Systems and methods for controlling the operation of a vapor compression cycle

Abstract

The present disclosure discloses a system and method for controlling the operation of a vapor compression cycle based on a hybrid model of the vapor compression cycle dynamics, the hybrid model including a physics-based model and a data-driven model. The method includes: performing a constrained Kalman smoother on observed variables collected over multiple time instances to jointly estimate parameters of the physics-based model and states of the vapor compression cycle; updating the data-driven model to minimize a difference between the states estimated by performing the constrained Kalman smoother and states predicted by the physics-based model; and updating the hybrid model using the estimated parameters of the physics-based model and the updated data-driven model to control the operation of the vapor compression cycle.

Description

[Technical Field]

[0001] TECHNICAL FIELD This disclosure relates to vapor compression cycles, and more particularly to systems and methods for controlling the operation of vapor compression cycles. [Background technology]

[0002] The vapor compression cycle is a fundamental technology in modern society due to its widespread use in air conditioning and heating applications. Its role is expected to grow in the future as it provides an effective means to decarbonize heating systems and utilize electrical energy generated from renewable sources such as solar or wind power. There is therefore widespread interest in further developing vapor compression cycle technology to be energy efficient and to meet performance requirements related to the health and comfort of users in buildings.

[0003] Various control techniques employed in vapor compression cycles use models that represent the underlying physics / dynamics of the vapor compression cycle to predict its behavior and control it. Accurate predictions of vapor compression cycle behavior can be used for control techniques such as model predictive control and estimation of performance parameters such as the cooling capacity provided by a heat exchanger (HEX). Vapor compression cycle models can also play a key role in the development of fault detection and diagnostic algorithms and are central to emerging digital twin technologies aimed at improving energy efficiency, streamlining maintenance, and maximizing user comfort.

[0004] Some approaches use physics-based models to predict the behavior of vapor compression cycles. Physics-based models are derived from first principles of physics, resulting in a set of high-dimensional, nonlinear differential-algebraic equations for a multiphysics system, such as a vapor compression cycle. Such models are typically formulated to meet application-specific physics-based or computational requirements and relate to the physical processes most relevant to the application. The simplifying assumptions associated with such requirements, such as lumped parameters and finite discretization, often lead to discrepancies between model predictions and data collected from the system. Addressing the discrepancies to improve the accuracy of model predictions is a challenging task that can require undue effort and complexity, and the resulting improvement in predictions is relatively small.

[0005] Alternatively, data-driven models are sometimes used to predict the behavior of vapor compression cycles. Data-driven models are developed using data collected from the system. However, data-driven models require large data sets containing complete state trajectories to achieve reasonable modeling accuracy. Because sensor data is limited, such large data sets are not available. Furthermore, data-driven models present various other challenges, such as the uninterpretability of data-driven models, a large parameter search space, and the lack of explicit consideration of the fundamental physical laws governing the system.

[0006] Therefore, there remains a need for a model of the dynamics of a vapor compression cycle to control the cycle. Summary of the Invention

[0007] It is an object of some embodiments to provide a system and method for controlling the operation of a vapor compression cycle using a hybrid model of vapor compression cycle dynamics, the hybrid model of vapor compression cycle dynamics including a physics-based model and a data-driven model, and to determine model attributes of the hybrid model.

[0008] Some embodiments are based on the recognition that modeling efforts for vapor compression cycles can benefit from a hybrid modeling paradigm that combines domain expertise represented by a physics-based model with a data-driven model to learn the behavior of the vapor compression cycle. Accordingly, the present disclosure provides a hybrid model of vapor compression cycle dynamics, including a physics-based model and a data-driven model. The physics-based model is configured to predict state transitions of the vapor compression cycle according to observed variables and control inputs to the vapor compression cycle based on parameters of the physics-based model. The physics-based model includes one or a combination of governing partial differential equations discretized in the spatial and time domains, lookup tables, and interpolation splines for calculating thermodynamic properties of the refrigerant of the vapor compression cycle. The data-driven model is trained using machine learning to estimate residual errors of the state transitions predicted by the physics-based model. The data-driven model may include a neural network.

[0009] Physics-based models are parameterized by a parameter vector θ, which includes the number of finite control volumes for the discretization of the governing partial differential equations, the geometric parameters of the vapor compression cycle, the properties of the materials used in the vapor compression cycle, the total mass of the refrigerant, etc. Data-driven models, e.g., neural networks, are parameterized by a vector w, which includes the weights and biases of each artificial neuron, as well as parameters defining the architecture of the neural network.

[0010] An objective of some embodiments is to estimate model attributes of a hybrid model based on observation variables collected over multiple time instances. The model attributes of the hybrid model include parameters of the physics-based model, i.e., parameter θ, and parameters of the data-driven model, i.e., parameter w. The observation variables include temperature and pressure measured by sensors installed at different locations within the vapor compression cycle. The estimated model attributes are preferably such that the contribution of the physics-based model is maximized in the hybrid model, while the data-driven model is utilized solely to correct modeling errors that cannot be corrected by the physics-based model alone. Thus, the data-driven model is utilized to learn residual dynamics based on the discrepancy between the physics-based model and the observation variables. Therefore, in some embodiments of the present disclosure, the parameters of the physics-based model and the data-driven model are determined by solving a joint optimization problem that minimizes a cost function including a penalty for the deviation between the predicted and actual outputs of the vapor compression cycle and a weighted norm of the output of the data-driven model.

[0011] Some embodiments recognize that simultaneously estimating the parameters θ of a physics-based model and the parameters w of a data-driven model is a challenging problem because they are fundamentally different variables. On the one hand, the parameters θ of a physics-based model are generally low-dimensional, but their derivatives with respect to the parameters θ are difficult to compute because they require derivatives of the solution of a differential equation. Furthermore, the dynamics of a vapor compression cycle are nonlinear, numerically stiff, and have derivative discontinuities due to phase changes associated with evaporation or condensation. On the other hand, the parameters w have large dimensions, but their derivatives can be efficiently computed using standard computational tools such as automatic differentiation.

[0012] Some embodiments of the present disclosure are based on the recognition that the computational challenges associated with a joint optimization problem can be addressed not by solving the joint optimization problem, but by decomposing it into two equivalent, tractable, unconstrained optimization problems that separately determine θ and w. For example, the joint optimization problem can be decomposed into a first optimization problem of jointly estimating the vapor compression cycle states and the parameters θ of a physics-based model, and a second optimization problem of determining the parameters w of a data-driven model.

[0013] Some embodiments recognize that the first optimization problem can be interpreted as a joint state and parameter estimation problem based on a physics-based model of a vapor compression cycle. Such an interpretation allows for a solution to be found using an optimal smoothing formulation. In particular, approximate solutions to the first optimization problem can be efficiently found using a wide range of nonlinear estimation methods. However, estimation methods typically do not guarantee that physics-based constraints, such as monotonicity of pressure in the refrigerant flow direction within a vapor compression cycle, are satisfied. Satisfaction of such physics-based constraints is important to ensure that the state estimate is physically realizable. Therefore, one embodiment uses a constrained Kalman smoother, such as a constrained extended Kalman smoother (C-EKS) or a constrained ensemble Kalman smoother (C-EnKS), that is tailored to estimating vapor compression cycles and enforces physics-based constraints during the joint estimation of the vapor compression cycle states and the parameters of the physics-based model.

[0014] Thus, a constrained Kalman smoother is used to solve the first optimization problem to estimate the parameters of the physics-based model and the states of the vapor compression cycle. In particular, the constrained Kalman smoother is performed on the observed variables collected over multiple time instances to estimate the parameters of the physics-based model and the states of the vapor compression cycle.

[0015] There is a difference between the states predicted by the physics-based model and the states estimated by running the constrained Kalman smoother. This difference is called the residual error. To compensate for the residual error, the parameters w of the data-driven model are determined to minimize a cumulative learning cost function consisting of the difference between the residual error and the output of the data-driven model corresponding to the same input that generated the error residual at that time. The residual error is a known constant within the second optimization problem; therefore, the data-driven model essentially attempts to learn the residual error for a given input state vector and control input vector.

[0016] To that end, some embodiments of the present disclosure are based on the recognition that the second optimization problem, which determines the parameters of the data-driven model, is a standard neural network training problem. According to one embodiment, the second optimization problem is solved using stochastic gradient descent to determine the parameters of the data-driven model.

[0017] Furthermore, the hybrid model is updated with parameters of the physics-based model estimated by performing the constrained Kalman smoother and parameters of the data-driven model determined by solving a second optimization problem using stochastic gradient descent. In other words, the updated hybrid model includes a physics-based model having parameters estimated by performing the constrained Kalman smoother and a data-driven model having parameters determined by solving a second optimization problem using stochastic gradient descent. Furthermore, the operation of the vapor compression cycle is controlled using the updated hybrid model. For example, control inputs to actuators of the vapor compression cycle are determined based on the updated hybrid model. The control inputs include, for example, compressor speed, fan speed, and expansion valve position. The operation of the vapor compression cycle is controlled in accordance with the control inputs.

[0018] Accordingly, one embodiment discloses a controller for controlling the operation of a vapor compression cycle based on a hybrid model of vapor compression cycle dynamics including a physics-based model and a data-driven model. The physics-based model is configured to predict state transitions of the vapor compression cycle according to observation variables and control inputs to the vapor compression cycle based on parameters of the physics-based model. The data-driven model is trained using machine learning to estimate residual errors of the state transitions predicted by the physics-based model. The controller includes a processor and a memory having instructions stored thereon. When executed by the processor, the instructions cause the controller to collect digital representations of observation variables of the operation of the vapor compression cycle over a plurality of time instances; perform a constrained Kalman smoother on the collected observation variables over the plurality of time instances to jointly estimate parameters of a physics-based model and states of the vapor compression cycle; minimize a cost function composed of residual errors of state transitions predicted by the physics-based model for the plurality of time instances and residual errors between the observation variables estimated by the constrained Kalman smoother and corresponding collected observation variables for the plurality of time instances; update a data-driven model to minimize a difference between the states estimated by performing the constrained Kalman smoother on the collected observation variables over the plurality of time instances and the states predicted by the physics-based model; update a hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; and control the operation of the vapor compression cycle using the updated hybrid model.

[0019] Accordingly, another embodiment discloses a method for controlling the operation of a vapor compression cycle based on a hybrid model of vapor compression cycle dynamics including a physics-based model and a data-driven model, wherein the physics-based model is configured to predict state transitions of the vapor compression cycle according to observed variables and control inputs to the vapor compression cycle based on parameters of the physics-based model, and the data-driven model is trained using machine learning to estimate residual errors of the state transitions predicted by the physics-based model. The method includes collecting digital representations of observation variables of the operation of the vapor compression cycle over a plurality of time instances; performing a constrained Kalman smoother on the collected observation variables over the plurality of time instances to jointly estimate parameters of a physics-based model and states of the vapor compression cycle, and minimizing a cost function consisting of residual errors of state transitions predicted by the physics-based model for the plurality of time instances and residual errors between the observation variables estimated by the constrained Kalman smoother and corresponding collected observation variables for the plurality of time instances; updating a data-driven model to minimize a difference between the states estimated by performing the constrained Kalman smoother on the collected observation variables over the plurality of time instances and the states predicted by the physics-based model; updating a hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; and controlling the operation of the vapor compression cycle using the updated hybrid model.

[0020] Accordingly, yet another embodiment discloses a non-transitory computer-readable storage medium containing a processor-executable program for executing a method for controlling operation of a vapor compression cycle based on a hybrid model of vapor compression cycle dynamics including a physics-based model and a data-driven model. The physics-based model is configured to predict state transitions of the vapor compression cycle according to observation variables and control inputs to the vapor compression cycle based on parameters of the physics-based model. The data-driven model is trained using machine learning to estimate residual errors of the state transitions predicted by the physics-based model. The method includes collecting digital representations of observation variables of the operation of the vapor compression cycle over a plurality of time instances; performing a constrained Kalman smoother on the collected observation variables over the plurality of time instances to jointly estimate parameters of a physics-based model and states of the vapor compression cycle, and minimizing a cost function consisting of residual errors of state transitions predicted by the physics-based model for the plurality of time instances and residual errors between the observation variables estimated by the constrained Kalman smoother and corresponding collected observation variables for the plurality of time instances; updating a data-driven model to minimize a difference between the states estimated by performing the constrained Kalman smoother on the collected observation variables over the plurality of time instances and the states predicted by the physics-based model; updating a hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; and controlling the operation of the vapor compression cycle using the updated hybrid model. [Brief explanation of the drawings]

[0021] [Figure 1A] FIG. 1 illustrates a vapor compression cycle according to an embodiment of the present disclosure. [Figure 1B] FIG. 2 is a block diagram of a controller for controlling the operation of a vapor compression cycle according to an embodiment of the present disclosure. [Figure 1C]FIG. 1 illustrates a hybrid model of vapor compression cycle dynamics according to some embodiments of the present disclosure. [Figure 1D] FIG. 1 is a schematic diagram illustrating decomposition of a joint optimization problem, according to some embodiments of the present disclosure. [Figure 2] FIG. 1 is a schematic diagram of a system architecture including a storage medium according to some embodiments of the present disclosure. [Figure 3] FIG. 1 is a schematic diagram of a cloud-based architecture according to some embodiments of the present disclosure. [Figure 4] FIG. 2 is a block diagram of a method for estimating states using a constrained ensemble Kalman smoother according to some embodiments of the present disclosure. [Figure 5A] FIG. 1 is a block diagram of a method for controlling the operation of a vapor compression cycle according to an embodiment of the present disclosure. [Figure 5B] FIG. 1 is a block diagram for controlling the operation of a vapor compression cycle using an updated hybrid model according to an embodiment of the present disclosure. [Figure 6] FIG. 1 is a schematic diagram of a computing device that can be used to implement the controller and methods of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0022] The presently disclosed embodiments are further described with reference to the accompanying drawings, which are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments.

[0023] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other instances, devices and methods are shown in block diagram form solely to avoid obscuring the present disclosure.

[0024] As used in this specification and claims, the terms "for example," "for example," and "such as," as well as the verbs "comprise," "have," and "include," and each of their other verb forms, when used in conjunction with a list of one or more components or other items, should be construed as open-ended, meaning that the list should not be considered as excluding other additional components or items. The term "based on" means based at least in part on. Furthermore, it should be understood that the style and terminology used herein are for purposes of description and should not be regarded as limiting. Any headings used herein are for convenience only and have no legal or limiting effect.

[0025] 1A illustrates a vapor compression cycle 100 according to an embodiment of the present disclosure. The vapor compression cycle 100 includes a compressor 101, a condensing heat exchanger 103, an expansion valve 105, and an evaporative heat exchanger 107 disposed in a space 109. Heat transfer from the condensing heat exchanger 103 is facilitated by the use of a fan 111, and heat transfer from the evaporative heat exchanger 107 is facilitated by the use of a fan 113. The vapor compression cycle 100 may include variable actuators, such as variable compressor speed, variable expansion valve position, and variable fan speed. The present disclosure provides numerous alternative equipment architectures for multiple heat exchangers, compressors, valves, and other components, such as accumulators or reservoirs, piping, and the illustration of the vapor compression cycle 100 is not intended to limit the scope or application of the present disclosure to any system.

[0026] In the vapor compression cycle 100, the compressor 101 compresses a low-pressure, low-temperature gas-phase fluid (refrigerant) to a high-pressure, high-temperature vapor state, which then enters the condensing heat exchanger 103. As the refrigerant passes through the condensing heat exchanger 103, the high-temperature, high-pressure refrigerant transfers its heat to the low-temperature ambient air through heat transfer facilitated by a fan 111. As the refrigerant transfers heat to the ambient air, the refrigerant gradually condenses to a high-pressure, low-temperature liquid state. The refrigerant then exits the condensing heat exchanger 103 and passes through an expansion valve 105, expanding to a low-pressure boiling state, from which it enters the evaporative heat exchanger 107. Because the air passing through the evaporative heat exchanger 107 is warmer than the refrigerant itself, the refrigerant gradually evaporates as it passes through the evaporative heat exchanger 107. The refrigerant exiting the evaporative heat exchanger 107 is in a low-pressure, low-temperature state. The low-pressure, low-temperature refrigerant then re-enters the compressor 101, and the cycle begins again.

[0027] Vapor compression cycle 100 operates with a set of nominal input values ​​for actuators, such as, for example, compressor 101 speed, fan 111 speed, expansion valve 105 position, and fan 113 speed. It is desirable or an objective for vapor compression cycle 100 to achieve a performance metric, such as regulating a variable, such as temperature or humidity, within space 109 or regulating a process variable, such as temperature or pressure, at one or more points within vapor compression cycle 100. To achieve such an objective, one or more sensors are installed at various locations within vapor compression cycle 100 to monitor the variables of interest. The variables of interest may include temperature, humidity, and / or pressure. For example, sensors such as sensor 115, sensor 117, sensor 119, sensor 123, and sensor 121 (collectively referred to as sensors 115, 117, 119, 121, and 123) are located at different locations. Sensors 115, 117, 119, and 121 monitor the temperature and / or pressure at their respective locations. Alternatively or additionally, measurements of variables within space 109, such as temperature or humidity, may be obtained via sensors such as sensor 123.

[0028] Information from sensors 115, 117, 119, 121, and 123 is input to a controller 125 associated with vapor compression cycle 100. Based on the information from sensors 115, 117, 119, 121, and 123, controller 125 may control the operation of vapor compression cycle 100. For example, based on the information from sensors 115, 117, 119, 121, and 123, controller 125 may modify actuator inputs, such as compressor 101 speed, fan 111 speed, expansion valve 105 position, and fan 113 speed, to achieve desired performance metrics.

[0029] 1B illustrates a block diagram of a controller 125 according to an embodiment of the present disclosure. The controller 125 includes a processor 127 and a memory 129. The processor 127 may be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 129 may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable memory system. Additionally, in some embodiments, the memory 129 may be implemented using a hard drive, an optical drive, a thumb drive, an array of drives, or any combination thereof.

[0030] Processor 127 is configured to collect digital representations of observed variables of the operation of vapor compression cycle 100 over multiple time instances. In one embodiment, processor 127 collects the digital representations of observed variables of the operation of vapor compression cycle 100 from sensors 115, 117, 119, 121, and 123. The observed variables include, for example, measurements of one or more of temperature and pressure at different locations within vapor compression cycle 100.

[0031] Controller 125 may employ a model representing the underlying physics / dynamics of vapor compression cycle 100 to predict the behavior of vapor compression cycle 100. Based on digital representations of collected observation variables, the model predicts the behavior of vapor compression cycle 100. Accurate predictions of the behavior of vapor compression cycle 100 can be used for various control techniques, such as model predictive control and estimation of performance parameters, such as the cooling capacity provided by a heat exchanger (HEX). Models of vapor compression cycle 100 can also play a key role in the development of fault detection and diagnostic algorithms and are central to emerging digital twin technologies aimed at improving energy efficiency, streamlining maintenance, and maximizing user comfort.

[0032] The model of vapor compression cycle 100 may be a physics-based model. A physics-based model is derived from first principles of physics, resulting in a set of high-dimensional, nonlinear, differential-algebraic equations for a multi-physics system, such as vapor compression cycle 100. Such models are typically formulated to meet application-specific physics-based or computational requirements and relate to the physical processes most relevant to the application. The simplifying assumptions associated with such requirements, such as lumped parameters and finite discretization, often lead to discrepancies between model predictions and data collected from the system (e.g., a vapor compression system (VCS)). Addressing the discrepancies to improve the accuracy of the model predictions is a challenging task that can require undue effort and complexity, and the resulting improvement in predictions is relatively small.

[0033] Alternatively, the model of vapor compression cycle 100 may be a data-driven model. A data-driven model is developed using data collected from the system. However, to achieve reasonable modeling accuracy, a data-driven model requires a large data set containing complete state trajectories. Because sensor data is limited, such large data sets are not available. Furthermore, data-driven models suffer from various other challenges, such as the uninterpretability of data-driven models, a large parameter search space, and the lack of explicit consideration of the fundamental physical laws governing the system.

[0034] Some embodiments are based on the recognition that modeling efforts for vapor compression cycle 100 can benefit from a hybrid modeling paradigm that combines domain expertise represented by physics-based models with data-driven models to learn the behavior of vapor compression cycle 100. Accordingly, the present disclosure provides a hybrid model 131 of the dynamics of vapor compression cycle 100. In one embodiment, hybrid model 131 is stored in memory 129. Hybrid model 131 is described below in FIG. 1C.

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[0036] An objective of some embodiments is to estimate model attributes of hybrid model 131 based on observed variables collected over multiple time instances. The model attributes of hybrid model 131 include parameters of physics-based model 133, i.e., parameter θ, and parameters of data-driven model 135, i.e., parameter w.

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[0042] Numerical optimization for solving (4) is challenging because equality constraints must be relaxed or incorporated using Lagrangian methods, and the parameters θ and w are fundamentally different optimization variables. On the one hand, the parameter θ is generally low-dimensional, but derivatives with respect to the parameter θ are difficult to compute because they require derivatives of the solution of differential equations. Furthermore, the dynamics of the vapor compression cycle 100 are nonlinear and numerically stiff, with derivative discontinuities due to phase changes associated with evaporation or condensation. On the other hand, although w has large dimensions, derivatives can be computed efficiently using standard computational tools such as automatic differentiation.

[0043] Some embodiments of the present disclosure are based on the recognition that the computational challenges associated with joint optimization (4) can be addressed not by solving the joint optimization problem (4), but by decomposing (4) into two equivalent tractable unconstrained optimization problems that determine θ and w separately, as described below in FIG. 1D.

[0044] 1D shows a schematic diagram illustrating the decomposition of joint optimization problem (4) 137, according to some embodiments of the present disclosure. Joint optimization problem (4) 137 is decomposed into a first optimization problem 139 of joint estimation of the states of vapor compression cycle 100 and parameters θ of physics-based model 133, and a second optimization problem 141 of determining parameters w of data-driven model 135.

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[0049] The Kalman smoothing algorithm is a non-causal data assimilation method that uses measurement data available at future time instances to improve estimates of past states using the Kalman estimation framework. Kalman smoothers are therefore suitable for batch processing of measurements or observed variables collected over multiple time instances. The Kalman smoothing method is based on the underlying function F pSolving (5) is guaranteed to be optimal if and h are linear in the optimization variables. Although the governing equations underlying the vapor compression cycle 100 are not linear, the Kalman smoothing algorithm remains advantageous for obtaining an approximate solution to (5) due to its reasonably good accuracy, computational efficiency, and simple implementation compared to sophisticated solvers that may otherwise be required to solve (5). Kalman smoothers for nonlinear systems can be realized in various formulations, such as the extended Kalman smoother and the ensemble Kalman smoother. The extended Kalman smoother, also known as the Rauch-Tung-Striebel (RTS) smoother, linearizes the nonlinear dynamics and uses Jacobian matrices for the propagation and update steps of the Kalman estimation process. The ensemble Kalman smoother is a Monte Carlo-type method that uses an ensemble of random particles sampled from the state distribution for the propagation stage and an empirically calculated covariance matrix for the update step. Ensemble Kalman smoothers are used in high-dimensional nonlinear systems such as vapor compression cycle 100 because they do not require the storage of high-dimensional covariance matrices required in extended Kalman smoothers.

[0050] Additionally, the Kalman smoother can be customized for specific vapor compression applications to achieve significantly faster solutions that also incorporate physics-based state constraints. For example, the refrigerant pressure in the heat exchanger must decrease in the direction of flow to satisfy fundamental physical relationships in the vapor compression cycle 100. If such constraints on the refrigerant pressure are not satisfied after state corrections are applied at a given time, the solver may not be able to successfully integrate the dynamic model forward over the next time interval because the perturbed pressure may cause unphysical changes in the direction of flow, violating fundamental assumptions of the dynamic model.

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[0055] Additionally, the processor 127 may calculate the parameters θ of the physics-based model 133. * and the parameter w of the data-driven model 135 * In other words, the updated hybrid model 131 is updated by the parameter θ * a physics-based model 133 with parameters w * and a data-driven model 135 having the updated hybrid model 131. Further, the processor 127 controls the operation of the vapor compression cycle 100 using the updated hybrid model 131. For example, based on the updated hybrid model 131, the processor 127 determines control inputs to actuators of the vapor compression cycle 100, such as the speed of the compressor 101, the speed of the fan 111, the position of the expansion valve 105, and the speed of the fan 113. Further, the processor 127 controls the actuators based on the determined control inputs.

[0056] In some embodiments, digital representations of observed variables of the operation of vapor compression cycle 100 collected from sensors 115, 117, 119, 121, and 123 are transmitted to a storage medium co-located in the same geographic location where vapor compression cycle 100 is located.

[0057] 2 shows a schematic diagram of system architecture 200 including storage medium 201, according to some embodiments of the present disclosure. Digital representations of observed variables of the operation of vapor compression cycle 100 collected over multiple time instances from sensors 115, 117, 119, 121, and 123, as well as control inputs provided by controller 125, are stored in storage medium 201. Additionally, in some embodiments, other internal information associated with controller 125, such as internal controller variables, discrete variables from control logic, or other information generated by controller 125, may be stored in storage medium 201. The storage medium may be co-located in the same geographic location where vapor compression cycle 100 is located.

[0058] Additionally, data from storage medium 201 is provided to controller 125 periodically, either periodically or when there is an event that requires an update of hybrid model 131, such as when a user requests information related to the operation of vapor compression cycle 100. In one embodiment, data provided from storage medium 203 may include digital representations of observed variables of the operation of the vapor compression cycle collected over multiple time instances.

[0059] Some embodiments are based on the recognition that some or all of the data stored in storage medium 201 may be stored using cloud computing resources, and in addition, updates to hybrid model 131 may be realized on a remote server. Such an embodiment is illustrated in FIG. 3.

[0060] 3 shows a schematic diagram of a cloud-based architecture 300 according to some embodiments of the present disclosure. Vapor compression cycle 100, controller 125, and storage medium 201 are considered system 301. System 301 communicates with remote server 303 (also referred to as a cloud computing system) via network 305. In this case, storage medium 201 may vary in size and may additionally or alternatively be present or absent depending on the ability and / or reliability of remote server 303 to access data from vapor compression cycle 100.

[0061] System 301 is configured to transmit some or all of the data (e.g., digital representations of observed variables and control inputs) to remote server 303 for storage, rather than maintaining the data in storage medium 201 co-located with vapor compression cycle 100. Additionally, remote server 303 may store model attributes of hybrid model 131, i.e., parameters θ of physics-based model 133 and parameters w of data-driven model 135.

[0062] The model attributes of the hybrid model 131 stored on the remote server 303 may be updated periodically or when an update trigger event occurs. Update trigger events include a user requesting information related to the operation of the vapor compression cycle 100, a request to replace a failed component (e.g., compressor, fan) of the vapor compression cycle 100 with a new component, a user requesting an update to the hybrid model 131, etc. For example, a failed component (e.g., compressor, fan) of the vapor compression cycle 100 may be replaced by an independent contractor during a maintenance service. Specification information for the newly installed component can be used to update the hybrid model 131 on the remote server 303 to mimic the physical vapor compression cycle 100 as accurately as possible.

[0063] For example, when an update trigger event occurs, the remote server 303 runs the constrained Kalman smoother 143 on the observation variables collected over multiple time instances to jointly estimate the parameters of the physics-based model 133 and the states of the vapor compression cycle 100 to minimize a cost function consisting of the residual error of the state transitions predicted by the physics-based model 133 and the residual error between the observation variables estimated by the constrained Kalman smoother for multiple time instances and the corresponding collected observation variables.

[0064] Additionally, the remote server 303 updates the data-driven model 135 to minimize the difference between the states estimated by running the constrained Kalman smoother 143 on the observed variables collected over multiple time instances and the states predicted by the physics-based model 133. The remote server 303 further updates the hybrid model using the estimated parameters of the physics-based model 133 and the updated data-driven model.

[0065] The remote server 303 further transmits the updated hybrid model to the controller 125 via the network 305. The controller 125 receives the updated hybrid model and controls the operation of the vapor compression cycle using the received updated hybrid model.

[0066] Cloud-based architecture 300 is advantageous. For example, only limited computing resources need be co-located with vapor compression cycle 100, and appropriate computing resources can be easily coordinated and scaled on remote server 303, i.e., in the cloud. Additionally, both data and estimates of the condition of vapor compression cycle 100 can be used simultaneously in a variety of different contexts, including, but not limited to, use in equipment service or maintenance scheduling or the development of next-generation systems. According to some embodiments, estimates of the condition of vapor compression cycle 100 may indicate the need for equipment maintenance that is not readily apparent from measured data. Cloud-based architecture 300 may make such information readily and asynchronously available to service companies, enabling them to automatically follow up with users and schedule maintenance calls. Additionally, the information provided to the service company enables the use of accurate diagnostic and service tools.

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[0068] FIG. 4 illustrates a block diagram of a method 400 for estimating states using a constrained ensemble Kalman smoother according to some embodiments of the present disclosure.

[0069] Method 400 begins with data 401 from the operation of vapor compression cycle 100 and a model 403 of vapor compression cycle 100. Data 401 includes a set of control inputs u and measurements, i.e., observed variables y, from sensors installed within vapor compression cycle 100. According to one embodiment, model 403 of vapor compression cycle 100 describes both the evolution of the state variables by a function f and the measurements as a function of the state variables by a second function h, which may potentially be a nonlinear function.

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[0071] In block 407, the covariance r (i)* The state variables, which are transformed to the range of ∇ ...

[0072] N data points may be available, but in the smoothing window, all N data points may be used, or a smaller set may be used. For example, the state update in the covariance range coordinate system at the first measurement time k=1 is calculated while applying the constraints, and then transformed back to the coordinate system of the original state variables.

[0073] If the end of the available data is reached, block 409 checks to see if measurement time k=1 is at the time of the last data point. Since measurement time k=1 is not equal to N, block 411 then solves the nonlinear model f forward from the first to the second measurement time k=2, and then updates the state variables again to account for the measurement at time k=2.

[0074] At time k=2, state corrections are applied to the state estimates at both times k=1 and k=2, and constraints are enforced at both times k=1 and k=2. This ensures that the state estimate at time k=1 takes into account the measurements at time k=2 and that the constraints are satisfied at both times. In such iterations, the length of the state estimate data gradually increases as additional data is incorporated until all N data points have been incorporated, and all of the state variables are continually updated to reflect the new information provided by the data points successively added to the growing smoothing window. Increasing the length of the smoothing window as more data points are incorporated can pose serious computational challenges, including prohibitive memory requirements and computational time.

[0075] To this end, in some embodiments, after a sufficient number of data points have been incorporated into the corrected state estimate, the length of the smoothing window, i.e., the number of data points in the smoothing window, l=k−m+1, may be fixed to be a constant so that data points available at times earlier than m are not considered in updating step 407. As each data point is processed, a final set of smoothed state estimates is output in block 413. The final set of smoothed state estimates comprises the state of vapor compression cycle 100.

[0076] In another embodiment, the constrained ensemble Kalman smoother 400 is adapted to jointly estimate the state and the parameters of the physics-based model. Within the scope of the joint estimation, the constrained ensemble Kalman smoother 400 estimates an augmented vector that includes both the state and the parameters of the physics-based model, while following the same general flow of the methodology of the constrained ensemble Kalman smoother 400.

[0077] Further, an overall method for controlling the operation of vapor compression cycle 100 is described below in FIG. 5A.

[0078] 5A shows a block diagram of a method 500 for controlling the operation of a vapor compression cycle 100 according to an embodiment of the present disclosure. At block 501, the method 500 includes collecting digital representations of observation variables and control inputs of the operation of the vapor compression cycle 100 over a plurality of time instances. At block 503, the method 500 includes running a constrained Kalman smoother 143 on the collected observation variables over the plurality of time instances to jointly estimate parameters of a physics-based model 133 and states of the vapor compression cycle 100, and minimizing a cost function comprised of the residual error of the state transitions predicted by the physics-based model 133 and the residual error between the observation variables estimated by the constrained Kalman smoother and the corresponding collected observation variables for the plurality of time instances.

[0079] At block 505, method 500 includes updating data-driven model 135 to minimize a difference between a state estimated by running constrained Kalman smoother 143 on observed variables collected over multiple time instances and a state predicted by physics-based model 133. At block 507, method 500 includes updating hybrid model 131 with parameters of estimated physics-based model 133 and the updated data-driven model. At block 509, method 500 includes controlling operation of vapor-compression cycle 100 using the updated hybrid model.

[0080]

number

[0081] Further, in block 513, control inputs to actuators of the vapor compression cycle 100 are determined based on the updated hybrid model and the unobserved variables. The control inputs may include one or more of the speed of the compressor 101, the speed of the fan 111, the position of the expansion valve 105, and the speed of the fan 113.

[0082] Further, in block 515, an actuator of the vapor compression cycle 100 is controlled in accordance with the determined control input to control the operation of the vapor compression cycle 100.

[0083] FIG. 6 shows a schematic diagram of a computing device that can be used to implement the controller 125 and method 500 of the present disclosure. The computing device 600 includes a power supply 601, a processor 603, a memory 605, and a storage device 607, all connected to a bus 609. Additionally, a high-speed interface 611, a low-speed interface 613, a high-speed expansion port 615, and a low-speed connection port 617 can be connected to the bus 609. Additionally, a low-speed expansion port 619 is connected to the bus 609. Furthermore, an input interface 621 can be connected to an external receiver 623 and an output interface 625 via the bus 609. The receiver 627 can be connected to an external transmitter 629 and a transmitter 631 via the bus 609. Also connected to the bus 609 are an external memory 633, an external sensor 635, a machine 637, and an environment 639. Additionally, one or more external input / output devices 641 can be connected to the bus 609. A network interface controller (NIC) 643 may be adapted to connect to a network 645 via bus 609, enabling, among other things, data or other data to be rendered on a third-party display device, a third-party imaging device, and / or a third-party printing device external to computing device 600.

[0084] The memory 605 can store instructions executable by the computing device 600, as well as any data that can be utilized by the methods and systems of the present disclosure. The memory 605 can include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable memory system. The memory 605 can be one or more volatile memory units and / or one or more non-volatile memory units. The memory 605 can also be another form of computer-readable medium, such as a magnetic disk or an optical disk.

[0085] The storage device 607 may be adapted to store supplemental data and / or software modules used by the computing device 600. The storage device 607 may include a hard drive, an optical drive, a thumb drive, an array of drives, or any combination thereof. Additionally, the storage device 607 may include a computer-readable medium such as a floppy disk device, a hard disk device, an optical disk device, or an array of devices including a tape device, a flash memory or other similar solid-state memory device, or a storage area network or other configuration of devices. The instructions may be stored on an information carrier. When executed by one or more processing devices (e.g., processor 603), the instructions perform one or more methods, such as those described above.

[0086] Computing device 600 may optionally be linked through bus 609 to a display interface or user interface (HMI) 647 adapted to connect computing device 600 to a display device 649 and keyboard 651. Display device 649 may include, among other things, a computer monitor, a camera, a television, a projector, or a mobile device. In some implementations, computing device 600 may include a printer interface for connecting to a printing device. The printing device may include, among other things, a liquid inkjet printer, a solid ink printer, a large-scale commercial printer, a thermal printer, a UV printer, or a dye sublimation printer.

[0087] The high-speed interface 611 manages bandwidth-intensive operations of the computing device 600, and the low-speed interface 613 manages low-bandwidth-intensive operations. Such an allocation of functions is merely an example. In some implementations, the high-speed interface 611 can be coupled to memory 605, a user interface (HMI) 646, a keyboard 651, and a display 649 (e.g., through a graphics processor or accelerator), and can be coupled to a high-speed expansion port 615 that can accept various expansion cards via a bus 609. In one implementation, the low-speed interface 613 is coupled to storage device 607 and a low-speed expansion port 617 via a bus 609. The low-speed expansion port 617, which can include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet), can be coupled to one or more input / output devices 641. The computing device 600 can be connected to a server 653 and a rack server 655. The computing device 600 can be implemented in several different forms. For example, the computing device 600 may be implemented as part of a rack server 655 .

[0088] The description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes are contemplated that may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0089] Specific details are provided in the following description to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements of the disclosed subject matter may be shown as components in block diagram form in order to avoid obscuring the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. Furthermore, like reference numbers and names in the various drawings indicate like elements.

[0090] Also, particular embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. While a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. Additionally, the order of operations may be rearranged. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any specifically described process may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, the termination of the function may correspond to a return of the function to the calling function or the main function.

[0091] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. The manual or automatic implementation may be performed, or at least assisted, through the use of machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor(s) may perform the necessary tasks.

[0092] The various methods or processes outlined herein may be coded as software executable on one or more processors employing any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0093] Embodiments of the present disclosure may be embodied as a method, an example of which is provided. The order of operations performed as part of this method may be determined in any suitable manner. Thus, embodiments may be configured to perform operations in an order different from that illustrated, which may include performing some operations simultaneously, even though in the example embodiment they are shown as a sequence of operations.

[0094] Furthermore, embodiments of the present disclosure and the functional operations described herein can be implemented in digital electronic circuitry, tangibly embodied computer software or firmware, computer hardware including the structures disclosed herein and their structural equivalents, or one or more combinations thereof. Furthermore, some embodiments of the present disclosure can be implemented as one or more computer programs, i.e., as one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by or to control the operation of a data processing apparatus. Furthermore, the program instructions can be encoded on an artificially generated propagated signal, such as a machine-generated electrical, optical, or electromagnetic signal, generated to encode information that is transmitted to a suitable receiving device for execution by the data processing apparatus. A computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or one or more combinations thereof.

[0095] According to embodiments of the present disclosure, the term "data processing apparatus" may encompass all types of apparatus, devices, and machines that process data, including, by way of example, a programmable processor, a computer, or multiple processors or computers. The apparatus may include special-purpose logic circuitry, such as an FPGA (field-programmable gate array) or an ASIC (application-specific integrated circuit). In addition to hardware, the apparatus may also include code that creates an execution environment for the computer program, such as code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or one or more combinations thereof.

[0096] A computer program (which may also be called or described as a program, software, software application, module, software module, script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, such as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in part of a file that holds other programs or data, for example, in one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple coordinated files, for example, a file that stores one or more modules, subprograms, or portions of code.

[0097] A computer program can be deployed to be executed on one computer or on multiple computers located at one location or distributed across multiple locations and interconnected by a communications network. Computers suitable for running computer programs may, by way of example, be based on general-purpose or special-purpose microprocessors or both, or any other type of central processing unit. Typically, a central processing unit receives instructions and data from a read-only memory or a random-access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data.

[0098] Typically, a computer also includes one or more mass storage devices, such as magnetic, magneto-optical, or optical disks, for storing data, or is operatively coupled to such disks to receive data from, transfer data to, or both. However, a computer need not have such devices. Furthermore, a computer can be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device, such as a universal serial bus (USB) flash drive, to name a few.

[0099] To provide for user interaction, embodiments of the subject matter described herein may be implemented on a computer having a display device, such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user, and a keyboard and pointing device, such as a mouse or trackball, that allows the user to provide input to the computer. Other types of devices may also be used to provide for user interaction. For example, feedback provided to the user may be any form of sensory feedback, such as visual feedback, auditory feedback, or tactile feedback, and input from the user may be received in any form, including acoustic, speech, or tactile input. Additionally, the computer may provide for user interaction by sending documents to and receiving documents from a device used by the user, for example, by sending a web page to a web browser on the user's client device in response to a request received from the web browser.

[0100] Embodiments of the subject matter described herein may be implemented in a computing system that includes a back-end component, e.g., a data server, or a middleware component, e.g., an application server, or a front-end component, e.g., a client computer having a graphical user interface or web browser that allows a user to interact with an implementation of the subject matter described herein, or any combination of one or more of such back-end, middleware, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication, e.g., a communications network. Examples of communications networks include local area networks ("LANs") and wide area networks ("WANs"), e.g., the Internet.

[0101] A computing system may include clients and servers. Clients and servers are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a mutual client-server relationship.

[0102] While the present disclosure has been described in terms of certain preferred embodiments, it should be understood that various other adaptations and modifications can be made within the spirit and scope of the disclosure. It is, therefore, the object of the following claims to cover all such variations and modifications that fall within the true spirit and scope of the disclosure.

Claims

1. 1. A controller for controlling operation of a vapor compression cycle based on a hybrid model of dynamics of the vapor compression cycle, the hybrid model including a physics-based model and a data-driven model, the physics-based model being configured to predict state transitions of the vapor compression cycle according to observation variables and control inputs to the vapor compression cycle based on parameters of the physics-based model, and the data-driven model being trained using machine learning to estimate residual errors of the state transitions predicted by the physics-based model, the controller comprising a processor and a memory having instructions stored thereon, the instructions, when executed by the processor, causing the controller to: collecting digital representations of observed variables of operation of the vapor compression cycle and control inputs over a plurality of time instances; performing a constrained Kalman smoother on the collected observation variables over a plurality of time instances to jointly estimate the parameters of the physics-based model and states of the vapor compression cycle, and minimizing a cost function comprised of a residual error of the state transitions predicted by the physics-based model for the plurality of time instances and a residual error between the collected observation variables and the estimated observation variables by the constrained Kalman smoother for the plurality of time instances; updating the data-driven model to minimize a difference between the state estimated by running the constrained Kalman smoother on the observed variables collected over multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; A controller that controls operation of the vapor compression cycle using the updated hybrid model.

2. 2. The controller of claim 1, wherein the physics-based model includes one or a combination of governing partial differential equations discretized in the space and time domains, look-up tables, and interpolating splines for calculating thermodynamic properties of a refrigerant in the vapor compression cycle.

3. 3. The controller of claim 2, wherein the parameters of the physics-based model include a number of finite control volumes for a discretization of a governing partial differential equation, geometric parameters of the vapor compression cycle, properties of materials used in the vapor compression cycle, and a total mass of the refrigerant.

4. The controller of claim 1 , wherein the data-driven model comprises a neural network.

5. The controller of claim 4 , wherein parameters of the data-driven model include an architecture, weights, and biases of the neural network.

6. The controller of claim 1 , wherein the observed variables include measurements of one or more of temperature and pressure at different locations within the vapor compression cycle.

7. The controller of claim 1 , wherein the control inputs to the vapor compression cycle include compressor speed, fan speed, and expansion valve position.

8. The controller of claim 1 , wherein the processor is further configured to transmit the digital representations of the observed variables of operation of the vapor compression cycle and the control inputs to a remote server for storage.

9. The remote server executing the constrained Kalman smoother on the collected observation variables over a plurality of time instances to jointly estimate the parameters of the physics-based model and the states of the vapor compression cycle, and minimizing the cost function consisting of the residual error of the state transitions predicted by the physics-based model for the plurality of time instances and the residual error between the collected observation variables and the estimated observation variables by the constrained Kalman smoother for the plurality of time instances; updating the data-driven model to minimize the difference between the state estimated by running the constrained Kalman smoother on the observed variables collected over multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; The controller of claim 8 , configured to transmit the updated hybrid model.

10. The processor further comprises: receiving an updated hybrid model; The controller of claim 9 , configured to determine unobserved variables of the vapor compression cycle using the received updated hybrid model.

11. The controller of claim 10 , wherein the processor is further configured to control operation of the vapor compression cycle using the received updated hybrid model.

12. 1. A method for controlling operation of a vapor compression cycle based on a hybrid model of the dynamics of the vapor compression cycle, the hybrid model including a physics-based model and a data-driven model, wherein the physics-based model is configured to predict state transitions of the vapor compression cycle according to observation variables and control inputs to the vapor compression cycle based on parameters of the physics-based model, and the data-driven model is trained by machine learning to estimate residual errors of the state transitions predicted by the physics-based model, the method comprising: collecting digital representations of observed variables and control inputs of the operation of the vapor compression cycle over a plurality of time instances; running a constrained Kalman smoother on the collected observation variables over a plurality of time instances to jointly estimate the parameters of the physics-based model and states of the vapor compression cycle, and minimizing a cost function comprised of a residual error of the state transitions predicted by the physics-based model for the plurality of time instances and a residual error between the collected observation variables and the estimated observation variables by the constrained Kalman smoother for the plurality of time instances; updating the data-driven model to minimize a difference between the state estimated by running the constrained Kalman smoother on the observed variables collected over multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; and controlling operation of the vapor compression cycle using the updated hybrid model.

13. 13. The method of claim 12, wherein the physics-based model includes one or a combination of governing partial differential equations discretized in the space and time domains, look-up tables, and interpolating splines for calculating thermodynamic properties of a refrigerant in the vapor compression cycle.

14. 14. The method of claim 13, wherein the parameters of the physics-based model include a number of finite control volumes for a discretization of a governing partial differential equation, geometric parameters of the vapor compression cycle, properties of materials used in the vapor compression cycle, and a total mass of the refrigerant.

15. The method of claim 12 , wherein the data-driven model comprises a neural network.

16. The method of claim 15 , wherein the parameters of the data-driven model include one or more of an architecture, weights, and biases of the neural network.

17. The method of claim 12 , wherein the observed variables include measurements of one or more of temperature and pressure at different locations within the vapor compression cycle.

18. The method of claim 12 , wherein the control inputs to the vapor compression cycle include compressor speed, fan speed, and expansion valve position.

19. 13. The method of claim 12, further comprising transmitting the digital representations of the observed variables of operation of the vapor compression cycle and the control inputs to a remote server for storage.

20. 1. A non-transitory computer-readable storage medium containing a processor-executable program for executing a method for controlling operation of a vapor compression cycle based on a hybrid model of the dynamics of the vapor compression cycle, the hybrid model including a physics-based model and a data-driven model, the physics-based model being configured to predict state transitions of the vapor compression cycle according to observation variables and control inputs to the vapor compression cycle based on parameters of the physics-based model, and the data-driven model being trained by machine learning to estimate residual errors of the state transitions predicted by the physics-based model, the method comprising: collecting digital representations of observed variables and control inputs of the operation of the vapor compression cycle over a plurality of time instances; running a constrained Kalman smoother on the collected observation variables over a plurality of time instances to jointly estimate the parameters of the physics-based model and states of the vapor compression cycle, and minimizing a cost function comprised of a residual error of the state transitions predicted by the physics-based model for the plurality of time instances and a residual error between the collected observation variables and the estimated observation variables by the constrained Kalman smoother for the plurality of time instances; updating the data-driven model to minimize a difference between the state estimated by running the constrained Kalman smoother on the observed variables collected over multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the estimated parameters of the physics-based model and the updated data-driven model; and controlling operation of the vapor compression cycle using the updated hybrid model.

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