Patent Publication Number: US-10317261-B2

Title: Systems and methods for controlling flow rate using differential pressure measurements

Description:
BACKGROUND 
     The present invention relates generally to heating, ventilating, air conditioning, or refrigeration (HVAC) systems. The present invention relates more particularly to systems and methods for estimating a flow rate through a HVAC device (e.g., a heat exchanger) based on a measured pressure differential across the HVAC device. 
     HVAC systems generally include a variety of HVAC devices configured to facilitate heating, cooling, refrigeration, and/or other HVAC applications. The flow rate of a refrigerant, coolant, or other working fluid through a HVAC device may be a useful quantity for purposes of determining a heating, cooling, or refrigeration load served by the HVAC device. The flow rate of a fluid through a HVAC device is typically measured using a flow rate sensor installed upstream or downstream of the HVAC device. However, flow rate sensors can be expensive, inaccurate, and are often difficult to properly calibrate and maintain. Flow rate measurements can also have a high uncertainty associated therewith. It would be desirable to provide a system or method for obtaining flow rate information that overcomes these and other disadvantages of conventional flow rate measurements. 
     SUMMARY 
     One implementation of the present disclosure is a system for estimating a mass or volumetric flow rate through a device. In some embodiments, the device is a HVAC device. The system includes one or more pressure sensors configured to measure a plurality of pressure differentials across a tested device and a flow rate sensor configured to measure a plurality of flow rates through the tested device. Each of the measured flow rates corresponds to one of the measured pressure differentials. The system further includes a regression model trainer configured to generate regression coefficients for a flow rate model using the measured pressure differentials and corresponding flow rates. The flow rate model estimates a flow rate as a function of a pressure differential. The system further includes a flow rate estimator configured to use the flow rate model to estimate a flow rate through a tested or untested device as a function of a new measured pressure differential across the tested or untested device. 
     In some embodiments, the tested device is a first heat exchanger and the untested device is a second heat exchanger that has one or more device characteristics in common with the first heat exchanger. The one or more device characteristics may include at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type. 
     In some embodiments, the flow rate estimator is a component of the tested device and the estimated flow rate is a flow rate through the tested device. In other embodiments, the flow rate estimator is a component of the untested device and the estimated flow rate is a flow rate through the untested device. In other embodiments, the flow rate estimator is a component of a controller for the tested or untested device. 
     In some embodiments, the system further includes a device clusterer configured to organize a plurality of devices into clusters based on one or more device characteristics associated with the devices. The device clusterer may be configured to select the untested device from a plurality of devices organized into a same cluster as the tested device. 
     In some embodiments, the device clusterer is configured to generate a clustered set of test data including (1) the measured pressure differentials and corresponding flow rates for the tested device and (2) measured pressure differentials and corresponding flow rates for one or more other devices organized into a same cluster as the tested device. The regression model trainer may use the clustered set of test data to generate the regression coefficients for the flow rate model. 
     In some embodiments, the system further includes an uncertainty calculator. The uncertainty calculator may be configured to determine an uncertainty of one or more of the regression coefficients in the flow rate model and generate a set of uncertainty model parameters based on the determined uncertainties. The uncertainty calculator may use the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate. 
     Another implementation of the present disclosure is a method for estimating a mass or volumetric flow rate through a tested device. In some embodiments, the device is a HVAC device. The method includes measuring pressure differentials across a tested device and corresponding flow rates through the tested device at a plurality of different pressure differentials and flow rates. The method further includes training a flow rate model using the measured pressure differentials and corresponding flow rates. The flow rate model estimates a flow rate as a function of a pressure differential. The method further includes measuring a new pressure differential across the tested device and estimating a new flow rate through the tested device using the new pressure differential as an input to the flow rate model. 
     In some embodiments, the method includes organizing a plurality of devices into clusters based on one or more device characteristics associated with the plurality of devices. The plurality of devices may include the tested device and one or more other devices. In some embodiments, the one or more device characteristics include at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type. 
     In some embodiments, the method includes generating a clustered set of test data including (1) the measured pressure differentials and corresponding flow rates for the tested device and (2) measured pressure differentials and corresponding flow rates for one or more of the other devices organized into a same cluster as the tested device. Training the flow rate model may include using the clustered set of test data to generate regression coefficients for the flow rate model. 
     In some embodiments, the method includes determining an uncertainty of one or more trained parameters in the flow rate model, generating a set of uncertainty model parameters based on the determined uncertainties, and using the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate. 
     Another implementation of the present disclosure is a method for estimating a mass or volumetric flow rate through a device. In some embodiments, the device is a HVAC device. The method includes measuring pressure differentials across a first device and corresponding flow rates through the first device at a plurality of different pressure differentials and flow rates. The method further includes training a flow rate model using the measured pressure differentials and corresponding flow rates. The flow rate model estimates a flow rate as a function of a pressure differential. The method further includes measuring a pressure differential across a second device that has one or more device characteristics in common with the first device. The method further includes estimating a flow rate through the second device using the measured pressure differential across the second device as an input to the flow rate model. 
     In some embodiments, the first device is a first heat exchanger and the second device is a second heat exchanger that has one or more device characteristics in common with the first heat exchanger. The one or more device characteristics may include at least one of a device model code, a material tube index, a number of heat exchange passes, and a water box type. 
     In some embodiments, the method includes organizing a plurality of devices into clusters based on one or more device characteristics associated with the plurality of devices. The plurality of devices may include the first device and one or more other devices. 
     In some embodiments, the method includes generating a clustered set of test data including (1) the measured pressure differentials and corresponding flow rates for the first device and (2) measured pressure differentials and corresponding flow rates for one or more of the other devices organized into a same cluster as the first device. Training the flow rate model may include using the clustered set of test data to generate regression coefficients for the flow rate model. 
     In some embodiments, the method includes determining an uncertainty of one or more trained parameters in the flow rate model, generating a set of uncertainty model parameters based on the determined uncertainties, and using the uncertainty model parameters, an idiosyncratic uncertainty, and a sensor uncertainty in an uncertainty model to determine an uncertainty of the estimated flow rate. 
     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 
         FIG. 1  is a perspective view of a building served by a building management system (BMS), according to an exemplary embodiment. 
         FIG. 2  is a block diagram of a waterside system which may be used in conjunction with the BMS of  FIG. 1 , according to an exemplary embodiment. 
         FIG. 3  is a block diagram of an airside system which may be used in conjunction with the BMS of  FIG. 1 , according to an exemplary embodiment. 
         FIG. 4  is a block diagram of the BMS of  FIG. 1 , according to an exemplary embodiment. 
         FIG. 5A  is block diagram of a HVAC device testing system configured to perform a field testing procedure to train a flow rate model that estimates a flow rate through a HVAC device as a function of a pressure differential across the HVAC device, according to an exemplary embodiment. 
         FIG. 5B  is block diagram of a HVAC device testing system configured to perform a factory testing procedure to train a flow rate model that estimates a flow rate through a HVAC device as a function of a pressure differential across similar HVAC devices, according to an exemplary embodiment. 
         FIG. 6  is a block diagram illustrating the HVAC device testing system of  FIG. 5  in greater detail, according to an exemplary embodiment. 
         FIG. 7  is a block diagram of a HVAC system that includes the HVAC device testing system of  FIG. 5  and uses model parameters generated by the HVAC device testing system to estimate flow rates through various tested and untested HVAC devices, according to an exemplary embodiment. 
         FIG. 8  is a flowchart of a process for estimating a flow rate through a tested HVAC device, according to an exemplary embodiment. 
         FIG. 9  is a flowchart of a process for estimating a flow rate through an untested HVAC device, according to an exemplary embodiment. 
         FIG. 10  is a graph plotting test data including measured pressure differentials and corresponding flow rates for a cluster of HVAC devices, and a flow rate model generated based on the measured test data, according to an exemplary embodiment. 
         FIG. 11  is a graph illustrating the accuracy of the flow rate model of  FIG. 10 , according to an exemplary embodiment. 
         FIG. 12  is a flowchart of a process for obtaining regression parameters for a HVAC device and using the regression parameters to estimate flow rate through the HVAC device, according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Referring generally to the FIGURES, systems and methods for estimating flow rates in a heating, ventilation, or air conditioning (HVAC) system using differential pressure measurements are shown, according to various exemplary embodiments. A HVAC device testing system is used to test the fluid flow characteristics of various HVAC devices (e.g., evaporators, condensers, chillers, etc.) in order to determine a relationship between two or more variables that characterize the fluid flow through the HVAC devices. In some embodiments, the variables tested by the HVAC device testing system include flow rate {dot over (F)} and differential pressure ΔP. The tested flow rate {dot over (F)} may be a mass flow rate {dot over (F)} m  or a volumetric flow rate {dot over (F)} V  of a fluid flow (i.e., a liquid or gas flow) through a tested HVAC device. The differential pressure ΔP may be a pressure drop across the tested HVAC device or a component thereof (i.e., a pressure differential). The HVAC device testing system collects (e.g., measures) multiple data points for the tested variables while the tested HVAC device is operated over a range of fluid flow conditions. For example, the HVAC device testing system may measure the differential pressure ΔP and the corresponding flow rate {dot over (F)} at a plurality of different pressures and/or flow rates. 
     The HVAC device testing system may use the collected data points to train a regression model that predicts one of the tested variables as a function of one or more of the other tested variables. For example, the HVAC device testing system may use the measured differential pressures ΔP and the corresponding flow rates {dot over (F)} to train a regression model that estimates flow rate {circumflex over (F)} as a function of differential pressure ΔP, as shown in the following equation:
 
 {circumflex over (F)}=aΔP   b  
 
where the parameters a and b are regression coefficients trained by the HVAC device testing system based on the measured test data.
 
     In some embodiments, the HVAC device testing system performs the testing procedure for multiple different HVAC devices. The HVAC device testing system may organize the tested HVAC devices into a plurality of groups or clusters based on one or more characteristics of the devices. For example, the HVAC device testing system may organize a set of tested heat exchangers into clusters based on device characteristics such as the device type, device manufacturer, model code, material tube index (MTI), number of passes, water box type, and/or any device characteristic that affects (or correlates with) the performance of the HVAC device with respect to any of the tested variables. In some embodiments, the HVAC device testing system combines the test data for multiple HVAC devices within the same cluster and uses the combined test data to train a regression model for the cluster. 
     The regression models and/or the regression coefficients trained by the HVAC device testing system may be stored within various HVAC devices. In some embodiments, a regression model is stored within the memory of the tested HVAC device. In some embodiments, a regression model is stored within other HVAC devices that have similar characteristics (e.g., model code, MTI, number of passes, water box type, etc.) to the tested HVAC device. In some embodiments, the regression models are stored in controllers for the HVAC devices rather than the HVAC devices themselves. 
     Once the testing procedure is complete, the flow rate sensor is no longer needed and may be removed from the tested HVAC device. In operation, the differential pressure ΔP across a tested or untested HVAC device may be measured using one or more pressure sensors. The HVAC device (or controller for the HVAC device) may use the stored regression model to automatically calculate the estimated flow rate {circumflex over (F)} as a function of the measured differential pressure ΔP. Advantageously, this feature allows the HVAC device (or controller for the HVAC device) to determine and/or report values for multiple correlated variables without requiring independent sensors to measure both variables. Additional advantages and features of the present invention are described in greater detail below. 
     HVAC and Building Management System 
     Referring now to  FIGS. 1-4 , an exemplary building management system (BMS) and HVAC system in which the systems and methods of the present invention may be implemented are shown, according to an exemplary embodiment. Although the present invention is described primarily with reference to HVAC devices in a building HVAC system, it should be understood that the systems and methods described herein can be used to determine flow rates through any type of system or device (e.g., industrial devices, food processing devices, irrigation devices, medical devices, sprinkler systems, building equipment, etc.) and are not limited to HVAC devices. 
     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 an HVAC system  100 . HVAC system  100  may 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 may 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  may 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 may 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  may 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 may 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  may 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  may 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  may 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. 
     Referring now to  FIG. 2 , a block diagram of a waterside system  200  is shown, according to an exemplary embodiment. In various embodiments, waterside system  200  may supplement or replace waterside system  120  in HVAC system  100  or may be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , waterside system  200  may 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  may 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 the thermal energy loads (e.g., hot water, cold water, heating, cooling, etc.) of a building or campus. For example, heater subplant  202  may 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  may 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  may 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 may be delivered to individual zones of building  10  to serve the 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.) may be used in place of or in addition to water to serve the 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 invention. 
     Each of subplants  202 - 212  may 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 may 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  may 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 . 
     Referring now to  FIG. 3 , a block diagram of an airside system  300  is shown, according to an exemplary embodiment. In various embodiments, airside system  300  may supplement or replace airside system  130  in HVAC system  100  or may be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , airside system  300  may 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 may 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  may 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  may be exhausted from AHU  302  through exhaust damper  316  as exhaust air  322 . 
     Each of dampers  316 - 320  may be operated by an actuator. For example, exhaust air damper  316  may be operated by actuator  324 , mixing damper  318  may be operated by actuator  326 , and outside air damper  320  may 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 may 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 may be collected, stored, or used by actuators  324 - 328 . AHU controller  330  may 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  may 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  may 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  may 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  may be controlled by an actuator. For example, valve  346  may be controlled by actuator  354  and valve  352  may 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 controller  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  may 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  may be separate (as shown in  FIG. 3 ) or integrated. In an integrated implementation, AHU controller  330  may 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  may 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  may be a computer workstation, a client terminal, a remote or local interface, or any other type of user interface device. Client device  368  may be a stationary terminal or a mobile device. For example, client device  368  may 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 . 
     Referring now to  FIG. 4 , a block diagram of a building management system (BMS)  400  is shown, according to an exemplary embodiment. BMS  400  may 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  may include any number of devices, controllers, and connections for completing its individual functions and control activities. HVAC subsystem  440  may include many of the same components as HVAC system  100 , as described with reference to  FIGS. 1-3 . For example, HVAC subsystem  440  may 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  may 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  may 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  may 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 WiFi transceiver for communicating via a wireless communications network. In another example, one or both of interfaces  407 ,  409  may 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  may 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.) may 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  may be or include volatile memory or non-volatile memory. Memory  408  may 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 an exemplary embodiment, 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  may 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  may 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  may 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  may 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  may 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  may 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  may 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 may 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 may 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 an exemplary embodiment, 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 may 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 may 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 may 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 may 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  may 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 an exemplary embodiment, 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  may 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  may 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  may 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  may 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  may 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  may 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  may 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  may 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 may 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  may 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 an exemplary embodiment, 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  may 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  may 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. 
     HVAC Device Testing 
     Referring now to  FIGS. 5A-5B , a HVAC device testing system  500  is shown, according to an exemplary embodiment. In various embodiments, HVAC device testing system  500  may be implemented as a component of BMS  400 , airside system  300 , waterside system  200 , HVAC system  100 , or as a separate system that interacts with any of systems  100 - 400 . HVAC device testing system  500  may be configured to test the fluid flow characteristics of various HVAC devices (e.g., evaporators, condensers, chillers, etc.) in order to determine a relationship between two or more variables that characterize the fluid flow through the HVAC devices.  FIG. 5A  illustrates a “field testing” implementation in which HVAC device testing system  500  is used to test a particular HVAC device that is currently in use at a customer site.  FIG. 5B  illustrates a “factory testing” implementation in which HVAC device testing system  500  is used to test various HVAC devices at the factory or other off-site location. Both of these implementations are described in greater detail below. 
     In some embodiments, the variables tested by HVAC device testing system  500  include flow rate {dot over (F)} and differential pressure ΔP. The tested flow rate {dot over (F)} may be a mass flow rate {dot over (F)} m  or a volumetric flow rate {dot over (F)} V  of a fluid flow  536  through a tested HVAC device  502 . In some embodiments, tested flow rate {dot over (F)} is measured by a flow rate sensor  504  installed downstream or upstream of the tested HVAC device  502 . In other embodiments, flow rate sensor  504  may be integrated with the tested HVAC device  502  and the tested flow rate {dot over (F)} may be provided as a data output from the tested HVAC device  502 . 
     The differential pressure ΔP may be a pressure drop across the tested HVAC device  502  or a component thereof. In some embodiments, the differential pressure ΔP is measured using an integrated (e.g., factory-installed) differential pressure sensor  505  within the tested HVAC device  502  and provided as a data output from the tested HVAC device  502 . In other embodiments, the differential pressure ΔP is calculated by subtracting a pressure P 2  downstream of the tested HVAC device from a pressure P 1  upstream of the tested HVAC device (i.e., ΔP=P 1 −P 2 ). The upstream pressure P 1  and the downstream pressure P 2  may be measured using an upstream pressure sensor  506  and a downstream pressure sensor  508 , as shown in  FIG. 6 . 
     Referring particularly to  FIG. 5A , a field testing implementation of HVAC device testing system  500  is shown, according to an exemplary embodiment. In the field testing implementation, HVAC device testing system  500  receives measurements of the tested variables for a particular HVAC device  502  that is currently in use at a customer site. HVAC device testing system  500  may be configured to collect (e.g., measure) multiple data points for the tested variables while the tested HVAC device  502  is operated over a range of fluid flow conditions. For example, HVAC device testing system  500  may measure the differential pressure ΔP and the corresponding flow rate {dot over (F)} at a plurality of different pressures and/or flow rates. 
     HVAC device testing system  500  may use the collected data points to train a regression model that predicts one of the tested variables as a function of one or more of the other tested variables. For example, HVAC device testing system  500  may use the measured differential pressures ΔP and the corresponding flow rates {dot over (F)} to train a regression model that estimates flow rate {circumflex over (F)} as a function of differential pressure ΔP, as shown in the following equation:
 
 {circumflex over (F)}=aΔP   b  
 
where the parameters a and b are regression coefficients trained by HVAC device testing system  500  based on the test data. It should be understood that the regression model {circumflex over (F)}=aΔP b  is merely exemplary and that other forms or types of regression models can be used by HVAC device testing system  500  in various embodiments.
 
     In the field testing implementation, HVAC device testing system  500  may provide the regression model and/or the regression coefficients to the tested HVAC device  502 . In some embodiments, the regression model is stored within the memory of the tested HVAC device  502 . For example, HVAC device testing system  500  is shown providing the regression coefficients a and b to the tested HVAC device  502 . 
     Once the testing procedure is complete, flow rate sensor  504  is no longer needed and may be removed from the tested HVAC device  502 . In operation, the differential pressure ΔP across the tested HVAC device  502  may be measured using an integrated pressure sensor  505  (as shown in  FIG. 5A ) or upstream and downstream pressure sensors  506  and  508  (as shown in  FIG. 6 ). The tested HVAC device  502  may use the stored regression model to automatically calculate the estimated flow rate {circumflex over (F)}. Advantageously, this feature allows the tested HVAC device  502  to determine and/or report values for multiple correlated variables without requiring independent sensors to measure both variables. 
     Referring now to  FIG. 5B , a factory testing implementation of HVAC device testing system  500  is shown, according to an exemplary embodiment. In the factory testing implementation, HVAC device testing system  500  performs the testing procedure for multiple different tested HVAC devices  502 . HVAC device testing system  500  may organize the tested HVAC devices  502  into a plurality of groups or clusters based on one or more characteristics of the tested HVAC devices  502 . For example, HVAC device testing system  500  may organize a set of tested heat exchangers into clusters based on device characteristics such as the device type, device manufacturer, model code, material tube index (MTI), number of heat exchange passes, water box type, and/or any device characteristic that affects (or correlates with) the performance of the HVAC device with respect to any of the tested variables. In some embodiments, HVAC device testing system  500  combines the test data for multiple HVAC devices within the same cluster and uses the combined test data to train a regression model for the cluster. 
     The regression models and/or the regression coefficients trained by HVAC device testing system  500  may be stored in a regression coefficients database  532 . Regression coefficients database  532  may store each set of regression coefficients a and b with one or more parameters that characterize the HVAC device or devices to which the set of regression coefficients apply (e.g., device type, device manufacturer, model code, MTI, etc.). The regression coefficients a and b can be retrieved from regression coefficients database  532  and stored within various untested HVAC devices  503  or controllers  507  for untested HVAC devices that have the same or similar characteristics as the tested HVAC devices  502  used to generate the regression coefficients. 
     In some embodiments, a regression model is stored within other HVAC devices that have similar characteristics (e.g., model code, MTI, number of passes, water box type, etc.) to the tested HVAC devices  502 . For example, regression coefficients database  532  is shown providing the regression coefficients a and b to an untested HVAC device  503 . In some embodiments, the regression models are stored in controllers for the HVAC devices rather than the HVAC devices themselves. For example, regression coefficients database  532  is shown providing the regression coefficients a and b to a controller  507  for an untested HVAC device  509 . The regression coefficients a and b can be stored within devices  503  and  507  prior to distribution to a customer (e.g., in the factory) or uploaded to devices  503  and  507  at a later time (e.g., via a communications network, via removable storage media, etc.). 
     In operation, the differential pressure ΔP across an untested HVAC device  503  or  509  may be measured using an integrated differential pressure sensor  505  (as shown in  FIG. 5B ) or upstream and downstream pressure sensors  506  and  508  (as shown in  FIG. 6 ). In various embodiments, the differential pressure measurements ΔP are provided to a controller  507  for an untested HVAC device  509  or used internally by the untested HVAC device  503 . The untested HVAC device  503  or controller  507  for the untested HVAC device  509  may use the stored regression model to automatically calculate the estimated flow rate {circumflex over (F)}. Advantageously, this feature allows the untested HVAC device  503  or controller  507  for the untested HVAC device  509  to determine and/or report values for multiple correlated variables without requiring independent sensors to measure both variables. Additional advantages and features of HVAC device testing system  500  are described in greater detail with reference to  FIG. 6 . 
     Referring now to  FIG. 6 , a block diagram illustrating HVAC device testing system  500  in greater detail is shown, according to an exemplary embodiment. HVAC device testing system  500  is shown to include a data communications interface  510  and a processing circuit  512 . Data communications interface  510  may include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting electronic data communications with tested HVAC devices (e.g., tested HVAC  502 ), untested HVAC devices (e.g., untested HVAC devices  503 ,  509 ), sensors (e.g., sensors  504 - 508 ), controllers (e.g., controller  507 , BMS controller  366 ), and/or other external systems or devices. Communications via interface  510  may 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, data communications interface  510  may include an Ethernet card and port for sending and receiving data via an Ethernet-based communications link or network. In another example, data communications interface  510  may include a WiFi transceiver for communicating via a wireless communications network. In some embodiments, data communications interface  510  is configured to communicate using the BACnet communications protocol. 
     Data communications interface  510  may receive measurements from one or more sensors (e.g., sensors  504 - 508 ) configured to measure the variables that characterize the fluid flow  536  through a tested HVAC device  502 . For example, data communications interface  510  may receive measured pressures and/or flow rates from sensors  504 - 508  and provide the measurements to processing circuit  512 . Processing circuit  512  may be communicably connected to data communications interface  510  such that processing circuit  512  and the various components thereof can send and receive data via communications interface  510 . 
     Processing circuit  512  is shown to include a processor  514  and memory  516 . Processor  514  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  516  (e.g., memory, memory unit, storage device, etc.) may 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  516  may be or include volatile memory or non-volatile memory. Memory  516  may 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 an exemplary embodiment, memory  516  is communicably connected to processor  514  via processing circuit  512  and includes computer code for executing (e.g., by processing circuit  512  and/or processor  514 ) one or more processes described herein. 
     In some embodiments, HVAC device testing system  500  and processing circuit  512  are implemented within a single computer (e.g., one server, one housing, etc.). In other embodiments various components of HVAC device testing system  500  may be distributed across multiple servers or computers that can exist in distributed locations. For example, data communications interface  510  may receive measurements from sensors  504 - 508  and send the measurements to a remote processing circuit  512  for further processing. In some embodiments, one or more components of processing circuit  512  are implemented using a cloud-based computing platform such as the PANOPTIX® brand building efficiency platform sold by Johnson Controls, Inc. 
     Still referring to  FIG. 6 , memory  516  is shown to include a test data collector  518 . Test data collector  518  may be configured to collect test data describing the flow characteristics of various tested HVAC devices  502 . Collected test data may include, for example, measured pressures, measured flow rates, measured temperatures, measured humidities, or any other type of measured data value that describes a fluid flow  536  through a tested HVAC device  502 . 
     Although only one tested HVAC device  502  is shown in  FIG. 6 , it should be understood that test data collector  518  may receive and store test data for any number and/or type of HVAC devices. In various embodiments, the tested HVAC devices  502  may be passive HVAC components or active HVAC components. Passive HVAC components may include, for example, heat exchangers (e.g., condensers, evaporators, cooling coils, heating coils, gas coolers, etc.), flow control elements (e.g., pipes, ducts, tubes, flow restrictors, etc.), and the like. Active HVAC components may include, for example, chillers, heaters, electronic valves, compressors, fans, or any other HVAC component that typically requires energy to operate. 
     Measured test data may be received from one or more sensors (e.g., sensors  504 - 508 ) via data communications interface  510 . In some embodiments, test data collector  518  receives measured test data from one or more factory-installed sensors in the tested HVAC device  502 . For example, tested HVAC device  502  may include a factory-installed differential pressure sensor configured to measure a pressure differential ΔP across HVAC device  502  or a portion thereof (as shown in  FIG. 5 ). In other embodiments, test data collector  518  receives measured test data from one or more sensors installed upstream or downstream of a tested HVAC device  502 . For example, test data collector  518  may receive an upstream pressure P 1  from an upstream pressure sensor  506  and a downstream pressure P 2  from a downstream pressure sensor  508  (as shown in  FIG. 6 ). In some embodiments, test data collector  518  receives measured test data from a flow sensor  504  installed upstream or downstream of tested HVAC device  502 . 
     In some embodiments, test data collector  518  receives measured values for two or more correlated variables such as flow rate {dot over (F)} and differential pressure ΔP. In other embodiments, test data collector  518  receives measured values for a single measured variable and associates the measured values with known or controlled values for the other correlated variable. For example, memory  516  is shown to include a flow modulator  520 . Flow modulator  520  may be configured to modulate (e.g., adjust, control, etc.) the flow rate {dot over (F)} through the tested HVAC device  502  such that measuring the flow rate {dot over (F)} is not required. In some embodiments, flow modulator  520  modulates the flow rate {dot over (F)} by providing a control signal to a fan or pump configured to affect the flow rate {dot over (F)} through HVAC device  502 . Flow modulator  520  may provide the known or controlled values for the flow rate {dot over (F)} to test data collector  518 . 
     Test data collector  518  may also collect data indicating device characteristics of the tested HVAC devices  502 . Device characteristics may include, for example, a device type (e.g., chiller, heat exchanger, pipe, etc.), a device manufacturer, a model code, a condenser or evaporator code, a material tube index, a number of passes, a water box type, and the like. Device characteristics may be provided by a user (e.g., via user interface  534  or network  446 ) and/or received via data communications interface  510  in conjunction with the measured test data. The measured test data and the device characteristics may be stored by test data collector  518  in a test database  530 . Each data point in test database  530  may include a measured pressure value and a corresponding measured flow rate value. In some embodiments, the measured test data may be stored along with an indication of one or more device characteristics describing the tested HVAC device  502  associated with the measured test data. 
     Still referring to  FIG. 6 , memory  516  is shown to include a test variable calculator  522 . Test variable calculator  522  may be configured to determine values for one or more calculated test variables based on the measured values collected by test data collector  518 . For example, the measured values collected by test data collector  518  may include an upstream pressure P 1  and a downstream pressure P 2 . Test variable calculator  522  may subtract the downstream pressure P 2  from the upstream pressure P 1  to calculate the pressure differential ΔP (i.e., ΔP=P 1 −P 2 ) across the tested HVAC device  502 . The calculated pressure differential ΔP may then be used as an input to the regression model to generate the regression coefficients. 
     In some embodiments, the test variables include calculated values such as enthalpy, entropy, fluid density, and/or other values that cannot be directly measured. Test variable calculator  522  may use thermodynamic relationships to determine values for one or more non-measured test variables. For example, test variable calculator  522  may calculate a fluid enthalpy as a function of a measured temperature and/or pressure. As another example, test variable calculator  522  may calculate a mass flow rate {dot over (F)} m  by multiplying a known fluid density ρ by a measured volumetric flow rate {dot over (F)} v  (i.e., {dot over (F)} m =ρ{dot over (F)} v ). The mass flow rate {dot over (F)} m  may then be used as an input to the regression model to generate the regression coefficients. In other embodiments, the volumetric flow rate {dot over (F)} v  is used as an input to the regression model to generate the regression coefficients without first converting to a mass flow rate. The calculated test variables may be stored alongside the measured test data in test database  530 . 
     Still referring to  FIG. 6 , memory  516  is shown to include a device clusterer  524 . Device clusterer  524  may be configured to organize the tested HVAC devices into a plurality of groups or clusters based on one or more characteristics of the tested HVAC devices. For example, device clusterer  524  may organize a set of tested heat exchangers into clusters based on heat exchanger characteristics such as the device type (e.g., condenser, evaporator, etc.), device manufacturer, model code, material tube index (MTI), number of passes, evaporator or condenser code, water box type, and/or any device characteristic that affects (or correlates with) the performance of the HVAC device with respect to any of the tested variables. 
     The device characteristics used by device clusterer  524  to organize HVAC devices into clusters are referred to herein as “clustering parameters.” In some embodiments, device clusterer  524  organizes the tested HVAC devices into a plurality of clusters such that all of the devices in each cluster have the same combination of clustering parameters. For example, all of the HVAC devices assigned to one cluster may have the same text string in their model name (e.g., “ABC˜” where “˜” is a wildcard), the same MTI number, and/or the same number of passes. In some embodiments, the clustering parameters are provided by a user (e.g., via user interface  534  or network  446 ) and/or received in conjunction with the measured test data. For example, device clusterer  524  may cause user interface  534  or client device  448  to display a prompt for a user to specify one or more clustering parameters used to organize the HVAC devices into clusters. 
     In other embodiments, device clusterer  524  automatically selects or generates one or more clustering parameters based on predefined clustering criteria (e.g., model name, MTI number, number of passes). For example, device clusterer  524  may automatically determine that HVAC devices with a model name that includes the text string “ABC” should be assigned to one cluster, whereas HVAC devices with a model name that includes the text string “DEF” should be assigned to another cluster. In some embodiments, device clusterer  524  automatically selects clustering parameters that are estimated to result in a best fit of the regression model to the clustered test data. 
     In some embodiments, device clusterer  524  combines the test data for multiple HVAC devices within the same cluster. For example, device clusterer  524  may organize the test data in test database  530  into a plurality of clustered sets. Each clustered set may include all of the test data (e.g., measured pressures and flow rates) corresponding to the HVAC devices within a particular cluster. Each clustered set of test data may be used by regression model trainer  526  to train a different set of regression coefficients. 
     Still referring to  FIG. 6 , memory  516  is shown to include a regression model trainer  526 . Regression model trainer  526  may be configured to train regression models based on the measured and/or calculated test data in test database  530 . Training a regression model may include using the test data to generate a set of coefficients for a regression model. In some embodiments, regression model trainer  526  trains a regression model using the test data from a single HVAC device. In other embodiments, regression model trainer  526  trains a regression model using a clustered set of test data for a set of related HVAC devices (e.g., HVAC devices that have shared device characteristics). 
     Regression model trainer  526  may be configured to perform a regression analysis in which the test data are modeled by a function which predicts a flow-related variable (e.g., an estimated flow rate {circumflex over (F)}) as a function of at least one other flow-related variable (e.g., differential pressure ΔP) and one or more model parameters (i.e., regression coefficients). In some embodiments, regression model trainer  526  performs a nonlinear regression to generate values for the regression coefficients a and b in the following nonlinear model:
 
 {circumflex over (F)}=aΔP   b  
 
where {circumflex over (F)} is a flow rate predicted by the model, ΔP is a pressure differential provided as an input to the model, and a and b are the regression coefficients or model parameters. The measured flow rates {dot over (F)} and the measured pressures ΔP from test database  530  may be provided as inputs to regression model trainer  526  and used to generate values for the regression coefficients a and b.
 
     Regression model trainer  526  may determine values for the regression coefficients a and b such that the resulting function best fits the test data. Regression model trainer  526  may use any of a variety of regression techniques to determine the values for a and b. For example, regression model trainer  526  may use least squares regression, ordinary least squares regression, partial least squares regression, total least squares regression, generalized least squares regression, weighted least squares regression, nonlinear least squares regression, non-negative least squares regression, iteratively reweighted least squares regression, ridge regression, Bayesian regression, or any other suitable regression technique. 
     The regression analysis performed by regression model trainer  526  may produce values for the regression coefficients a and b, containment limits ±L for the regression coefficients a and b, a R 2  value indicating the accuracy of the fit, and a random error uncertainty (RMSE). The containment limits ±L may define a range of values (e.g., maximum and minimum values) for each of the regression coefficients a and b based on a predefined containment probability (e.g., 95%, 99%, etc.). In some embodiments, the RMSE value and/or the containment limits are used by uncertainty calculator  528  to determine an uncertainty in the flow rate {circumflex over (F)} estimated by the regression model. Regression model trainer  526  may store the regression coefficients a and b, the containment limits, and/or the RMSE value in regression coefficients database  532 . 
     In some embodiments, HVAC device testing system  500  stores the trained regression model (i.e., the model equation and the regression coefficients) within the memory of the tested HVAC device(s)  502 . Each of the trained regression models corresponds to a set of test data used to train the regression model and may be stored within the memory of the HVAC device(s) from which the corresponding test data was collected. The tested HVAC device(s)  502  may then use the trained regression model (e.g., during operation) to estimate a flow rate {circumflex over (F)} based on a measured differential pressure ΔP. 
     In some embodiments, HVAC device testing system  500  stores the trained regression model within the memory of one or more untested HVAC devices that are similar to the tested HVAC devices  502 . For example, the trained regression model for a cluster of tested HVAC devices may be stored in one or more untested HVAC devices that satisfy the clustering parameters for the cluster (i.e., devices that would have been organized into the same cluster as the tested HVAC devices based on the clustering parameters). For example, if a cluster includes all two-pass heat exchangers with a MTI of 321 and a model name that includes the string “ABC,” the regression coefficients generated for that cluster may be stored within an untested heat exchanger that also has these device characteristics (e.g., a new model of heat exchanger in the “ABC” family). The untested HVAC device may then use the trained regression model (e.g., during operation) to estimate a flow rate {circumflex over (F)} based on a measured differential pressure ΔP. 
     In some embodiments, HVAC device testing system  500  provides the trained regression model and/or the regression coefficients to another system or device. For example, the trained regression models and/or the regression coefficients may be provided to a BMS controller (e.g., BMS controller  366 ), a supervisory controller, and/or a local controller for the HVAC devices. The controller may then use the trained regression model to estimate a flow rate {circumflex over (F)} through the HVAC devices based on a measured differential pressure ΔP. 
     In some embodiments, the regression coefficients are provided to FDD layer  416  for use in fault detection and diagnostics. For example, FDD layer  416  may compare the regression coefficients with a previous set of regression coefficients based on a previous set of test data. A fault may be detected by FDD layer  416  if the regression coefficients have changed significantly from their previous values. The trained regression model and/or the regression coefficients may be stored locally, provided to an external system or device, and/or presented to a user via user interface  534 . 
     Still referring to  FIG. 6 , memory  516  is shown to include an uncertainty calculator  528 . Uncertainty calculator  528  may be configured to determine the uncertainties associated with various measured or calculated values. In some embodiments, uncertainty calculator  528  determines the uncertainty μ a  associated with the regression coefficient a, the uncertainty μ b  associated with the regression coefficient b, and the uncertainty μ ΔP  associated with the differential pressure measurements ΔP. Uncertainty calculator  528  may use the uncertainties μ a , μ b , and μ ΔP  to calculate (or generate a formula for calculating) the uncertainty μ {dot over (F)}  associated with the flow rate {circumflex over (F)} estimated by the regression model. 
     In some embodiments, uncertainty calculator  528  estimates the uncertainty μ ΔP  associated with the differential pressure measurements ΔP using a Type A uncertainty estimation. A Type A uncertainty estimation may involve data sampling and statistical analysis. For example, uncertainty calculator  528  may obtain n independent differential pressure measurements ΔP under the same operating conditions. If the uncertainty were zero, all of the independent differential pressure measurements ΔP would ideally be the same; however, measurement uncertainty causes the measured pressures ΔP to vary. Uncertainty calculator  528  may estimate Type A uncertainty using the following equation: 
               μ     Δ   ⁢           ⁢   P       =       s     Δ   ⁢           ⁢   P       n           
where s ΔP  is the standard deviation of the differential pressure measurements ΔP and n is the number of differential pressure measurements.
 
     In other embodiments, uncertainty calculator  528  estimates the uncertainty μ ΔP  associated with the differential pressure measurements ΔP using a Type B uncertainty estimation. A Type B uncertainty estimation may be based on heuristics obtained from recollected experience and/or manufacturer-specified containment limits and containment probabilities. For example, if the measurement error is normally distributed, uncertainty calculator  528  may estimate Type B uncertainty using the following equation: 
               μ     Δ   ⁢           ⁢   P       =     L       ϕ     -   1       ⁡     (       1   +   p     2     )               
where L represents the containment limits (e.g., ±L), p is the containment probability (e.g., 95%, 99%, etc.), and ϕ −1  is the inverse normal distribution function. The containment limits ±L and the containment probability p may be obtained from manufacturer specifications for the differential pressure sensor used to measure the differential pressure values ΔP.
 
     In some embodiments, uncertainty calculator  528  uses the Type B uncertainty estimation to estimate the uncertainties μ a  and μ b  associated with the regression model coefficients a and b. The regression analysis performed by regression model trainer  526  may generate values for the regression model coefficients a and b, as well as containment limits L and a containment probability p. For example, the regression analysis for an exemplary set of test data may produce the following information:
         a=198.2 [194.4, 202] 95%   b=0.5759 [0.5691, 0.5827] 95%   SSE=3.07E3   R 2 =0.9983   RMSE=8.6592
 
which indicates that the containment limits L a  for a are ±3.8 (i.e., a=198.2±3.8), the containment limits L b  for b are ±0.0068 (i.e., b=0.5759±0.0068), and that the containment probability p is 95% (i.e., p=0.95). From this information, uncertainty calculator  528  can estimate the uncertainties μ a  and μ b  using the following equations:
       

     
       
         
           
             
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               a 
             
             = 
             
               
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     In some embodiments, uncertainty calculator  528  calculates (or generates a formula for calculating) the uncertainty μ F  associated with the flow rate {circumflex over (F)} estimated by the regression model. As previously described, the model for calculating flow rate {dot over (F)} may have the form {circumflex over (F)}=aΔP b . The uncertainty μ F  may have depend on uncertainties μ a  and μ b  associated with the regression model coefficients a and b, the random error uncertainty (RMSE), and the uncertainty μ ΔP  associated with the differential pressure measurements ΔP. In some embodiments, a, b, and ΔP are independent and each is normally distributed. 
     Uncertainty calculator  528  may calculate the flow rate uncertainty μ F  using an uncertainty model, as shown in the following equations: 
     
       
         
           
             
                 
             
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     In some embodiments, uncertainty calculator  528  assumes that the test data has no uncertainty (i.e., μ ΔP =0). With this assumption, the uncertainty model can be simplified as follows: 
     
       
         
           
             
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     Uncertainty calculator  528  may provide the uncertainty model and/or the uncertainty model parameters (i.e., the values for μ a , μ b , and/or μ ΔP ) to an external system or device. For example, the uncertainty model and/or model parameters may be provided to the tested HVAC devices, untested HVAC devices, controllers for such devices, a user device, or any other system or device. In some embodiments, the uncertainty model and/or model parameters are provided to the same devices that receive the regression model coefficients a and b, as described with reference to regression model trainer  526 . In some embodiments, uncertainty calculator  528  inserts the values for a, b, and RMSE (generated by regression model trainer  526 ) and the values for μ a , μ b , and μ ΔP  (generated by uncertainty calculator  528 ) into the uncertainty model such that the only remaining unknown variables are μ F  and ΔP. The HVAC devices and/or controllers may use uncertainty model in conjunction with current pressure measurements ΔP to calculate the uncertainty μ F  in the estimated flow rate {circumflex over (F)}. 
     Flow Rate Estimation 
     Referring now to  FIG. 7 , a block diagram illustrating a HVAC system  700  is shown, according to an exemplary embodiment. HVAC system  700  is shown to include a variety of tested and untested HVAC devices  702 - 712 . HVAC devices  702 ,  706 , and  710  are tested HVAC devices, whereas HVAC devices  704 ,  708 , and  712  are untested HVAC devices. A tested HVAC device may be any HVAC device for which test data are measured and provided to HVAC device testing system  500 . Test data may include pressure measurements (e.g., P 1 , P 2 , ΔP) indicating a pressure differential across a tested HVAC device and flow rate measurements (e.g., {dot over (F)}) indicating a corresponding flow rate through the tested HVAC device. For example, tested HVAC devices  702 ,  706 , and  710  are shown providing pressure/flow measurements  716 ,  718 , and  720 , respectively, to HVAC device testing system  500 . An untested HVAC device may be any HVAC device that does not provide measured test data to HVAC device testing system  500  for purposes of generating a flow rate model. 
     HVAC devices  702 - 712  are organized into a plurality of clusters (i.e., cluster A, cluster B, and cluster C) based on one or more clustering parameters. HVAC devices  702 - 704  belong to cluster A; HVAC devices  706 - 708  belong to cluster B, and HVAC devices  710 - 712  belong to cluster C. In some embodiments, device clusterer  524  organizes HVAC devices  702 - 712  into clusters A-C such that all of the devices in each cluster have the same combination of clustering parameters. For example, all of the HVAC devices assigned to cluster A have the same text string in their model name, the same MTI number, and/or the same number of passes. 
     HVAC device testing system  500  may use each set of pressure/flow measurements  716 - 720  to generate a corresponding set of model parameters  722 - 726 . For example, HVAC device testing system  500  may use pressure/flow measurements  716  to generate model parameters  722  for cluster A. Similarly, HVAC device testing system  500  may use pressure/flow measurements  718  and  720  to generate model parameters  724  for cluster B and model parameters  726  for cluster C. Each set of model parameters  722 - 726  may include regression model parameters (e.g., a and b in the regression model {circumflex over (F)}=aΔP b ) and/or uncertainty model parameters (e.g., μ a , μ b , μ ΔP , and RSME in the uncertainty model μ F =√{square root over ((ΔP b ) 2 μ a   2 +(a·ln(ΔP)·ΔP b ) 2 μ b   2 +RMSE 2 +(a·b·ΔP b-1 ) 2 μ ΔP   2 ))}. The regression model parameters a and b and the uncertainty model parameters μ a , μ b , μ ΔP , and RSME may be generated by regression model trainer  526  and/or uncertainty calculator  528 , as described with reference to  FIG. 6 . 
     HVAC device testing system  500  may provide each set of model parameters to the tested and/or untested HVAC devices for the corresponding cluster. For example, HVAC device testing system  500  may provide model parameters  722  to tested HVAC devices  702  and untested HVAC devices  704 . HVAC device testing system  500  may provide model parameters  724  to tested HVAC devices  706  and untested HVAC devices  708 . HVAC device testing system  500  may provide model parameters  726  to tested HVAC devices  710  and untested HVAC devices  712 . In some embodiments, HVAC device testing system  500  provides the model parameters to a controller for the HVAC devices rather than the HVAC devices themselves. For example, HVAC device testing system  500  is shown providing model parameters  726  to a controller  714  for untested HVAC devices  712 . 
     Devices  702 - 714  may use model parameters  722 - 726  to calculate an estimated flow rate {circumflex over (F)} as a function of a differential pressure measurement ΔP. The estimated flow rate {circumflex over (F)} may be calculated using the following equation:
 
 {circumflex over (F)}=aΔP   b  
 
where the differential pressure measurement ΔP is a new differential pressure measurement measured by HVAC devices  702 - 712  or otherwise made available to devices  702 - 714 . The new differential pressure measurement ΔP may be a more recent measurement not included in pressure/flow measurements  716 - 720 . In some embodiments, devices  702 - 714  use model parameters  722 - 726  to calculate an estimated flow rate uncertainty μ F  according to the following equation:
 
     
       
         
           
             
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     In some embodiments, devices  702 - 714  use the estimated flow rates {circumflex over (F)} and/or uncertainties μ F  for load prediction, fault detection and diagnostics, energy monitoring/reporting, or other applications in which a flow rate value may be useful. For example, controller  714  may use the estimated flow rates {circumflex over (F)} and/or uncertainties μ F  to generate a control signal u provided to HVAC devices  712 . In some embodiments, the estimated flow rates {circumflex over (F)} and/or uncertainties μ F  are reported to a supervisory controller or a client device via a communications network. 
     Referring now to  FIG. 8 , a flowchart of a process  800  for determining a flow rate through a HVAC device is shown, according to an exemplary embodiment. In some embodiments, process  800  is performed by one or more components of HVAC system  100 , waterside system  200 , airside system  300 , BMS  400 , HVAC device testing system  500 , and/or a HVAC system  700 , as described with reference to  FIGS. 1-7 . 
     Process  800  is shown to include measuring differential pressures across a HVAC device and corresponding flow rates through the HVAC device (step  802 ). The HVAC device may be any active or passive component in a HVAC system. For example, the HVAC device may be a heat exchanger (e.g., condenser, evaporator, cooling coil, heating coil, gas cooler, etc.), flow control element (e.g., pipe, duct, tube, flow restrictor, etc.), chiller, heater, electronic valve, compressor, fan, or any other HVAC component. The differential pressures ΔP and flow rates {dot over (F)} may be measured at a plurality of different operating conditions (e.g., a plurality of different differential pressure values and corresponding flow rate values). In some embodiments, the differential pressure ΔP or the flow rate {dot over (F)} may be a controlled variable. In other embodiments, both the differential pressure ΔP and the flow rate {dot over (F)} are uncontrolled variables. 
     Step  802  may include measuring a differential pressure ΔP and flow rate {dot over (F)} using one or more sensors. In some embodiments, one or more of the sensors are factory-installed sensors integrated with the HVAC device (e.g., a differential pressure sensor within the HVAC device). In some embodiments, one or more of the sensors are positioned upstream or downstream of the HVAC device (e.g., an upstream pressure sensor, a downstream pressure sensor, a flow rate sensor, etc.). The differential pressure ΔP may be measured directly or calculated from a pair of pressure measurements across the HVAC device. The flow rate {dot over (F)} may be a mass flow rate or a volumetric flow rate. In some embodiments, the flow rate {dot over (F)} is measured using a temporary flow rate sensor that is installed for testing purposes only and removed once the testing process is complete. 
     Still referring to  FIG. 8 , process  800  is shown to include training a flow rate model using the measured differential pressures and corresponding flow rates (step  804 ). In some embodiments, the flow rate model is a nonlinear model that estimates a flow rate {circumflex over (F)} as a function of a differential pressure ΔP and one or more model parameters. For example, the flow rate model may have the form:
 
 {circumflex over (F)}=aΔP   b  
 
where a and b are the model parameters.
 
     Step  804  may include using the measured differential pressures ΔP and flow rates {dot over (F)} as training data to determine values for the model parameters a and b. Any of a variety of regression techniques may be used to determine the values for a and b. For example, step  804  may include using least squares regression, ordinary least squares regression, partial least squares regression, total least squares regression, generalized least squares regression, weighted least squares regression, nonlinear least squares regression, non-negative least squares regression, iteratively reweighted least squares regression, ridge regression, Bayesian regression, or any other suitable regression technique to determine values for the model parameters a and b based on the measured data received in step  802 . 
     In some embodiments, step  804  includes combining the measured differential pressures ΔP and flow rates {dot over (F)} received in step  802  with another set of measured differential pressures ΔP and flow rates {dot over (F)} for another HVAC device. For example, the measured data received in step  802  may be combined with the measured data for another HVAC device within the same cluster. HVAC devices within the same cluster may have one or more shared characteristics such as device type (e.g., condenser, evaporator, etc.), device manufacturer, model code, material tube index (MTI), number of passes, evaporator or condenser code, water box type, and/or any device characteristic that affects (or correlates with) the performance of the HVAC device with respect to any of the variables measured in step  802 . 
     In some embodiments, step  804  includes identifying one or more HVAC devices in the same cluster as the HVAC device for which the data is received in step  802 . Step  804  may include combining the measured data from the identified HVAC device with the measured data received in step  802  to form a clustered set of test data. Each clustered set may include all of the test data (e.g., measured pressures and flow rates) corresponding to the HVAC devices within a particular cluster. In some embodiments, the flow rate model in step  804  is trained using all of the measured data in the clustered set. 
     In some embodiments, step  804  includes determining an uncertainty in the flow rate model parameters a and b (e.g., μ a , μ b ), an uncertainty in the measured pressure ΔP (e.g., μ ΔP ), and/or a random error uncertainty (e.g., RSME) as described with reference to  FIG. 6 . In some embodiments, step  804  includes providing the flow rate model parameters a and b and/or the uncertainty model parameters μ a , μ b , μ ΔP , and RSME to the HVAC device or a controller for the HVAC device. 
     Still referring to  FIG. 8 , process  800  is shown to include measuring a new differential pressure across the HVAC device (step  806 ). The new differential pressure ΔP new  may be another (e.g., updated or more recent) differential pressure value measured in a similar manner to the differential pressures received in step  802 . For example, the new differential pressure ΔP new  may be measured by a factory-installed differential pressure sensor or calculated based on an upstream pressure measurement and a downstream pressure measurement. 
     Process  800  is shown to include estimating a new flow rate through the HVAC device using the new differential pressure as an input to the flow rate model (step  808 ). Step  808  may include estimating the flow rate {circumflex over (F)} using the flow rate model trained in step  804 :
 
 {circumflex over (F)}=aΔP   b  
 
where the values for a and b are determined in step  804  and the new differential pressure measurement ΔP new  received in step  806  is substituted for the differential pressure variable ΔP. In some embodiments, step  808  includes calculating an uncertainty μ F  for the estimated flow rate {circumflex over (F)}, as described with reference to uncertainty calculator  528 .
 
     In various embodiments, step  808  is performed by the HVAC device, a controller for the HVAC device, or any other system or device that receives the flow rate model generated in step  804 . The estimated flow rate {circumflex over (F)} may be provided as an output from the HVAC device along with the new differential pressure measurement ΔP new . Advantageously, this allows the HVAC device to determine or report values for two or more correlated variables without requiring independent sensors to measure each variable. 
     Referring now to  FIG. 9 , a flowchart of a process  900  for determining a flow rate through an untested HVAC device is shown, according to an exemplary embodiment. In some embodiments, process  900  is performed by one or more components of HVAC system  100 , waterside system  200 , airside system  300 , BMS  400 , HVAC device testing system  500 , and/or a HVAC system  700 , as described with reference to  FIGS. 1-7 . 
     Process  900  is shown to include measuring differential pressures across a first HVAC device and corresponding flow rates through the first HVAC device (step  902 ). The first HVAC device may be any active or passive component in a HVAC system. For example, the first HVAC device may be a heat exchanger (e.g., condenser, evaporator, cooling coil, heating coil, gas cooler, etc.), flow control element (e.g., pipe, duct, tube, flow restrictor, etc.), chiller, heater, electronic valve, compressor, fan, or any other HVAC component. The differential pressures ΔP and flow rates {dot over (F)} may be measured at a plurality of different operating conditions (e.g., a plurality of different differential pressure values and corresponding flow rate values). In some embodiments, the differential pressure ΔP or the flow rate {dot over (F)} may be a controlled variable. In other embodiments, both the differential pressure ΔP and the flow rate {dot over (F)} are uncontrolled variables. 
     Step  902  may include measuring a differential pressure ΔP and flow rate {dot over (F)} using one or more sensors. In some embodiments, one or more of the sensors are factory-installed sensors integrated with the first HVAC device (e.g., a differential pressure sensor within the first HVAC device). In some embodiments, one or more of the sensors are positioned upstream or downstream of the first HVAC device (e.g., an upstream pressure sensor, a downstream pressure sensor, a flow rate sensor, etc.). The differential pressure ΔP may be measured directly or calculated from a pair of pressure measurements across the first HVAC device. The flow rate {dot over (F)} may be a mass flow rate or a volumetric flow rate. In some embodiments, the flow rate {dot over (F)} is measured using a temporary flow rate sensor that is installed for testing purposes only and removed once the testing process is complete. 
     Still referring to  FIG. 9 , process  900  is shown to include training a flow rate model using the measured differential pressures and corresponding flow rates (step  904 ). In some embodiments, the flow rate model is a nonlinear model that estimates a flow rate {circumflex over (F)} as a function of a differential pressure ΔP and one or more model parameters. For example, the flow rate model may have the form:
 
 {circumflex over (F)}=aΔP   b  
 
where a and b are the model parameters.
 
     Step  904  may include using the measured differential pressures ΔP and flow rates {dot over (F)} as training data to determine values for the model parameters a and b. Any of a variety of regression techniques may be used to determine the values for a and b. For example, step  904  may include using least squares regression, ordinary least squares regression, partial least squares regression, total least squares regression, generalized least squares regression, weighted least squares regression, nonlinear least squares regression, non-negative least squares regression, iteratively reweighted least squares regression, ridge regression, Bayesian regression, or any other suitable regression technique to determine values for the model parameters a and b based on the measured data received in step  902 . 
     In some embodiments, step  904  includes combining the measured differential pressures ΔP and flow rates {dot over (F)} received in step  902  with another set of measured differential pressures ΔP and flow rates {dot over (F)} for another HVAC device. For example, the measured data received in step  902  may be combined with the measured data for another HVAC device within the same cluster. In some embodiments, step  904  includes identifying one or more HVAC devices in the same cluster as the first HVAC device. Step  904  may include combining the measured data from the identified HVAC device with the measured data received in step  902  to form a clustered set of test data. Each clustered set may include all of the test data (e.g., measured pressures and flow rates) corresponding to the HVAC devices within a particular cluster. In some embodiments, the flow rate model in step  904  is trained using all of the measured data in the clustered set. In some embodiments, step  904  includes determining an uncertainty in the flow rate model parameters a and b (e.g., μ a , μ b ), an uncertainty in the measured pressure ΔP (e.g., μ ΔP ), and/or a random error uncertainty (e.g., RSME) as described with reference to  FIG. 6 . 
     Still referring to  FIG. 9 , process  900  is shown to include measuring a differential pressure across a second HVAC device that has one or more shared characteristics with the first HVAC device (step  906 ). Shared characteristics may include, for example, device type (e.g., condenser, evaporator, etc.), device manufacturer, model code, material tube index (MTI), number of passes, evaporator or condenser code, water box type, and/or any device characteristic that affects (or correlates with) the performance of the first HVAC device with respect to any of the variables measured in step  902 . In some embodiments, step  906  includes identifying the second HVAC device based on one or more shared characteristics with the first HVAC device. The second HVAC device may be identified as any device in the same cluster as the first HVAC device. 
     The differential pressure across the second HVAC device may be measured in a similar manner to the differential pressures received in step  902 . For example, the differential pressure across the second HVAC device may be measured by a factory-installed differential pressure sensor or calculated based on an upstream pressure measurement and a downstream pressure measurement. 
     Process  900  is shown to include estimating a flow rate through the second HVAC device using the measured differential pressure across the second HVAC device as an input to the flow rate model (step  908 ). Step  908  may include estimating the flow rate {circumflex over (F)} through the second HVAC device using the flow rate model trained in step  904 :
 
 {circumflex over (F)}=aΔP   b  
 
where the values for a and b are determined in step  904  and the differential pressure measurement received in step  906  is substituted for the differential pressure variable ΔP. In some embodiments, step  908  includes calculating an uncertainty μ F  for the estimated flow rate {circumflex over (F)}, as described with reference to uncertainty calculator  528 .
 
     In various embodiments, step  908  is performed by the second HVAC device, a controller for the second HVAC device, or any other system or device that receives the flow rate model generated in step  904 . The estimated flow rate {circumflex over (F)} may be provided as an output from the second HVAC device along with the differential pressure measurement across the second HVAC device. Advantageously, this allows the second HVAC device to determine or report values for two or more correlated variables without requiring independent sensors to measure each variable. 
     Referring now to  FIG. 10 , a graph  1000  of a nonlinear regression model is shown, according to an exemplary embodiment. Graph  1000  plots flow rate {dot over (F)} vs. differential pressure ΔP for a cluster of tested HVAC devices. Each of the HVAC devices represented in graph  1000  has device characteristics that satisfy a given set of clustering parameters. For example, each of the HVAC devices represented in graph  1000  has a model name that includes the text string “YK˜M4˜” where the “˜” character is a wildcard (e.g., YKMQM4H9-EUG, YKMRM4K1-CWGS, YKM2M4K1-CAGS, etc.). Each of the HVAC devices represented in graph  1000  also is a two-pass heat exchanger with a MTI of 266. Device clusterer  524  may use these and/or other clustering parameters to select the HVAC devices that are included in graph  1000 . 
     Graph  1000  is shown to include several sets of test data  1002 - 1016 . Each set of test data  1002 - 1016  corresponds to a tested HVAC device within the cluster. For example, test data  1002  corresponds to the HVAC device “YKMQM4H9-EUG,” test data  1004  corresponds to the HVAC device “YKMRM4K1-CWGS,” test data  1006  corresponds to the HVAC device “YKM2M4K1-CBGS,” and so on. Each data point of test data  1002 - 1016  includes a differential pressure value ΔP and a corresponding flow rate value {dot over (F)}. Test data  1002 - 1016  may be collected using one or more sensors configured to measure the differential pressures ΔP and the corresponding flow rates {dot over (F)} for the tested HVAC devices. Test data  1002 - 1016  may be combined into a clustered set of test data and used to train a regression model. 
     Graph  1000  is shown to include a flow rate model  1018 . As shown in  FIG. 10 , flow rate model  1018  is a nonlinear regression model. For example, flow rate model  1018  may have the form {dot over (F)}=aΔP b , where the coefficients a and b are trained using test data  1002 - 1016 . Regression model trainer  526  may use any of a variety of regression analyses to determine optimal values for coefficients a and b, as described with reference to  FIG. 6 . The optimal values may be values which result in the best fit of flow rate model  1018  to test data  1002 - 1016 . For example, the regression analysis performed by regression model trainer  526  may generate the regression coefficients a=951.2 and b=0.4775, as shown in parameter display  1020 . The regression coefficients a and b and/or the flow rate model  1018  may be provided to the tested HVAC devices in the cluster and/or untested HVAC devices that satisfy the clustering parameters. The HVAC devices may then use flow rate model  1018  to estimate a flow rate {circumflex over (F)} as a function of a measured differential pressure ΔP. 
     The regression analysis performed by regression model trainer  526  may also generate containment limits for the regression coefficients a and b. For example, parameter display  1020  indicates that the containment limits for a are [925.9 976.5] (i.e., a=951.2±25.3), whereas the containment limits for b are [0.4689 0.4862] (i.e., b=0.4775±0.0087). A containment probability of 95% is provided for each of the containment limits. The regression analysis performed by regression model trainer  526  may also generate a RMSE value, shown in parameter display  1020  as RMSE=96.83. 
     The parameters shown in parameter display  1020  may be used by uncertainty calculator  528  to generate the parameters of an uncertainty model (e.g., μ a , μ b , RSME, etc.), as described with reference to  FIG. 6 . The uncertainty model parameters and/or the uncertainty model may be provided to the tested HVAC devices in the cluster and/or untested HVAC devices that satisfy the clustering parameters. The HVAC devices may then use uncertainty model to calculate an uncertainty μ F  in the estimated flow rate {circumflex over (F)} as a function of a measured differential pressure ΔP and the uncertainty model parameters. 
     Referring now to  FIG. 11 , a graph  1100  of the flow rate model percentage error is shown, according to an exemplary embodiment. Graph  1100  plots the percentage error of flow rate model  1018  with respect to the actual flow rate values included in test data  1002 - 1016 . As evidenced by graph  1100 , flow rate model  1018  has a maximum error of approximately 8%, with the majority of the error values within ±2%. These results indicate that flow rate model  1018  is highly accurate and can be used to provide an accurate estimate of the flow rate {circumflex over (F)}. 
     Referring now to  FIG. 12 , a flowchart of a process  1200  for determining a flow rate through a HVAC device is shown, according to an exemplary embodiment. In some embodiments, process  1200  is performed by one or more components of HVAC system  100 , waterside system  200 , airside system  300 , BMS  400 , HVAC device testing system  500 , and/or a HVAC system  700 , as described with reference to  FIGS. 1-7 . Process  1200  may be used to automatically obtain regression coefficients for a HVAC device and use the regression coefficients to estimate a flow rate through the HVAC device. 
     Process  1200  is shown to include identifying the HVAC device (step  1202 ). The HVAC device may be any active or passive component in a HVAC system. For example, the HVAC device may be a heat exchanger (e.g., condenser, evaporator, cooling coil, heating coil, gas cooler, etc.), flow control element (e.g., pipe, duct, tube, flow restrictor, etc.), chiller, heater, electronic valve, compressor, fan, or any other HVAC component. Step  1202  may include identifying one or more characteristics of the device such as the device type, device manufacturer, model code, material tube index (MTI), number of heat exchange passes, water box type, and/or any device characteristic that describes the HVAC device. 
     Process  1200  is shown to include accessing a database of regression coefficients (step  1204 ). The database of regression coefficients may be a local database or a remote database accessible via a communications network (e.g., a LAN, the Internet, etc.). The database of regression coefficients may include sets of regression coefficients a and b for different types of HVAC devices. Each set of regression coefficients a and b may be stored in the regression coefficients database with one or more parameters that characterize the HVAC device or devices to which the set of regression coefficients apply (e.g., device type, device manufacturer, model code, MTI, etc.). In some embodiments, the database of regression coefficients is populated by performing the HVAC device testing procedure described with reference to  FIGS. 5B-6 . 
     Still referring to  FIG. 12 , process  1200  is shown to include determining whether coefficients are available for the identified HVAC device (step  1206 ). Step  1206  may include determining whether any of the sets regression coefficients in the regression coefficients database are stored with parameters that match the characteristics of the identified HVAC device. If a match is found, step  1206  may include determining that coefficients are available for the identified HVAC device (i.e., the result of step  1206  is “yes”) and the corresponding set of regression coefficients may be retrieved from the regression coefficients database (step  1210 ). However, if a match is not found, step  1206  may include determining that coefficients are not available for the identified HVAC device (i.e., the result of step  1206  is “no”) and the HVAC testing procedure may be performed to obtain the regression coefficients for the identified HVAC device (step  1208 ). In some embodiments, the HVAC device testing procedure is the same or similar to the field testing procedure described with reference to  FIG. 5A . The regression coefficients may be stored within the HVAC device or a controller for the HVAC device. 
     Process  1200  is shown to include measuring a differential pressure across the HVAC device (step  1212 ) and using the measured differential pressure and the regression coefficients to estimate flow rate through the HVAC device (step  1214 ). The differential pressure across the HVAC device may be measured by a factory-installed differential pressure sensor or calculated based on an upstream pressure measurement and a downstream pressure measurement. Step  1214  may include estimating the flow rate {circumflex over (F)} through the HVAC device using a flow rate model trained with the regression coefficients received in step  1208  or step  1210 . For example, step  1214  may include calculating flow rate using the model:
 
 {circumflex over (F)}=aΔP   b  
 
where the values for a and b are the regression coefficients obtained in step  1208  or step  1210  and ΔP is the differential pressure measurement obtained in step  1212 .
 
     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 may be reversed or otherwise varied and the nature or number of discrete elements or positions may 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 may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions may 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 may 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. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. 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 may 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.