Patent Publication Number: US-2018031290-A1

Title: Vapor cycle refrigeration system filter life estimation

Description:
BACKGROUND 
     The present disclosure relates generally to vapor cycle refrigeration systems, and in particular to determining a remaining useful life of a filter of a vapor cycle refrigeration system using reduced order modeling techniques. 
     Complex systems, such as those implemented onboard aircraft, often include operational parameters that may not be sensed by physical sensors of the system. For example, aircraft air-conditioning packs implementing vapor cycle refrigeration techniques may not have sensor readings to measure parameters such as a differential pressure across system filters. Knowledge of these unmeasured parameters can be useful for protective control modes, system health diagnostics, and planned maintenance activities. It may be possible to sense these parameters with physical sensors, but at added cost, complexity, and weight to the system. 
     SUMMARY 
     In one example, a method includes operating a vapor cycle refrigeration system of an aircraft. The method further includes measuring, via a plurality of sensors, operational parameters of the vapor cycle refrigeration system while the vapor cycle refrigeration system is operating, and transmitting the measured operational parameters to a computer system. The method further includes generating, by the computer system using a first reduced order model that corresponds to an unclogged state of a filter of the aircraft vapor cycle refrigeration system, a first predicted discharge pressure of a compressor of the aircraft vapor cycle refrigeration system based on the measured operational parameters. The method further includes generating, by the computer system using a second reduced order model that corresponds to a clogged state of the filter, a second predicted discharge pressure of the compressor based on the measured operational parameters. The method further includes determining, by the computer system, a remaining useful life of the filter based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure of the compressor, and outputting, by the computer system, an indication of the remaining useful life of the filter. 
     In another example, a system includes a vapor cycle refrigeration system of an aircraft and a computer system. The vapor cycle refrigeration system includes a plurality of sensors, a compressor, and a filter. The plurality of sensors are configured to measure operational parameters of the vapor cycle refrigeration system. The compressor is configured to compress refrigerant of the vapor cycle refrigeration system. The filter is disposed within a flow path of the refrigerant. The computer system includes at least one processor and computer-readable memory. The computer-readable memory is encoded with instructions that, when executed by the at least one processor, cause the computer system to receive the operational parameters of the vapor cycle refrigeration system measured by the plurality of sensors, and generate, using a first reduced order model that corresponds to an unclogged state of the filter, a first predicted discharge pressure of the compressor based on the received operational parameters. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to generate, using a second reduced order model that corresponds to a clogged state of the filter, a second predicted discharge pressure of the compressor based on the received operational parameters. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to determine a remaining useful life of the filter based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure of the compressor. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to output an indication of the remaining useful life of the filter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic block diagram illustrating an example system including an aircraft vapor cycle refrigeration system and a computer system that determines a remaining useful life of a filter of the vapor cycle refrigeration system using reduced order models. 
         FIG. 2  is a flow diagram illustrating example operations to generate a reduced order model that can be utilized to determine a remaining useful life of a filter of a vapor cycle refrigeration system. 
         FIG. 3  is a flow diagram illustrating example operations to determine a remaining useful life of a filter of a vapor cycle refrigeration system using reduced order models. 
     
    
    
     DETAILED DESCRIPTION 
     As described herein, a computer system utilizes reduced order modeling techniques to determine a remaining useful life of a filter of an aircraft vapor cycle refrigeration system. The filter, disposed within a flow path of refrigerant of the system, gathers debris and particles that may be generated during normal system operation. Accordingly, the filter helps to prevent circulation of the debris that could eventually cause evaporator fouling, throttling valve clogging, or compressor damage. However, as the filter collects debris, its impedance of the flow of refrigerant increases. This increased impedance in turn causes a system compressor to increase the refrigerant pressure to overcome the filter impedance. A compressor discharge pressure that exceeds a maximum protective threshold pressure can cause the compressor to shutdown (i.e., halt operation) to prevent damage to the compressor or other system components. As such, replacement (or cleaning) of the filter prior to system shutdown is desirable to prevent inoperability of the cooling system and the corresponding loss of service and revenue from, e.g., commercial flights. 
     According to techniques of this disclosure, a computer system utilizes reduced order models to generate predicted discharge pressures of a compressor, the predicted discharge pressures corresponding to both clogged and unclogged states of the filter. The computer system determines a remaining useful life (RUL) of the filter based on the predicted discharge pressures and a measured discharge pressure of the compressor. The computer system outputs an indication of the RUL of the filter including, e.g., a percentage of filtering capacity remaining prior to reaching a clogged filter state that can result in compressor shutdown, an indication of a remaining system runtime prior to reaching the clogged filter state, or other indications of RUL of the filter. As such, the system can determine a RUL of the filter without requiring dedicated pressure or other sensors, such as a differential pressure sensor (or multiple pressure sensors) for measuring a difference in pressure of the refrigerant across the filter. The use of predicted pressures generated by the reduced order models enables the computer system to account for relatively high refrigerant pressures that may be due to normal system operation, rather than clogging of the filter. Moreover, the reduced order of the models (as compared to a higher-fidelity model) lowers the computational complexity of the models, thereby decreasing runtime of the models, requirements of the computer, and complexity of model implementation. 
       FIG. 1  is a schematic block diagram illustrating system  10  that includes aircraft vapor cycle refrigeration system  12  and computer system  14  that determines a remaining useful life (RUL) of filter  16  using reduced order models. As illustrated in  FIG. 1 , system  10  further includes data acquisition system  18  and display  20 . Vapor cycle refrigeration system  12  includes controller  22 , condenser  24 , expansion orifice  26 , flash tank  28 , throttling valve  29 , evaporator  30 , compressor  32 , heat sink inlet temperature sensor T HSI , compressor suction temperature sensor T CS , compressor suction pressure sensor P CS , compressor discharge temperature sensor T CD , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor motor current sensor I. Computer system  14  includes reduced order model (ROM) module  34  and filter RUL module  36 . The arrowed lines extending between condenser  24 , filter  16 , expansion orifice  26 , flash tank  28 , throttling valve  29 , evaporator  30 , and compressor  32  indicate a flow and direction of refrigerant circulated in vapor cycle refrigeration system  12 . 
     Refrigerant is supplied to compressor  32  in vapor form from both flash tank  28  and evaporator  30 . Compressor  32  compresses the refrigerant to a higher pressure and supplies the compressed refrigerant in vapor form to condenser  24 . Condenser  24  condenses the compressed vapor refrigerant to liquid form using cooling liquid and/or gaseous flow supplied through the heat sink inlet. Heat from the compressed refrigerant is transferred from the refrigerant to the cooling liquid and/or gaseous flow supplied to condenser  24  through the heat sink inlet and is carried away from vapor cycle refrigeration system  12  via the heat sink outlet. The condensed, liquid refrigerant is supplied from condenser  24  through filter  16  to expansion orifice  26 . Filter  16  is disposed within a flow path of the refrigerant and includes filter media, such as fibrous filter media sized to trap particles and other debris that may be present within the liquid refrigerant while allowing the liquid refrigerant to pass through the media. While in the example of  FIG. 1 , filter  16  is disposed downstream of condenser  24  and upstream of expansion orifice  26 , filter  16  can be disposed in any location of vapor cycle refrigeration system  12  in which refrigerant is conveyed in liquid form, such as downstream of flash tank  28  and upstream of throttling valve  29 . 
     Condensed liquid refrigerant passed through filter  16  is supplied through expansion orifice  26 . As the liquid refrigerant passes through expansion orifice  26 , a rapid pressure reduction of the liquid refrigerant occurs causing an evaporation of a portion of the refrigerant and resulting in two-phase refrigerant (i.e., liquid phase and vapor phase) that is supplied to flash tank  28  where phase separation occurs through, e.g., gravity separation. Expansion orifice  26  can be a fixed orifice configured to cause the pressure reduction in the refrigerant. In some examples, expansion orifice  26  can be implemented as a valve, the position of which is controlled via, e.g., controller  22  to cause and/or control the pressure reduction of the refrigerant. 
     Vapor-form refrigerant is supplied from flash tank  28  to compressor  32 . Liquid refrigerant, cooled by both the heat transfer in condenser  24  and the rapid pressure reduction through expansion orifice  26 , is supplied to throttling valve  29 . A position of throttling valve  29 , sometimes referred to as an expansion valve, is controlled by a motor (not illustrated) via commands from controller  22  to cause a rapid pressure reduction of the liquid refrigerant as it passes through throttling valve  29 , thereby causing an evaporation of a portion of the refrigerant (having a further cooling effect on the refrigerant) and resulting in a two-phase refrigerant (i.e., liquid phase and vapor phase) that is supplied to evaporator  30 . 
     Evaporator  30  cools inlet air as it is passed through evaporator  30  through an evaporation process in which the liquid refrigerant is converted (i.e., evaporated) from the liquid state to a mostly or entirely gaseous state. The evaporation process absorbs heat from the inlet air, thereby cooling the inlet air and providing conditioned air for, e.g., a cabin, galley, or other air conditioning system. The evaporated refrigerant is supplied from evaporator  30  to compressor  32 . As such, vapor cycle refrigeration system  12  provides a closed-loop cycle of refrigerant in which heat is transferred from an inlet air supply to the refrigerant to provide cooled, conditioned air, and rejected from vapor cycle refrigeration system  12  via the heat sink inlet and the heat sink outlet at condenser  24 . 
     As liquid refrigerant passes through filter  16 , particles or other debris that may be present in the refrigerant (e.g., created during normal operation of system components) are collected within the filtration media of filter  16 . As filter  16  begins to clog with particles, the impedance of filter  16  to flow of the refrigerant increases. In response, compressor  32  increases the discharge pressure to maintain operational pressures of the refrigerant downstream of filter  16 . Compressor  32  and/or controller  22 , however, maintain the discharge pressure of compressor  32  to a pressure that is below a maximum threshold pressure to prevent physical damage to compressor  32  and/or other components of vapor cycle refrigeration system  12  that could occur at refrigerant pressures above the maximum threshold pressure. 
     As illustrated in  FIG. 1 , vapor cycle refrigeration system includes controller  22 . Controller  22  can be any electronic device that is operationally coupled (e.g., electrically and/or communicatively coupled) to components of vapor cycle refrigeration system  12  to control real-time operation of the components of the system and to receive inputs from various sensors positioned throughout vapor cycle refrigeration system  12 . As illustrated in  FIG. 1 , controller  22  is operationally connected to receive inputs from compressor suction temperature sensor T CS , compressor discharge temperature sensor T CD , heat sink inlet temperature sensor T HSI , compressor suction pressure sensor P CS , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor motor current sensor I. 
     Compressor suction temperature sensor T CS  and compressor suction pressure sensor P CS  are positioned at or near an upstream inlet of compressor  32  to measure a temperature and pressure of refrigerant entering the upstream (or suction) inlet of compressor  32 . Compressor discharge temperature sensor T CD  and compressor discharge pressure sensor P CD  are positioned at or near a downstream outlet of compressor  32  to measure a temperature and pressure of refrigerant exiting the downstream (or discharge) outlet of compressor  32 . Compressor speed sensor N and compressor current sensor I are integral to or positioned adjacent to compressor  32 . Compressor speed sensor N is configured to sense an operational speed of compressor  32 , such as a rotational speed of a shaft of compressor  32 . Compressor current sensor I is configured to sense an amount of electrical current draw of compressor  32  from a power source integral to or remote from vapor cycle refrigeration system  12 . Heat sink inlet temperature sensor T HSI  is positioned at or near the heat sink inlet of condenser  24  to sense a temperature of the cooling liquid and/or gaseous flow through the heat sink inlet. 
     As further illustrated in  FIG. 1 , system  10  includes data acquisition system  18 , display  20 , and computer system  14 . Data acquisition system  18  includes one or more electronic components configured to receive various discrete, analog, and/or digital parameters from sensors and/or systems of an aircraft that includes system  10  and distribute the received parameters to consuming systems. Display  20  can be a display device positioned in, e.g., a cockpit of the aircraft. In some examples, display  20  can include one or more input devices, such as buttons or touch-sensitive components to receive input from a user (e.g., user confirmation or acknowledgments of displayed data). Computer system  14  can be a remote, ground-based computer system or a computer system of an aircraft that includes system  10 . For example, computer system  14  can be part of a ground-based maintenance system that receives aircraft operational data and processes the data for diagnostic or other maintenance activities. In other examples, computer system  14  can be part of an on-board avionics system, such as an aircraft prognostics and health management system. 
     Controller  22 , as illustrated in  FIG. 1 , is communicatively coupled to data acquisition system  18  via one or more wired or wireless communication channels, or both. For example, controller  22  can be connected to data acquisition system  18  via an aircraft data bus implementing the Aeronautical Radio, Inc. (ARINC)  429  or other communication protocol. Data acquisition system  18  is communicatively coupled to display  20  (e.g., via the ARINC  429  data bus or other communication channels) to transmit data that is displayed at display  20  and/or receive data (e.g., user input data) from display  20 . Data acquisition system  18  is communicatively coupled with computer system  14  via one or more wired and/or wireless communication channels. For instance, in examples where computer system  14  is a ground-based computer system, data acquisition system  18  can be communicatively coupled with computer system  14  via one or more wireless communication channels, such as cellular communications, wireless Internet communications (e.g., WiFi), or other wireless communication channels. 
     Each of computer system  14  and controller  22  include one or more processors and computer-readable memory encoded with instructions that, when executed by the one or more processors, cause computer system  14  and controller  22  to operate in accordance with techniques described herein. Examples of the one or more processors include any one or more of a microprocessor, a controller, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other equivalent discrete or integrated logic circuitry. Computer-readable memory of computer system  14  and controller  22  can be configured to store information with computer system  14  and controller  22  during operation. The computer-readable memory can be described, in some examples, as computer-readable storage media. In some examples, a computer-readable storage medium can include a non-transitory medium. The term “non-transitory” can indicate that the storage medium is not embodied in a carrier wave or a propagated signal. In certain examples, a non-transitory storage medium can store data that can, over time, change (e.g., in RAM or cache). Computer-readable memory of computer system  14  and controller  22  can include volatile and non-volatile memories. Examples of volatile memories can include random access memories (RAM), dynamic random access memories (DRAM), static random access memories (SRAM), and other forms of volatile memories Examples of non-volatile memories can include magnetic hard discs, optical discs, floppy discs, flash memories, or forms of electrically programmable memories (EPROM) or electrically erasable and programmable (EEPROM) memories. 
     Computer system  14 , as illustrated in  FIG. 1 , includes ROM module  34  and filter RUL module  36 . As described herein, computer system  14  utilizes ROM module  34  to generate predicted discharge pressures of compressor  32  corresponding to an unclogged state of filter  16  and a clogged state of filter  16 . Computer system  14  utilizes filter RUL module  36  to determine a remaining useful life of filter  16  based on the predicted discharge pressures from ROM module  34  and a measured discharge pressure sensed by compressor discharge pressure sensor P CD . 
     The reduced order models utilized by ROM module  34  can be generated based on a high-fidelity physics-based model of vapor cycle refrigeration system  12  or operational data captured during operation of vapor cycle refrigeration system  12  (e.g., test data), as is further described below. ROM module  34  can utilize a first reduced order model that is adapted to generate a first predicted discharge pressure of compressor  32  corresponding to an unclogged state of filter  16  based on a set of measured input parameters of vapor cycle refrigeration system  12 . ROM module  34  can utilize a second reduced order model that is adapted to generate a second predicted discharge pressure of compressor  32  corresponding to a clogged state of filter  16  based on the set of measured input parameters of vapor cycle refrigeration system  12 . Each of the first and second reduced order models can be implemented using the following equation: 
         P   pred   =b   0 +Σ i   b   i   x   i   c     i   +Σ j   b   j ( X ) j   c     j     Equation (1)
 
     where:
         P pred  is a predicted discharge pressure of the compressor (i.e., the first predicted discharge pressure corresponding to the unclogged state of filter  16  or the second predicted discharge pressure corresponding to the clogged state of filter  16 );   b 0  is a constant;   b i  and b j  are multiplicative regression coefficients;   c i  and c j  are exponential regression coefficients;   x i  are first order parameters, each corresponding to one of the set of measured input operational parameters; and   X j  are interaction terms, each corresponding to a multiplicative product of two or more of the measured input operational parameters.       

     ROM module  34  can receive a set of measured input parameters from one or more of compressor suction temperature sensor T CS , compressor discharge temperature sensor T CD , heat sink inlet temperature sensor T HSI , compressor suction pressure sensor P CS , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor current sensor I. ROM module  34  can determine the first predicted discharge pressure of compressor  32  corresponding to the unclogged state of filter  16  using Equation (1) having constant b 0 , multiplicative regression coefficients b i  and b j , and exponential regression coefficients c i  and c j  that are configured to produce a predicted pressure P pred  that estimates a discharge pressure of compressor  32  during operation of vapor cycle refrigeration system  12  having an unclogged state of filter  16 . ROM module  34  can determine the second predicted discharge pressure of compressor  32  corresponding to the clogged state of filter  16  using Equation (1) having constant b 0 , multiplicative regression coefficients b i  and b j , and exponential regression coefficients c i  and c j  that are configured to produce a predicted pressure P pred  that estimates a discharge pressure of compressor  32  during operation of vapor cycle refrigeration system  12  having a clogged state of filter  16 . 
     Filter RUL module  36  utilizes the first predicted discharge pressure corresponding to the unclogged state of filter  16 , the second predicted discharge pressure corresponding to the clogged state of filter  16 , and a measured pressure from compressor discharge pressure sensor P CD  to determine a remaining useful life of filter  16 . For example, RUL module  36  can determine the remaining useful life of filter  16  using the following equation: 
     
       
         
           
             
               
                 
                   
                     Filter 
                     life 
                   
                   = 
                   
                     
                       min 
                        
                       
                         ( 
                         
                           1 
                           , 
                           
                             1 
                             - 
                             
                               
                                 
                                   P 
                                   dis 
                                 
                                 - 
                                 
                                   P 
                                   disClean 
                                 
                               
                               
                                 
                                   P 
                                   disClogged 
                                 
                                 - 
                                 
                                   P 
                                   disClean 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     × 
                     100 
                      
                     % 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     where:
         Filter life  is the remaining useful life of the filter;   P dis  is the measured discharge pressure received from compressor discharge pressure sensor P CD ;   P disClean  is the first predicted discharge pressure corresponding to the unclogged state of filter  16 ;   P disClogged  is the second predicted discharge pressure corresponding to the clogged state of filter  16 ; and   the min operator selects the minimum value of the two operands.       

     Computer system  14  can output an indication of the remaining useful life of filter  16 , such as to a display device of computer system  14  (not illustrated), data acquisition system  18 , or other consuming system. While Equation (2) above is adapted to produce a remaining useful life of filter  16  that is expressed as a percentage of filtering capacity of filter  16  remaining prior to reaching a clogged filter state that can result in protective shutdown of compressor  32 , in some examples, the remaining useful life of filter  16  output by computer system  14  can include other indications of the remaining useful life. For instance, RUL module  36  can determine an estimated remaining runtime of vapor cycle refrigeration system  12  prior to reaching the clogged state of filter  16  based on a runtime of vapor cycle refrigeration system  12  since installation (or cleaning) of filter  16  and the determined percentage of filtering capacity of filter  16  remaining prior to reaching the clogged filter state. 
     In operation, computer system  14  transmits a data upload request to data acquisition system  18  to request an upload of measured operational parameters of vapor cycle refrigeration system  12  during operation of vapor cycle refrigeration system  12 . The upload request can be periodic, such as on a per-flight basis, a per-runtime basis, or other periods. Data acquisition system  18 , in response to receiving the data upload request, retrieves measured operational parameters of vapor cycle refrigeration system  12  from controller  22  and transmits the received parameters to computer system  14 . The measured operational parameters can include, e.g., measured parameters from compressor suction temperature sensor T CS , compressor discharge temperature sensor T CD , heat sink inlet temperature sensor T HSI , compressor suction pressure sensor P CS , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor current sensor I. 
     ROM module  34  determines a first predicted discharge pressure of compressor  32  based on the measured operational parameters using a first reduced order model that corresponds to an unclogged state of filter  16 . ROM module  23  determines a second predicted discharge pressure of compressor  32  based on the measured operational parameters using a second reduced order model that corresponds to a clogged state of filter  16 . Filter RUL module  36  determines a remaining useful life of filter  16  based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure sensed by compressor discharge pressure sensor P CD . 
     Computer system  14  outputs an indication of the remaining useful life of filter  16 , such as to a display of computer system  14  (e.g., for use by maintenance personnel), data acquisition system  18  (e.g., for further transmission to an aircraft prognostics and health management system), or to one or more other consuming systems. As such, system  10  implementing techniques of this disclosure determines a remaining useful life of filter  16  that can be monitored over time to enable maintenance personnel and/or prognostic systems to predict (and plan for) maintenance of filter  16  prior to a degree of clogging of filter  16  that could result in inoperability of vapor cycle refrigeration system  12 . 
       FIG. 2  is a flow diagram illustrating example operations to generate a reduced order model that can be utilized to determine a remaining useful life of a filter of a vapor cycle refrigeration system. For purposes of clarity and ease of discussion, the example operations are described below within the context of system  10  of  FIG. 1 . While described with respect to the generation of a single reduced order model, the example operations of  FIG. 2  can be used by ROM module  34  to generate multiple reduced order models corresponding to multiple operational states of filter  16 , such as an unclogged state of filter  16 , a clogged state of filter  16 , or other defined states of filter  16 . 
     A reference discharge pressure for compressor  32  of vapor cycle refrigeration system  12  which the reduced order models will try to predict is generated and collected (Step  38 ) via methods such as high fidelity modeling results and/or laboratory or field test data collection. The reference discharge pressure of compressor  32  is determined for a selected state of filter  16 , such as one of an unclogged state and a clogged state of filter  16 . The unclogged state of filter  16  corresponds to an operational state and corresponding impedance to flow of refrigerant in which filter  16  contains substantially only filter media without foreign debris. The clogged state of filter  16  corresponds to an operational state in which filter  16  exhibits an impedance to refrigerant flow that results in an operational discharge pressure of compressor  32  that is near or exceeds a predefined maximum protective threshold pressure. In some examples, computer system  14  can determine the reference discharge pressure of compressor  32  over an operational envelope of vapor cycle refrigeration system  12  using a high-fidelity physics-based model that simulates operational parameters of each component of vapor cycle refrigeration system  12 . In another example, computer system  14  can determine a reference discharge pressure of compressor  32  using stored operational parameters of vapor cycle refrigeration  12  that were stored during previous operation of vapor cycle refrigeration cycle  12  with the corresponding state of filter  16  during, for example, test data collection in the field or laboratory (e.g., an unclogged state, a clogged state, or other states of filter  16 ). 
     An initial permutation of input parameters is determined (Step  40 ). For example, a first permutation of input parameters x i  and interaction terms X j  from Equation (1) can be determined. A predicted compressor discharge pressure of compressor  32  is generated using Equation (1) and the selected set of input parameters (Step  42 ). For instance, ROM module  34  can generate predicted compressor discharge pressure P pred  using Equation (1) with the selected set (e.g., the first permutation) of input parameters x i  and terms X j . The deviation of interaction the determined predicted discharge pressure of compressor  32  from the reference discharge pressure is determined (Step  44 ). For example, ROM module  34  can determine the difference between the predicted discharge pressure P pred  and the reference discharge pressure collected via high fidelity modeling results or laboratory test data collection corresponding to the selected state of filter  16  (e.g., one of the unclogged or clogged state of filter  16 ). The deviation of the predicted discharge pressure from the collected reference discharge pressure is associated with the selected permutation of input parameters and stored in computer-readable memory of computer system  14  (Step  46 ). 
     Computer system  14  determines whether each permutation of input parameters has been selected (Step  48 ). In response to determining that at least one permutation of input parameters has not been selected (“NO” branch of  48 ), computer system  14  selects a new permutation of the set of input parameters (Step  50 ) and determines a predicted discharge pressure P pred  of compressor  32  using the new permutation of input parameters (Step  42 ). In response to determining that each permutation of input parameters has been selected (“YES” branch of  48 ), computer system  14  selects the input parameter set corresponding to the least deviation from the reference discharge pressure (Step  52 ). For example, computer system  14  can select the least deviation from the set of stored deviations of predicted discharge pressures from the reference discharge pressure. Computer system  14  can select the associated permutation of input parameters as the set of input parameters that are used for the reduced order model to determine the predicted discharge pressure corresponding to the selected state of filter  16 . As such, computer system  14  can determine the set of input parameters from among the set of possible input parameters that produce a least deviation from the reference discharge pressure. 
     In another embodiment, an initial statistical test is first conducted to determine which input parameters x i  and interaction terms X j  from Equation (1) show the greatest sensitivity and correlation to the reference discharge pressure. Input parameters and interaction terms that do not pass the statistical test are omitted from Equation (1) and not used further. An optimizer is then use to determine the regression coefficients to give the best fit to the reference discharge pressure in Equation (1). 
       FIG. 3  is a flow diagram illustrating example operations to determine a remaining useful life of a filter of a vapor cycle refrigeration system using reduced order models. For purposes of clarity and ease of discussion, the example operations are described below within the context of system  10  of  FIG. 1 . Operational parameters of vapor cycle refrigeration system  12  are measured via a plurality of sensors while vapor cycle refrigeration system  12  is operating (Step  54 ). For example, compressor suction temperature sensor T CS , compressor discharge temperature sensor T CD , heat sink inlet temperature sensor T HSI , compressor suction pressure sensor P CS , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor motor current sensor I can measure operational parameters of vapor cycle refrigeration system  12  during operation of vapor cycle refrigeration system  12 . The measured operational parameters are transmitted to computer system  14  (Step  56 ). For instance, data acquisition system  18  can transmit a data upload request to controller  22  to request the transmission of the operational parameters from controller  22  to data acquisition system  18 . Controller  22  can transmit the operational parameters sensed by compressor suction temperature sensor T CS , compressor discharge temperature sensor T CD , heat sink inlet temperature sensor T HSI , compressor suction pressure sensor P CS , compressor discharge pressure sensor P CD , compressor speed sensor N, and compressor motor current sensor I to data acquisition system  18  in response to receiving the data upload request. Data acquisition system  18  can transmit the measured operational parameters to computer system  14  via, e.g., one or more wired and/or wireless communication channels. 
     ROM module  34  generates, using a first reduced order model that corresponds to an unclogged state of filter  16 , a first predicted discharge pressure of compressor  32  based on the measured operational parameters (Step  58 ). ROM module  34  generates, using a second reduced order model that corresponds to a clogged state of filter  16 , a second predicted discharge pressure of compressor  32  based on the measured operational parameters (Step  60 ). Filter RUL module  36  determines a remaining useful life of filter  16  based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure sensed by compressor discharge pressure sensor P CD  (Step  62 ). For example, filter RUL module  36  can determine the remaining useful life of filter  16  using Equation (2). Computer system  14  outputs an indication of the remaining useful life of filter  16  (Step  64 ). 
     Accordingly, system  10  implementing techniques of this disclosure determines a remaining useful life of filter  16  that can be monitored over time to enable maintenance personnel and/or prognostic systems to plan for maintenance of filter  16  prior to a level of clogging that could result in unplanned inoperability of vapor cycle refrigeration system  12 . 
     Discussion of Possible Embodiments 
     The following are non-exclusive descriptions of possible embodiments of the present invention. 
     A method includes operating a vapor cycle refrigeration system of an aircraft, measuring, via a plurality of sensors, operational parameters of the vapor cycle refrigeration system while the vapor cycle refrigeration system is operating, and transmitting the measured operational parameters to a computer system. The method further includes generating, by the computer system using a first reduced order model that corresponds to an unclogged state of a filter of the aircraft vapor cycle refrigeration system, a first predicted discharge pressure of a compressor of the aircraft vapor cycle refrigeration system based on the measured operational parameters. The method further includes generating, by the computer system using a second reduced order model that corresponds to a clogged state of the filter, a second predicted discharge pressure of the compressor based on the measured operational parameters. The method further includes determining, by the computer system, a remaining useful life of the filter based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure of the compressor, and outputting, by the computer system, an indication of the remaining useful life of the filter. 
     The method of the preceding paragraph can optionally include, additionally and/or alternatively, any one or more of the following features, configurations, operations and/or additional components: 
     A further embodiment of the foregoing method, wherein determining the remaining useful life of the filter can include determining the remaining useful life of the filter according to the following equation: 
     
       
         
           
             
               
                 Filter 
                 life 
               
               = 
               
                 
                   min 
                    
                   
                     ( 
                     
                       1 
                       , 
                       
                         1 
                         - 
                         
                           
                             
                               P 
                               dis 
                             
                             - 
                             
                               P 
                               disClean 
                             
                           
                           
                             
                               P 
                               disClogged 
                             
                             - 
                             
                               P 
                               disClean 
                             
                           
                         
                       
                     
                     ) 
                   
                 
                 × 
                 100 
                  
                 % 
               
             
             ; 
           
         
       
     
     where: Filter life  is the remaining useful life of the filter; P dis  is the measured discharge pressure of the compressor; P disClean  is the first predicted discharge pressure of the compressor; and P disClogged  is the second predicted discharge pressure of the compressor. 
     A further embodiment of any of the foregoing methods, wherein each of the first reduced order model and the second reduced order model can be of the following form: P pred =b 0 +Σ i b i x i   c     i   +Σ j b j (X) j   c     j   ; where: P pred  is a predicted discharge pressure of the compressor; b 0  is a constant; b i  and b j  are multiplicative regression coefficients; c i  and c j  are exponential regression coefficients; x i  are first order parameters, each corresponding to one of the measured operational parameters; and X j  are interaction terms, each corresponding to a multiplicative product of two or more of the measured operational parameters. 
     A further embodiment of any of the foregoing methods, further comprising selecting the first order parameters x i  from a set of candidate first order parameters and selecting the interaction terms X j  from a set of candidate interaction terms based on determining that the first order parameters x i  and the interaction terms X j  result in the predicted discharge pressure P pred  that is within a threshold deviation from a reference discharge pressure of the compressor. 
     A further embodiment of any of the foregoing methods, further comprising: generating the first reduced order model using a high-fidelity physics-based model of the vapor cycle refrigeration system having a simulated unclogged state of the filter; and generating the second reduced order model using the high-fidelity physics-based model having a simulated clogged state of the filter. 
     A further embodiment of any of the foregoing methods, further comprising: generating the first reduced order model using first stored operational parameters of the vapor cycle refrigeration system that were stored during previous operation of the vapor cycle refrigeration system with the unclogged state of the filter; and generating the second reduced order model using second stored operational parameters of the vapor cycle refrigeration system that were stored during previous operation of the vapor cycle refrigeration system with the clogged state of the filter 
     A further embodiment of any of the foregoing methods, wherein computer system can be a remote, ground-based computer system. 
     A further embodiment of any of the foregoing methods, further comprising: receiving, by a controller device of the vapor cycle refrigeration system, a data upload request from a data acquisition system of an aircraft that includes the vapor cycle refrigeration system. Transmitting the plurality of measured operational parameters to the computer system can include: transmitting the plurality of measured operational parameters from the controller device of the vapor cycle refrigeration system to the data acquisition system in response to receiving the data upload request; and transmitting the plurality of measured operational parameters from the data acquisition system to the computer system. 
     A further embodiment of any of the foregoing methods, wherein the indication of the remaining useful life of the filter can include an indication of an estimated amount of remaining run-time of the vapor cycle refrigeration system before the remaining useful life of the filter reaches an unacceptable level. 
     A further embodiment of any of the foregoing methods, wherein the operational parameters include one or more of a compressor suction temperature, a compressor discharge temperature, a heat sink inlet temperature, a compressor suction pressure, a compressor discharge pressure, a compressor speed, and a compressor motor current draw. 
     A system includes a vapor cycle refrigeration system of an aircraft and a computer system. The vapor cycle refrigeration system includes a plurality of sensors, a compressor, and a filter. The plurality of sensors are configured to measure operational parameters of the vapor cycle refrigeration system. The compressor is configured to compress refrigerant of the vapor cycle refrigeration system. The filter is disposed within a flow path of the refrigerant. The computer system includes at least one processor and computer-readable memory. The computer-readable memory is encoded with instructions that, when executed by the at least one processor, cause the computer system to receive the operational parameters of the vapor cycle refrigeration system measured by the plurality of sensors, and generate, using a first reduced order model that corresponds to an unclogged state of the filter, a first predicted discharge pressure of the compressor based on the received operational parameters. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to generate, using a second reduced order model that corresponds to a clogged state of the filter, a second predicted discharge pressure of the compressor based on the received operational parameters. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to determine a remaining useful life of the filter based on the first predicted discharge pressure, the second predicted discharge pressure, and a measured discharge pressure of the compressor. The computer-readable memory is further encoded with instructions that, when executed by the at least one processor, cause the computer system to output an indication of the remaining useful life of the filter. 
     The system of the preceding paragraph can optionally include, additionally and/or alternatively, any one or more of the following features, configurations, operations and/or additional components: 
     A further embodiment of the foregoing system, wherein the computer system can be encoded with instructions that, when executed by the at least one processor, cause the computer system to determine the remaining useful life of the filter according to the following equation: 
     
       
         
           
             
               
                 Filter 
                 life 
               
               = 
               
                 
                   min 
                    
                   
                     ( 
                     
                       1 
                       , 
                       
                         1 
                         - 
                         
                           
                             
                               P 
                               dis 
                             
                             - 
                             
                               P 
                               disClean 
                             
                           
                           
                             
                               P 
                               disClogged 
                             
                             - 
                             
                               P 
                               disClean 
                             
                           
                         
                       
                     
                     ) 
                   
                 
                 × 
                 100 
                  
                 % 
               
             
             ; 
           
         
       
     
     where Filter life  is the remaining useful life of the filter; P dis  is the measured discharge pressure of the compressor; P disClean  is the first predicted discharge pressure of the compressor; and P disClogged  is the second predicted discharge pressure of the compressor. 
     A further embodiment of the foregoing system, wherein each of the first reduced order model and the second reduced order model can be of the following form: P pred =b 0 +Σ i  b i x i   c     i   +Σ j b j (X) i   c     j   ; where: P pred  is a predicted discharge pressure of the compressor; b 0  is a constant; b i  and b j  are multiplicative regression coefficients; c i  and c j  are exponential regression coefficients; x i  are first order parameters, each corresponding to one of the measured operational parameters; and X j  are interaction terms, each corresponding to a multiplicative product of two or more of the measured operational parameters. 
     A further embodiment of the foregoing system, wherein the computer-readable memory can be further encoded with instructions that, when executed by the at least one processor, cause the computer system to select the first order parameters x i  from a set of candidate first order parameters and select the interaction terms X j  from a set of candidate interaction terms based on determining that the first order parameters x i  and the interaction terms X j  result in the predicted discharge pressure Ppred that is within a threshold deviation from a reference discharge pressure of the compressor. 
     A further embodiment of the foregoing system, wherein the computer-readable memory can be further encoded with instructions that, when executed by the at least one processor, cause the computer system to: generate the first reduced order model using a high-fidelity physics-based model of the vapor cycle refrigeration system having a simulated unclogged state of the filter; and generate the second reduced order model using the high-fidelity physics-based model having a simulated clogged state of the filter. 
     A further embodiment of the foregoing system, wherein the computer-readable memory can be further encoded with instructions that, when executed by the at least one processor, cause the computer system to: generate the first reduced order model using first stored operational parameters of the vapor cycle refrigeration system that were stored during previous operation of the vapor cycle refrigeration system with the unclogged state of the filter; and generate the second reduced order model using second stored operational parameters of the vapor cycle refrigeration system that were stored during previous operation of the vapor cycle refrigeration system with the clogged state of the filter. 
     A further embodiment of the foregoing system, wherein the computer-system can be a remote, ground-based computer system. 
     A further embodiment of the foregoing system, wherein the vapor cycle refrigeration system can further include a controller device operatively connected to the plurality of sensors and to a data acquisition system of the aircraft. The controller device can be configured to transmit the operational parameters of the vapor cycle refrigeration system measured by the plurality of sensors to the data acquisition system in response to receiving a data upload request from the data acquisition system. 
     A further embodiment of the foregoing system, wherein the computer system can be further encoded with instructions that, when executed by the at least one processor, cause the computer system to determine an estimated amount of remaining run-time of the vapor cycle refrigeration system before the remaining useful life of the filter reaches an unacceptable level. 
     A further embodiment of the foregoing system, wherein the plurality of sensors can include one or more of a compressor suction temperature sensor, a compressor discharge temperature sensor, a heat sink inlet temperature sensor, a compressor suction pressure sensor, a compressor discharge pressure sensor, a compressor speed sensor, and a compressor motor current sensor. 
     While the invention has been described with reference to an exemplary embodiment(s), it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment(s) disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.