System and method for controlling operation of vapor compression cycle

Abstract

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

Description

Technical Field

[0001] This disclosure relates to a vapor compression cycle, and more specifically, to a system and method for controlling the operation of a vapor compression cycle. Background Technology

[0002] Vapor compression cycles have become a fundamental technology in modern society due to their widespread application in air conditioning and space heating. As vapor compression cycles offer an effective method for decarbonizing heating systems and utilizing electricity generated from renewable energy sources such as solar or wind power, they are expected to play an increasingly important role in the coming years. Therefore, there is widespread interest in further developing vapor compression cycle technology to ensure it is both energy-efficient and meets performance requirements related to the health and comfort of building occupants.

[0003] A range of control techniques employed in the vapor compression cycle utilize models representing the underlying physics / dynamics of the cycle to predict and control its behavior. Accurate predictions of vapor compression cycle behavior can be used for control techniques such as model predictive control and performance parameter estimation, including the cooling capacity provided by heat exchangers (HEX). Vapor compression cycle models also play a crucial role in the development of fault detection and diagnostic algorithms and are essential for emerging digital twin technologies aimed at improving energy efficiency, simplifying maintenance, and maximizing user comfort.

[0004] Some methods use physics-based models to predict the behavior of vapor compression cycles. These physics-based models are derived from the first principles of physics, thus constructing a set of high-dimensional nonlinear differential-algebraic equations for multi-physics systems such as vapor compression cycles. Such models are typically built to meet the physics-based or computational requirements of a specific application and involve the physical processes most relevant to the application. The simplifications that accompany these requirements (e.g., lumped parameters and finite discretization) often lead to a mismatch between model predictions and the data collected from the system. Addressing this mismatch to improve model prediction accuracy is not easy and can require unusual effort and complexity, resulting in relatively small improvements in prediction.

[0005] Alternatively, a data-driven model can be used to predict the behavior of a vapor compression cycle. This data-driven model is developed using data collected from the system. However, this data-driven model requires a large dataset containing the full-state trajectory to achieve reasonable modeling accuracy. Such large datasets are difficult to obtain due to the limited availability of sensor data. Furthermore, data-driven models face a number of other challenges, such as the lack of interpretability, an excessively large parameter search space, and the absence of explicit consideration of the fundamental physical laws of the control system.

[0006] Therefore, a kinetic model for controlling the vapor compression cycle is still needed. Summary of the Invention

[0007] Some embodiments aim to provide a system and method for controlling the operation of a vapor compression cycle using a hybrid kinetic model of the vapor compression cycle. This hybrid kinetic model of the vapor compression cycle includes both a physics-based model and a data-driven model. Some embodiments also aim to determine the model properties of this hybrid model.

[0008] Some implementations are based on the understanding that modeling of 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. Therefore, this disclosure provides a hybrid dynamic model of a vapor compression cycle incorporating both a physics-based model and a data-driven model. The physics-based model is configured to predict state transitions of the vapor compression cycle based on observed variables and control inputs of the vapor compression cycle, using parameters from the physics-based model. The physics-based model includes one or a combination of dominant partial differential equations, lookup tables, and interpolation splines, discretized in the spatial and temporal domains, for calculating the thermodynamic properties of the refrigerant in the vapor compression cycle. The data-driven model is trained using machine learning to estimate the residuals 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 multiple finite control volumes used to discretize the dominant partial differential equations, geometric parameters of the vapor compression cycle, material properties used in the vapor compression cycle, total mass of the refrigerant, etc. On the other hand, data-driven models (such as neural networks) are parameterized by a vector w, which contains the weights and biases of each artificial neuron and parameters defining the architecture of the neural network.

[0010] Some implementations aim to estimate model properties of a hybrid model based on observed variables collected over multiple time instances. The model properties 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). Observed variables include temperature and pressure measured by sensors installed at different locations within the vapor compression cycle. It is desired that the estimated model properties maximize the contribution of the physics-based model to the hybrid model, while the data-driven model is used only to correct modeling errors that cannot be corrected by the physics-based model alone. Therefore, the data-driven model is used to learn residual dynamics based on the mismatch between the physics-based model and the observed variables. Thus, in embodiments of this 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 that includes a penalty for the deviation between the predicted and actual outputs of the vapor compression cycle and a weighted norm of the data-driven model output.

[0011] Some implementations are based on the understanding 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 typically low-dimensional, but their derivatives are difficult to compute because they require differentiating the solutions to the differential equations. Furthermore, the kinetics of a vapor compression cycle are nonlinear, numerically rigid, and exhibit derivative discontinuities due to phase transitions accompanying evaporation or condensation. On the other hand, the parameters w are high-dimensional, but their derivatives can be efficiently computed using standard computational tools such as automatic differentiation.

[0012] Some embodiments of this disclosure are based on the understanding that the computational challenges associated with joint optimization problems can be solved by decomposing the joint optimization problem into two equivalent and tractable unconstrained optimization problems that determine θ and w respectively, rather than solving the joint optimization problem. For example, the joint optimization problem can be decomposed into: a first optimization problem for jointly estimating the state of a vapor compression cycle and the parameters θ of a physics-based model; and a second optimization problem for determining the parameters w of a data-driven model.

[0013] Some implementations are based on the understanding 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. This interpretation allows for the use of optimal smoothing formulas to determine the solution. In particular, approximate solutions to the first optimization problem can be efficiently determined using nonlinear estimation methods of various ranges. However, typically, estimation methods do not guarantee that physics-based constraints, such as the monotonicity of pressure in the refrigerant flow direction during the vapor compression cycle, will be satisfied. Satisfying these physics-based constraints is crucial to ensuring that the state estimation is physically feasible. Therefore, one implementation uses a constrained Kalman smoother, such as a constrained extended Kalman smoother (C-EKS) or a constrained ensemble Kalman smoother (C-EnKS), specifically designed for the estimation of vapor compression cycles, and enforces physics-based constraints during the joint estimation of the vapor compression cycle's state and the parameters of the physics-based model.

[0014] Therefore, a constrained Kalman smoother is used to solve the first optimization problem to estimate the parameters of the physics-based model and the state of the vapor compression cycle. Specifically, the constrained Kalman smoother is performed on the observations collected over multiple time instances to estimate the parameters of the physics-based model and the state of the vapor compression cycle.

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

[0016] Therefore, some embodiments of this disclosure are based on the understanding that the second optimization problem for determining the parameters of a data-driven model is a standard neural network training problem. According to embodiments, stochastic gradient descent is used to solve the second optimization problem to determine the parameters of the data-driven model.

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

[0018] Therefore, one embodiment discloses a controller for controlling the operation of a vapor compression cycle based on a kinetic hybrid model, the hybrid model comprising 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 based on parameters of the physics-based model according to observed variables of the vapor compression cycle and control inputs, and wherein the data-driven model is trained by machine learning to estimate residuals of the state transitions predicted by the physics-based model, the controller comprising: a processor; and a memory storing instructions that, when executed by the processor, cause the controller to: collect digital representations of the observed variables of the operation of the vapor compression cycle at multiple time instances; and process the observed variables collected at the multiple time instances... The process involves: executing a constrained Kalman smoother to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle to minimize a cost function consisting of residuals of the state transitions predicted by the physics-based model at multiple time instances, and residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables; updating the data-driven model to minimize the difference between the state estimated by executing the constrained Kalman smoother on the observed variables collected at multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the updated data-driven model and the estimated parameters of the physics-based model; and using the updated hybrid model to control the operation of the vapor compression cycle.

[0019] Therefore, another embodiment discloses a method for controlling the operation of a vapor compression cycle using a hybrid kinetic model based on the vapor compression cycle, the hybrid model comprising 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 based on parameters of the physics-based model according to observed variables and control inputs of the vapor compression cycle, and wherein the data-driven model is trained by machine learning to estimate residuals of the state transitions predicted by the physics-based model. The method includes: collecting digital representations of observed variables of the operation of the vapor compression cycle at multiple time instances; performing a constrained Kalman smoother on the observed variables collected at the multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle to minimize a cost function, the cost function consisting of residuals of the state transitions predicted by the physics-based model at the multiple time instances and residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables; updating the data-driven model to minimize the difference between the state estimated by performing the constrained Kalman smoother on the observed variables collected at the multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the updated estimated parameters of the data-driven model and the physics-based model; and using the updated hybrid model to control the operation of the vapor compression cycle.

[0020] Therefore, another embodiment discloses a non-transitory computer-readable storage medium on which a program is implemented, the program being executable by a processor to perform a method for controlling the operation of a vapor compression cycle based on a kinetic hybrid model, the hybrid model comprising 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 based on parameters of the physics-based model according to observed variables and control inputs of the vapor compression cycle, and wherein the data-driven model is trained by machine learning to estimate residuals of the state transitions predicted by the physics-based model. The method includes: collecting digital representations of observed variables of the operation of the vapor compression cycle at multiple time instances; performing a constrained Kalman smoother on the observed variables collected at the multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle to minimize a cost function, the cost function consisting of residuals of the state transitions predicted by the physics-based model at the multiple time instances and residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables; updating the data-driven model to minimize the difference between the state estimated by performing the constrained Kalman smoother on the observed variables collected at the multiple time instances and the state predicted by the physics-based model; updating the hybrid model using the updated estimated parameters of the data-driven model and the physics-based model; and using the updated hybrid model to control the operation of the vapor compression cycle. Attached Figure Description

[0021] Figure 1A A vapor compression cycle according to an embodiment of the present disclosure is shown.

[0022] Figure 1B A block diagram of a controller for controlling the operation of a vapor compression cycle according to an embodiment of the present disclosure is shown.

[0023] Figure 1C A kinetic hybrid model of a vapor compression cycle according to some embodiments of the present disclosure is shown.

[0024] Figure 1D A schematic diagram illustrating the decomposition of a joint optimization problem according to some embodiments of the present disclosure is shown.

[0025] Figure 2 A schematic diagram of a system architecture including a storage medium according to some embodiments of the present disclosure is shown.

[0026] Figure 3A schematic diagram of a cloud-based architecture according to some embodiments of the present disclosure is shown.

[0027] Figure 4 A block diagram is shown of a method for estimating a state using a constraint set Kalman smoother, according to some embodiments of the present disclosure.

[0028] Figure 5A A block diagram of a method for controlling the operation of a vapor compression cycle according to an embodiment of the present disclosure is shown.

[0029] Figure 5B A block diagram is shown illustrating the use of an updated hybrid model to control the operation of a vapor compression cycle according to an embodiment of this disclosure.

[0030] Figure 6 A schematic diagram of a computing device that can be used to implement the controller and method of this disclosure is shown. Detailed Implementation

[0031] The currently disclosed embodiments will be further explained in conjunction with the accompanying drawings. The drawings are not necessarily drawn to scale, but generally focus on illustrating the principles of the currently disclosed embodiments.

[0032] In the following description, numerous specific details are set forth for purposes of explanation in order to provide a thorough understanding of this disclosure. However, it will be apparent to those skilled in the art that this disclosure may be practiced without these specific details. In other instances, apparatuses and methods are shown only as block diagrams to avoid obscuring this disclosure.

[0033] As used in this specification and claims, the terms “for example,” “such as,” and “like,” as well as the verbs “comprising,” “having,” “including,” and other verb forms thereof, when used in conjunction with a list of one or more components or other items, are interpreted as open-ended, meaning that the list should not be construed as excluding other additional components or items. The term “based on” means at least partially based on. Furthermore, it should be understood that the wording and terminology used herein are for descriptive purposes and should not be considered restrictive. Any headings used in this specification are for convenience only and have no legal or restrictive effect.

[0034] Figure 1AA vapor compression cycle 100 according to an embodiment of the present disclosure is shown. The vapor compression cycle 100 includes a compressor 101, a condensing heat exchanger 103, an expansion valve 105, and an evaporating heat exchanger 107 located within a space 109. Heat transfer in the condensing heat exchanger 103 is facilitated by a fan 111, while heat transfer in the evaporating heat exchanger 107 is facilitated by 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. Many alternative device architectures are involved in this disclosure, which include multiple heat exchangers, compressors, valves, and other components such as accumulators or reservoirs, piping, etc. The description of the vapor compression cycle 100 is not intended to limit the scope or application of this disclosure to any system.

[0035] In the vapor compression cycle 100, the compressor 101 compresses the low-pressure, low-temperature gaseous fluid (refrigerant) into a high-pressure, high-temperature vapor state, which then enters the condensing heat exchanger 103. As the refrigerant flows through the condensing heat exchanger 103, heat transfer facilitated by the fan 111 causes the high-temperature, high-pressure refrigerant to transfer its heat to the cooler ambient air. As the refrigerant transfers heat to the ambient air, it gradually condenses until it reaches a high-pressure, low-temperature liquid state. Furthermore, the refrigerant leaves the condensing heat exchanger 103, flows through the expansion valve 105, expands to a low-pressure boiling state, and then enters the evaporating heat exchanger 107. Because the air flowing through the evaporating heat exchanger 107 is warmer than the refrigerant itself, the refrigerant gradually evaporates as it flows through the evaporating heat exchanger 107. The refrigerant leaving the evaporating heat exchanger 107 is in a low-pressure, low-temperature state. The low-pressure, low-temperature refrigerant re-enters the compressor 101, and the same cycle repeats.

[0036] The vapor compression cycle 100 operates with a set of rated actuator input values, such as the speed of compressor 101, the speed of fan 111, the position of expansion valve 105, the speed of fan 113, etc. The desired or objective is for the vapor compression cycle 100 to achieve performance metrics, such as regulating variables like temperature or humidity in space 109, or regulating process variables like temperature or pressure at one or more points within the vapor compression cycle 100. To achieve these objectives, one or more sensors are installed at various locations within the vapor compression cycle 100 to monitor variables of interest. These 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 (such as temperature or humidity) in space 109 can be obtained via sensors (such as sensor 123).

[0037] Information from sensors 115, 117, 119, 121, and 123 is input to a controller 125 associated with the vapor compression cycle 100. Based on the information from sensors 115, 117, 119, 121, and 123, the controller 125 can control the operation of the vapor compression cycle 100. For example, based on the information from sensors 115, 117, 119, 121, and 123, the controller 125 can change the input values ​​of the actuators, such as the speed of compressor 101, the speed of fan 111, the position of expansion valve 105, and the speed of fan 113, to achieve a desired performance metric.

[0038] Figure 1B A block diagram of a controller 125 according to an embodiment of the present disclosure is shown. 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 other configuration. The memory 129 may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable storage system. Furthermore, in some embodiments, the memory 129 may be implemented using a hard disk drive, an optical disk drive, a USB flash drive, a drive array, or any combination thereof.

[0039] Processor 127 is configured to collect digital representations of observed variables of the operation of vapor compression cycle 100 at multiple time instances. In one embodiment, processor 127 collects digital representations of observed variables of the operation of vapor compression cycle 100 from sensors 115, 117, 119, 121, and 123. Observed variables include, for example, measurements of one or more of temperature and pressure at different locations within vapor compression cycle 100.

[0040] The controller 125 can employ a low-level physical / dynamic model representing the vapor compression cycle 100 to predict its behavior. Based on a numerical representation of the collected observed variables, the model predicts the behavior of the vapor compression cycle 100. Accurate prediction of the behavior of the vapor compression cycle 100 can be used in a range of control techniques, such as model predictive control and performance parameter estimation, such as the cooling capacity provided by a heat exchanger (HEX). The model of the vapor compression cycle 100 can also play a significant role in the development of fault detection and diagnostic algorithms and is crucial for emerging digital twin technologies aimed at improving energy efficiency, simplifying maintenance, and maximizing user comfort.

[0041] The model for the vapor compression cycle 100 can be a physics-based model. This physics-based model originates from the first principles of physics, thus constructing a set of high-dimensional nonlinear differential-algebraic equations for the metaphysical system (such as the vapor compression cycle 100). Such models are typically constructed to meet the physics-based or computational requirements of a specific application and involve the physical processes most relevant to the application. The simplifications accompanying these requirements (e.g., lumped parameters and finite discretization) often result in a mismatch between model predictions and data collected from the system (e.g., the vapor compression system (VCS)). Addressing this mismatch to improve the accuracy of model predictions is not easy and may require unusual effort and complexity, resulting in relatively small improvements in prediction.

[0042] Alternatively, the model of the vapor compression cycle 100 can be a data-driven model. This data-driven model is developed using data collected from the system. However, such a model requires a large dataset containing the full-state trajectory to achieve reasonable modeling accuracy. Due to the limited availability of sensor data, such large datasets are difficult to obtain. Furthermore, data-driven models face a number of other challenges, such as the lack of interpretability, an excessively large parameter search space, and the absence of explicit consideration of the fundamental physical laws of the control system.

[0043] Some implementations are based on the understanding that modeling the vapor compression cycle 100 may 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 100. Therefore, this disclosure provides a kinetic hybrid model 131 for the vapor compression cycle 100. In an implementation, the hybrid model 131 is stored in memory 129. The hybrid model 131 is as follows: Figure 1C As stated above.

[0044] Figure 1C A kinetic hybrid model 131 of a vapor compression cycle 100 according to some embodiments of the present disclosure is shown. The kinetic hybrid model 131 of the vapor compression cycle 100 includes a physics-based model 133 and a data-driven model 135. The physics-based model 133 is configured to predict state transitions of the vapor compression cycle 100 based on observed variables and control inputs of the vapor compression cycle 100, using parameters of the physics-based model 133. The physics-based model 133 includes one or a combination of dominant partial differential equations, lookup tables, and interpolation splines, discretized in the spatial and time domains, for calculating the thermodynamic properties of the refrigerant in the vapor compression cycle 100. The data-driven model 135 is trained via machine learning to estimate residuals of the state transitions predicted by the physics-based model 133. The data-driven model 135 may include a neural network. Mathematically, the hybrid model 131 is provided as follows:

[0045] x k+1 =F p (x k ,u k ,θ)+F d (x k ,u k ,w) (1)

[0046] Where, x k It is a steam compression cycle 100 at time t k The state vector, u k It is a steam compression cycle 100 at time t k The vector of control input. Vector u k This includes control inputs from the controller 125, 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. Additionally, vector u... k It may also include variables that affect the behavior of the vapor compression cycle 100, such as the temperature and relative humidity of space 109 and the surrounding outdoor environment. In equation (1), F p This represents a physics-based model parameterized by a parameter vector θ, which includes multiple finite control volumes for discretizing the dominant partial differential equations, geometric parameters of the vapor compression cycle, material properties used in the vapor compression cycle 100, the total mass of the refrigerant, etc. On the other hand, F d This represents a data-driven model, such as a neural network, parameterized by a vector w, which contains the weights and biases of each artificial neuron and the parameters that define the architecture of the neural network.

[0047] Some implementations aim to estimate the model properties of the mixture model 131 based on observations collected over multiple time instances. The model properties of the mixture model 131 include the parameters of the physics-based model 133 (i.e., parameter θ) and the parameters of the data-driven model 135 (i.e., parameter w).

[0048] The observed variable can be represented by the following measurement equation:

[0049] y k =h(x k ,u k ,θ)+η (2)

[0050] Where η is a normally distributed variable N(0,R). Measurement model h(x) k ,u k ,θ) will be the state vector x k and control input vector u k As input, to predict the observed variable y kFurthermore, η accounts for random perturbations (such as sensor noise) that disrupt the measurements. The observed variable y k This includes temperature and pressure measured by sensors 115, 117, 119, 121 and 123 installed at different locations in the vapor compression cycle 100.

[0051] Processor 127 is configured to estimate the model properties of hybrid model 131, namely, parameters θ and w, by solving the following joint optimization problem.

[0052]

[0053] Constrained by x k+1 =F p (x k ,u k ,θ)+F d (x k ,u k ,w),k=0,...,K-1 (3)

[0054] The observed variables are collected and stored at multiple time instances k = 1, 2, ..., K.

[0055] The first term in problem (3) directly penalizes the data-driven model F. d The data-driven model, weighted by a positive definite matrix P, contributes to the performance of the hybrid model (1), while enforcing the equality constraints defined in the hybrid model. The choice of the first term of the cost function is based on the understanding that the obvious cost is simply minimized (e.g., ||x|). k+1 -F p (x k ,u k ,θ)-F d (x k ,u k The combination of parameters (θ, w) might lead to unexpected solutions. For example, in extreme cases, there might exist an optimal combination of parameters (θ). * ,w * ), making F p (x k ,u k ,θ * The kinetic information for F = 0 and the vapor compression cycle 100 comes solely from the data-driven model, discarding information from the physics-based model. Conversely, we expect the physics-based model F... p It can provide most of the explanation for the behavior of the vapor compression cycle 100 because of the physics-based model F. p It is often more robust and can generalize better to new or unknown data. In the extreme case, if there exists a parameter θ... * Make x k+1 -Fp (x k ,u k ,θ * If ) = 0, then formula (3) determines these parameters and discards any contribution from the data-driven model.

[0056] The second penalty prediction measure h(x) in question (3) k ,u k (θ) and observed variable y k The deviation between the measurements is weighted by the covariance matrix R of the sensor noise that perturbs the measurements. Finally, the last term in problem (3) considers the uncertainty of the initial state, since the initial conditions are usually unknown and are assumed to follow a normal distribution.

[0057] In data-driven modeling methods such as neural networks, the optimal parameters (θ) are typically determined by minimizing the cost function across multiple trajectories of the system. * ,w * To improve modeling accuracy and optimize generalization performance, problem (3) can be formulated as a joint optimization problem:

[0058]

[0059] Subject to Here, the superscript i represents the i-th trajectory in the training dataset containing a total of N trajectories.

[0060] Numerical optimization (4) is challenging because it requires relaxing or merging equality constraints using the Lagrangian method, and the parameters θ and w are fundamentally different optimization variables. On the one hand, the parameter θ is typically low-dimensional, but its derivatives with respect to θ are difficult to compute because they require differentiation of the solution to the differential equation. Furthermore, the kinetics of the vapor compression cycle 100 are nonlinear, numerically rigid, and have derivative discontinuities due to phase transitions accompanying evaporation or condensation. On the other hand, w has a large dimension, but its derivatives can be computed efficiently using standard computational tools such as automatic differentiation.

[0061] Some embodiments of this disclosure are based on the understanding that the computational challenges associated with joint optimization (4) can be solved by decomposing (4) into two equivalent and tractable unconstrained optimization problems that determine θ and w respectively, rather than solving the joint optimization problem (4), as follows: Figure 1D As stated above.

[0062] Figure 1DA schematic diagram of the decomposition of the joint optimization problem (4) according to some embodiments of the present disclosure is shown. The joint optimization problem (4) 137 is decomposed into: a first optimization problem 139, which is used to jointly estimate the state of the vapor compression cycle 100 and the parameters θ of the physics-based model 133; and a second optimization problem 141, which is used to determine the parameters w of the data-driven model 135.

[0063] The first optimization problem 139 involves minimizing a cost function composed of residuals of state transitions predicted by the physics-based model 133 over multiple time instances, and residuals between observed variables estimated by a constrained Kalman smoother and the collected corresponding observed variables over multiple time instances. Mathematically, the first optimization problem 139 is expressed as:

[0064]

[0065] The second optimization problem 141 is represented as:

[0066]

[0067] in,

[0068] Solve the first optimization problem (5) 139 to estimate the parameters θ of the physics-based model 133 for all time instances of the collected observation variables. * and state

[0069] Some implementations are based on the following understanding: the first optimization problem (5) 139, namely, the joint estimation of the state and parameters of the physical model 133, can be interpreted as θ and The maximum a posteriori estimate is obtained, where the VCS is affected by Gaussian perturbation. Therefore, the first optimization problem (5)139 can be solved efficiently using the four-dimensional variational (4DVar) data assimilation method. In practice, for reasons of computational cost and scalability, optimal smoothing methods (such as Kalman smoothers) are usually used to solve the first optimization problem (5)139.

[0070] Kalman smoothing is a noncausal data assimilation method that leverages available measurement data from future time instances to improve estimations of past states using the Kalman estimation framework. Therefore, Kalman smoothers are well-suited for batch processing of measurements or observations collected across multiple time instances. If the underlying function F... pIf h is linear among the optimization variables, then the Kalman smoothing method is guaranteed to be optimal in solving (5). Although the underlying governing equations of the vapor compression cycle 100 are not linear, the Kalman smoothing algorithm is still advantageous in obtaining an approximate solution to (5) because it has comparable accuracy, computational efficiency, and a simpler implementation compared to the complex solvers that might be required to solve (5). Kalman smoothers for nonlinear systems can be implemented using various formulas, 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 the Jacobian matrix for the propagation and update steps of the Kalman estimation process. The ensemble Kalman smoother is a Monte Carlo-like method in which a set of random particles sampled from the state distribution is used for the propagation phase and an empirically calculated covariance matrix is ​​used in the update step. For high-dimensional nonlinear systems like the vapor compression cycle 100, the ensemble Kalman smoother is used because it avoids the need for storing the high-dimensional covariance matrix required by the extended Kalman smoother.

[0071] Furthermore, the Kalman smoother can be customized for specific vapor compression applications to obtain significantly faster solutions that also incorporate physics-based state constraints. For example, to satisfy the fundamental physical relationships in vapor compression cycle 100, the refrigerant pressure in the heat exchanger must decrease in the flow direction. If this constraint on refrigerant pressure is not satisfied after applying state corrections at a given time, the solver may fail to successfully perform forward integration of the kinetic model in the next time interval because the perturbed pressure could cause non-physical changes in the flow direction, violating the fundamental assumptions of the kinetic model.

[0072] Therefore, the first optimization problem (5) 139 is solved using a constrained Kalman smoother 143 to estimate the parameters θ of the physics-based model 133. * and state In particular, processor 127 performs a constrained Kalman smoother on the observed variables collected at multiple time instances to estimate the parameters θ of the physics-based model 133 by minimizing the cost function of (5). * and state

[0073] There is a difference between the state predicted by the physics-based model 133 and the state estimated by performing a constrained Kalman smoother. This difference is called the residual. The residual can be calculated as follows:

[0074]

[0075] To compensate for the residuals, the parameters w of the data-driven model 135 should be determined to minimize the cumulative learning cost function, which consists of the difference between the residuals and the output of the data-driven model 135 (corresponding to the same input that produces the error residual at that moment). Residuals Within the scope of the second optimization problem, the constants are known; therefore, the data-driven model 135 is essentially an attempt to learn the residuals of a given input state vector and control input vector.

[0076] Therefore, some embodiments of this disclosure are based on the following understanding: determining the parameter w * The second optimization problem (6) 141 is a standard neural network training problem. According to the implementation, stochastic gradient descent 145 is used to solve the second optimization problem (6) 141 to determine the parameters w of the data-driven model 135. * The data-driven model 135 uses a training dataset containing ordered tuples. Training is performed using the data-driven model 135. The input to the model is (...). Furthermore, the output of the data-driven model 135 is the residual.

[0077] Furthermore, processor 127 uses the parameters θ of physics-based model 133. * And the parameters w of the data-driven model 135 * To update the mixture model 131. In other words, the updated mixture model 131 includes models with parameters θ. * The physics-based model 133 and the model with parameter w * The data-driven model 135. Furthermore, the processor 127 uses an updated hybrid model 131 to control the operation of the vapor compression cycle 100. For example, based on the updated hybrid model 131, the processor 127 determines the control inputs to the 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. Furthermore, the processor 127 controls the actuators based on the determined control inputs.

[0078] In some implementations, digital representations of observed variables of the operation of the vapor compression cycle 100 collected from sensors 115, 117, 119, 121, and 123 are sent to a storage medium located in the same geographic area as the vapor compression cycle 100.

[0079] Figure 2A schematic diagram of a system architecture 200 including a storage medium 201 according to some embodiments of the present disclosure is shown. Digital representations of observed variables of the operation of the vapor compression cycle 100 collected from sensors 115, 117, 119, 121, and 123 at multiple time instances, as well as control inputs provided by the controller 125, are stored in the storage medium 201. Furthermore, in some embodiments, other internal information associated with the controller 125 (such as internal controller variables, discrete variables from control logic, or other information generated by the controller 125) may also be stored in the storage medium 201. The storage medium may be located in the same geographical location as the vapor compression cycle 100.

[0080] Furthermore, the data in storage medium 201 is provided to controller 125 periodically, or at regular intervals, or when an event occurs that requires updating hybrid model 131 (e.g., when a user requests information related to the operation of vapor compression cycle 100). In embodiments, the data provided by storage medium 201 may include digital representations of observed variables of the operation of vapor compression cycle collected over multiple time instances.

[0081] Some implementations are based on the understanding that some or all of the data stored in storage medium 201 can be stored using cloud computing resources, and that updates to hybrid model 131 can be implemented on a remote server. Figure 3 Such an implementation method is described in the document.

[0082] Figure 3 A schematic diagram of a cloud-based architecture 300 according to some embodiments of the present disclosure is shown. A vapor compression cycle 100, a controller 125, and a storage medium 201 are considered as system 301. System 301 communicates with a remote server 303 (also referred to as a cloud computing system) via a network 305. In this case, the size of the storage medium 201 may vary. Alternatively, the storage medium 201 may be present or absent depending on the remote server 303's ability and / or reliability to access data from the vapor compression cycle 100.

[0083] System 301 is configured to send some or all of the data (e.g., digital representations of observed variables and control inputs) to a remote server 303 for storage, instead of storing the data in a storage medium 201 located in the same location as the vapor compression cycle 100. Furthermore, the remote server 303 can store model properties of the hybrid model 131, namely, the parameters θ of the physics-based model 133 and the parameters w of the data-driven model 135.

[0084] The model attributes of the hybrid model 131 stored in the remote server 303 can be updated at regular intervals or when an update trigger event occurs. Update trigger events include user requests for information related to the operation of the vapor compression cycle 100, replacement of a faulty component of the vapor compression cycle 100 (e.g., compressor, fan) with a new component, and user requests to update the hybrid model 131. For example, a faulty component of the vapor compression cycle 100 (e.g., compressor, fan) can be replaced by an independent contractor during maintenance services. The specification information of the newly installed component can be used to update the hybrid model 131 on the remote server 303 to simulate the physical vapor compression cycle 100 as closely as possible.

[0085] For example, when an update trigger event occurs, remote server 303 performs a constrained Kalman smoother 143 on the observed variables collected across multiple time instances to jointly estimate the parameters of the physics-based model 133 and the state of the vapor compression cycle 100 to minimize a cost function consisting of the residuals of the state transitions predicted by the physics-based model 133 and the residuals between the observed variables estimated by the constrained Kalman smoother across multiple time instances and the corresponding collected observed variables.

[0086] Furthermore, remote server 303 updates data-driven model 135 to minimize the difference between the state estimated by performing a constrained Kalman smoother 143 on observed variables collected at multiple time instances and the state predicted by physics-based model 133. Remote server 303 further updates the hybrid model using the estimated parameters of the updated data-driven model and physics-based model 133.

[0087] The remote server 303 further sends the updated hybrid model to the controller 125 via the network 305. The controller 125 receives the updated hybrid model and uses it to control the operation of the vapor compression cycle.

[0088] The cloud-based architecture 300 offers advantages. For example, limited computing resources can be co-located with the vapor compression cycle 100, and appropriate computing resources can be easily adjusted and scaled in a remote server 303 (i.e., the cloud). Furthermore, the data and estimates of the vapor compression cycle 100's condition can be used simultaneously for a variety of different scenarios, including but not limited to equipment servicing or maintenance planning, or for the development of next-generation systems. According to some implementations, estimates of the vapor compression cycle 100's condition can indicate equipment maintenance needs that are not easily discernible from measurement data. The cloud-based architecture 300 allows such information to be easily and asynchronously provided to service companies, enabling them to automatically follow up with users and schedule maintenance requests. Moreover, the information provided to service companies enables the use of precise diagnostic and service tools.

[0089] In the implementation, the parameters θ are used to estimate the physics-based model 133. * and state The constrained Kalman smoother is a constrained set Kalman smoother. The constrained set Kalman smoother is as follows: Figure 4 As shown.

[0090] Figure 4 A block diagram of a method 400 for estimating a state using a constraint set Kalman smoother, according to some embodiments of the present disclosure, is shown.

[0091] Method 400 begins with data 401 of the operation of the vapor compression cycle 100 and a model 403 of the vapor compression cycle 100. Data 401 includes a set of control inputs u and measured values, i.e., observed variables y from sensors installed in the vapor compression cycle 100. According to an embodiment, the model 403 of the vapor compression cycle 100 describes the evolution of the state variables via a function f and describes the measured values ​​as a function of the state variables via a second function h, which may be a nonlinear function.

[0092] In box 405, data 401 and model 403 are used to make the initial state set. The initialization is performed on an unconstrained set Kalman smoother of size M. The method for initializing a constrained set Kalman smoother involves determining a consistent initialization of model 403 given a set of user-specified initial conditions, and then perturbing the initial state with a set of random perturbations having estimated model covariance.

[0093] In box 407, by solving the constrained optimization problem, the transformation is made to the covariance r. (i)* The state variables within the range are updated for each measurement in data 401 within a smoothing window. The transformed corrected values ​​are then transformed back to the coordinate system of the original state variables to obtain the corrected enhanced state estimate. While this implementation of the constrained smoothing method 400 is not built for real-time applications, solving the constrained optimization problem in box 407 for each sample of each available data point can be computationally expensive. Therefore, in some implementations, the update step in box 407 can be replaced by a two-stage process, in which, in the first stage, the update is performed without constraints. After this update is applied, in the second stage, if the corrected enhanced state estimate obtained in the first stage violates constraints, only the constrained optimization problem in box 407 is solved. If the constraints are satisfied after the correction in the first stage, the second stage is skipped.

[0094] Although there may be N available data points, all N data points can be used, or a smaller set can be used within a smoothing window. For example, while applying constraints, the state update in the coordinate system of the covariance range at the first measurement time k=1 is calculated, and then transformed back to the coordinate system of the original state variables.

[0095] In box 409, if the end of available data has been reached, it is checked whether the measurement time k=1 is the time of the last data point. Since the measurement time k=1 is not equal to N, in box 411, the nonlinear model f is solved in the forward direction from the first measurement time to the second measurement time k=2, and then the state variables are updated again to take into account the measurement value at time k=2.

[0096] At time k=2, state correction is 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 measurement at time k=2 and satisfies the constraints at both times. In this iteration, as additional data is incorporated, the length of data covered by the state estimate gradually increases until all N data points are incorporated, and all state variables are continuously updated to reflect the new information provided by the data points added sequentially to the ever-growing smoothing window. With the incorporation of more data points, the increasing length of the smoothing window can present significant computational challenges, such as excessive storage requirements and computation time.

[0097] Therefore, in some implementations, 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) can be fixed as a constant so that the data points available at the time before m are not considered in update step 407. Once each data point has been processed, the final set of smoothed state estimates is output in box 413. The final set of smoothed state estimates contains the state of the vapor compression cycle 100.

[0098] In another implementation, the constraint set Kalman smoother 400 is suitable for jointly estimating the state and parameters of a physics-based model. Within the scope of the joint estimation, the constraint set Kalman smoother 400 estimates an augmentation vector comprising both the state and parameters of the physics-based model, while following a general process similar to the general process of the constraint set Kalman smoother 400 method.

[0099] In addition, below Figure 5A A general method for controlling the operation of the vapor compression cycle 100 is described.

[0100] Figure 5AA block diagram of a method 500 for controlling the operation of a vapor compression cycle 100 according to an embodiment of the present disclosure is shown. In block 501, method 500 includes collecting digital representations of observed variables and control inputs of the operation of the vapor compression cycle 100 at multiple time instances. In block 503, method 500 includes performing a constrained Kalman smoother 143 on the observed variables collected at the multiple time instances to jointly estimate the parameters of a physics-based model 133 and the state of the vapor compression cycle 100 to minimize a cost function consisting of residuals of state transitions predicted by the physics-based model 133 and residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables.

[0101] In box 505, method 500 includes updating the data-driven model 135 to minimize the difference between the state estimated by performing a constrained Kalman smoother 143 on observed variables collected at multiple time instances and the state predicted by the physics-based model 133. In box 507, method 500 includes updating the hybrid model 131 using the estimated parameters of the physics-based model 133 and the updated data-driven model. In box 509, method 500 includes using the updated hybrid model to control the operation of the vapor compression cycle 100.

[0102] Figure 5B A block diagram is shown illustrating the use of an updated hybrid model to control the operation of a vapor compression cycle 100 according to an embodiment of the present disclosure. In block 511, the updated hybrid model is used to determine unobserved variables of the vapor compression cycle 100. Unobserved variables correspond to variables that are difficult to measure or cannot be directly measured. For example, unobserved variables may include the refrigerant charge in the vapor compression cycle 100, the heat energy delivered by one or more heat exchangers of the vapor compression cycle 100, and the thermodynamic mass of the refrigerant flow at the inlet or outlet of one or more heat exchangers of the vapor compression cycle 100. For example, unobserved variables of the vapor compression cycle 100 The parameters θ of the updated hybrid model based on the physics model 133 * ,state And determined by known control inputs, as shown below:

[0103]

[0104] Here, g(.) is a known function that maps its independent variable to an unobserved variable.

[0105] Furthermore, in block 513, the control inputs for the actuator of the vapor compression cycle 100 are determined based on the updated hybrid model and unobserved variables. The control inputs may include one or more of the speed of compressor 101, the speed of fan 111, the position of expansion valve 105, and the speed of fan 113.

[0106] Furthermore, in block 515, the actuator of the vapor compression cycle 100 is controlled according to the determined control input to control the operation of the vapor compression cycle 100.

[0107] Figure 6 A schematic diagram of a computing device 600 is shown that can be used to implement the controller 125 and method 500 of this disclosure. The computing device 600 includes a power supply 601, a processor 603, a memory 605, and a storage device 607, all of which are connected to a bus 609. Furthermore, 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. A receiver 627 can be connected to an external transmitter 629 and a transmitter 631 via the bus 609. External memory 633, external sensors 635, a machine 637, and an environment 639 can also be connected to the bus 609. Furthermore, one or more external input / output devices 641 can be connected to the bus 609. The network interface controller (NIC) 643 may be adapted to be connected to the network 645 via the bus 609, wherein data or other data may be presented on a third-party display device, a third-party imaging device and / or a third-party printing device outside the computing device 600.

[0108] Memory 605 may store instructions executable by computing device 600 and any data usable by the methods and systems of this disclosure. Memory 605 may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable storage system. Memory 605 may be one or more volatile memory cells and / or one or more non-volatile memory cells. Memory 605 may also be another form of computer-readable medium such as a magnetic disk or optical disk.

[0109] Storage device 607 may be adapted to store supplementary data and / or software modules used by computing device 600. Storage device 607 may include a hard disk drive, optical disk drive, USB flash drive, drive array, or any combination thereof. Furthermore, storage device 607 may also include computer-readable media such as floppy disk devices, hard disk devices, optical disk devices, magnetic tape devices, flash memory or other similar solid-state storage devices, or device arrays including devices in a storage area network or other configuration. Instructions may be stored in an information carrier. When the instructions are executed by one or more processing devices (e.g., processor 603), one or more methods such as those described above will be performed.

[0110] The computing device 600 may optionally be linked to a display interface or user interface (HMI) 647 via a bus 609. The HMI 647 is adapted to connect the computing device 600 to a display device 649 and a keyboard 651, wherein the display device 649 may include a computer monitor, camera, television, projector, or mobile device, etc. In some implementations, the computing device 600 may include a printer interface for connecting to a printing device, wherein the printing device may include a liquid inkjet printer, solid inkjet printer, large format printer, thermal printer, UV printer, or dye-sublimation printer, etc.

[0111] High-speed interface 611 manages bandwidth-intensive operations of computing device 600, while low-speed interface 613 manages low-bandwidth-intensive operations. This functional allocation is merely illustrative. In some implementations, high-speed interface 611 may be connected to memory 605, user interface (HMI) 646, keyboard 651, and display 649 (e.g., via a graphics processor or accelerator), as well as high-speed expansion port 615, which can connect to various expansion cards via bus 609. In some implementations, low-speed interface 613 is connected to storage device 607 and low-speed expansion port 617 via bus 609. Low-speed expansion port 617, which may include various communication ports (e.g., USB, Bluetooth, Ethernet, Wireless Ethernet), may be connected to one or more input / output devices 641. Computing device 600 may be connected to server 653 and rack server 655. Computing device 600 may be implemented in a variety of different forms. For example, computing device 600 may be implemented as part of rack server 655.

[0112] This specification provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of this disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with a feasible description of implementing one or more exemplary embodiments. Various changes to the function and arrangement of the elements are contemplated without departing from the spirit and scope of the subject matter disclosed in the appended claims.

[0113] Specific details are set forth in the following description to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form to avoid obscuring the embodiments with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, the same reference numerals and names in the various figures denote the same elements.

[0114] Furthermore, various implementations can be described as processes shown in flowcharts, flow diagrams, data flow diagrams, structure diagrams, or block diagrams. Although flowcharts can describe operations as sequential processes, many operations can be executed in parallel or simultaneously. Moreover, the order of operations can be rearranged. A process may terminate upon completion of its operations, but may have additional steps not discussed or included in the diagrams. Furthermore, not all operations in any particular described process may occur in all implementations. A process may correspond to a method, function, program, subroutine, subroutine, etc. When a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or the main function.

[0115] Furthermore, implementations of the disclosed subject matter can be carried out, at least partially, manually or automatically. They can be performed, or at least assisted by, using machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof, for manual or automatic implementation. When implemented in software, firmware, middleware, or microcode, program code or code segments for performing the necessary tasks can be stored in a machine-readable medium. The processor can then perform the necessary tasks.

[0116] The various methods or processes outlined herein can be encoded as software that can be executed on one or more processors employing any of a variety of operating systems or platforms. Furthermore, such software can be written using a variety of suitable programming languages ​​and / or programming or scripting tools, and can also be compiled into executable machine language code or intermediate code that executes on a framework or virtual machine. Typically, in various implementations, the functionality of program modules can be combined or distributed as needed.

[0117] Implementations of this disclosure can be embodied as a method, examples of which have been provided. Actions performed as part of this method can be ordered in any suitable manner. Therefore, implementations can be constructed in which actions are performed in a different order than those shown, which may include performing some actions simultaneously, even if these actions are shown as sequential actions in the illustrative embodiments.

[0118] Furthermore, the embodiments of this disclosure and the functional operations described in this specification can be implemented in digital electronic circuits, in tangibly implemented computer software or firmware, in computer hardware (including the structures disclosed in this specification and their equivalents), or in one or more combinations thereof. Additionally, some embodiments of this disclosure can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier, for execution by a data processing device or for controlling the operation of a data processing device. Furthermore, program instructions can be encoded on artificially generated propagation signals (e.g., machine-generated electrical, optical, or electromagnetic signals) that are generated to encode information for transmission to a suitable receiver device for execution by the data processing device. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of these.

[0119] According to embodiments of this disclosure, the term "data processing apparatus" can encompass all kinds of devices, apparatuses, and machines for processing data, including, for example, programmable processors, computers, or multiple processors or computers. The apparatus may include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits). In addition to hardware, the apparatus may also include code that creates an execution environment for associated computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0120] A computer program (which may also be referred to or described as a program, software, software application, module, software module, script, or code) can be written in any programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but does not necessarily, correspond to a file in a file system. A program may be stored as a portion of a file that holds other programs or data, such as one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinating files, such as a file storing one or more modules, subroutines, or portions of code.

[0121] Computer programs can be deployed to execute on one or more computers located at a single site or distributed across multiple sites and interconnected via a communication network. For example, a computer suitable for executing a computer program can be based on a general-purpose or special-purpose microprocessor, or both, or any other type of central processing unit (CPU). Typically, the CPU receives instructions and data from read-only memory (ROM) or random access memory (RAM), or both. The basic components of a computer are the CPU for executing or running instructions and one or more memory devices for storing instructions and data.

[0122] Typically, a computer will also include one or more mass storage devices (e.g., disks, magneto-optical disks, or optical disks) for storing data, or operatively coupled to receive data from or transfer data to, or both. However, a computer does not need to have such a device. Furthermore, a computer may 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 just a few.

[0123] To enable interaction with the user, embodiments of the subject matter described herein can be implemented on a computer having a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback, such as visual, auditory, or tactile feedback; and input from the user can be received in any form, including acoustic, voice, or tactile input. Furthermore, the computer can interact with the user by sending documents to and receiving documents from the device used by the user; for example, by sending a webpage to a web browser on the user's client device in response to a request received from a web browser.

[0124] The embodiments of the subject matter described in this specification can be implemented in a computing system that includes, for example, a back-end component as a data server, or a middleware component including, for example, an application server, or a front-end component including, for example, a client computer having a graphical user interface or a web browser (through which a user can interact with the implementation of the subject matter described in this specification), or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected via digital data communication (e.g., a communication network) of any form or medium. Examples of communication networks include local area networks (“LANs”) and wide area networks (“WANs”), such as the Internet.

[0125] A computing system may include clients and servers. Clients and servers are typically geographically separated and usually interact through a communication network. The relationship between clients and servers is established through computer programs running on their respective computers, and they have a client-server relationship with each other.

[0126] Although this disclosure has been described with reference to certain preferred embodiments, it should be understood that various other modifications and variations can be made within the spirit and scope of this disclosure. Therefore, the appended claims cover all such changes and variations within the true spirit and scope of this disclosure.

Claims

1. A controller for controlling the operation of a vapor compression cycle based on a hybrid kinetic model, the hybrid model comprising 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 based on observed variables and control inputs of the vapor compression cycle using parameters of the physics-based model, wherein the data-driven model is trained via machine learning to estimate residuals of the state transitions predicted by the physics-based model, and the controller includes: a processor; and a memory storing instructions that, when executed by the processor, cause the controller to: A digital representation of the observed variables and control inputs of the operation of the vapor compression cycle is collected at multiple time instances; A constrained Kalman smoother is applied to the observed variables collected at multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle, so as to minimize a cost function that includes the residuals of the state transitions predicted by the physics-based model at the multiple time instances, and the residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables. The data-driven model is updated to minimize the difference between the state estimated by applying the constrained Kalman smoother to the observed variables collected at multiple time instances and the state predicted by the physics-based model. The hybrid model is updated using the estimated parameters of the updated data-driven model and the physics-based model; and The operation of the vapor compression cycle is controlled using an updated hybrid model.

2. The controller according to claim 1, wherein, The physics-based model includes one or a combination of dominant partial differential equations, lookup tables, and interpolation splines, discretized in the spatial and time domains, used to calculate the thermodynamic properties of the refrigerant in the vapor compression cycle.

3. The controller according to claim 2, wherein, The parameters of the physics-based model include multiple finite control volumes for discretizing the dominant partial differential equations, the geometric parameters of the vapor compression cycle, the properties of the materials used in the vapor compression cycle, and the total mass of the refrigerant.

4. The controller according to claim 1, wherein, The data-driven model includes neural networks.

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

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

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

8. The controller according to claim 1, wherein, The processor is also configured to send the observed variables of the operation of the vapor compression cycle and the digital representation of the control input to a remote server for storage.

9. The controller according to claim 8, wherein, The remote server is configured as follows: The constrained Kalman smoother is applied to the observed variables collected at multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle, in order to minimize the cost function, which includes the residuals of the state transitions predicted by the physics-based model at the multiple time instances, and the residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables. The data-driven model is updated to minimize the difference between the state estimated by applying the constrained Kalman smoother to the observed variables collected at multiple time instances and the state predicted by the physics-based model. The hybrid model is updated using the estimated parameters of the updated data-driven model and the physics-based model; as well as Send the updated hybrid model.

10. The controller according to claim 9, wherein, The processor is also configured to: Receive the updated hybrid model; and The received updated hybrid model is used to determine the unobserved variables of the vapor compression cycle.

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

12. A method for controlling the operation of a vapor compression cycle based on a hybrid kinetic model, the hybrid model comprising 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 based on the parameters of the physics-based model according to observed variables and control inputs of the vapor compression cycle, wherein the data-driven model is trained by machine learning to estimate residuals of the state transitions predicted by the physics-based model, and the method includes the following steps: A digital representation of the observed variables and control inputs of the operation of the vapor compression cycle is collected at multiple time instances; A constrained Kalman smoother is applied to the observed variables collected at multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle, so as to minimize a cost function that includes the residuals of the state transitions predicted by the physics-based model at the multiple time instances, and the residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables. The data-driven model is updated to minimize the difference between the state estimated by applying the constrained Kalman smoother to the observed variables collected at multiple time instances and the state predicted by the physics-based model. The hybrid model is updated using the estimated parameters of the updated data-driven model and the physics-based model; and The operation of the vapor compression cycle is controlled using an updated hybrid model.

13. The method according to claim 12, wherein, The physics-based model includes one or a combination of dominant partial differential equations, lookup tables, and interpolation splines, discretized in the spatial and time domains, used to calculate the thermodynamic properties of the refrigerant in the vapor compression cycle.

14. The method according to claim 13, wherein, The parameters of the physics-based model include multiple finite control volumes for discretizing the dominant partial differential equations, the geometric parameters of the vapor compression cycle, the properties of the materials used in the vapor compression cycle, and the total mass of the refrigerant.

15. The method according to claim 12, wherein, The data-driven model includes neural networks.

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

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

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

19. The method according to claim 12, wherein, The method further includes the step of sending the observed variables of the operation of the vapor compression cycle and the digital representation of the control input to a remote server for storage.

20. A non-transitory computer-readable storage medium having a program implemented thereon, the program being executable by a processor to perform a method for controlling the operation of a vapor compression cycle based on a kinetic hybrid model, the hybrid model comprising 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 based on the parameters of the physics-based model according to observed variables and control inputs of the vapor compression cycle, wherein the data-driven model is trained by machine learning to estimate residuals of the state transitions predicted by the physics-based model, and the method includes the following steps: A digital representation of the observed variables and control inputs of the operation of the vapor compression cycle is collected at multiple time instances; A constrained Kalman smoother is applied to the observed variables collected at multiple time instances to jointly estimate the parameters of the physics-based model and the state of the vapor compression cycle, so as to minimize a cost function that includes the residuals of the state transitions predicted by the physics-based model at the multiple time instances, and the residuals between the observed variables estimated by the constrained Kalman smoother at the multiple time instances and the corresponding collected observed variables. The data-driven model is updated to minimize the difference between the state estimated by applying the constrained Kalman smoother to the observed variables collected at multiple time instances and the state predicted by the physics-based model. The hybrid model is updated using the estimated parameters of the updated data-driven model and the physics-based model; and The operation of the vapor compression cycle is controlled using an updated hybrid model.

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