Patent Publication Number: US-2020284457-A1

Title: Hvac system with automated device pairing

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 15/400,926 filed Jan. 6, 2017, the entirety of which is incorporated by reference herein. 
    
    
     BACKGROUND 
     The present disclosure relates generally to heating, ventilation, and air conditioning (HVAC) systems for a building. The present disclosure relates more particularly to systems and methods for automatically establishing relationships between sensors and actuation devices in a building HVAC system. 
     Building HVAC systems typically include many different sensors and actuation devices. The sensors measure various environmental variables (e.g., temperature, humidity, air flow, etc.) and provide sensor readings to a controller. In a feedback control system, a controller uses the sensor readings to generate appropriate control signals for the actuation devices (e.g., chillers, boilers, valves, actuators, etc.) which operate to affect the environmental variables measured by the sensors. Some buildings have hundreds of sensors and actuation devices. It can be cumbersome, error prone, and time consuming to manually identify the associations between sensors and their corresponding actuation devices. Additionally, buildings evolve over time which can change existing relationships between sensors and actuation devices. For example, remodeling a building can break existing relationships between paired sensors and actuation devices or create new relationships that did not previously exist. 
     Some building HVAC systems record time series data (e.g., trend data, historical data, etc.) for various measured or calculated variables. Time series data can be used for many purposes including, for example, fault detection, benchmarking, executing queries, and other data analysis applications. Some data analysis applications compare two or more time series as part of the analysis. However, it can be difficult to compare time series to each other due to dimensional mismatches resulting from different sampling rates, different units of measurement, and other factors. Without the ability to accurately compare time series data, performing actions such as finding similar trends, executing queries on a broad data set, running diagnostic algorithms, conducting benchmarking, reporting on compliance across portfolio of systems or buildings, and other actions can be challenging. 
     SUMMARY 
     One implementation of the present disclosure is a heating, ventilation, and air conditioning (HVAC) system for a building. The HVAC system includes a number of actuation devices operable to affect one or more variables in the building, a number of sensors configured to measure the variables affected by the actuation devices, and a controller. The controller is configured to operate the actuation devices to affect one or more of the measured variables by providing an actuation signal to the actuation devices and to receive sensor response signals from the sensors. The sensor response signals indicate an effect of the actuation signal on the measured variables. For each of the sensor response signals, the controller is configured to calculate a similarity metric indicating a similarity between the sensor response signal and the actuation signal. The controller is configured to automatically establish a device pairing including one of the actuation devices and one of the sensors based on the similarity metrics. 
     In some embodiments, the device pairing defines a control relationship between the actuation device in the device pairing and the sensor in the device pairing. The control relationship can indicate that the actuation device in the device pairing is operable to control a variable measured by the sensor in the device pairing. 
     In some embodiments, the controller is configured to automatically create a feedback control loop including the actuation device in the device pairing and the sensor in the device pairing. The controller can use the feedback control loop to generate and provide control signals to the actuation device in the device pairing based on measurements received from the sensor in the device pairing. 
     In some embodiments, the controller is configured to calculate the similarity metrics based on differences between samples of the actuation signal and corresponding samples of each of the sensor response signals. 
     In some embodiments, the controller is configured to determine, for each of the sensor response signals, a delay time of the sensor response signal relative to the actuation signal. The controller can identify a sensor corresponding to the sensor response signal having a minimum of the delay times and can establish the device pairing such that the identified sensor is included in the device pairing. 
     In some embodiments, the controller is configured to generate an actuation signal time series including a plurality of samples of the actuation signal and generate a sensor response time series for each of the sensor response signals. Each sensor response time series may include a plurality of samples of one of the measured variables. In some embodiments, the controller calculates the similarity metrics by comparing the actuation signal time series to each of the sensor response time series. 
     In some embodiments, the controller is configured to detect a dimensional mismatch between the actuation signal time series and one or more of the sensor response time series and correct the dimensional mismatch by modifying at least one of the actuation signal time series and one or more of the sensor response time series. 
     In some embodiments, the controller is configured to apply a discrete cosine transformation (DCT) to the actuation signal and each of the sensor response signals. Each DCT may generate a plurality of DCT coefficients. The controller can calculate the similarity metrics by comparing the DCT coefficients resulting from the DCT of the actuation signal to DCT coefficients resulting from the DCT of each sensor response signal. 
     In some embodiments, the controller is configured to receive baseline sensor signals from each of the plurality of sensors. The baseline sensor signals may indicate values of the measured variables during a time period before the actuation signal is provided to the actuation devices. For each of the baseline sensor signals, the controller can calculate a similarity metric indicating a similarity between the baseline sensor signal and the actuation signal. 
     In some embodiments, the controller is configured to determine, for each of the plurality of sensors, whether the similarity metric calculated based on the sensor response signal indicates a greater similarity than the similarity metric calculated based on the baseline sensor signal. In some embodiments, the controller establishes the device pairing in response to a determination that the similarity metric calculated based on the sensor response signal indicates a greater similarity than the similarity metric calculated based on the baseline sensor signal. 
     Another implementation of the present disclosure is a method for establishing device pairings in a heating, ventilation, and air conditioning (HVAC) system for a building. The method includes operating one or more actuation devices to affect one or more measured variables in the building by providing an actuation signal to the actuation devices and receiving sensor response signals from a plurality of sensors configured to measure the variables affected by the actuation devices. The sensor response signals indicate an effect of the actuation signal on the measured variables. The method includes calculating a similarity metric for each of the sensor response signals. Each similarity metric indicates a similarity between the actuation signal and one of the sensor response signals. The method includes automatically establishing a device pairing including one of the actuation devices and one of the sensors based on the similarity metrics. 
     In some embodiments, the device pairing defines a control relationship between the actuation device in the device pairing and the sensor in the device pairing. The control relationship may indicate that the actuation device in the device pairing is operable to control a variable measured by the sensor in the device pairing. 
     In some embodiments, the method includes automatically creating a feedback control loop including the actuation device in the device pairing and the sensor in the device pairing. The method may include using the feedback control loop to generate and provide control signals to the actuation device in the device pairing based on measurements received from the sensor in the device pairing. 
     In some embodiments, the similarity metrics are calculated based on differences between samples of the actuation signal and corresponding samples of each of the sensor response signals. 
     In some embodiments, the method includes determining, for each of the sensor response signals, a delay time of the sensor response signal relative to the actuation signal. The method may include identifying a sensor corresponding to the sensor response signal having a minimum of the delay times and establishing the device pairing such that the identified sensor is included in the device pairing. 
     In some embodiments, the method includes generating an actuation signal time series including a plurality of samples of the actuation signal and generating a sensor response time series for each of the sensor response signals. Each sensor response time series may include a plurality of samples of one of the measured variables. The method may include calculating the similarity metrics by comparing the actuation signal time series to each of the sensor response time series. 
     In some embodiments, the method includes detecting a dimensional mismatch between the actuation signal time series and one or more of the sensor response time series and correcting the dimensional mismatch by modifying at least one of the actuation signal time series and one or more of the sensor response time series. 
     In some embodiments, the method includes applying a discrete cosine transformation (DCT) to the actuation signal and each of the sensor response signals. Each DCT may generate a plurality of DCT coefficients. The method may include calculating the similarity metrics by comparing the DCT coefficients resulting from the DCT of the actuation signal to DCT coefficients resulting from the DCT of each sensor response signal. 
     In some embodiments, the method includes receiving baseline sensor signals from each of the plurality of sensors. The baseline sensor signals may indicate values of the measured variables during a time period before the actuation signal is provided to the actuation devices. The method may include, for each of the baseline sensor signals, calculating a similarity metric indicating a similarity between the baseline sensor signal and the actuation signal. 
     In some embodiments, the method includes determining, for each of the plurality of sensors, whether the similarity metric calculated based on the sensor response signal indicates a greater similarity than the similarity metric calculated based on the baseline sensor signal. The method may include establishing the device pairing in response to a determination that the similarity metric calculated based on the sensor response signal indicates a greater similarity than the similarity metric calculated based on the baseline sensor signal. 
     Those skilled in the art will appreciate that the summary is illustrative only and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the devices and/or processes described herein, as defined solely by the claims, will become apparent in the detailed description set forth herein and taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Some embodiments will become more fully understood from the following detailed description, taken in conjunction with the accompanying drawings, wherein like reference numerals refer to like elements, in which: 
         FIG. 1  is a drawing of a building equipped with a heating, ventilation, and air conditioning (HVAC) system, according to an exemplary embodiment; 
         FIG. 2  is a drawing of a waterside system which can be used in combination with the HVAC system of  FIG. 1 , according to an exemplary embodiment; 
         FIG. 3  is a drawing of an airside system which can be used in combination with the HVAC system of  FIG. 1 , according to an exemplary embodiment; 
         FIG. 4  is a block diagram of a building management system which can be used to monitor and control the building and HVAC system of  FIG. 1 , according to an exemplary embodiment; 
         FIG. 5  is a block diagram of another building management system which can be used to monitor and control the building and HVAC system of  FIG. 1 , according to an exemplary embodiment; 
         FIG. 6A  is a block diagram of a HVAC system including sensors, actuation devices, and a controller, which can be implemented in the building of  FIG. 1 , according to an exemplary embodiment; 
         FIG. 6B  is a block diagram illustrating a portion of the HVAC system of  FIG. 6A  in greater detail including a smart actuator which can be configured to perform automated device pairing, according to an exemplary embodiment; 
         FIG. 6C  is a block diagram illustrating a portion of the HVAC system of  FIG. 6A  in greater detail including a smart chiller which can be configured to perform automated device pairing, according to an exemplary embodiment; 
         FIG. 6D  is a block diagram illustrating a portion of the HVAC system of  FIG. 6A  in greater detail including a smart thermostat which can be configured to perform automated device pairing, according to an exemplary embodiment; 
         FIG. 7  is a graph illustrating different types of signals and time series evaluated by the controller of  FIG. 6A , according to an exemplary embodiment; 
         FIG. 8  is a graph illustrating dimensional mismatch handling performed by the controller of  FIG. 6A , according to an exemplary embodiment; 
         FIG. 9  is a flowchart of a process for establishing device pairings between sensors and actuation devices, which can be performed by the controller of  FIG. 6A , according to an exemplary embodiment; and 
         FIG. 10  is a flowchart of a process for handling dimensional mismatches between actuation signal time series and sensor response time series, which can be performed by the controller of  FIG. 6A , according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Referring generally to the FIGURES, a heating, ventilation, and air conditioning (HVAC) system with automated device pairing and dimensional mismatch handling are shown according to various exemplary embodiments. The HVAC system includes a plurality of sensors and actuation devices (e.g., chillers, boilers, fans, dampers, actuators, valves, etc.). The sensors measure various environmental variables in the building (e.g., zone temperature, humidity, air flow, etc.). The actuation devices operate to affect the measured variables by providing heating, cooling, airflow, etc. to the building. A controller provides actuation signals to the actuation devices and receives sensor response signals from the sensors. The controller uses the sensor response signals to determine an effect of the actuation signals on the measured variables. 
     In some embodiments, the controller automatically establishes device pairings between sensors and actuation devices based on the sensor response signals. For each combination of an actuation signal and a sensor response signal, the controller can calculate a similarity metric. The similarity metric indicates the similarity or closeness between the sensor response signal and the actuation signal. The controller can use the similarity metrics to identify which of the sensor response signals most closely matches each actuation signal. The controller can then establish a device pairing between the actuation device and the sensor corresponding to the matching actuation signal and sensor response signal. 
     In some embodiments, the controller stores time series data for the actuation signals and sensor response signals. Different variables can be measured at different sampling rates, which can lead do dimensional mismatches between two or more time series that span the same range of times. For example, a time series sampled at a rate often samples per second may include twice the number of samples as a different time series sampled at a rate of five samples per second. The controller can automatically handle dimensional mismatches between two or more time series by performing a discrete cosine transformation for each time series. 
     A discrete cosine transformation (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. Performing the DCT may result in a set of DCT coefficients for each time series. The DCT coefficients represent the magnitudes of the cosine functions in the summation. The controller can apply a quantization process to the DCT coefficients in each set such that only a predetermined number of the DCT coefficients in each set are retained. The remaining DCT coefficients can be discarded or replaced with zeros, which has the effect of removing some of the higher frequency cosine functions from the summation. The controller can compare two or more time series by comparing the DCT coefficients resulting from each DCT. Advantageously, this allows for direct comparison between the transformed time series without requiring decompression, interpolation, synchronization, or other processing steps. Other features and advantages of the HVAC system and controller are described in greater detail below. 
     Building HVAC Systems and Building Management Systems 
     Referring now to  FIGS. 1-5 , several building management systems (BMS) and HVAC systems in which the systems and methods of the present disclosure can be implemented are shown, according to some embodiments. In brief overview,  FIG. 1  shows a building  10  equipped with a HVAC system  100 .  FIG. 2  is a block diagram of a waterside system  200  which can be used to serve building  10 .  FIG. 3  is a block diagram of an airside system  300  which can be used to serve building  10 .  FIG. 4  is a block diagram of a BMS which can be used to monitor and control building  10 .  FIG. 5  is a block diagram of another BMS which can be used to monitor and control building  10 . 
     Building and HVAC System 
     Referring particularly to  FIG. 1 , a perspective view of a building  10  is shown. Building  10  is served by a BMS. A BMS is, in general, a system of devices configured to control, monitor, and manage equipment in or around a building or building area. A BMS can include, for example, a HVAC system, a security system, a lighting system, a fire alerting system, any other system that is capable of managing building functions or devices, or any combination thereof. 
     The BMS that serves building  10  includes a HVAC system  100 . HVAC system  100  can include a plurality of HVAC devices (e.g., heaters, chillers, air handling units, pumps, fans, thermal energy storage, etc.) configured to provide heating, cooling, ventilation, or other services for building  10 . For example, HVAC system  100  is shown to include a waterside system  120  and an airside system  130 . Waterside system  120  may provide a heated or chilled fluid to an air handling unit of airside system  130 . Airside system  130  may use the heated or chilled fluid to heat or cool an airflow provided to building  10 . An exemplary waterside system and airside system which can be used in HVAC system  100  are described in greater detail with reference to  FIGS. 2-3 . 
     HVAC system  100  is shown to include a chiller  102 , a boiler  104 , and a rooftop air handling unit (AHU)  106 . Waterside system  120  may use boiler  104  and chiller  102  to heat or cool a working fluid (e.g., water, glycol, etc.) and may circulate the working fluid to AHU  106 . In various embodiments, the HVAC devices of waterside system  120  can be located in or around building  10  (as shown in  FIG. 1 ) or at an offsite location such as a central plant (e.g., a chiller plant, a steam plant, a heat plant, etc.). The working fluid can be heated in boiler  104  or cooled in chiller  102 , depending on whether heating or cooling is required in building  10 . Boiler  104  may add heat to the circulated fluid, for example, by burning a combustible material (e.g., natural gas) or using an electric heating element. Chiller  102  may place the circulated fluid in a heat exchange relationship with another fluid (e.g., a refrigerant) in a heat exchanger (e.g., an evaporator) to absorb heat from the circulated fluid. The working fluid from chiller  102  and/or boiler  104  can be transported to AHU  106  via piping  108 . 
     AHU  106  may place the working fluid in a heat exchange relationship with an airflow passing through AHU  106  (e.g., via one or more stages of cooling coils and/or heating coils). The airflow can be, for example, outside air, return air from within building  10 , or a combination of both. AHU  106  may transfer heat between the airflow and the working fluid to provide heating or cooling for the airflow. For example, AHU  106  can include one or more fans or blowers configured to pass the airflow over or through a heat exchanger containing the working fluid. The working fluid may then return to chiller  102  or boiler  104  via piping  110 . 
     Airside system  130  may deliver the airflow supplied by AHU  106  (i.e., the supply airflow) to building  10  via air supply ducts  112  and may provide return air from building  10  to AHU  106  via air return ducts  114 . In some embodiments, airside system  130  includes multiple variable air volume (VAV) units  116 . For example, airside system  130  is shown to include a separate VAV unit  116  on each floor or zone of building  10 . VAV units  116  can include dampers or other flow control elements that can be operated to control an amount of the supply airflow provided to individual zones of building  10 . In other embodiments, airside system  130  delivers the supply airflow into one or more zones of building  10  (e.g., via supply ducts  112 ) without using intermediate VAV units  116  or other flow control elements. AHU  106  can include various sensors (e.g., temperature sensors, pressure sensors, etc.) configured to measure attributes of the supply airflow. AHU  106  may receive input from sensors located within AHU  106  and/or within the building zone and may adjust the flow rate, temperature, or other attributes of the supply airflow through AHU  106  to achieve setpoint conditions for the building zone. 
     Waterside System 
     Referring now to  FIG. 2 , a block diagram of a waterside system  200  is shown, according to some embodiments. In various embodiments, waterside system  200  may supplement or replace waterside system  120  in HVAC system  100  or can be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , waterside system  200  can include a subset of the HVAC devices in HVAC system  100  (e.g., boiler  104 , chiller  102 , pumps, valves, etc.) and may operate to supply a heated or chilled fluid to AHU  106 . The HVAC devices of waterside system  200  can be located within building  10  (e.g., as components of waterside system  120 ) or at an offsite location such as a central plant. 
     In  FIG. 2 , waterside system  200  is shown as a central plant having a plurality of subplants  202 - 212 . Subplants  202 - 212  are shown to include a heater subplant  202 , a heat recovery chiller subplant  204 , a chiller subplant  206 , a cooling tower subplant  208 , a hot thermal energy storage (TES) subplant  210 , and a cold thermal energy storage (TES) subplant  212 . Subplants  202 - 212  consume resources (e.g., water, natural gas, electricity, etc.) from utilities to serve thermal energy loads (e.g., hot water, cold water, heating, cooling, etc.) of a building or campus. For example, heater subplant  202  can be configured to heat water in a hot water loop  214  that circulates the hot water between heater subplant  202  and building  10 . Chiller subplant  206  can be configured to chill water in a cold water loop  216  that circulates the cold water between chiller subplant  206  building  10 . Heat recovery chiller subplant  204  can be configured to transfer heat from cold water loop  216  to hot water loop  214  to provide additional heating for the hot water and additional cooling for the cold water. Condenser water loop  218  may absorb heat from the cold water in chiller subplant  206  and reject the absorbed heat in cooling tower subplant  208  or transfer the absorbed heat to hot water loop  214 . Hot TES subplant  210  and cold TES subplant  212  may store hot and cold thermal energy, respectively, for subsequent use. 
     Hot water loop  214  and cold water loop  216  may deliver the heated and/or chilled water to air handlers located on the rooftop of building  10  (e.g., AHU  106 ) or to individual floors or zones of building  10  (e.g., VAV units  116 ). The air handlers push air past heat exchangers (e.g., heating coils or cooling coils) through which the water flows to provide heating or cooling for the air. The heated or cooled air can be delivered to individual zones of building  10  to serve thermal energy loads of building  10 . The water then returns to subplants  202 - 212  to receive further heating or cooling. 
     Although subplants  202 - 212  are shown and described as heating and cooling water for circulation to a building, it is understood that any other type of working fluid (e.g., glycol, CO2, etc.) can be used in place of or in addition to water to serve thermal energy loads. In other embodiments, subplants  202 - 212  may provide heating and/or cooling directly to the building or campus without requiring an intermediate heat transfer fluid. These and other variations to waterside system  200  are within the teachings of the present disclosure. 
     Each of subplants  202 - 212  can include a variety of equipment configured to facilitate the functions of the subplant. For example, heater subplant  202  is shown to include a plurality of heating elements  220  (e.g., boilers, electric heaters, etc.) configured to add heat to the hot water in hot water loop  214 . Heater subplant  202  is also shown to include several pumps  222  and  224  configured to circulate the hot water in hot water loop  214  and to control the flow rate of the hot water through individual heating elements  220 . Chiller subplant  206  is shown to include a plurality of chillers  232  configured to remove heat from the cold water in cold water loop  216 . Chiller subplant  206  is also shown to include several pumps  234  and  236  configured to circulate the cold water in cold water loop  216  and to control the flow rate of the cold water through individual chillers  232 . 
     Heat recovery chiller subplant  204  is shown to include a plurality of heat recovery heat exchangers  226  (e.g., refrigeration circuits) configured to transfer heat from cold water loop  216  to hot water loop  214 . Heat recovery chiller subplant  204  is also shown to include several pumps  228  and  230  configured to circulate the hot water and/or cold water through heat recovery heat exchangers  226  and to control the flow rate of the water through individual heat recovery heat exchangers  226 . Cooling tower subplant  208  is shown to include a plurality of cooling towers  238  configured to remove heat from the condenser water in condenser water loop  218 . Cooling tower subplant  208  is also shown to include several pumps  240  configured to circulate the condenser water in condenser water loop  218  and to control the flow rate of the condenser water through individual cooling towers  238 . 
     Hot TES subplant  210  is shown to include a hot TES tank  242  configured to store the hot water for later use. Hot TES subplant  210  may also include one or more pumps or valves configured to control the flow rate of the hot water into or out of hot TES tank  242 . Cold TES subplant  212  is shown to include cold TES tanks  244  configured to store the cold water for later use. Cold TES subplant  212  may also include one or more pumps or valves configured to control the flow rate of the cold water into or out of cold TES tanks  244 . 
     In some embodiments, one or more of the pumps in waterside system  200  (e.g., pumps  222 ,  224 ,  228 ,  230 ,  234 ,  236 , and/or  240 ) or pipelines in waterside system  200  include an isolation valve associated therewith. Isolation valves can be integrated with the pumps or positioned upstream or downstream of the pumps to control the fluid flows in waterside system  200 . In various embodiments, waterside system  200  can include more, fewer, or different types of devices and/or subplants based on the particular configuration of waterside system  200  and the types of loads served by waterside system  200 . 
     Airside System 
     Referring now to  FIG. 3 , a block diagram of an airside system  300  is shown, according to some embodiments. In various embodiments, airside system  300  may supplement or replace airside system  130  in HVAC system  100  or can be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , airside system  300  can include a subset of the HVAC devices in HVAC system  100  (e.g., AHU  106 , VAV units  116 , ducts  112 - 114 , fans, dampers, etc.) and can be located in or around building  10 . Airside system  300  may operate to heat or cool an airflow provided to building  10  using a heated or chilled fluid provided by waterside system  200 . 
     In  FIG. 3 , airside system  300  is shown to include an economizer-type air handling unit (AHU)  302 . Economizer-type AHUs vary the amount of outside air and return air used by the air handling unit for heating or cooling. For example, AHU  302  may receive return air  304  from building zone  306  via return air duct  308  and may deliver supply air  310  to building zone  306  via supply air duct  312 . In some embodiments, AHU  302  is a rooftop unit located on the roof of building  10  (e.g., AHU  106  as shown in  FIG. 1 ) or otherwise positioned to receive both return air  304  and outside air  314 . AHU  302  can be configured to operate exhaust air damper  316 , mixing damper  318 , and outside air damper  320  to control an amount of outside air  314  and return air  304  that combine to form supply air  310 . Any return air  304  that does not pass through mixing damper  318  can be exhausted from AHU  302  through exhaust damper  316  as exhaust air  322 . 
     Each of dampers  316 - 320  can be operated by an actuator. For example, exhaust air damper  316  can be operated by actuator  324 , mixing damper  318  can be operated by actuator  326 , and outside air damper  320  can be operated by actuator  328 . Actuators  324 - 328  may communicate with an AHU controller  330  via a communications link  332 . Actuators  324 - 328  may receive control signals from AHU controller  330  and may provide feedback signals to AHU controller  330 . Feedback signals can include, for example, an indication of a current actuator or damper position, an amount of torque or force exerted by the actuator, diagnostic information (e.g., results of diagnostic tests performed by actuators  324 - 328 ), status information, commissioning information, configuration settings, calibration data, and/or other types of information or data that can be collected, stored, or used by actuators  324 - 328 . AHU controller  330  can be an economizer controller configured to use one or more control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, feedback control algorithms, etc.) to control actuators  324 - 328 . 
     Still referring to  FIG. 3 , AHU  302  is shown to include a cooling coil  334 , a heating coil  336 , and a fan  338  positioned within supply air duct  312 . Fan  338  can be configured to force supply air  310  through cooling coil  334  and/or heating coil  336  and provide supply air  310  to building zone  306 . AHU controller  330  may communicate with fan  338  via communications link  340  to control a flow rate of supply air  310 . In some embodiments, AHU controller  330  controls an amount of heating or cooling applied to supply air  310  by modulating a speed of fan  338 . 
     Cooling coil  334  may receive a chilled fluid from waterside system  200  (e.g., from cold water loop  216 ) via piping  342  and may return the chilled fluid to waterside system  200  via piping  344 . Valve  346  can be positioned along piping  342  or piping  344  to control a flow rate of the chilled fluid through cooling coil  334 . In some embodiments, cooling coil  334  includes multiple stages of cooling coils that can be independently activated and deactivated (e.g., by AHU controller  330 , by BMS controller  366 , etc.) to modulate an amount of cooling applied to supply air  310 . 
     Heating coil  336  may receive a heated fluid from waterside system  200  (e.g., from hot water loop  214 ) via piping  348  and may return the heated fluid to waterside system  200  via piping  350 . Valve  352  can be positioned along piping  348  or piping  350  to control a flow rate of the heated fluid through heating coil  336 . In some embodiments, heating coil  336  includes multiple stages of heating coils that can be independently activated and deactivated (e.g., by AHU controller  330 , by BMS controller  366 , etc.) to modulate an amount of heating applied to supply air  310 . 
     Each of valves  346  and  352  can be controlled by an actuator. For example, valve  346  can be controlled by actuator  354  and valve  352  can be controlled by actuator  356 . Actuators  354 - 356  may communicate with AHU controller  330  via communications links  358 - 360 . Actuators  354 - 356  may receive control signals from AHU controller  330  and may provide feedback signals to controller  330 . In some embodiments, AHU controller  330  receives a measurement of the supply air temperature from a temperature sensor  362  positioned in supply air duct  312  (e.g., downstream of cooling coil  334  and/or heating coil  336 ). AHU controller  330  may also receive a measurement of the temperature of building zone  306  from a temperature sensor  364  located in building zone  306 . 
     In some embodiments, AHU controller  330  operates valves  346  and  352  via actuators  354 - 356  to modulate an amount of heating or cooling provided to supply air  310  (e.g., to achieve a setpoint temperature for supply air  310  or to maintain the temperature of supply air  310  within a setpoint temperature range). The positions of valves  346  and  352  affect the amount of heating or cooling provided to supply air  310  by cooling coil  334  or heating coil  336  and may correlate with the amount of energy consumed to achieve a desired supply air temperature. AHU  330  may control the temperature of supply air  310  and/or building zone  306  by activating or deactivating coils  334 - 336 , adjusting a speed of fan  338 , or a combination of both. 
     Still referring to  FIG. 3 , airside system  300  is shown to include a building management system (BMS) controller  366  and a client device  368 . BMS controller  366  can include one or more computer systems (e.g., servers, supervisory controllers, subsystem controllers, etc.) that serve as system level controllers, application or data servers, head nodes, or master controllers for airside system  300 , waterside system  200 , HVAC system  100 , and/or other controllable systems that serve building  10 . BMS controller  366  may communicate with multiple downstream building systems or subsystems (e.g., HVAC system  100 , a security system, a lighting system, waterside system  200 , etc.) via a communications link  370  according to like or disparate protocols (e.g., LON, BACnet, etc.). In various embodiments, AHU controller  330  and BMS controller  366  can be separate (as shown in  FIG. 3 ) or integrated. In an integrated implementation, AHU controller  330  can be a software module configured for execution by a processor of BMS controller  366 . 
     In some embodiments, AHU controller  330  receives information from BMS controller  366  (e.g., commands, setpoints, operating boundaries, etc.) and provides information to BMS controller  366  (e.g., temperature measurements, valve or actuator positions, operating statuses, diagnostics, etc.). For example, AHU controller  330  may provide BMS controller  366  with temperature measurements from temperature sensors  362 - 364 , equipment on/off states, equipment operating capacities, and/or any other information that can be used by BMS controller  366  to monitor or control a variable state or condition within building zone  306 . 
     Client device  368  can include one or more human-machine interfaces or client interfaces (e.g., graphical user interfaces, reporting interfaces, text-based computer interfaces, client-facing web services, web servers that provide pages to web clients, etc.) for controlling, viewing, or otherwise interacting with HVAC system  100 , its subsystems, and/or devices. Client device  368  can be a computer workstation, a client terminal, a remote or local interface, or any other type of user interface device. Client device  368  can be a stationary terminal or a mobile device. For example, client device  368  can be a desktop computer, a computer server with a user interface, a laptop computer, a tablet, a smartphone, a PDA, or any other type of mobile or non-mobile device. Client device  368  may communicate with BMS controller  366  and/or AHU controller  330  via communications link  372 . 
     Building Management Systems 
     Referring now to  FIG. 4 , a block diagram of a building management system (BMS)  400  is shown, according to some embodiments. BMS  400  can be implemented in building  10  to automatically monitor and control various building functions. BMS  400  is shown to include BMS controller  366  and a plurality of building subsystems  428 . Building subsystems  428  are shown to include a building electrical subsystem  434 , an information communication technology (ICT) subsystem  436 , a security subsystem  438 , a HVAC subsystem  440 , a lighting subsystem  442 , a lift/escalators subsystem  432 , and a fire safety subsystem  430 . In various embodiments, building subsystems  428  can include fewer, additional, or alternative subsystems. For example, building subsystems  428  may also or alternatively include a refrigeration subsystem, an advertising or signage subsystem, a cooking subsystem, a vending subsystem, a printer or copy service subsystem, or any other type of building subsystem that uses controllable equipment and/or sensors to monitor or control building  10 . In some embodiments, building subsystems  428  include waterside system  200  and/or airside system  300 , as described with reference to  FIGS. 2-3 . 
     Each of building subsystems  428  can include any number of devices, controllers, and connections for completing its individual functions and control activities. HVAC subsystem  440  can include many of the same components as HVAC system  100 , as described with reference to  FIGS. 1-3 . For example, HVAC subsystem  440  can include a chiller, a boiler, any number of air handling units, economizers, field controllers, supervisory controllers, actuators, temperature sensors, and other devices for controlling the temperature, humidity, airflow, or other variable conditions within building  10 . Lighting subsystem  442  can include any number of light fixtures, ballasts, lighting sensors, dimmers, or other devices configured to controllably adjust the amount of light provided to a building space. Security subsystem  438  can include occupancy sensors, video surveillance cameras, digital video recorders, video processing servers, intrusion detection devices, access control devices and servers, or other security-related devices. 
     Still referring to  FIG. 4 , BMS controller  366  is shown to include a communications interface  407  and a BMS interface  409 . Interface  407  may facilitate communications between BMS controller  366  and external applications (e.g., monitoring and reporting applications  422 , enterprise control applications  426 , remote systems and applications  444 , applications residing on client devices  448 , etc.) for allowing user control, monitoring, and adjustment to BMS controller  366  and/or subsystems  428 . Interface  407  may also facilitate communications between BMS controller  366  and client devices  448 . BMS interface  409  may facilitate communications between BMS controller  366  and building subsystems  428  (e.g., HVAC, lighting security, lifts, power distribution, business, etc.). 
     Interfaces  407 ,  409  can be or include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with building subsystems  428  or other external systems or devices. In various embodiments, communications via interfaces  407 ,  409  can be direct (e.g., local wired or wireless communications) or via a communications network  446  (e.g., a WAN, the Internet, a cellular network, etc.). For example, interfaces  407 ,  409  can include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network. In another example, interfaces  407 ,  409  can include a Wi-Fi transceiver for communicating via a wireless communications network. In another example, one or both of interfaces  407 ,  409  can include cellular or mobile phone communications transceivers. In one embodiment, communications interface  407  is a power line communications interface and BMS interface  409  is an Ethernet interface. In other embodiments, both communications interface  407  and BMS interface  409  are Ethernet interfaces or are the same Ethernet interface. 
     Still referring to  FIG. 4 , BMS controller  366  is shown to include a processing circuit  404  including a processor  406  and memory  408 . Processing circuit  404  can be communicably connected to BMS interface  409  and/or communications interface  407  such that processing circuit  404  and the various components thereof can send and receive data via interfaces  407 ,  409 . Processor  406  can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components. 
     Memory  408  (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory  408  can be or include volatile memory or non-volatile memory. Memory  408  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present application. According to some embodiments, memory  408  is communicably connected to processor  406  via processing circuit  404  and includes computer code for executing (e.g., by processing circuit  404  and/or processor  406 ) one or more processes described herein. 
     In some embodiments, BMS controller  366  is implemented within a single computer (e.g., one server, one housing, etc.). In various other embodiments BMS controller  366  can be distributed across multiple servers or computers (e.g., that can exist in distributed locations). Further, while  FIG. 4  shows applications  422  and  426  as existing outside of BMS controller  366 , in some embodiments, applications  422  and  426  can be hosted within BMS controller  366  (e.g., within memory  408 ). 
     Still referring to  FIG. 4 , memory  408  is shown to include an enterprise integration layer  410 , an automated measurement and validation (AM&amp;V) layer  412 , a demand response (DR) layer  414 , a fault detection and diagnostics (FDD) layer  416 , an integrated control layer  418 , and a building subsystem integration later  420 . Layers  410 - 420  can be configured to receive inputs from building subsystems  428  and other data sources, determine optimal control actions for building subsystems  428  based on the inputs, generate control signals based on the optimal control actions, and provide the generated control signals to building subsystems  428 . The following paragraphs describe some of the general functions performed by each of layers  410 - 420  in BMS  400 . 
     Enterprise integration layer  410  can be configured to serve clients or local applications with information and services to support a variety of enterprise-level applications. For example, enterprise control applications  426  can be configured to provide subsystem-spanning control to a graphical user interface (GUI) or to any number of enterprise-level business applications (e.g., accounting systems, user identification systems, etc.). Enterprise control applications  426  may also or alternatively be configured to provide configuration GUIs for configuring BMS controller  366 . In yet other embodiments, enterprise control applications  426  can work with layers  410 - 420  to optimize building performance (e.g., efficiency, energy use, comfort, or safety) based on inputs received at interface  407  and/or BMS interface  409 . 
     Building subsystem integration layer  420  can be configured to manage communications between BMS controller  366  and building subsystems  428 . For example, building subsystem integration layer  420  may receive sensor data and input signals from building subsystems  428  and provide output data and control signals to building subsystems  428 . Building subsystem integration layer  420  may also be configured to manage communications between building subsystems  428 . Building subsystem integration layer  420  translate communications (e.g., sensor data, input signals, output signals, etc.) across a plurality of multi-vendor/multi-protocol systems. 
     Demand response layer  414  can be configured to optimize resource usage (e.g., electricity use, natural gas use, water use, etc.) and/or the monetary cost of such resource usage in response to satisfy the demand of building  10 . The optimization can be based on time-of-use prices, curtailment signals, energy availability, or other data received from utility providers, distributed energy generation systems  424 , from energy storage  427  (e.g., hot TES  242 , cold TES  244 , etc.), or from other sources. Demand response layer  414  may receive inputs from other layers of BMS controller  366  (e.g., building subsystem integration layer  420 , integrated control layer  418 , etc.). The inputs received from other layers can include environmental or sensor inputs such as temperature, carbon dioxide levels, relative humidity levels, air quality sensor outputs, occupancy sensor outputs, room schedules, and the like. The inputs may also include inputs such as electrical use (e.g., expressed in kWh), thermal load measurements, pricing information, projected pricing, smoothed pricing, curtailment signals from utilities, and the like. 
     According to some embodiments, demand response layer  414  includes control logic for responding to the data and signals it receives. These responses can include communicating with the control algorithms in integrated control layer  418 , changing control strategies, changing setpoints, or activating/deactivating building equipment or subsystems in a controlled manner. Demand response layer  414  may also include control logic configured to determine when to utilize stored energy. For example, demand response layer  414  may determine to begin using energy from energy storage  427  just prior to the beginning of a peak use hour. 
     In some embodiments, demand response layer  414  includes a control module configured to actively initiate control actions (e.g., automatically changing setpoints) which minimize energy costs based on one or more inputs representative of or based on demand (e.g., price, a curtailment signal, a demand level, etc.). In some embodiments, demand response layer  414  uses equipment models to determine an optimal set of control actions. The equipment models can include, for example, thermodynamic models describing the inputs, outputs, and/or functions performed by various sets of building equipment. Equipment models may represent collections of building equipment (e.g., subplants, chiller arrays, etc.) or individual devices (e.g., individual chillers, heaters, pumps, etc.). 
     Demand response layer  414  may further include or draw upon one or more demand response policy definitions (e.g., databases, XML files, etc.). The policy definitions can be edited or adjusted by a user (e.g., via a graphical user interface) so that the control actions initiated in response to demand inputs can be tailored for the user&#39;s application, desired comfort level, particular building equipment, or based on other concerns. For example, the demand response policy definitions can specify which equipment can be turned on or off in response to particular demand inputs, how long a system or piece of equipment should be turned off, what setpoints can be changed, what the allowable set point adjustment range is, how long to hold a high demand setpoint before returning to a normally scheduled setpoint, how close to approach capacity limits, which equipment modes to utilize, the energy transfer rates (e.g., the maximum rate, an alarm rate, other rate boundary information, etc.) into and out of energy storage devices (e.g., thermal storage tanks, battery banks, etc.), and when to dispatch on-site generation of energy (e.g., via fuel cells, a motor generator set, etc.). 
     Integrated control layer  418  can be configured to use the data input or output of building subsystem integration layer  420  and/or demand response later  414  to make control decisions. Due to the subsystem integration provided by building subsystem integration layer  420 , integrated control layer  418  can integrate control activities of the subsystems  428  such that the subsystems  428  behave as a single integrated supersystem. In some embodiments, integrated control layer  418  includes control logic that uses inputs and outputs from a plurality of building subsystems to provide greater comfort and energy savings relative to the comfort and energy savings that separate subsystems could provide alone. For example, integrated control layer  418  can be configured to use an input from a first subsystem to make an energy-saving control decision for a second subsystem. Results of these decisions can be communicated back to building subsystem integration layer  420 . 
     Integrated control layer  418  is shown to be logically below demand response layer  414 . Integrated control layer  418  can be configured to enhance the effectiveness of demand response layer  414  by enabling building subsystems  428  and their respective control loops to be controlled in coordination with demand response layer  414 . This configuration may advantageously reduce disruptive demand response behavior relative to conventional systems. For example, integrated control layer  418  can be configured to assure that a demand response-driven upward adjustment to the setpoint for chilled water temperature (or another component that directly or indirectly affects temperature) does not result in an increase in fan energy (or other energy used to cool a space) that would result in greater total building energy use than was saved at the chiller. 
     Integrated control layer  418  can be configured to provide feedback to demand response layer  414  so that demand response layer  414  checks that constraints (e.g., temperature, lighting levels, etc.) are properly maintained even while demanded load shedding is in progress. The constraints may also include setpoint or sensed boundaries relating to safety, equipment operating limits and performance, comfort, fire codes, electrical codes, energy codes, and the like. Integrated control layer  418  is also logically below fault detection and diagnostics layer  416  and automated measurement and validation layer  412 . Integrated control layer  418  can be configured to provide calculated inputs (e.g., aggregations) to these higher levels based on outputs from more than one building subsystem. 
     Automated measurement and validation (AM&amp;V) layer  412  can be configured to verify that control strategies commanded by integrated control layer  418  or demand response layer  414  are working properly (e.g., using data aggregated by AM&amp;V layer  412 , integrated control layer  418 , building subsystem integration layer  420 , FDD layer  416 , or otherwise). The calculations made by AM&amp;V layer  412  can be based on building system energy models and/or equipment models for individual BMS devices or subsystems. For example, AM&amp;V layer  412  may compare a model-predicted output with an actual output from building subsystems  428  to determine an accuracy of the model. 
     Fault detection and diagnostics (FDD) layer  416  can be configured to provide on-going fault detection for building subsystems  428 , building subsystem devices (i.e., building equipment), and control algorithms used by demand response layer  414  and integrated control layer  418 . FDD layer  416  may receive data inputs from integrated control layer  418 , directly from one or more building subsystems or devices, or from another data source. FDD layer  416  may automatically diagnose and respond to detected faults. The responses to detected or diagnosed faults can include providing an alert message to a user, a maintenance scheduling system, or a control algorithm configured to attempt to repair the fault or to work-around the fault. 
     FDD layer  416  can be configured to output a specific identification of the faulty component or cause of the fault (e.g., loose damper linkage) using detailed subsystem inputs available at building subsystem integration layer  420 . In other exemplary embodiments, FDD layer  416  is configured to provide “fault” events to integrated control layer  418  which executes control strategies and policies in response to the received fault events. According to some embodiments, FDD layer  416  (or a policy executed by an integrated control engine or business rules engine) may shut-down systems or direct control activities around faulty devices or systems to reduce energy waste, extend equipment life, or assure proper control response. 
     FDD layer  416  can be configured to store or access a variety of different system data stores (or data points for live data). FDD layer  416  may use some content of the data stores to identify faults at the equipment level (e.g., specific chiller, specific AHU, specific terminal unit, etc.) and other content to identify faults at component or subsystem levels. For example, building subsystems  428  may generate temporal (i.e., time-series) data indicating the performance of BMS  400  and the various components thereof. The data generated by building subsystems  428  can include measured or calculated values that exhibit statistical characteristics and provide information about how the corresponding system or process (e.g., a temperature control process, a flow control process, etc.) is performing in terms of error from its setpoint. These processes can be examined by FDD layer  416  to expose when the system begins to degrade in performance and alert a user to repair the fault before it becomes more severe. 
     Referring now to  FIG. 5 , a block diagram of another building management system (BMS)  500  is shown, according to some embodiments. BMS  500  can be used to monitor and control the devices of HVAC system  100 , waterside system  200 , airside system  300 , building subsystems  428 , as well as other types of BMS devices (e.g., lighting equipment, security equipment, etc.) and/or HVAC equipment. 
     BMS  500  provides a system architecture that facilitates automatic equipment discovery and equipment model distribution. Equipment discovery can occur on multiple levels of BMS  500  across multiple different communications busses (e.g., a system bus  554 , zone buses  556 - 560  and  564 , sensor/actuator bus  566 , etc.) and across multiple different communications protocols. In some embodiments, equipment discovery is accomplished using active node tables, which provide status information for devices connected to each communications bus. For example, each communications bus can be monitored for new devices by monitoring the corresponding active node table for new nodes. When a new device is detected, BMS  500  can begin interacting with the new device (e.g., sending control signals, using data from the device) without user interaction. 
     Some devices in BMS  500  present themselves to the network using equipment models. An equipment model defines equipment object attributes, view definitions, schedules, trends, and the associated BACnet value objects (e.g., analog value, binary value, multistate value, etc.) that are used for integration with other systems. Some devices in BMS  500  store their own equipment models. Other devices in BMS  500  have equipment models stored externally (e.g., within other devices). For example, a zone coordinator  508  can store the equipment model for a bypass damper  528 . In some embodiments, zone coordinator  508  automatically creates the equipment model for bypass damper  528  or other devices on zone bus  558 . Other zone coordinators can also create equipment models for devices connected to their zone busses. The equipment model for a device can be created automatically based on the types of data points exposed by the device on the zone bus, device type, and/or other device attributes. Several examples of automatic equipment discovery and equipment model distribution are discussed in greater detail below. 
     Still referring to  FIG. 5 , BMS  500  is shown to include a system manager  502 ; several zone coordinators  506 ,  508 ,  510  and  518 ; and several zone controllers  524 ,  530 ,  532 ,  536 ,  548 , and  550 . System manager  502  can monitor data points in BMS  500  and report monitored variables to various monitoring and/or control applications. System manager  502  can communicate with client devices  504  (e.g., user devices, desktop computers, laptop computers, mobile devices, etc.) via a data communications link  574  (e.g., BACnet IP, Ethernet, wired or wireless communications, etc.). System manager  502  can provide a user interface to client devices  504  via data communications link  574 . The user interface may allow users to monitor and/or control BMS  500  via client devices  504 . 
     In some embodiments, system manager  502  is connected with zone coordinators  506 - 510  and  518  via a system bus  554 . System manager  502  can be configured to communicate with zone coordinators  506 - 510  and  518  via system bus  554  using a master-slave token passing (MSTP) protocol or any other communications protocol. System bus  554  can also connect system manager  502  with other devices such as a constant volume (CV) rooftop unit (RTU)  512 , an input/output module (IOM)  514 , a thermostat controller  516  (e.g., a TEC5000 series thermostat controller), and a network automation engine (NAE) or third-party controller  520 . RTU  512  can be configured to communicate directly with system manager  502  and can be connected directly to system bus  554 . Other RTUs can communicate with system manager  502  via an intermediate device. For example, a wired input  562  can connect a third-party RTU  542  to thermostat controller  516 , which connects to system bus  554 . 
     System manager  502  can provide a user interface for any device containing an equipment model. Devices such as zone coordinators  506 - 510  and  518  and thermostat controller  516  can provide their equipment models to system manager  502  via system bus  554 . In some embodiments, system manager  502  automatically creates equipment models for connected devices that do not contain an equipment model (e.g., IOM  514 , third party controller  520 , etc.). For example, system manager  502  can create an equipment model for any device that responds to a device tree request. The equipment models created by system manager  502  can be stored within system manager  502 . System manager  502  can then provide a user interface for devices that do not contain their own equipment models using the equipment models created by system manager  502 . In some embodiments, system manager  502  stores a view definition for each type of equipment connected via system bus  554  and uses the stored view definition to generate a user interface for the equipment. 
     Each zone coordinator  506 - 510  and  518  can be connected with one or more of zone controllers  524 ,  530 - 532 ,  536 , and  548 - 550  via zone buses  556 ,  558 ,  560 , and  564 . Zone coordinators  506 - 510  and  518  can communicate with zone controllers  524 ,  530 - 532 ,  536 , and  548 - 550  via zone busses  556 - 560  and  564  using a MSTP protocol or any other communications protocol. Zone busses  556 - 560  and  564  can also connect zone coordinators  506 - 510  and  518  with other types of devices such as variable air volume (VAV) RTUs  522  and  540 , changeover bypass (COBP) RTUs  526  and  552 , bypass dampers  528  and  546 , and PEAK controllers  534  and  544 . 
     Zone coordinators  506 - 510  and  518  can be configured to monitor and command various zoning systems. In some embodiments, each zone coordinator  506 - 510  and  518  monitors and commands a separate zoning system and is connected to the zoning system via a separate zone bus. For example, zone coordinator  506  can be connected to VAV RTU  522  and zone controller  524  via zone bus  556 . Zone coordinator  508  can be connected to COBP RTU  526 , bypass damper  528 , COBP zone controller  530 , and VAV zone controller  532  via zone bus  558 . Zone coordinator  510  can be connected to PEAK controller  534  and VAV zone controller  536  via zone bus  560 . Zone coordinator  518  can be connected to PEAK controller  544 , bypass damper  546 , COBP zone controller  548 , and VAV zone controller  550  via zone bus  564 . 
     A single model of zone coordinator  506 - 510  and  518  can be configured to handle multiple different types of zoning systems (e.g., a VAV zoning system, a COBP zoning system, etc.). Each zoning system can include a RTU, one or more zone controllers, and/or a bypass damper. For example, zone coordinators  506  and  510  are shown as Verasys VAV engines (VVEs) connected to VAV RTUs  522  and  540 , respectively. Zone coordinator  506  is connected directly to VAV RTU  522  via zone bus  556 , whereas zone coordinator  510  is connected to a third-party VAV RTU  540  via a wired input  568  provided to PEAK controller  534 . Zone coordinators  508  and  518  are shown as Verasys COBP engines (VCEs) connected to COBP RTUs  526  and  552 , respectively. Zone coordinator  508  is connected directly to COBP RTU  526  via zone bus  558 , whereas zone coordinator  518  is connected to a third-party COBP RTU  552  via a wired input  570  provided to PEAK controller  544 . 
     Zone controllers  524 ,  530 - 532 ,  536 , and  548 - 550  can communicate with individual BMS devices (e.g., sensors, actuators, etc.) via sensor/actuator (SA) busses. For example, VAV zone controller  536  is shown connected to networked sensors  538  via SA bus  566 . Zone controller  536  can communicate with networked sensors  538  using a MSTP protocol or any other communications protocol. Although only one SA bus  566  is shown in  FIG. 5 , it should be understood that each zone controller  524 ,  530 - 532 ,  536 , and  548 - 550  can be connected to a different SA bus. Each SA bus can connect a zone controller with various sensors (e.g., temperature sensors, humidity sensors, pressure sensors, light sensors, occupancy sensors, etc.), actuators (e.g., damper actuators, valve actuators, etc.) and/or other types of controllable equipment (e.g., chillers, heaters, fans, pumps, etc.). 
     Each zone controller  524 ,  530 - 532 ,  536 , and  548 - 550  can be configured to monitor and control a different building zone. Zone controllers  524 ,  530 - 532 ,  536 , and  548 - 550  can use the inputs and outputs provided via their SA busses to monitor and control various building zones. For example, a zone controller  536  can use a temperature input received from networked sensors  538  via SA bus  566  (e.g., a measured temperature of a building zone) as feedback in a temperature control algorithm. Zone controllers  524 ,  530 - 532 ,  536 , and  548 - 550  can use various types of control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, feedback control algorithms, etc.) to control a variable state or condition (e.g., temperature, humidity, airflow, lighting, etc.) in or around building  10 . 
     HVAC System with Automated Device Pairing and Dimensional Mismatch Handling 
     Referring now to  FIG. 6A , a block diagram of a HVAC system  600  is shown, according to an exemplary embodiment. HVAC system  600  is shown to include a controller  602 , an input module  630 , an output module  632 , several sensors  640 , and several actuation devices  650 . In brief overview, controller  602  receives sensor readings from sensors  640  via input module  630  and uses the sensor readings to generate actuation signals (e.g., control signals, setpoints, operating commands, etc.) for actuation devices  650 . Controller  602  provides the actuation signals to actuation devices  650  via output module  632 . Actuation devices  650  operate to affect an environmental condition in a building (e.g., temperature, humidity, airflow, etc.), which can be measured by sensors  640  and provided as a feedback to controller  602 . 
     Controller  602  can be any type of controller in a HVAC system or BMS. In some embodiments, controller  602  is a zone controller configured to monitor and control a building zone. For example, controller  602  can be a zone temperature controller, a zone humidity controller, a zone lighting controller, a VAV zone controller (e.g., VAV zone controllers  524 ,  532 ,  536 ,  550 ), a COBP zone controller (e.g., COPB controller  530 ,  548 ), or any other type of controller for a building zone. In other embodiments, controller  602  is a system controller or subsystem controller. For example, controller  602  can be a BMS controller (e.g., BMS controller  366 ), a central plant controller, a subplant controller, a supervisory controller for a HVAC system or any other type of building subsystem (e.g., a controller for any of building subsystems  428 ). In some embodiments, controller  602  is a field controller or device controller configured to monitor and control the performance of a set of HVAC devices or other building equipment. For example, controller  602  can be an AHU controller (e.g., AHU controller  330 ), a thermostat controller (e.g., thermostat controller  516 ), a rooftop unit controller, a chiller controller, a damper controller, or any other type of controller in a HVAC system or BMS. 
     Sensors  640  can include any of a variety of physical sensors configured to measure a variable state or condition in a building. For example, sensors  640  are shown to include temperature sensors  641 , humidity sensors  642 , airflow sensors  643 , lighting sensors  644 , pressure sensors  645 , and voltage sensors  646 . Sensors  640  can be distributed throughout a building and configured to measure various environmental conditions at different locations in the building. For example, one of temperature sensors  641  can be located in a first zone of the building and configured to measure the temperature of the first zone, whereas another of temperature sensors  641  can be located in a second zone of the building and configured to measure the temperature of the second zone. Similarly, sensors  640  can be distributed throughout a HVAC system and configured to measure conditions at different locations in the HVAC system. For example, one of temperature sensors  641  can be a supply air temperature sensor configured to measure the temperature of the airflow provided to a building zone from an AHU, whereas another of temperature sensors  641  can be a return air temperature sensor configured to measure the temperature of the airflow returning from the building zone to the AHU. 
     Sensors  640  are shown providing sensor readings to controller  602  via input module  630 . The sensor readings can include analog inputs, digital inputs, measurements, data samples, and/or other types of data generated by sensors  640 . In some embodiments, sensors  640  provide analog inputs to input module  630  and input module  630  converts the analog inputs to digital data samples. Each data sample can include a data point and associated metadata. The data point can include a measured value attribute indicating the value of the measured variable and a time attribute indicating the time at which the measured value was observed. The metadata can include a unit of measure (e.g., degrees C., degrees F., kPa, volts, Watts, m/s, etc.), a sampling rate, a source description, a location, a purpose, or other attributes describing the associated data point. Controller  602  can receive the sensor readings from input module  630  and store the sensor readings as time series data in a time series database  616  (described in greater detail below). Controller  602  can use the sensor readings and/or time series data to generate appropriate actuation signals for actuation devices  650 . 
     Actuation devices  650  can include any of a variety of physical devices configured to affect a variable state or condition in a building. For example, actuation devices  650  are shown to include chillers  651 , heaters  652 , valves  653 , air handling units (AHUs)  654 , dampers  655 , and actuators  656 . Although only a few types of actuation devices  650  are shown, it should be understood that actuation devices  650  can include any type of equipment or device configured to affect building conditions. For example, actuation devices  650  can power relays, switches, lights, pumps, fans, cooling towers, or other types of building equipment or central plant equipment. Actuation devices  650  can include some or all of the equipment in building  10 , HVAC system  100 , waterside system  200 , airside system  300 , BMS  400 , and/or BMS  500 , as described with reference to  FIGS. 1-5 . Actuation devices  650  can operate to affect various building conditions including temperature, humidity, airflow, lighting, air quality, power consumption, or any other variable state or condition in a building. 
     Actuation devices  650  are shown receiving actuation signals from controller  602  via output module  632 . In some embodiments, the actuation signals are control signals for actuation devices  650  (e.g., operating setpoints, on/off commands, etc.). For example, the actuation signals can include commands to activate or deactivate individual chillers  651  or heaters  652  and/or commands to operate chillers  651  or heaters  652  at a variable capacity (e.g., operate at 20% capacity, 40% capacity, etc.). The actuation signals can include position setpoints for valves  653 , dampers  655 , or actuators  656 . The position setpoints can include commands to move to a fully closed position, a 50% open position, a fully open position, or any intermediate position. 
     In some embodiments, the actuation signals are provided directly to actuation devices  650  from controller  602  and used to adjust a physical operation of actuation devices  650  (e.g., if controller  602  directly controls actuation devices  650 ). In other embodiments, the actuation signals are provided to an intermediate controller for actuation devices  650 . For example, controller  602  can provide a setpoint to a local controller for one or more of actuation devices  650 . The local controller can then generate control signals for actuation devices  650  to achieve the setpoint received from controller  602 . 
     Controller  602  can use the sensor readings from sensors  640  as feedback to determine appropriate actuation signals for actuation devices  650 . Controller  602  can be configured to use one or more feedback control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, etc.) to control actuation devices  650  based on the sensor readings. For example, if the sensor reading from one of temperature sensors  641  indicates that the temperature of a particular building zone is below a temperature setpoint for the building zone, controller  602  can provide an actuation signal to one of heaters  652 , dampers  655 , or AHUs  654  to increase the amount of heating provided to the building zone. 
     In some embodiments, the feedback control actions performed by controller  602  require knowledge of the relationships between sensors  640  and actuation devices  650 . For example, in order to drive the temperature measured by a particular temperature measured toward a setpoint, controller  602  may need to identify which of actuation devices  650  is configured to affect the measured temperature. In other words, controller  602  may need to identify causal relationships between various sensors  640  and actuation devices  650 . If such relationships are not already known, controller  602  can perform an automated device pairing process to establish associations between various sensors  640  and actuation devices  650 . 
     Some buildings have hundreds of sensors  640  and actuation devices  650 . It can be cumbersome, error prone, and time consuming to manually identify the associations between sensors  640  and their corresponding actuation devices  650 . Additionally, building evolve over time which can change existing relationships between sensors  640  and actuation devices  650 . For example, remodeling a building can break existing relationships between paired sensors  640  and actuation devices  650  or create new relationships that did not previously exist. Advantageously, the automated device pairing process performed by controller  602  can automatically identify causal relationships between various sensors  640  and actuation devices  650  (e.g., heater A affects temperature sensor B, damper C affects flow sensor D, etc.). Once the causal relationships have been identified, controller  602  can store associations between related sensors  640  and actuation devices  650  and use the stored associations to perform control actions. 
     Still referring to  FIG. 6A , controller  602  is shown to include a communications interface  604  and a processing circuit  606 . Communications interface  604  can include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with external systems or devices (e.g., input module  630 , output module  632 , sensors  640 , actuation devices  650 , etc.). Data communications via communications interface  604  can be direct (e.g., local wired or wireless communications) or via a communications network (e.g., a LAN, a WAN, the Internet, a cellular network, etc.). For example, communications interface  604  can include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network, a Wi-Fi transceiver for communicating via a wireless communications network, and/or cellular or mobile phone communications transceivers for communicating via a cellular communications network. 
     Processing circuit  606  is shown to include a processor  608  and memory  610 . Processing circuit  606  can be communicably connected to communications interface  604  such that processing circuit  606  and the various components thereof can send and receive data via communications interface  604 . Processor  608  can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components. 
     Memory  610  (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory  610  can be or include volatile memory or non-volatile memory. Memory  610  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present application. In some embodiments, memory  610  is communicably connected to processor  608  via processing circuit  606  and includes computer code for executing (e.g., by processing circuit  606  and/or processor  608 ) one or more processes described herein. 
     Still referring to  FIG. 6A , controller  602  is shown to include virtual sensors  614  and virtual actuation devices  612 . Virtual sensors  614  can include logical representations of one or more physical sensors  640 . For example, virtual sensors  614  can include data objects (e.g., BACnet objects, JSON objects, etc.), each of which corresponds to a particular physical sensor  640  and functions as a logical representation of the corresponding physical sensor  640  within the memory  610  of controller  602 . Virtual sensors  614  can include various attributes which describe the corresponding physical sensors  640  and include the sensor readings from the corresponding physical sensors  640 . An example of a virtual sensor  614  shown below: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 { 
               
            
           
           
               
               
            
               
                   
                 “unique identifier” : “ucis-2327-2127-sded-iesa”, 
               
               
                   
                 “signature” : “7b1c018bf975c88fbe9df6292bf370b1”, 
               
               
                   
                 “BACnet object” : { 
               
            
           
           
               
               
            
               
                   
                 “object identifier” : “analog input #1101”, 
               
               
                   
                 “object name” : “507_SP2.RET_AIR”, 
               
               
                   
                 “description” : “return air temp”, 
               
               
                   
                 “device type” : “thermistor”, 
               
               
                   
                 “object type” : “analog input”, 
               
               
                   
                 “units” : “DEG_F”, 
               
               
                   
                 “present value” : “68” 
               
               
                   
                 “update interval” : “15 min”, 
               
               
                   
                 “status flags” : [ 
               
            
           
           
               
               
            
               
                   
                 “in alarm”, 
               
               
                   
                 “fault”, 
               
               
                   
                 “overridden”, 
               
               
                   
                 “out of service” 
               
            
           
           
               
               
            
               
                   
                 ], 
               
               
                   
                 “event status” : “normal”, 
               
               
                   
                 “reliability” : “no fault detected”, 
               
               
                   
                 “out of service” : “false”, 
               
            
           
           
               
               
            
               
                   
                 } 
               
            
           
           
               
               
            
               
                   
                 } 
               
               
                   
                   
               
            
           
         
       
     
     Virtual sensors  614  can include a unique identifier attribute and a signature attribute. In some embodiments, the unique identifier attribute is a text string uniquely identifying a particular virtual sensor  614  (e.g., ucis-2327-2127-sded-iesa). The signature attribute can be generated by controller  602  as a function of the BACnet object attribute values. For example, controller  602  can generate the signature attribute using the following function: 
       Signature=MD5(CONCAT(“analog input #1101”,“507_SP2.RET_AIR”,“return air temp”,“thermistor”,“analog input”,“DEG_F”,“15 min”,“68”)
 
     where the CONCAT ( ) function is a string concatenation function of the attribute values and the MD5 ( ) function is a hashing function producing a hash value (e.g., a 128 bit hash value). When any of the attribute values change, the signature attribute will also change. Accordingly, the signature attribute enables capturing of source data changes, including changes in the present value of the sensor reading. 
     Virtual sensors  614  can include a BACnet object attribute with various sub-attributes describing the corresponding physical sensors  640 . For example, virtual sensors  614  can include an object identifier attribute which identifies the type of input (e.g., analog input, digital input, enumerated value input, binary input, etc.), an object name attribute which names the corresponding physical sensor (e.g., 507_SP2.RET_AIR), a description attribute which provides a description of the measured value (e.g., return air temperature, supply air temperature, relative humidity, etc.), and a device type attribute which indicates the type of physical sensor  640  represented by the virtual sensor  614  (e.g., thermistor, thermocouple, limit switch, piezoelectric, etc.). 
     Virtual sensors  614  can include a present value attribute which indicates the present value of the sensor reading (e.g.,  68 ), a units attribute which indicates the unit of measure of the present value attribute (e.g., degrees F., degrees C., kPa, volts, etc.), and an update interval attribute which indicates how often the present value attribute is updated (e.g., 15 minutes, 1 minute, 1 second, etc.). In some embodiments, virtual sensors  614  include status attributes (e.g., status flags, event status, reliability, etc.) which indicate the current status of the corresponding physical sensor  640 . The attributes of virtual sensors  614  can be updated in real time (e.g., continuously or periodically as defined by the update interval) to reflect the current sensor readings and/or the status of the corresponding physical sensors  640 . In some embodiments, virtual sensors  614  include software agents which monitor the sensor readings and other information (e.g., metadata) received from sensors  640  and update the corresponding attribute values accordingly. 
     Similarly, virtual actuation devices  612  can include logical representations of one or more physical actuation devices  650 . For example, virtual actuation devices  612  can include data objects (e.g., BACnet objects, JSON objects, etc.), each of which corresponds to a particular physical actuation device  650  and functions as a logical representation of the corresponding physical actuation device  650  within the memory  610  of controller  602 . Virtual actuation devices  612  can include various attributes which describe the corresponding physical actuation devices  650 . In some embodiments, virtual actuation devices  612  include some or all of the same attributes of virtual sensors  614 , as previously described. In some embodiments, virtual actuation devices  612  include a present value attribute which includes the most recent value of the actuation signal provided to the virtual actuation device. 
     Still referring to  FIG. 6A , controller  602  is shown to include a time series database  616 . Virtual sensors  614  are shown providing sensor readings to time series database  616 , whereas virtual actuation devices  612  are shown providing actuation signals to time series database  616 . The sensor readings provided by virtual sensors  614  can include a series of sensor readings collected by each of sensors  640  over time. Similarly, the actuation signals provided by virtual actuation devices  612  can include a series of values of the actuation signals provided to each of actuation devices  650  over time. Time series database  616  can store the sensor readings and actuation signals as time series data for each of sensors  640  and actuation devices  650 . Each time series corresponds to one of sensors  640  or actuation devices  650  and includes a series of data values received from the corresponding sensor  640  or provided to the corresponding actuation device  650 . 
     In some embodiments, each time series is a partially ordered tuple of a particular data point and associated metadata, as shown in the following equation: 
       Timeseries=&lt;Data Point,Metadata&gt; 
     Each data point may include a series of data values (e.g., sensor reading values or actuation signal values) and corresponding times at which those values were measured or provided. An example of a Data Point is shown in the following equation: 
       Data Point=&lt;time,value&gt; 
     where each of time and value can include a vector of time series values. Metadata can include various attributes of the corresponding data point, as shown in the following equation: 
       Metadata=&lt;unit,sampling rate,source description,location,purpose, . . . &gt; 
     where each item of Metadata represents one of the attributes (and corresponding attribute values) of the virtual sensor  614  or virtual actuation device  612  from which the time series values of the associated data point were received. Time series database  616  can store each time series for use by other components of controller  602 . 
     In some embodiments, time series database  616  stores each time series of actuation signal values as an actuation signal time series t(x) as shown in the following equation: 
         t ( x )={ t   1   ,t   2   ,t   3   , . . . ,t   N-1   ,t   N } 
     where each element t i  of the actuation signal time series t(x) is the value of the actuation signal at a particular time (i.e., a sample of the actuation signal) and N is the total number of elements in the actuation signal time series t(x). Similarly, time series database  616  can store each time series of sensor reading values as a sensor response time series r(x) as shown in the following equation: 
         r ( x )={ r   1   ,r   2   ,r   3   , . . . ,r   M-1   ,r   M } 
     where each element r i  of the sensor response time series r(x) is the value of the sensor response signal at a particular time (i.e., a sample of the sensor response signal) and M is the total number of elements in the sensor response time series r(x). 
     Controller  602  can automatically identify causal relationships between various sensors  640  and actuation devices  650  based on the time series data associated therewith. For example, for each actuation signal time series t(x), controller  602  can identify one or more of the sensor response time series r(x) which closely match the actuation signal time series. In some embodiments, controller  602  uses a distance function to determine which of the sensor response time series r(x) most closely match the actuation signal time series t(x). As described in detail below, the distance function may compare corresponding values t i  and r i  of each time series to calculate a similarity metric or similarity score for pairs of actuation signal time series t(x) and sensor response time series r(x). 
     In some embodiments, the similarity metric calculation performed by controller  602  requires the actuation signal time series t(x) and sensor response time series r(x) to have the same number of samples (i.e., N=M) and/or sampling rate to allow the corresponding values t i  and r i  of each time series to be identified and compared. However, some time series can have different numbers of samples (i.e., N≠M), which can be collected at different sampling rates. This is referred to as a dimensional mismatch between time series. A dimensional mismatch between time series can complicate the similarity metric calculation since it can be difficult to determine the corresponding values t i  and r i  of each time series. However, controller  602  can automatically identify and compensate for dimensional mismatches between time series. 
     Still referring to  FIG. 6A , controller  602  is shown to include a dimensional mismatch identifier  618 . Dimensional mismatch identifier  618  is configured to identify dimensional mismatches between various actuation signal time series t(x) and sensor response time series r(x). As described above, a dimensional mismatch may occur when two time series have a different number of samples and/or sampling rates. In some embodiments, dimensional mismatch identifier  618  determines the size of each time series. For example, dimensional mismatch identifier  618  can determine the number of samples N in the actuation signal time series t(x) and the number of samples M in the sensor response time series r(x). Dimensional mismatch identifier  618  can detect a dimensional mismatch in response to a determination that the number of samples N in the actuation signal time series t(x) is different from the number of samples M in the sensor response time series r(x) (i.e., N≠M). 
     In some embodiments, dimensional mismatch identifier  618  determines the sampling rate of each time series. In some embodiments, the sampling rate of a time series may be stored as metadata associated with the time series in time series database  616 . Dimensional mismatch identifier  618  can determine the sampling rate of a time series by reading the sampling rate from the metadata in time series database  616 . In other embodiments, dimensional mismatch identifier  618  calculates the sampling rate for one or more time series based on the size of the time series and the range of time spanned by the time series. 
     Dimensional mismatch identifier  618  can identify a start time and an end time for the time series by reading the timestamps associated with the first and last data samples in the time series. Dimensional mismatch identifier  618  can then calculate the sampling rate by dividing the size of the time series by the difference between the end time and the start time, as shown in the following equation: 
     
       
         
           
             sampling_rate 
             = 
             
               
                 size_of 
                  
                 _timeseries 
               
               
                 end_time 
                 - 
                 start_time 
               
             
           
         
       
     
     where size_of_timeseries is the number of samples M or N in the time series, end_time is the timestamp associated with the last sample in the time series, start_time is the timestamp associated with the first sample in the time series, and sampling_rate is the sampling rate of the time series, expressed as the number of samples per unit time (e.g., 0.8 samples/hour). Dimensional mismatch identifier  618  can detect a dimensional mismatch in response to a determination that two time series have different sampling rates. 
     Dimensional mismatch identifier  618  can be configured to correct a dimensional mismatch between two time series. In some embodiments, dimensional mismatch identifier  618  corrects dimensional mismatch by increasing the number of samples of the time series with the fewer number of samples (e.g., by interpolating between samples). In other embodiments, dimensional mismatch identifier  618  corrects dimensional mismatch by reducing the number of samples of the time series with the greater number of samples (e.g., by discarding extra samples). In other embodiments, dimensional mismatch identifier  618  merely identifies a dimensional mismatch to other components of controller  602  which are configured to address the dimensional mismatch. For example, dimensional mismatch identifier  618  is shown reporting a dimensional mismatch to discrete cosine transformer  620 . 
     Still referring to  FIG. 6A , controller  602  is shown to include a discrete cosine transformer  620 . Discrete cosine transformer  620  can be configured to perform a discrete cosine transform (DCT) for each actuation signal time series t(x) and sensor response time series r(x). A DCT expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. There are eight standard DCT variants, commonly referred to as DCT-I, DCT-II, DCT-III, DCT-IV, DCT-V, DCT-VI, DCT-VII, and DCT-VIII. One of these variants (i.e., DCT-II) is discussed in detail below. However, it should be understood that discrete cosine transformer  620  can use any standard or non-standard DCT variant in other embodiments. 
     In some embodiments, discrete cosine transformer  620  performs a DCT for each actuation signal time series t(x) using the following equation: 
     
       
         
           
             
               T 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   N 
                   - 
                   1 
                 
               
                
               
                 
                   t 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         N 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               N 
               - 
               1 
             
           
         
       
     
     where T(k) is the kth coefficient of the DCT of the actuation signal time series t(x), t i  is the ith sample of the actuation signal time series t(x), and N is the number of samples of the actuation signal time series t(x). Discrete cosine transformer  620  can generate an array T of the DCT coefficients (e.g., T=[T(0), T(1), T(2), . . . , T(N−2), T(N−1)]) where the length of the array T is the same as the number of samples N of the actuation signal time series t(x). 
     Similarly, discrete cosine transformer  620  can perform a DCT for each sensor response time series r(x) using the following equation: 
     
       
         
           
             
               R 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   M 
                   - 
                   1 
                 
               
                
               
                 
                   r 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         M 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               M 
               - 
               1 
             
           
         
       
     
     where R(k) is the kth coefficient of the DCT of the sensor response time series r(x), r i  is the ith sample of the sensor response time series r(x), and M is the number of samples of the sensor response time series r(x). Discrete cosine transformer  620  can generate an array R of the DCT coefficients (e.g., R=[R(0), R(1), R(2), . . . , R(M−2), R(M−1)]) where the length of the array R is the same as the number of samples M of the sensor response time series r(x). 
     The following example illustrates the result of applying DCT to an input time series X(n). The input time series X(n) can be an actuation signal time series t(x) or a sensor response time series r(x) as previously described. The samples of the input time series X(n) are shown in the following array: 
         X ( n )=[1.00,1.70,2.00,2.00,4.30,4.50,3.00,3.00,2.30,2.20,2.20,2.30] 
     where the input time series X(n) includes twelve time series values X(1), . . . , X(12). Applying DCT to the input time series X(n) results in a set of DCT coefficients, shown in the following array: 
         Y ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52,−0.20,−0.93,−0.63,0.32,0.50,−0.06]
 
     where the array of DCT coefficients Y(k) includes twelve DCT coefficients Y(1), . . . , Y(12). 
     Still referring to  FIG. 6A , controller  602  is shown to include a DCT quantizer  622 . DCT quantizer  622  can be configured to apply a quantization process to the sets of DCT coefficients generated by discrete cosine transformer  620 . As described above, the DCT process performed by discrete cosine transformer  620  converts an input data time series X(n) into a sum of cosine functions which oscillate at different frequencies. The cosine function with the lowest frequency is typically first in the summation, followed by cosine functions with successively higher frequencies. Accordingly, the DCT coefficient which occurs first in the array of DCT coefficients Y(k) represents the magnitude of the lowest frequency cosine function. Each of the following DCT coefficients represents the magnitude of a cosine function with a successively higher oscillation frequency. 
     DCT quantizer  622  can apply a quantization process to the sets of DCT coefficients by filling some of the higher frequency DCT coefficients with zeros. This has the effect of removing some of the higher frequency components (i.e., cosine functions) from the summation while retaining the lower frequency components. In some embodiments, DCT quantizer  622  performs the quantization process using a predetermined quantization level. The quantization level may define the number of the DCT coefficients which are retained (i.e., not filled with zeros). For example, a quantization level of six may retain the DCT coefficients applied to the six lowest frequency cosine functions (e.g., the first six DCT coefficients in the array) while the remaining DCT coefficients are filled with zeros. 
     The following example illustrates the result of a quantization process which can be performed by DCT quantizer  622 . DCT quantizer  622  can modify the array of DCT coefficients Y(k) shown above to form the following quantized array QY(k): 
         QY ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52,0.00,0.00,0.00,0.00,0.00,0.00]
 
     In this example, a quantization level of six is applied, meaning that only the first six DCT coefficients are retained from the original array of DCT coefficients Y(k). The remaining DCT coefficients are filled with zeros. True compression can be achieved by not storing the zeros. For example, DCT quantizer  622  can store the following compressed array C(k): 
         C ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52]
 
     in which the coefficients filled with zeros are discarded to produce a compressed array with a length equal to the quantization level applied. In this example, the compressed array C(k) has a length of six resulting from the use of a quantization level of six. In various embodiments, DCT quantizer  622  can use a quantization level of six or any other quantization level to produce compressed arrays of various lengths. 
     In some embodiments, DCT quantizer  622  automatically determines the quantization level to apply based on the number of samples in each of the original actuation signal time series t(x) and sensor response time series r(x). As described above, the number of DCT coefficients produced by discrete cosine transformer  620  for a given input time series X(n) may be equal to the number of samples in the time series X(n) prior to performing DCT. For example, an input time series X 1 (n) with twelve samples may result in twelve DCT coefficients in the resultant DCT coefficient array Y 1 (k), whereas an input time series X 2 (n) with ten samples may result in ten DCT coefficients in the resultant DCT coefficient array Y 2 (k). In some embodiments, DCT quantizer  622  identifies the actuation signal time series t(x) or sensor response time series r(x) with the fewest samples and applies a quantization level equal to the number of samples in the identified time series. 
     In some embodiments, DCT quantizer  622  applies the same quantization level to the sets of DCT coefficients corresponding to each of the original actuation signal time series t(x) and sensor response time series r(x). Using the same quantization level for each of the original time series may result in the same number of compressed DCT coefficients being stored for each of the original actuation signal time series t(x) and sensor response time series r(x). In some embodiments, the number of stored DCT coefficients is equal to the number of samples in the original time series with the fewest samples. Advantageously, this allows for direct comparison of the DCT coefficients in the compressed arrays C(k) generated for each of the original time series without requiring decompression, interpolation, synchronization, or other processing steps after the compressed arrays C(k) are generated. 
     In some embodiments, DCT quantizer  622  generates a compressed time series Ta based on each compressed array of DCT coefficients. DCT quantizer  622  can store the compressed time series T α  using the following data structure: 
         T   α = α,δ,ρ,κ, ψ , υ 1 ,υ 2 , . . . υ p     
 
     where α is the time series ID of the source time series (e.g., the actuation signal time series t(x) or sensor response time series r(x)), δ is the dimension of the source time series (e.g., the number of samples in the source time series), ρ is the quantization level applied by DCT quantizer  622 , κ is a pointer for metadata,  ψ  indicates the start time and end time of samples in the source time series, and  υ 1 , υ 2 , . . . υ p    is the array of compressed DCT coefficients. An example of a compressed time series stored using this data structure is as follows: 
         T   203 = 203,12,6, 2016:10:05:12:00:00,2016:10:05:13:00:00 , 8.80,−0.57,−2.65,−1.15,0.81,0.52   
 
     where  203  is the time series ID of the source time series, 12 is size of the source time series (e.g., 12 samples in the source time series), 6 is the quantization level applied by DCT quantizer  622 , 2016:10:05:12:00:00 is the start time of the source time series (e.g., the timestamp of the earliest sample in the source time series), 2016:10:05:13:00:00 is the end time of the source time series (e.g., the timestamp of the latest sample in the source time series), and the array  8.80, −0.57, −2.65, −1.15, 0.81, 0.52  includes the compressed DCT coefficients generated by DCT quantizer  622 . 
     Still referring to  FIG. 6A , controller  602  is shown to include a similarity calculator  624 . Similarity calculator  624  can be configured to determine whether two time series are similar to each other based on the compressed DCT coefficients and/or compressed time series generated by DCT quantizer  622 . In some embodiments, similarity calculator  624  determines whether any of the sensor response time series r(x) are similar to a given actuation signal time series t(x). Similarity calculator  624  can repeat this process for each actuation signal time series t(x) to determine whether any of the sensor response time series r(x) are similar to each actuation signal time series t(x). 
     In some embodiments, similarity calculator  624  determines whether two time series are similar to each other by calculating a similarity metric for the two time series. The similarity metric can be based on the compressed DCT coefficients generated by DCT quantizer  622  for the two time series. For example, the compressed DCT coefficients generated for a given actuation signal time series t(x) can be represented by an array T, whereas the compressed DCT coefficients generated for a given sensor response time series r(x) can be represented by an array R. The arrays T and R can be particular instances of the compressed array C(k) generated by DCT quantizer  622  for the actuation signal time series t(x) and the sensor response time series r(x), respectively. Each array T and R can include a predetermined number N of DCT coefficients, defined by the quantization level applied by DCT quantizer  622 . Examples of arrays T and R are as follows: 
     
       
      
       T= 
       
       t 
       1 
       ,t 
       2 
       , . . . t 
       N 
       
      
     
     
       
      
       R= 
       
       r 
       1 
       ,r 
       2 
       , . . . ,r 
       N 
       
      
     
     Similarity calculator  624  can calculate a similarity metric for the source time series t(x) and r(x) based on the corresponding arrays T and R of compressed DCT coefficients. In some embodiments, similarity calculator  624  calculates the similarity metric using the following equation: 
     
       
         
           
             
               d 
                
               
                 ( 
                 
                   T 
                   , 
                   R 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   N 
                 
               
                
               
                 
                   
                     
                       ( 
                       
                         
                           t 
                           i 
                         
                         - 
                         
                           r 
                           i 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 
                   δ 
                   i 
                 
               
             
           
         
       
     
     where t i  is the ith DCT coefficient in the array T based on the actuation signal time series t(x), r i  is the ith DCT coefficient in the array R based on the sensor response time series r(x), δ i  is the standard deviation of the ith DCT coefficients, and N is the number of DCT coefficients in each array T and R. Low values of the similarity metric d(T, R) indicate a greater similarity, whereas high values of the similarity metric d (T, R) indicate a lesser similarity. Similarity calculator  624  can calculate a similarity metric for each pairing of an actuation signal time series t(x) and a sensor response time series r(x). 
     Still referring to  FIG. 6A , controller  602  is shown to include a device pairing generator  626 . Device pairing generator  626  is shown receiving the similarity metrics from similarity calculator  624 . Device pairing generator  626  can be configured to generate device pairings based on the similarity metrics. Each device pairing may include one of sensors  640  and one of actuation devices  650 . A device pairing may indicate that the actuation device  650  in the device pairing is configured to affect the variable measured by the sensor  640  in the device pairing. For each potential device pairing (i.e., for each combination of a sensor  640  and an activation device  650 ), device pairing generator  626  can identify the corresponding arrays T and R of compressed DCT coefficients and the calculated similarity metric d(T, R) based on the arrays T and R. Device pairing generator  626  can use the similarity metric d(T, R) to determine whether to generate a device pairing between the given sensor  640  and the given actuation device  650 . 
     In some embodiments, device pairing generator  626  generates device pairings by comparing the similarity metric d(T, R) to a threshold value. Device pairing generator  626  can be configured to generate a device pairing between a sensor  640  and an actuation device  650  if the similarity metric d(T, R) is less than the threshold value (e.g., d(T, R)&lt;threshold). The threshold value can be a predefined value or a calculated value (e.g., a standard deviation of the DCT coefficients). 
     In some embodiments, the threshold value is a similarity metric between the actuation signal time series t(x) and a baseline (e.g., average) sensor signal time series a(x) over a predetermined time period. The baseline sensor signal time series a(x) can indicate the average sensor response from a particular sensor  640  before the actuation signal is applied to the actuation device  650  (e.g., baseline sensor readings), whereas the sensor response time series r(x) can indicate the sensor response from the same sensor  640  after the actuation signal is applied to the actuation device  650 . If the actuation device  650  affects the sensor  640 , the actuation signal time series t(x) is expected to be more similar to the sensor response time series r(x) than the baseline sensor signal time series a(x). Accordingly, the similarity metric d(T, R) between the actuation signal time series t(x) and the sensor response time series r(x) is expected to be lower (i.e., more similar) than the similarity metric d(T, A) between the actuation signal time series t(x) and the baseline sensor signal time series a(x). 
     In some embodiments, time series database  616  stores a baseline sensor signal time series a(x) for each of sensors  640  based on sensor readings from sensors  640  before the actuation signal is applied to actuation devices  650 . Time series database  616  can also store a sensor response time series r(x) for each of sensors  640  based on sensor readings from sensors  640  while the actuation signal is applied to actuation devices  650  or after the actuation signal is applied to actuation devices  650 . Discrete cosine transformer  620  and DCT quantizer  622  can generate DCT coefficients and compressed DCT coefficients for each baseline sensor signal time series a(x), sensor response time series r(x), and actuation signal time series t(x). Similarity calculator  624  can then calculate a similarity metric d(T, R) between each actuation signal time series t(x) and sensor response time series r(x) and a similarity metric d(T, A) between each actuation signal time series t(x) and baseline sensor signal time series a(x). Device pairing generator  626  can generate a device pairing between a sensor  640  and an actuation device  650  if the similarity metric d (T, R) for a given combination of a sensor  640  and an actuation device  650  is less than the similarity metric d(T,A) for the sensor  640  and the actuation device  650 . 
     In some embodiments, device pairing generator  626  generates device pairings by comparing the similarity metrics d(T, R) for various combinations of sensors  640  and actuation devices  650 . For each actuation device  650 , device pairing generator  626  can identify the similarity metrics d(T, R) calculated for the actuation device  650  in combination with each of sensors  640 . Each similarity metric d(T, R) indicates the similarity (i.e., the closeness) between the actuation signal time series t(x) associated with the actuation device  650  and the sensor response time series r(x) associated with one of sensors  640 . For example, the similarity metric d(T 1 , R 1 ) may indicate the similarity between a first actuation device  650  (corresponding to array T 1 ) and a first sensor  640  (corresponding to array R 1 ), whereas the similarity metric d(T 1 , R 2 ) may indicate the similarity between the first actuation device  650  and a second sensor  640  (corresponding to array R 2 ). Device paring generator  626  can identify all of the similarity metrics associated with a given actuation device  650  (e.g., d(T 1 , R 1 ), . . . , d(T 1 , R P ), where P is the total number of sensors  640  and/or sensor response time series r(x)). 
     Device pairing generator  626  can determine which of the identified similarity metrics is the lowest for a given actuation device  650 . The lowest similarity metric indicates the closest match between the actuation signal time series t(x) associated with the actuation device  650  and the sensor response time series r(x) associated with one of sensors  640 . Device pairing generator  626  can generate a device pairing between the actuation device  650  and the sensor  640  having the lowest similarity metric d(T, R) with the actuation device  650 . If the actuation device  650  has the same similarity metric with multiple sensors  640  (e.g., d(T 1 , R 1 )=d(T 1 , R 2 )), device pairing generator  626  can examine the time delay Δw between the actuation signal time series t(x) associated with the actuation device  650  and sensor response time series r(x) associated with each of sensors  640 . The time delay Δw may indicate the delay between the time w 1  at which the actuation signal is applied to the actuation device  650  and the time w 2  at which the effects of the actuation signal are evident in the sensor response (e.g., Δw=w 2 −w 1 ). Device pairing generator  626  can determine which of the sensors  640  has the lowest time delay Δw and can generate a device pairing between the actuation device  650  and the sensor  640  with the lowest time delay Δw. 
     Device pairing generator  626  can generate one or more device pairings for each of actuation devices  650 . Each device pairing can identify one of actuation devices  650  and one of sensors  640 . A device pairing between an actuation device  650  and a sensor  640  indicates that the actuation device  650  is capable of affecting the value measured by the sensor. Device pairing generator  626  can provide the device pairings to device controller  628 . Device controller  628  can use the device pairings to generate the actuation signals for actuation devices  650 . In some embodiments, device controller  628  uses the device pairings to automatically generate and store causal relationships between various sensors  640  and actuation devices  650 . 
     In some embodiments, device controller  628  uses the device pairings to create kits of causally related devices. Each kit may be a logical grouping or set of devices in HVAC system  600  which includes one or more of sensors  640  and one or more of actuation devices  650 . In some embodiments, each kit includes all of the sensors  640  and actuation devices  650  that are linked to each other by the device pairings generated by device pairing generator  626 . Each device in a given kit may have a device pairing with at least one other device in the kit. For example, a temperature sensor for a building zone may have a device pairing with a chiller which is operable to affect the temperature of the building zone. The temperature sensor may also have device pairings with an air handling unit and an airflow damper which operate to provide airflow to the building zone. The kit generated by device controller  628  may include the temperature sensor and all of the actuation devices which operate to affect the temperature of the building zone (e.g., the chiller, the air handling unit, the airflow damper, etc.). 
     In some embodiments, device controller  628  uses the kits to detect and diagnose faults or performance issues in the building. For example, a temperature fault for a building zone (e.g., temperature out of range) can be detected by a temperature sensor located in the building zone. However, the temperature fault may originate from a fault in one or more of the actuation devices  650  which affect the temperature measured by the temperature sensor. Device controller  628  can use the kits of causally related devices to identify one or more actuation devices  650  (e.g., a chiller, a heater, an air handling unit, a damper, etc.) which operate to affect the variable in fault (e.g., the temperature measured by the temperature sensor). Device controller  628  can then test the actuation devices  650  in the kit to determine whether any of the actuation devices  650  are operating abnormally and diagnose the cause of the fault. 
     In some embodiments, device controller  628  uses the kits to generate recommendations for resolving the fault. For example, device controller  628  may recommend that all of the actuation devices  650  in a kit be tested or investigated in order to determine which of the actuation devices  650  is contributing to a detected fault associated with a sensor  640  in the kit. In some embodiments, the recommendation is based on a duration of the fault. For example, if the fault has been occurring for an amount of time which is less than a duration threshold, device controller  628  may recommend that one or more of the devices in the kit be investigated or tested. However, if the fault has been occurring for an amount of time which exceeds the duration threshold, device controller  628  may recommend that one or more of the devices in the kit be replaced, repaired, or changed in order to resolve the fault. 
     In some embodiments, device controller  628  provides actuation devices  650  with test signals as part of the device pairing process. The test signals may be predetermined signals or sequences of control operations which differ from the control signals provided to actuation devices  650  during normal operation. In some embodiments, the test signals are the actuation signals t(x) used by other components of controller  602  to generate the device pairings. Device controller  628  can provide the test signals to actuation devices  650  via communications interface  604  and to virtual actuation devices  612 . Virtual actuation devices  612  can update their status in real time based on the test signals. 
     In some embodiments, device controller  628  uses the device pairings to create feedback control loops for HVAC system  600 . Each feedback control loop can receive a feedback signal from one or more of sensors  640  and can provide a control signal to one or more of actuation devices  650 . Device controller  628  can use the device pairings to define the sensors  640  and actuation devices  650  in each control loop. For example, device controller  628  can create a control loop which receives a feedback signal from the sensor  640  in a device pairing and provides a control signal to the actuation device  650  in the device pairing. Device controller  628  can map the sensor readings from the sensor  640  in the device pairing to the feedback signal in the control loop. Similarly, device controller  628  can map the actuation signals provided to the actuation device  650  in the device pairing to the control signal in the control loop. 
     Device controller  628  can use the feedback control loops to generate the actuation signals for actuation devices  650 . Device controller  628  can use state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, or any other type of control methodology to generate the actuation signals for actuation devices  650  based on the sensor readings. For example, if the sensor reading from one of temperature sensors  641  indicates that the temperature of a particular building zone is below a temperature setpoint for the building zone, device controller  628  can provide an actuation signal to one of heaters  652 , dampers  655 , or AHUs  654  to increase the amount of heating provided to the building zone. Advantageously, the relationships between actuation devices  650  and sensors  640  can be identified automatically based on the device pairings to allow device controller  628  to determine which of actuation devices  650  can be operated to affect a given sensor reading. 
     Referring now to  FIG. 6B , a block diagram illustrating a portion of HVAC system  600  in greater detail is shown, according to an exemplary embodiment. HVAC system  600  is shown to include a smart actuator  658 , sensors  640 , and a valve/damper  672 . Smart actuator  658  may be one of actuation devices  650  or a separate actuator in HVAC system  600 . Valve/damper  672  may be an airflow damper, a fluid control valve, an expansion valve, or any other type of flow control device in HVAC system  600 . Smart actuator  658  can be configured to operate valve/damper  672  (e.g., by opening and closing valve/damper  672 ) based on sensor readings received from sensors  640 . Advantageously, smart actuator  658  can automatically determine which of sensors  640  is affected by valve/damper  672  and can operate valve/damper  672  based on the sensor readings from the affected sensor or sensors  640 . 
     Smart actuator  658  is shown to include an actuation device  674  having a motor  676  and a drive device  678 . Drive device  678  may be mechanically coupled to valve/damper  672  and configured to open and close valve/damper  672  when operated by motor  676 . Motor  676  may be mechanically coupled to drive device  678  and configured to operate drive device  678  based on actuation signals received from processing circuit  606 . Unlike conventional actuators, smart actuator  658  can independently and automatically determine appropriate actuation signals for actuation device  674  without requiring input from an external controller. 
     Smart actuator  658  is shown to include a communications interface  680  and a processing circuit  606 . Communications interface  680  may be the same or similar to communications interface  604 , as described with reference to  FIG. 6A . Communications interface  680  can include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with external systems or devices (e.g., sensors  640 , user devices, supervisory controllers, etc.). Data communications via communications interface  680  can be direct (e.g., local wired or wireless communications) or via a communications network (e.g., a LAN, a WAN, the Internet, a cellular network, etc.). For example, communications interface  680  can include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network, a Wi-Fi transceiver for communicating via a wireless communications network, and/or cellular or mobile phone communications transceivers for communicating via a cellular communications network. 
     Processing circuit  606  may include some or all of the components of processing circuit  606  shown in  FIG. 6A . For example, processing circuit  606  is shown to include a processor  608  and memory  608 . Processing circuit  606  can be communicably connected to communications interface  680  such that processing circuit  606  and the various components thereof can send and receive data via communications interface  680 . Processor  608  can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components. 
     Memory  610  (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory  610  can be or include volatile memory or non-volatile memory. Memory  610  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present application. In some embodiments, memory  610  is communicably connected to processor  608  via processing circuit  606  and includes computer code for executing (e.g., by processing circuit  606  and/or processor  608 ) one or more processes described herein. 
     Memory  610  may include some or all of the components of memory  610  shown in  FIG. 6A . For example, memory  610  may include virtual actuation devices  612 , virtual sensors  614 , time series database  616 , dimensional mismatch identifier  618 , discrete cosine transformer  620 , DCT quantizer  622 , similarity calculator  624 , device pairing generator  626 , and device controller  628 . When implemented in smart actuator  658 , device pairing generator  626  can generate pairings between actuation device  674  and one or more of sensors  640  using the techniques described with reference to  FIG. 6A . In other words, device pairing generator  626  can determine which of sensors  640  is/are affected by actuation device  674 . Device controller  628  can use the device pairings and the sensor readings from the affected sensors  640  to generate actuation signals for actuation device  674 . 
     Referring now to  FIG. 6C , a block diagram illustrating another portion of HVAC system  600  in greater detail is shown, according to an exemplary embodiment. HVAC system  600  is shown to include a smart chiller  659 , sensors  640 , and a building zone  670 . Smart chiller  659  may be one of actuation devices  650  or a separate chiller in HVAC system  600 . Smart chiller  659  can be configured to provide cooling for building zone  670  based on sensor readings received from sensors  640 . For example, smart chiller  659  is shown to include a refrigeration circuit  660  having a compressor  662 , a condenser  664 , an expansion device  666 , and an evaporator  668 . Compressor  662  can be configured to circulate a refrigerant between condenser  664  and evaporator  668  based on actuation signals received from processing circuit  606 . Evaporator  668  can provide cooling for an airflow provided to building zone  670  either directly (e.g., by directly chilling the airflow) or via an intermediate coolant (e.g., by chilling a coolant which is used to chill the airflow). Unlike conventional chillers, smart chiller  659  can independently and automatically determine appropriate actuation signals for refrigeration circuit  660  without requiring input from an external controller. 
     Smart chiller  659  can automatically determine which of sensors  640  is/are affected by refrigeration circuit  660  and can operate refrigeration circuit  660  based on the sensor readings from the affected sensor(s)  640 . For example, sensors  640  are shown to include a zone A temperature sensor  641   a , a zone B temperature sensor  641   b , and a zone C temperature sensor  641 C. One or more of temperature sensors  641   a - 641   c  may be located in building zone  670  and configured to measure the temperature of building zone  670 . However, the locations of temperature sensors  641   a - 641   c  may be unknown to smart chiller  659  when smart chiller  659  is first installed. Smart chiller  659  can use the device pairing techniques described with reference to  FIG. 6A  to determine which of temperature sensors  641   a - 641   c  is affected by refrigeration circuit  660 . 
     Smart chiller  659  is shown to include a communications interface  680  and a processing circuit  606 . Communications interface  680  may be the same or similar to communications interface  604 , as described with reference to  FIG. 6A . Communications interface  680  can include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with external systems or devices (e.g., sensors  640 , user devices, supervisory controllers, etc.). Data communications via communications interface  680  can be direct (e.g., local wired or wireless communications) or via a communications network (e.g., a LAN, a WAN, the Internet, a cellular network, etc.). For example, communications interface  680  can include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network, a Wi-Fi transceiver for communicating via a wireless communications network, and/or cellular or mobile phone communications transceivers for communicating via a cellular communications network. 
     Processing circuit  606  may include some or all of the components of processing circuit  606  shown in  FIG. 6A . For example, processing circuit  606  is shown to include a processor  608  and memory  608 . Processing circuit  606  can be communicably connected to communications interface  680  such that processing circuit  606  and the various components thereof can send and receive data via communications interface  680 . Processor  608  can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components. 
     Memory  610  (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory  610  can be or include volatile memory or non-volatile memory. Memory  610  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present application. In some embodiments, memory  610  is communicably connected to processor  608  via processing circuit  606  and includes computer code for executing (e.g., by processing circuit  606  and/or processor  608 ) one or more processes described herein. 
     Memory  610  may include some or all of the components of memory  610  shown in  FIG. 6A . For example, memory  610  may include virtual actuation devices  612 , virtual sensors  614 , time series database  616 , dimensional mismatch identifier  618 , discrete cosine transformer  620 , DCT quantizer  622 , similarity calculator  624 , device pairing generator  626 , and device controller  628 . When implemented in smart chiller  659 , device pairing generator  626  can generate pairings between smart chiller  659  and one or more of sensors  640 . In other words, device pairing generator  626  can determine which of sensors  640  is/are affected by smart chiller  659 . Device controller  628  can use the device pairings and the sensor readings from the affected sensors  640  to generate actuation signals for compressor  662  and/or other components of refrigeration circuit  660 . 
     Referring now to  FIG. 6D , a block diagram illustrating another portion of HVAC system  600  in greater detail is shown, according to an exemplary embodiment. HVAC system  600  is shown to include a smart thermostat  648 , actuation devices  650 , and a building zone  670 . Smart thermostat  648  is shown to include sensors  640 . Sensors  640  can include a temperature sensor  641 , humidity sensor  642 , or any other type of sensor  640 , as described with reference to  FIG. 6A . Sensors  640  can be configured to measure various environmental conditions or variables within building zone  670 . For example, temperature sensor  641  can measure the temperature of building zone  670 , whereas humidity sensor  642  can measure the humidity of building zone  670 . Smart thermostat  648  can independently and automatically determine appropriate actuation signals for actuation devices  650  without requiring input from an external controller. 
     Smart thermostat  648  can automatically determine which of actuation devices  650  affect the environmental conditions of building zone  670  and can operate actuation devices  650  to control the environmental conditions measured by sensors  640 . For example, actuation devices  650  are shown to include several chillers  651 , several heaters  652 , and several air handling units  654 . One or more of actuation devices  650  may operate to affect conditions within building zone  670 . However, smart thermostat  648  may be unaware of such causal relationships when smart thermostat  648  is initially installed. Smart thermostat  648  can use the device pairing techniques described with reference to  FIG. 6A  to determine which of actuation devices  650  can be operated to control conditions within building zone  670 . 
     Smart thermostat  648  is shown to include a communications interface  680  and a processing circuit  606 . Communications interface  680  may be the same or similar to communications interface  604 , as described with reference to  FIG. 6A . Communications interface  680  can include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with external systems or devices (e.g., actuation devices  650 , user devices, supervisory controllers, etc.). Data communications via communications interface  680  can be direct (e.g., local wired or wireless communications) or via a communications network (e.g., a LAN, a WAN, the Internet, a cellular network, etc.). For example, communications interface  680  can include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network, a Wi-Fi transceiver for communicating via a wireless communications network, and/or cellular or mobile phone communications transceivers for communicating via a cellular communications network. 
     Processing circuit  606  may include some or all of the components of processing circuit  606  shown in  FIG. 6A . For example, processing circuit  606  is shown to include a processor  608  and memory  608 . Processing circuit  606  can be communicably connected to communications interface  680  such that processing circuit  606  and the various components thereof can send and receive data via communications interface  680 . Processor  608  can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components. 
     Memory  610  (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory  610  can be or include volatile memory or non-volatile memory. Memory  610  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present application. In some embodiments, memory  610  is communicably connected to processor  608  via processing circuit  606  and includes computer code for executing (e.g., by processing circuit  606  and/or processor  608 ) one or more processes described herein. 
     Memory  610  may include some or all of the components of memory  610  shown in  FIG. 6A . For example, memory  610  may include virtual actuation devices  612 , virtual sensors  614 , time series database  616 , dimensional mismatch identifier  618 , discrete cosine transformer  620 , DCT quantizer  622 , similarity calculator  624 , device pairing generator  626 , and device controller  628 . When implemented in smart thermostat  648 , device pairing generator  626  can generate pairings between sensors  640  and one or more of actuation devices  650 . In other words, device pairing generator  626  can determine which of actuation devices  650  affect the variables or conditions measured by sensors  640 . Device controller  628  can use the device pairings and the sensor readings from sensors  640  to generate actuation signals for actuation devices  650 . 
     Example Graphs 
     Referring now to  FIG. 7  a graph  700  illustrating the different types of signals evaluated by controller  602  is shown, according to an exemplary embodiment. In graph  700 , line  702  represents an actuation signal t(x), line  706  represents a sensor response signal r(x), and line  710  represents a baseline sensor signal a(x). The actuation signal t(x) can be provided to one or more of actuation devices  650 , as previously described. In the example shown in  FIG. 7 , the actuation signal t(x) is a setpoint signal (e.g., a temperature setpoint) which can be provided as an input to actuation devices  650  (e.g., controllable HVAC equipment) which operate to affect the temperature of a building zone. In some embodiments, the actuation signal t(x) is a predetermined test signal which differs from the normal actuation signals provided to actuation devices  650 . For example, the actuation signal t(x) is shown as a step increase from 68° F. to 72° F., which is held for a predetermined time period, followed by a step decrease from 72° F. back to 68° F. The actuation signal t(x) causes actuation devices  650  to increase an amount of heating provided to the building zone, which causes the temperature of the building zone to increase. 
     The sensor response signal r(x) can be received from one or more of sensors  640 , as previously described. In the example shown in  FIG. 7 , the sensor response signal r(x) is a measured temperature signal received from a temperature sensor located in the building zone controlled by actuation devices  650 . The temperature of the building zone begins to increase shortly after the actuation signal t(x) is increased, which results in an increase in the sensor response signal r(x). Similarly, the temperature of the building zone begins to decrease shortly after the actuation signal t(x) is decreased, which results in a decrease in the sensor response signal r(x). The time delay between the actuation signal t(x) and the sensor response signal r(x) is shown as delay time Δw. 
     The baseline sensor signal a(x) can be received from the same sensor  640  which provides the sensor response signal r(x). However, the baseline sensor signal a(x) indicates the sensor readings from the sensor  640  from a time period before the actuation signal t(x) is provided to actuation devices  650 . The signals shown in graph  700  are characteristic of a sensor  640  and an actuation device  650  which have a causal relationship with each other. For example, the sensor response signal r(x) closely matches the actuation signal t(x), whereas the baseline sensor signal a(x) is significantly different from both the actuation signal t(x) and the sensor response signal r(x). In other words, the sensor response signal r(x) is correlated with the actuation signal t(x), which indicates a causal relationship between the corresponding actuation device  650  and sensor  640 . 
     Still referring to  FIG. 7 , graph  700  is shown to include a line  704  representing the discrete cosine transform (DCT) of the actuation signal t(x), a line  708  representing the DCT of the sensor response signal r(x), and a line  712  representing the DCT of the baseline sensor signal a(x). Discrete cosine transformer  620  can be configured to generate DCTs of the various time series signals received or generated by controller  602 , as previously described. In graph  700 , the DCTs represented by lines  704 ,  708 , and  712  are continuous functions (i.e., summations of cosine functions) which results in a smooth curves for each of lines  704 ,  708 , and  712 . Advantageously, the DCT functions reduce any noise present in the signals t(x), r(x), and a(x), and can be evaluated at any point. In some embodiments, controller  602  compares the DCTs of the actuation signal t(x), sensor response signal r(x), and baseline sensor signal a(x) rather than the original signals to determine whether a causal relationship exists between a particular sensor  640  and a particular actuation device  650 . 
     Referring now to  FIG. 8  a graph  800  illustrating the dimensional mismatch handling performed by controller  602  is shown, according to an exemplary embodiment. In graph  800 , line  802  represents samples of actuation signal time series t(x) provided to one or more of actuation devices  650 , whereas line  804  represents samples of a sensor response time series r(x) received from one or more of sensors  640 . The actuation signal time series t(x) and the sensor response time series r(x) cover the same time period. However, sampling rate used to generate the samples of the sensor response time series r(x) is twice the sampling rate used to generate the samples of the actuation time series t(x), which results in twice as many samples of the sensor response time series r(x) being collected during the same time period. In other words, the sensor response time series r(x) includes twice as many samples (e.g., 24 samples) as the actuation signal time series t(x) (e.g., 12 samples). 
     In order to compare the actuation signal time series t(x) and the sensor response time series r(x), controller  602  can generate DCTs of each time series. As described with reference to  FIG. 6A , discrete cosine transformer  620  can generate DCT coefficients for the actuation signal time series t(x) using the following equation: 
     
       
         
           
             
               T 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   N 
                   - 
                   1 
                 
               
                
               
                 
                   t 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         N 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               N 
               - 
               1 
             
           
         
       
     
     where T(k) is the kth coefficient of the DCT of the actuation signal time series t(x), t i  is the ith sample of the actuation signal time series t(x), and N is the number of samples of the actuation signal time series t(x). Discrete cosine transformer  620  can generate an array T of the DCT coefficients (e.g., T=[T(0), T(1), T(2), . . . , T(N−2), T(N−1)]) where the length of the array T is the same as the number of samples N of the actuation signal time series t(x) (e.g., 12 samples). 
     Similarly, discrete cosine transformer  620  can generate DCT coefficients for the sensor response time series r(x) using the following equation: 
     
       
         
           
             
               R 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   M 
                   - 
                   1 
                 
               
                
               
                 
                   r 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         M 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               M 
               - 
               1 
             
           
         
       
     
     where R(k) is the kth coefficient of the DCT of the sensor response time series r(x), r i  is the ith sample of the sensor response time series r(x), and M is the number of samples of the sensor response time series r(x). Discrete cosine transformer  620  can generate an array R of the DCT coefficients (e.g., R=[R(0), R(1), R(2), . . . , R(M−2), R(M−1)]) where the length of the array R is the same as the number of samples M of the sensor response time series r(x) (e.g., 24 samples). 
     To make the arrays T and R the same dimension, DCT quantizer  622  can perform a quantization process. In some embodiments, DCT quantizer  622  performs the quantization process using a predetermined quantization level. The quantization level may define the number of the DCT coefficients in each array T and R which are retained (i.e., not filled with zeros). For example, a quantization level of twelve may retain the first twelve DCT coefficients in each array T and R while the remaining DCT coefficients are filled with zeros. In the example shown in  FIG. 8 , DCT quantizer  622  applies a quantization level of twelve to each array T and R of DCT coefficients. This quantization level has no effect on the array T since the array T only contains 12 DCT coefficients. However, applying a quantization level of twelve to the array R has the effect of filling the final twelve DCT coefficients with zeros such that only the first twelve DCT coefficients in array R are retained. 
     Still referring to  FIG. 8 , graph  800  is shown to include a line  806  representing the inverse DCT of the actuation signal time series t(x) and a line  808  representing the inverse DCT of the sensor response time series r(x). Lines  806 - 808  illustrate the similarity between the quantized DCT functions based on the actuation signal time series t(x) and the sensor response time series r(x). As discussed with reference to  FIG. 6A , similarity calculator  624  can evaluate the similarity between two or more DCT functions without reconstructing the inverse DCT (e.g., by calculating a distance between the DCT coefficients). However, the inverse DCTs are shown in graph  800  to illustrate how controller  602  can reduce the dimension of the sensor response time series r(x) to match the dimension of the actuation signal time series t(x) (or vice versa) by performing a discrete cosine transform and applying a quantization process. 
     Flow Diagrams 
     Referring now to  FIG. 9 , a flowchart of a process  900  for establishing device pairings between sensors and actuation devices is shown, according to an exemplary embodiment. In some embodiments, process  900  is performed by one or more components of controller  602 , as described with reference to  FIG. 6A . Process  900  can be used in a building and/or a building HVAC system to automatically establish device pairings between various sensors and causally-related actuation devices. The device pairings can then be used to automatically generate control loops for use in controlling the actuation devices. 
     Process  900  is shown to include collecting baseline sensor measurements from a plurality of sensors (step  902 ). The sensors can include some or all of sensors  640 , as described with reference to  FIG. 6A . For example, the sensors can include temperature sensors, humidity sensors, airflow sensors, lighting sensors, pressure sensors, voltage sensors, or any other type of sensor in a building and/or a building HVAC system. The sensors can be distributed throughout a building and configured to measure various environmental conditions at different locations in the building. For example, one temperature sensor can be located in a first zone of the building and configured to measure the temperature of the first zone, whereas another temperature sensor can be located in a second zone of the building and configured to measure the temperature of the second zone. Similarly, the sensors can be distributed throughout a HVAC system and configured to measure conditions at different locations in the HVAC system. For example, one of temperature sensor can be a supply air temperature sensor configured to measure the temperature of the airflow provided to a building zone from an AHU, whereas another temperature sensor can be a return air temperature sensor configured to measure the temperature of the airflow returning from the building zone to the AHU. 
     The baseline sensor measurements may be received from the plurality of sensors during a baseline time period before an actuation signal or test signal is provided to actuation devices  650 . In some embodiments, the baseline temperature measurements are used to generate a baseline sensor signal time series a(x). The baseline sensor signal time series a(x) may indicate the average sensor readings from the plurality of sensors before the actuation signal or test signal is provided to the actuation devices  650 . 
     In some embodiments, step  902  includes storing the baseline sensor signal time series a(x) in a time series database (e.g., time series database  616 ). The time series database can store the baseline sensor measurements from each of the plurality of sensors as separate baseline sensor signal time series a(x) as shown in the following equation: 
         a ( x )={ a   1   ,a   2   ,a   3   , . . . ,a   P-1   ,t   P } 
     where each element a i  of the baseline sensor signal time series a(x) is the value of a baseline sensor signal at a particular time (i.e., a sample of the baseline sensor signal) and P is the total number of elements in the baseline sensor signal time series a(x). 
     Still referring to  FIG. 9 , process  900  is shown to include providing an actuation signal to an actuation device (step  904 ). The actuation device can include any of actuation devices  650 , as described with reference to  FIG. 6A . For example, the actuation device can include a chiller, heater, valve, air handling unit (AHU), damper, actuator, and/or any other physical device configured to affect a variable state or condition in a building or building HVAC system. The actuation device can include any of the equipment in building  10 , HVAC system  100 , waterside system  200 , airside system  300 , BMS  400 , and/or BMS  500 , as described with reference to  FIGS. 1-5 . The actuation device can operate to affect various building conditions including temperature, humidity, airflow, lighting, air quality, power consumption, or any other variable state or condition in a building. In some embodiments, the actuation device receives the actuation signal from a controller (e.g., controller  602 ) via an output module. 
     In some embodiments, the actuation signal is a control signal for the actuation devices (e.g., operating setpoints, on/off commands, etc.). For example, the actuation signal can include commands to activate or deactivate the actuation device and/or commands to operate the actuation device a variable capacity (e.g., operate at 20% capacity, 40% capacity, etc.). If the actuation device is a device with a variable position (e.g., a valve, a damper, an actuator, etc.) the actuation signal can include position setpoints for the actuation device. The position setpoints can include commands to move to a fully closed position, a 50% open position, a fully open position, or any intermediate position. In some embodiments, the actuation signal is a predetermined test signal which differs from the normal actuation signals provided to the actuation device. 
     In some embodiments, the actuation signal is provided directly to the actuation device from the controller and used to adjust a physical operation of the actuation device (e.g., if the controller directly controls the actuation device). In other embodiments, the actuation signal is provided to an intermediate controller for the actuation devices. For example, a supervisory controller can provide a setpoint to a local controller for the actuation device. The local controller can then generate control signals for the actuation devices to achieve the setpoint received from the supervisory controller. 
     In some embodiments, step  904  includes using the actuation signal to generate an actuation signal time series t(x). The actuation signal time series t(x) can be stored in the time series database. The time series database can store each time series of actuation signal values as an actuation signal time series t(x) as shown in the following equation: 
         t ( x )={ t   1   ,t   2   ,t   3   , . . . ,t   N-1   ,t   N } 
     where each element t i  of the actuation signal time series t(x) is the value of the actuation signal at a particular time (i.e., a sample of the actuation signal) and N is the total number of elements in the actuation signal time series t(x). 
     Still referring to  FIG. 9 , process  900  is shown to include recording sensor response signals from the plurality of sensors in response to the actuation signal (step  906 ). The sensor response signals indicate the effect of the actuation device on the variables measured by the plurality of sensors. If a causal relationship exists between the actuation device and a particular sensor (i.e., the actuation device can affect the value measured by the sensor), the sensor response signal may change in response to providing the actuation signal to the actuation device. However, if no causal relationship exists between the actuation device and the sensor (i.e., the actuation device is not capable of affecting the value measured by the sensor), the sensor response signal may not change in response to providing the actuation signal to the actuation device. 
     In some embodiments, step  906  includes generating time series of sensor response values. Each time series of sensor response values can be stored in the time series database as a sensor response time series r(x) as shown in the following equation: 
         r ( x )={ r   1   ,r   2   ,r   3   , . . . ,r   M-1   ,r   M } 
     where each element r i  of the sensor response time series r(x) is the value of the sensor response signal at a particular time (i.e., a sample of the sensor response signal) and M is the total number of elements in the sensor response time series r(x). 
     Process  900  is shown to include determining a similarity between the actuation signal and each sensor response signal (step  908 ). In some embodiments, step  908  includes calculating a similarity metric or similarity score indicating a similarity (e.g., a distance) between the actuation signal time series t(x) and each of the sensor response time series r(x). The following equation can be used to calculate the similarity metric between the actuation signal time series t(x) and a given sensor response time series r(x): 
     
       
         
           
             
               d 
                
               
                 ( 
                 
                   
                     t 
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   , 
                   
                     r 
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   N 
                 
               
                
               
                 
                   
                     
                       ( 
                       
                         
                           t 
                           i 
                         
                         - 
                         
                           r 
                           i 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 
                   δ 
                   i 
                 
               
             
           
         
       
     
     where t i  is the ith sample in the actuation signal time series t(x), r i  is the ith sample in the sensor response time series r(x), δ i  is the standard deviation of the ith samples, and N is the number of samples in each time series. Low values of the similarity metric d(t(x), r(x)) indicate a greater similarity (i.e., a lower distance between time series), whereas high values of the similarity metric d(t(x), r(x)) indicate a lesser similarity (i.e., a greater distance between time series). Step  908  can include calculating a similarity metric for each pairing of the actuation signal time series t(x) with one of the sensor response time series r(x). 
     The previous equation for calculating the similarity metric can be used if both the actuation signal time series t(x) and the sensor response time series r(x) have the same number of samples. However, if the actuation signal time series t(x) and the sensor response time series r(x) have different numbers of samples, additional processing may be required. For example, step  908  may include performing a discrete cosine transformation (DCT) of the actuation signal time series t(x) and each sensor response time series r(x) to generate sets of DCT coefficients for each time series. The sets of DCT coefficients can then be quantized, as described with reference to  FIG. 6A , to produce arrays of compressed DCT coefficients for each time series. The similarity metrics can then be calculated based on the compressed DCT coefficients generated for each time series. 
     The compressed DCT coefficients generated for the actuation signal time series t(x) can be represented by an array T, and the compressed DCT coefficients generated for a given sensor response time series r(x) can be represented by an array R. The arrays T and R can be particular instances of the compressed array C(k) generated by DCT quantizer  622  for the actuation signal time series t(x) and the sensor response time series r(x), respectively. Each array T and R can include a predetermined number N of DCT coefficients, defined by the quantization level applied by DCT quantizer  622 . Examples of arrays T and R are as follows: 
     
       
      
       T= 
       
       t 
       1 
       ,t 
       2 
       , . . . t 
       N 
       
      
     
     
       
      
       R= 
       
       r 
       1 
       ,r 
       2 
       , . . . ,r 
       N 
       
      
     
     Step  908  can include generating an array T of DCT coefficients for the actuation signal time series t(x) and an array R of DCT coefficients for each of the sensor response time series r(x). 
     In some embodiments, step  908  includes calculating a similarity metric for the source time series t(x) and r(x) based on the corresponding arrays T and R of compressed DCT coefficients. Step  908  can include calculating the similarity metric using the following equation: 
     
       
         
           
             
               d 
                
               
                 ( 
                 
                   T 
                   , 
                   R 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   N 
                 
               
                
               
                 
                   
                     
                       ( 
                       
                         
                           t 
                           i 
                         
                         - 
                         
                           r 
                           i 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 
                   δ 
                   i 
                 
               
             
           
         
       
     
     where t i  is the ith DCT coefficient in the array T based on the actuation signal time series t(x), r i  is the ith DCT coefficient in the array R based on the sensor response time series r(x), δ i  is the standard deviation of the ith DCT coefficients, and N is the number of DCT coefficients in each array T and R. Low values of the similarity metric d(T, R) indicate a greater similarity, whereas high values of the similarity metric d(T, R) indicate a lesser similarity. Step  908  can include calculating a similarity metric for each pairing of the array T based on the actuation signal time series t(x) with one of the arrays R based on one of the sensor response time series r(x). 
     Still referring to  FIG. 9 , process  900  is shown to include identifying the sensor response signal with the greatest similarity to the actuation signal and the corresponding sensor (step  910 ). Step  910  can include comparing the similarity metrics d(T, R) calculated for the actuation device in combination with each of the plurality of sensors. Each similarity metric d (T, R) indicates the similarity (i.e., the closeness) between the actuation signal time series t(x) associated with the actuation device and the sensor response time series r(x) associated with one of the sensors. For example, the similarity metric d(T 1 , R 1 ) may indicate the similarity between the actuation device and a first sensor of the plurality of sensors (corresponding to array R 1 ), whereas the similarity metric d(T 1 , R 2 ) may indicate the similarity between the actuation device and a second sensor of the plurality of sensors (corresponding to array R 2 ). 
     Step  910  can include identifying all of the similarity metrics associated with the actuation device (e.g., d(T 1 , R 1 ), . . . , d(T 1 , R P ), where P is the total number of sensors and/or sensor response time series r(x)). In some embodiments, step  910  includes determining which of the identified similarity metrics is the lowest. The lowest similarity metric may indicate the closest match between the actuation signal time series t(x) associated with the actuation device and the sensor response time series r(x) associated with one of the sensors. In other embodiments, step  910  can include determining which of the identified similarity metrics is the highest. For example, other techniques for calculating the similarity metric may produce larger similarity metrics when two time series match more closely. Regardless of how the similarity metric is calculated, step  910  can include identifying the similarity metric which indicates the closest match between the actuation signal time series t(x) and the corresponding sensor response time series r(x). 
     If the actuation device has the same similarity metric with multiple sensors (e.g., d(T 1 , R 1 )=d(T 1 , R 2 )), step  910  can include examining the time delay Δw between the actuation signal time series t(x) associated with the actuation device and sensor response time series r(x) associated with each of the sensors. The time delay Δw may indicate the delay between the time w 1  at which the actuation signal is applied to the actuation device and the time w 2  at which the effects of the actuation signal are evident in each sensor response (e.g., Δw=w 2 −w 1 ). Step  910  can include identifying the sensor and/or sensor response time series r(x) with the lowest time delay Δw relative to the actuation signal time series t(x). 
     Still referring to  FIG. 9 , process  900  is shown to include establishing a device pairing between the actuation device and the identified sensor (step  912 ). The device pairing can include the actuation device and the sensor identified in step  910 . The device pairing between the actuation device and the sensor indicates that the actuation device is capable of affecting the value measured by the sensor. In some embodiments step  910  includes using the device pairing to automatically generate and store causal relationships between the actuation device and the identified sensor. 
     Process  900  is shown to include using the device pairing to generate and provide control signals to the actuation device (step  914 ). Step  914  can include using the device pairing to create a feedback control loop for HVAC system  600 . The feedback control loop can receive a feedback signal from the identified sensor and can provide a control signal to the actuation device. Step  914  can include using the device pairing to define the sensor and actuation device in the control loop. For example, step  914  can include creating a control loop which receives a feedback signal from the sensor in the device pairing and provides a control signal to the actuation device in the device pairing. Step  914  can include mapping the sensor readings from the sensor in the device pairing to the feedback signal in the control loop. Similarly, step  914  can include mapping the actuation signals provided to the actuation device in the device pairing to the control signal in the control loop. 
     Step  914  can include using the feedback control loop to generate actuation signals for the actuation device. Step  914  can include using state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, or any other type of control methodology to generate the actuation signals for the actuation device based on the sensor readings. For example, if the sensor reading from the sensor indicates that the temperature of a particular building zone is below a temperature setpoint for the building zone, step  914  can include providing an actuation signal to the actuation device to increase the amount of heating provided to the building zone. Advantageously, process  900  can be performed to automatically establish relationships between various actuation devices and sensors based on the device pairings to allow controller  602  to determine which of the actuation devices can be operated to affect a given sensor reading. 
     Referring now to  FIG. 10 , a flowchart of a process  1000  for handling dimensional mismatches between actuation signal time series and sensor response time series is shown, according to an exemplary embodiment. In some embodiments, process  1000  is performed by one or more components of controller  602 , as described with reference to  FIG. 6A . Process  1000  can be used in a building and/or a building HVAC system to automatically establish device pairings between various sensors and actuation devices when the time series have different sampling rates and/or different numbers of samples. The device pairings can then be used to automatically generate control loops for use in controlling the actuation devices. 
     Process  1000  is shown to include performing a discrete cosine transformation (DCT) of actuation signal time series t(x) and sensor response time series r(x) to generate sets of DCT coefficients (step  1002 ). In some embodiments, step  1002  is performed by discrete cosine transformer  620 , as described with reference to  FIG. 6A . Step  1002  can include performing a DCT for each actuation signal time series t(x) and sensor response time series r(x). A DCT expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. There are eight standard DCT variants, commonly referred to as DCT-I, DCT-II, DCT-III, DCT-IV, DCT-V, DCT-VI, DCT-VII, and DCT-VIII. One of these variants (i.e., DCT-II) is discussed in detail below. However, it should be understood that step  1002  can use any standard or non-standard DCT variant in other embodiments. 
     In some embodiments, step  1002  includes performing a DCT for each actuation signal time series t(x) using the following equation: 
     
       
         
           
             
               T 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   N 
                   - 
                   1 
                 
               
                
               
                 
                   t 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         N 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               N 
               - 
               1 
             
           
         
       
     
     where T(k) is the kth coefficient of the DCT of the actuation signal time series t(x), t i  is the ith sample of the actuation signal time series t(x), and N is the number of samples of the actuation signal time series t(x). Step  1002  can include generating an array T of the DCT coefficients (e.g., T=[T(0), T(1), T(2), . . . , T(N−2), T(N−1)]) where the length of the array T is the same as the number of samples N of the actuation signal time series t(x). 
     Similarly, step  1002  can include performing a DCT for each sensor response time series r(x) using the following equation: 
     
       
         
           
             
               R 
                
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   M 
                   - 
                   1 
                 
               
                
               
                 
                   r 
                   i 
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         π 
                         M 
                       
                        
                       
                         ( 
                         
                           i 
                           + 
                           
                             1 
                             2 
                           
                         
                         ) 
                       
                        
                       k 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               = 
               0 
             
             , 
             … 
              
             
                 
             
             , 
             
               M 
               - 
               1 
             
           
         
       
     
     where R(k) is the kth coefficient of the DCT of the sensor response time series r(x), r i  is the ith sample of the sensor response time series r(x), and M is the number of samples of the sensor response time series r(x). Step  1002  can include generating an array R of the DCT coefficients (e.g., R=[R(0), R(1), R(2), . . . , R(M−2), R(M−1)]) where the length of the array R is the same as the number of samples M of the sensor response time series r(x). 
     The following example illustrates the result of applying DCT to an input time series X(n). The input time series X(n) can be an actuation signal time series t(x) or a sensor response time series r(x) as previously described. The samples of the input time series X(n) are shown in the following array: 
         X ( n )=[1.00,1.70,2.00,2.00,4.30,4.50,3.00,3.00,2.30,2.20,2.20,2.30] 
     where the input time series X(n) includes twelve time series values X(1), . . . ,X(12). Applying DCT to the input time series X(n) results in a set of DCT coefficients, shown in the following array: 
         Y ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52,−0.20,−0.93,−0.63,0.32,0.50,−0.06]
 
     where the array of DCT coefficients Y(k) includes twelve DCT coefficients Y(1), . . . , Y(12). 
     Still referring to  FIG. 10 , process  1000  is shown to include identifying a dimensional mismatch between the actuation signal time series t(x) and the sensor response time series r(x) (step  1004 ). In some embodiment, step  1004  is performed by dimensional mismatch identifier  618 , as described with reference to  FIG. 6A . A dimensional mismatch may occur when two time series have a different number of samples and/or sampling rates. In some embodiments, step  1004  includes determining the size of each time series. For example, step  1004  can include determining the number of samples N in the actuation signal time series t(x) and the number of samples M in the sensor response time series r(x). The number of samples N and M can be determined by counting the number of samples in the original time series t(x) and r(x) or the number of elements in each of the arrays of DCT coefficients T and R. Step  1004  can include identifying a dimensional mismatch in response to a determination that the number of samples N in the actuation signal time series t(x) or the array T is different from the number of samples M in the sensor response time series r(x) or the array R (i.e., N≠M). 
     In some embodiments, step  1004  includes determining the sampling rate of each time series. In some embodiments, the sampling rate of a time series may be stored as metadata associated with the time series in time series database  616 . Step  1004  can include determining the sampling rate of a time series by reading the sampling rate from the metadata in time series database  616 . In other embodiments, step  1004  includes calculating the sampling rate for one or more time series based on the size of the time series and the range of time spanned by the time series. 
     Step  1004  can include identifying a start time and an end time for the time series by reading the timestamps associated with the first and last data samples in the time series. Step  1004  can include calculating the sampling rate by dividing the size of the time series by the difference between the end time and the start time, as shown in the following equation: 
     
       
         
           
             sampling_rate 
             = 
             
               
                 size_of 
                  
                 _timeseries 
               
               
                 end_time 
                 - 
                 start_time 
               
             
           
         
       
     
     where size_of_timeseries is the number of samples M or N in the time series, end_time is the timestamp associated with the last sample in the time series, start_time is the timestamp associated with the first sample in the time series, and sampling_rate is the sampling rate of the time series, expressed as the number of samples per unit time (e.g., 0.8 samples/hour). Step  1004  can include identifying a dimensional mismatch in response to a determination that two time series have different sampling rates. 
     In some embodiments, step  1004  includes correcting a dimensional mismatch by increasing the number of samples of the time series with the fewer number of samples (e.g., by interpolating between samples). In other embodiments, step  1004  includes correcting dimensional mismatch by reducing the number of samples of the time series with the greater number of samples (e.g., by discarding extra samples). In other embodiments, step  1004  merely identifies a dimensional mismatch which is corrected by subsequent steps of process  1000 . 
     Still referring to  FIG. 10 , process  1000  is shown to include applying a quantization to the sets of DCT coefficients generated in step  1002  to equalize the number of DCT coefficients in each set (step  1006 ). In some embodiments, step  1006  is performed by DCT quantizer  622 , as described with reference to  FIG. 6A . Step  1006  can be performed in response to a determination in step  1004  that a dimensional mismatch exists between the actuation signal time series t(x) and the sensor response time series r(x). 
     As described above, the DCT process performed in step  1002  converts an input data time series X(n) into a sum of cosine functions which oscillate at different frequencies. The cosine function with the lowest frequency is typically first in the summation, followed by cosine functions with successively higher frequencies. Accordingly, the DCT coefficient which occurs first in the array of DCT coefficients Y(k) represents the magnitude of the lowest frequency cosine function. Each of the following DCT coefficients represents the magnitude of a cosine function with a successively higher oscillation frequency. 
     Step  1006  can include applying a quantization process to the sets of DCT coefficients by filling some of the higher frequency DCT coefficients with zeros. This has the effect of removing some of the higher frequency components (i.e., cosine functions) from the summation while retaining the lower frequency components. In some embodiments, step  1006  includes performing the quantization process using a predetermined quantization level. The quantization level may define the number of the DCT coefficients which are retained (i.e., not filled with zeros). For example, a quantization level of six may retain the DCT coefficients applied to the six lowest frequency cosine functions (e.g., the first six DCT coefficients in the array) while the remaining DCT coefficients are filled with zeros. 
     The following example illustrates the result of a quantization process which can be performed in step  1006 . Step  1006  can include modifying the array of DCT coefficients Y(k) shown above to form the following quantized array QY(k): 
         QY ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52,0.00,0.00,0.00,0.00,0.00,0.00]
 
     In this example, a quantization level of six is applied, meaning that only the first six DCT coefficients are retained from the original array of DCT coefficients Y(k). The remaining DCT coefficients are filled with zeros. True compression can be achieved by not storing the zeros. For example, step  1006  can include storing the following compressed array C(k): 
         C ( k )=[8.80,−0.57,−2.65,−1.15,0.81,0.52]
 
     in which the coefficients filled with zeros are discarded to produce a compressed array with a length equal to the quantization level applied. In this example, the compressed array C(k) has a length of six resulting from the use of a quantization level of six. In various embodiments, step  1006  can use a quantization level of six or any other quantization level to produce compressed arrays of various lengths. 
     In some embodiments, step  1006  includes automatically determining the quantization level to apply based on the number of samples in each of the original actuation signal time series t(x) and sensor response time series r(x). As described above, the number of DCT coefficients produced in step  1002  for a given input time series X(n) may be equal to the number of samples in the time series X(n) prior to performing DCT. For example, an input time series X 1 (n) with twelve samples may result in twelve DCT coefficients in the resultant DCT coefficient array Y 1 (k), whereas an input time series X 2 (n) with ten samples may result in ten DCT coefficients in the resultant DCT coefficient array Y 2  (k). In some embodiments, step  1006  includes identifying the actuation signal time series t(x) or sensor response time series r(x) with the fewest samples and applies a quantization level equal to the number of samples in the identified time series. 
     In some embodiments, step  1006  includes applying the same quantization level to the sets of DCT coefficients corresponding to each of the original actuation signal time series t(x) and sensor response time series r(x). Using the same quantization level for each of the original time series may result in the same number of compressed DCT coefficients being stored for each of the original actuation signal time series t(x) and sensor response time series r(x). In some embodiments, the number of stored DCT coefficients is equal to the number of samples in the original time series with the fewest samples. Advantageously, this allows for direct comparison of the DCT coefficients in the compressed arrays C(k) generated for each of the original time series without requiring decompression, interpolation, synchronization, or other processing steps after the compressed arrays C(k) are generated. 
     In some embodiments, step  1006  includes generating a compressed time series T α  based on each compressed array of DCT coefficients. Step  1006  can include storing the compressed time series T α  using the following data structure: 
         T   α = α,δ,ρ,κ, ψ , υ 1 ,υ 2 , . . . υ p     
 
     where α is the time series ID of the source time series (e.g., the actuation signal time series t(x) or sensor response time series r(x)), δ is the dimension of the source time series (e.g., the number of samples in the source time series), ρ is the quantization level applied by in step  1006 , κ is a pointer for metadata,  ψ  indicates the start time and end time of samples in the source time series, and  υ 1 , υ 2 , . . . υ p    is the array of compressed DCT coefficients. An example of a compressed time series stored using this data structure is as follows: 
         T   203 = 203,12,6, 2016:10:05:12:00:00,2016:10:05:13:00:00 , 8.80,−0.57,−2.65,−1.15,0.81,0.52   
 
     where  203  is the time series ID of the source time series, 12 is size of the source time series (e.g., 12 samples in the source time series), 6 is the quantization level applied by in step  1006 , 2016:10:05:12:00:00 is the start time of the source time series (e.g., the timestamp of the earliest sample in the source time series), 2016:10:05:13:00:00 is the end time of the source time series (e.g., the timestamp of the latest sample in the source time series), and the array  8.80, −0.57, −2.65, −1.15, 0.81, 0.52  includes the compressed DCT coefficients generated in step  1006 . 
     Still referring to  FIG. 10 , process  1000  is shown to include determining a similarity between the actuation signal time series t(x) and the sensor response time series r(x) based on the quantized sets of DCT coefficients (step  1008 ). The quantized DCT coefficients generated for the actuation signal time series t(x) can be represented by an array T, and the compressed DCT coefficients generated for a given sensor response time series r(x) can be represented by an array R. The arrays T and R can be particular instances of the compressed array C(k) generated in step  1006  for the actuation signal time series t(x) and the sensor response time series r(x), respectively. Each array T and R can include a predetermined number N of DCT coefficients, defined by the quantization level applied in step  1006 . Examples of arrays T and R are as follows: 
     
       
      
       T= 
       
       t 
       1 
       ,t 
       2 
       , . . . t 
       N 
       
      
     
     
       
      
       R= 
       
       r 
       1 
       ,r 
       2 
       , . . . ,r 
       N 
       
      
     
     In some embodiments, step  1008  includes calculating a similarity metric for the source time series t(x) and r(x) based on the corresponding arrays T and R of compressed DCT coefficients. Step  1008  can include calculating the similarity metric using the following equation: 
     
       
         
           
             
               d 
                
               
                 ( 
                 
                   T 
                   , 
                   R 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   N 
                 
               
                
               
                 
                   
                     
                       ( 
                       
                         
                           t 
                           i 
                         
                         - 
                         
                           r 
                           i 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 
                   δ 
                   i 
                 
               
             
           
         
       
     
     where t i  is the ith DCT coefficient in the array T based on the actuation signal time series t(x), r i  is the ith DCT coefficient in the array R based on the sensor response time series r(x), δ i  is the standard deviation of the ith DCT coefficients, and N is the number of DCT coefficients in each array T and R. Low values of the similarity metric d(T, R) indicate a greater similarity, whereas high values of the similarity metric d (T, R) indicate a lesser similarity. 
     Process  1000  is shown to include establishing a device pairing between an actuation device and a sensor based on the similarity between the corresponding time series (step  1010 ). The actuation device in step  1010  may be the specific actuation device to which the actuation signal t(x) is provided, whereas the sensor in step  1010  may be the specific sensor from which the sensor response signal r(x) is received. In some embodiments, step  1010  includes comparing the similarity metric d(T, R) calculated in step  1008  to a threshold value. Step  1010  can include generating a device pairing between the sensor and the actuation device if the similarity metric d(T, R) is less than the threshold value (e.g., d(T, R)&lt;threshold). The threshold value can be a predefined value or a calculated value (e.g., a standard deviation of the DCT coefficients). 
     In some embodiments, the threshold value is a similarity metric between the actuation signal time series t(x) and a baseline (e.g., average) sensor signal time series a(x) over a predetermined time period. The baseline sensor signal time series a(x) can indicate the average sensor response from the sensor before the actuation signal is applied to the actuation device (e.g., baseline sensor readings), whereas the sensor response time series r(x) can indicate the sensor response from the same sensor after the actuation signal is applied to the actuation device. If the actuation device affects the sensor, the actuation signal time series t(x) is expected to be more similar to the sensor response time series r(x) than the baseline sensor signal time series a(x). Accordingly, the similarity metric d(T, R) between the actuation signal time series t(x) and the sensor response time series r(x) is expected to be lower (i.e., more similar) than the similarity metric d(T, A) between the actuation signal time series t(x) and the baseline sensor signal time series a(x). 
     In some embodiments, step  1010  includes generating DCT coefficients and compressed DCT coefficients for each baseline sensor signal time series a(x), sensor response time series r(x), and actuation signal time series t(x). Step  1010  can include calculating a similarity metric d(T, R) between the actuation signal time series t(x) and the sensor response time series r(x) associated with the temperature sensor. Step  1010  can also include calculating a baseline similarity metric d(T, A) between the actuation signal time series t(x) and baseline sensor signal time series a(x) associated with the same temperature sensor. Step  1010  can include generating a device pairing between the sensor and the actuation device if the similarity metric d(T, R) for the combination of the sensor and the actuation device indicates a greater similarity (e.g., a lower similarity metric) than the baseline similarity metric d(T, A) for the sensor and the actuation device. 
     In some embodiments, step  1010  includes comparing the similarity metrics d(T, R) calculated for the actuation device in combination with each of a plurality of sensors. Each similarity metric d(T, R) indicates the similarity (i.e., the closeness) between the actuation signal time series t(x) associated with the actuation device and the sensor response time series r(x) associated with one of the sensors. For example, the similarity metric d(T 1 , R 1 ) may indicate the similarity between the actuation device and a first sensor of the plurality of sensors (corresponding to array R 1 ), whereas the similarity metric d(T 1 , R 2 ) may indicate the similarity between the actuation device and a second sensor of the plurality of sensors (corresponding to array R 2 ). 
     Step  1010  can include identifying all of the similarity metrics associated with the actuation device (e.g., d(T 1 , R 1 ), . . . , d(T 1 , R p ), where P is the total number of sensors and/or sensor response time series r(x)). In some embodiments, step  1010  includes determining which of the identified similarity metrics is the lowest. The lowest similarity metric may indicate the closest match between the actuation signal time series t(x) associated with the actuation device and the sensor response time series r(x) associated with one of the sensors. In other embodiments, step  1010  can include determining which of the identified similarity metrics is the highest. For example, other techniques for calculating the similarity metric may produce larger similarity metrics when two time series match more closely. Regardless of how the similarity metric is calculated, step  1010  can include identifying the similarity metric which indicates the closest match between the actuation signal time series t(x) and the corresponding sensor response time series r(x). 
     If the actuation device has the same similarity metric with multiple sensors (e.g., d(T 1 , R 1 )=d(T 1 , R 2 )), step  1010  can include examining the time delay Δw between the actuation signal time series t(x) associated with the actuation device and sensor response time series r(x) associated with each of the sensors. The time delay Δw may indicate the delay between the time w 1  at which the actuation signal is applied to the actuation device and the time w 2  at which the effects of the actuation signal are evident in each sensor response (e.g., Δw=w 2 −w 1 ). Step  1010  can include identifying the sensor and/or sensor response time series r(x) with the lowest time delay Δw relative to the actuation signal time series t(x). 
     Still referring to  FIG. 10 , process  1000  is shown to include using the device pairing to generate and provide control signals to the actuation device (step  1012 ). Step  1012  can include using the device pairing to create a feedback control loop for HVAC system  600 . The feedback control loop can receive a feedback signal from the identified sensor and can provide a control signal to the actuation device. Step  1012  can include using the device pairing to define the sensor and actuation device in the control loop. For example, step  1012  can include creating a control loop which receives a feedback signal from the sensor in the device pairing and provides a control signal to the actuation device in the device pairing. Step  1012  can include mapping the sensor readings from the sensor in the device pairing to the feedback signal in the control loop. Similarly, step  1012  can include mapping the actuation signals provided to the actuation device in the device pairing to the control signal in the control loop. 
     Step  1012  can include using the feedback control loop to generate actuation signals for the actuation device. Step  1012  can include using state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, or any other type of control methodology to generate the actuation signals for the actuation device based on the sensor readings. For example, if the sensor reading from the sensor indicates that the temperature of a particular building zone is below a temperature setpoint for the building zone, step  1012  can include providing an actuation signal to the actuation device to increase the amount of heating provided to the building zone. Advantageously, process  1000  can be performed to automatically establish relationships between various actuation devices and sensors based on the device pairings to allow controller  602  to determine which of the actuation devices can be operated to affect a given sensor reading. 
     Configuration of Exemplary Embodiments 
     The construction and arrangement of the systems and methods as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements can be reversed or otherwise varied and the nature or number of discrete elements or positions can be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps can be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions can be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure. 
     The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure can be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Embodiments within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions. 
     Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also two or more steps can be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.