Control of a vapor compression system using a stochastic surrogate model.

Abstract

A controller for controlling a vapor compression system is provided. The controller is configured to estimate an operating cost of the VCS for each of the different combinations of setpoints by controlling operation of the VCS using different combinations of setpoints for different actuators of the VCS, and to calculate a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints for different actuators of the VCS and their corresponding operating costs using Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs. The probabilistic surrogate model defines at least a first second moment of the operating costs in the probabilistic mapping. The controller is further configured to select an optimal combination of setpoints that is most likely to be a global minimum in the surrogate model according to a gain function of the first second moment of the operating costs.

Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE This disclosure relates generally to vapor compression systems, and more particularly to apparatus and methods for controlling the operation of a vapor compression system. [Background technology]

[0002] Vapor compression systems, such as heat pumps, refrigeration systems, and air conditioning systems, are widely used in industrial and domestic applications. The introduction of variable speed compressors, variable position valves, and variable speed fans into the vapor compression cycle has greatly improved the operating adaptability of vapor compression systems. The efficiency of a vapor compression system can be improved by controlling the variable components of the vapor compression system. In other words, by providing control inputs to the vapor compression system, the efficiency can be improved. For example, by adjusting the speed of the compressor, the flow rate of the refrigerant can be adjusted. By changing the speed of the evaporator fan and the condenser fan, the heat transfer between the air and the heat exchanger can be modified. By changing the opening of the expansion valve, the pressure loss between the high pressure and low pressure of the vapor compression system can be affected, which affects the flow rate of the refrigerant and the corresponding superheat temperature at the evaporator outlet.

[0003] The combination of control inputs to a vapor compression system that delivers a particular amount of heat is often not unique, and various combinations of control inputs consume different amounts of energy. Therefore, it is desirable to operate the vapor compression system using a combination of control inputs that minimizes the energy and maximizes the energy efficiency of the vapor compression system.

[0004] Some approaches to maximizing energy efficiency rely on mathematical models used to represent the physics of the vapor compression system. Such model-based approaches attempt to describe the thermodynamic behavior of the vapor compression system and the effect of the control inputs of the vapor compression system on its energy consumption. In such model-based approaches, traditional analytical models are used to predict the combination of control inputs that meets the heat load requirements and minimizes energy.

[0005] However, using mathematical models in this manner to predict combinations of control inputs has drawbacks. For example, the mathematical models rely on simplifying assumptions to generate mathematically tractable representations. Such assumptions ignore important effects or do not consider facility-specific characteristics such as room size, causing the mathematical models to deviate from the actual behavior of the vapor compression system. Also, mathematical models are difficult to derive and calibrate. For example, parameters describing the operation of the components of the vapor compression system, e.g., the compressor, are experimentally determined for each type of compressor used, and the mathematical model of the vapor compression system may include many such parameters. Thus, determining the values ​​of the parameters of each mathematical model is a tedious process. Also, vapor compression systems may change over time. A mathematical model that accurately describes the operation of a vapor compression system at one time may become inaccurate at a later time due to changes in the vapor compression system, e.g., due to the accumulation of refrigerant leaking gradually or corrosion of the heat exchanger.

[0006] Some techniques aim to optimize the control inputs without using mathematical models. For example, extremum-seeking controllers (ESCs) are used to optimize the control inputs without models. However, ESCs can take hours to converge to an optimal set point. Also, because disturbances acting on the vapor compression system have faster dynamics, the optimal set point may change before the ESCs can converge. This slow convergence characteristic of ESCs prevents optimizing the performance of a vapor compression system in real time.

[0007] Furthermore, ESC numerically constructs local gradients and searches for local optima until they reach a local optimum. Such a process can be slow. For example, if the ESC control gains are too small and the basis functions being optimized contain small gradients, convergence will be slow. Conversely, if the ESC control gains are too large and the basis functions are nonlinear, the iterative solution of ESC may overshoot the optimal set point due to large gradients. Thus, ESC cannot handle nonconvex problems with highly nonlinear dynamics.

[0008] To overcome the slow convergence characteristics of the ESC, a filter is used. The filter isolates the phase effects of the transient part of the response to the perturbation. However, the design of the filter is complex and requires extensive information about the vapor compression system. Summary of the Invention

[0009] It is an object of some embodiments to provide a data-driven approach to determine an optimal combination of set points that minimizes power consumption of a vapor compression system without using an analytical model of the underlying system dynamics. Such an object can be achieved by formulating a surrogate model. It is also an object of some embodiments to provide a Bayesian optimization warm-start method that requires a surrogate model to accelerate the convergence of an extremum-seeking controller (ESC).

[0010] Vapor compression systems (VCS), such as heat pumps, refrigeration systems, and air conditioning systems, are widely used in industrial and domestic applications. The introduction of variable speed compressors, variable position valves, and variable speed fans into the vapor compression cycle has greatly improved the operational adaptability of vapor compression systems. Specifically, the combination of control inputs to a VCS that delivers a particular amount of heat is often not unique, and different combinations of control inputs may have different operating costs. For example, a VCS operating according to two different combinations of control inputs that control the state of the actuators of the VCS may deliver the same heat capacity but consume different amounts of energy. It is therefore desirable to operate the VCS with a combination of control inputs that optimizes the operating costs, e.g., a combination of control inputs that minimizes the energy consumption and / or maximizes the energy efficiency of the VCS.

[0011] Control methods that address the energy efficiency of VCSs can be divided into two categories: model-based control methods and data-driven control methods. Model-based methods attempt to describe the impact of VCS control inputs on the thermodynamic behavior and energy consumption of the VCS. In such model-based methods, traditional analytical models are used to predict the combination of control inputs that meets the heat load requirements and minimizes the energy consumption. However, analytical models for different configurations of VCSs are difficult to derive, calibrate, and update over time. For example, it is difficult to formulate analytical models for multi-zone vapor compression systems (MZ-VCSs) that include at least one compressor connected to multiple heat exchangers located in one or more indoor zones. In other words, the complexity of MZ-VCSs may preclude the use of corresponding analytical models.

[0012] In the absence of an accurate model of the dynamic system (e.g., VCS), some control methods use driving data generated by the dynamic system in real time to build a control policy that stabilizes the dynamics of the dynamic system. Designing a control policy using driving data in this way is called data-driven control. There are two types of data-driven control methods: indirect and direct. Indirect methods include building a surrogate model of the dynamic system and leveraging the surrogate model to design a controller. Direct methods include building a control policy directly based on driving data without building an intermediate model. A disadvantage of indirect methods is that they may require a large amount of data at the model building stage. Conversely, direct methods require less data, but even state-of-the-art direct control methods have difficulty handling the state and input constraints required to maintain safe operation of a closed-loop control system such as a VCS.

[0013] To that end, it is an objective of some embodiments to provide an indirect data-driven control method for closed-loop control of a VCS. Such a closed-loop control method may not suffer from the complexity of model-based control methods and direct data-driven control methods. However, to provide such indirect data-driven control, it is necessary to generate a surrogate model that can efficiently manage the operation of the VCS.

[0014] Some embodiments are based on the recognition that there are several obstacles in constructing a surrogate model for controlling the VCS. For example, constructing the surrogate model requires exploring a large and practically infinite continuous space of values ​​of the control inputs to the actuators of the VCS. To address this challenge, some embodiments replace the surrogate model of the control inputs to the actuators of the VCS with a surrogate model of the setpoints of the different actuators that the VCS control needs to achieve and / or track. In this way, the optimization of the VCS control is decoupled from the actual control, and the space of setpoints can be sampled without jeopardizing the continuous control of the different actuators of the VCS.

[0015] The surrogate model provides a mapping between various combinations of setpoints of different actuators of the VCS and the corresponding operating costs of the VCS. As used herein, a "setpoint" refers to a desired value of a variable of the VCS. The term setpoint applies to any particular value of a particular set of control signals, thermodynamic parameters, and environmental parameters. For example, the term "setpoint" may refer to a particular state of a component of the VCS. The different actuators of the VCS may include one or more of an actuator controlling a position of an expansion valve of the VCS, an indoor fan of the VCS, an outdoor fan of the VCS, and a damper actuator, etc. According to an embodiment, the operating cost corresponding to a setpoint combination is the power consumption of the VCS operating according to the setpoint combination. Additionally, the surrogate model 102 may be used to control the operation of the VCS.

[0016] Some embodiments are based on the recognition that by using various search techniques, such as gradient descent, on the surrogate model, an optimal combination of setpoints that reduces the operating cost of the VCS can be selected. However, decoupling the control from the actual VCS control slows down the dynamic response of the VCS, which creates other challenges. For example, the surrogate model needs to map the setpoints and the operating cost of the VCS in a steady state. However, it takes time (e.g., 15 minutes) for the VCS to reach a steady state corresponding to the setpoints. Also, if the optimization and control of the setpoints are decoupled, an additional feedback controller needs to be used to iteratively change the state of the actuators to the setpoints, which then requires additional time to stabilize the output of the VCS.

[0017] Therefore, separating the setpoint optimization from the actual VCS control poses the inherent challenges of (1) how to estimate the VCS operating cost in the transient time without waiting for the steady state of VCS operation, and (2) how to reduce the number of sample sets of setpoint combinations and corresponding operating costs required to build a surrogate model.

[0018] Some embodiments address these inherent challenges by constructing a probabilistic surrogate model using Bayesian optimization of combinations of setpoints and their corresponding estimated operating costs. The probabilistic surrogate model provides a mapping between various combinations of setpoints for different actuators of the VCS and a probability distribution of the corresponding operating costs. The surrogate model corresponds to a probabilistic surrogate model. The probabilistic nature of the surrogate model includes (1) uncertainties that can be incorporated into the probabilistic surrogate model and thus used to estimate the operating costs of the VCS without waiting for a steady state of VCS operation, and (2) uncertainties that can be used to guide the surrogate model construction process to account for such uncertainties in order to reduce the number of samples required to construct the surrogate model.

[0019] According to one embodiment, the probabilistic surrogate model can be constructed using a probabilistic machine learning algorithm (e.g., Gaussian process regression) that maps combinations of set points to a probability distribution of corresponding estimated operating costs, such that at least the first second moment of the operating costs is defined in the probabilistic mapping. In one embodiment, at least the first second moment can include a mean value of the operating costs and a squared variance (also referred to as a confidence range) of the operating costs. For example, for a particular combination of set points, the surrogate model provides not only a predicted value of the power consumption, but also a confidence range of the predicted power consumption (e.g., the predicted value of the power consumption is 1000W, and the confidence range is 95% that the predicted power consumption lies between 960W and 1040W).

[0020] Additionally, some embodiments aim to select the next setpoint (also referred to as "data point") combination that should be queried. As used herein, querying a setpoint (or data point) combination refers to evaluating an objective using the setpoint combination (e.g., operating a vapor compression system according to the setpoint combination). Some embodiments use a gain function of the first second moment of the operating cost to select the next setpoint combination to query.

[0021] The acquisition function uses the probabilistic mapping provided by the surrogate model to select the next setpoint combination to query. Thus, the acquisition function is used as a guide to determine the next data point to sample / query. In one embodiment, the acquisition function is maximized to select the optimal setpoint combination that is most likely to be a global minimum of the surrogate model to query and optimize the operation of the VCS. The construction of such a surrogate model and its utilization are part of Bayesian optimization. In other words, Bayesian optimization includes a surrogate model that uses Gaussian process regression to provide a probabilistic mapping, and an acquisition function that utilizes the probabilistic mapping provided by the surrogate model to direct the resulting setpoint query.

[0022] The selected optimal combination of set points is applied to a feedback controller associated with the VCS. The feedback controller is configured to determine control commands corresponding to the selected optimal combination of set points. Further, the feedback controller modifies states of actuators of the VCS according to the selected optimal combination of set points by controlling operation of the VCS based on the control commands. The feedback controller is any one or a combination of a PI controller, a PID controller, an MPC controller, or a robust controller.

[0023] Further, the vapor compression system provides a performance output (e.g., power consumption) for the optimal combination of selected set points. Further, the optimal combination of selected set points and the corresponding performance output are used to update the surrogate model using Bayesian optimization. As a result, an updated surrogate model is obtained. Further, a new optimal combination of set points for controlling the VCS is selected and the surrogate model is updated by applying the same acquisition function to the updated surrogate model. In a similar manner, the surrogate model is updated at each iteration. Such an iterative process is performed online, i.e., during real-time operation of the vapor compression system, until a termination condition is met. The termination condition may be the number of iterations. The number of iterations may be arbitrary or may be defined by the user. The iterative update of the surrogate model provides an accurate surrogate model. At each iteration, the surrogate model is updated and used in combination with the acquisition function to determine the optimal set points, so that the surrogate model in combination with the acquisition function acts as a set point optimizer.

[0024] Some embodiments are based on the realization that for a non-convex function containing multiple minima, if ESC is started in a region containing a minima, then ESC will only determine the local minimum and not the global minimum.

[0025] Some embodiments are based on the realization that for non-convex functions, determining the global minimum involves identifying a good initial guess, i.e., starting the ESC in a region where the function is locally convex and contains the global minimum. Furthermore, a gradient estimate is used within the region to identify the global minimum. Without a good initial guess, gradient-based algorithms may converge slowly and get stuck in local minima.

[0026] Some embodiments are based on the recognition that a surrogate model can be used to initiate ESC in a region that is most likely to contain a global minimum. In particular, a Bayesian Optimization (BO) framework that uses a surrogate model can be formulated to initiate ESC in a region that is most likely to contain a global minimum. The solution obtained by the BO framework can then be used as an initial guess for an Adam-accelerated extremum-seeking control that can be used to obtain the global minimum.

[0027] Some embodiments are based on the recognition that if an analytical form of the operating cost function is available, the gradient of the operating cost used by the extremum-seeking controller to adjust the optimal combination of selected set points can be easily calculated. However, for controlling a VCS, such an analytical function is usually not available. However, some embodiments are based on the recognition that instead of such an analytical function, a probabilistic surrogate model can be used to calculate the gradient of the operating cost based on successive estimates of the operating cost for the adjusted set point combination. Specifically, one embodiment includes directly obtaining the gradient of the kernel matrix of the Gaussian process for each set point. In this way, the probabilistic surrogate model is used for both the warm start of the ESC and the control of the ESC.

[0028] Optimization based on surrogate modeling (e.g., Bayesian optimization warm start ESC) offers decisive advantages. For example, machine learning methods allow building a surrogate model of the vapor compression system's input to the performance output, e.g., via Gaussian process regression, despite the noise of the measurements. However, model-free methods (e.g., ESC) estimate gradients directly from noisy data, which may lead to undesirable effects such as oscillations or divergence in the neighborhood of the optimal input. Surrogate modeling also allows learning an input-output model once a termination criterion is achieved and storing it, e.g., on the cloud, to provide a good initial guess (warm start) for the inputs in subsequent operations. Moreover, convergence rates improve with surrogate modeling via smooth regressors, since smooth optimization methods such as linear and quadratic methods can be used directly on the surrogate model.

[0029] Accordingly, one embodiment discloses a controller for controlling operation of a vapor compression system (VCS), comprising at least one processor and a memory storing instructions that, when executed by the at least one processor, cause the controller to perform the following operations: estimating an operating cost of the VCS for each of the different combinations of setpoints by controlling operation of the VCS using different combinations of setpoints of different actuators of the VCS, and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints of different actuators of the VCS and their corresponding operating costs using Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first second moment of the operating costs in the probabilistic mapping. The operations include selecting an optimal combination of setpoints that is most likely to be a global minimum in the surrogate model according to a gain function of the first second moment of the operating costs, and modifying states of the actuators of the VCS according to the corresponding setpoints in the selected optimal combination by sending the selected optimal combination of setpoints to a feedback controller.

[0030] Another embodiment discloses a method for controlling the operation of a vapor compression system (VCS). The method includes estimating an operating cost of the VCS for each of the different combinations of setpoints by controlling the operation of the VCS using different combinations of setpoints of different actuators of the VCS, and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints of different actuators of the VCS and their corresponding operating costs using Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first second moment of the operating costs in the probabilistic mapping. The method includes selecting an optimal combination of setpoints that is most likely to be a global minimum in the surrogate model according to an acquisition function of the first second moment of the operating costs, and modifying the states of the actuators of the VCS according to the corresponding setpoints in the selected optimal combination by sending the selected optimal combination of setpoints to a feedback controller.

[0031] Yet another embodiment discloses a non-transitory computer-readable storage medium embodied with a program executable by a processor to execute a method for controlling operation of a vapor compression system (VCS). The method includes estimating an operating cost of the VCS for each of the different combinations of setpoints by controlling operation of the VCS using different combinations of setpoints of different actuators of the VCS, and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints of different actuators of the VCS and their corresponding operating costs using Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first second moment of the operating costs in the probabilistic mapping. The method includes selecting an optimal combination of setpoints that is most likely to be a global minimum in the surrogate model according to an acquisition function of the first second moment of the operating costs, and modifying states of the actuators of the VCS according to the corresponding setpoints in the selected optimal combination by sending the selected optimal combination of setpoints to a feedback controller. [Brief description of the drawings]

[0032] [Figure 1A] 1 is a schematic diagram illustrating the principles used by some embodiments to separate the control of a vapor compression system. FIG. [Figure 1B] 1 is a schematic diagram illustrating principles used by some embodiments to control the operation of a vapor compression system. [Figure 1C] FIG. 13 illustrates the average predicted values ​​and confidence ranges provided by the surrogate model according to some embodiments. [Figure 1D] FIG. 2 illustrates a curve of an acquisition function according to some embodiments. [Diagram 2] 1 is a block diagram illustrating a controller for controlling operation of a vapor compression system according to some embodiments. [Diagram 3]FIG. 1 is a block diagram illustrating a Gaussian process for determining a surrogate model in accordance with some embodiments. [Figure 4] FIG. 2 is a block diagram for selecting the next data point to query according to some embodiments. [Diagram 5] FIG. 1 is a schematic diagram illustrating a time-varying extremum-seeking controller (TV-ESC) using principles of the Adam algorithm, according to some embodiments. [Figure 6] FIG. 13 illustrates adaptation of stride length based on mean and standard deviation of gradient data according to some embodiments. [Figure 7A] FIG. 2 illustrates an example convex function in accordance with some embodiments. [Figure 7B] FIG. 2 illustrates an example non-convex function in accordance with some embodiments. [Figure 8] FIG. 1 illustrates a flowchart of Bayesian optimization warm-start ESC according to some embodiments. [Figure 9A] FIG. 1 is a block diagram illustrating a multi-zone vapor compression system (MZ-VCS) in accordance with some embodiments. [Figure 9B] FIG. 1 is a block diagram illustrating a multi-zone vapor compression system (MZ-VCS) in accordance with some embodiments. [Figure 10] FIG. 1 illustrates performance results for standard time-varying ESC, Adam acceleration time-varying ESC, and Bayesian optimized warm start ESC, according to some embodiments. [Figure 11] FIG. 13 illustrates performance results of standard time-varying ESC and Bayesian optimized warm-start ESC for a composite system, according to some embodiments. [Figure 12] FIG. 1 illustrates control of a heating, ventilation, and air conditioning (HVAC system) using a controller according to some embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] 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. It will be apparent to one skilled in the art that one or more embodiments can be practiced without these specific details. Additionally, the apparatus and methods are shown as block diagrams in order to avoid obscuring the present disclosure.

[0034] As used in this specification and claims, the terms "for example," "for example," "such as," and the verbs "comprise," "have," "include," and other verb forms thereof, when used with a list of one or more components or other items, should be construed as open ended, meaning not to exclude other additional components or items from this list. The term "based on" means based at least in part on. Furthermore, it should be understood that the phrases and terms used herein are for the purpose of description and should not be considered as limiting unless specifically defined as limiting. Any headings used herein are for convenience only and have no legal or limiting effect.

[0035] FIG. 1A is a schematic diagram illustrating the principle used by some embodiments to separate the control of a vapor compression system. Vapor compression systems (VCS), such as heat pumps, refrigeration systems, and air conditioning systems, are widely used in industrial and domestic applications. The introduction of variable speed compressors, variable position valves, and variable speed fans into the vapor compression cycle has greatly improved the operational adaptability of vapor compression systems. In particular, the combination of control inputs to a VCS that delivers a particular amount of heat is often not unique, and different combinations of control inputs may have different operating costs. For example, a VCS that operates according to two different combinations of control inputs that control the state of the actuators of the VCS may be able to deliver the same heat capacity but consume different amounts of energy. Therefore, it is desirable to operate the VCS with a combination of control inputs that optimizes the operating cost, e.g., a combination of control inputs that minimizes the energy consumption and / or maximizes the energy efficiency of the VCS.

[0036] Control methods that address the energy efficiency of VCSs can be divided into two categories: model-based control methods and data-driven control methods. Model-based methods attempt to describe the impact of VCS control inputs on the thermodynamic behavior and energy consumption of the VCS. In such model-based methods, traditional analytical models are used to predict the combination of control inputs that meets the heat load requirements and minimizes the energy consumption. However, analytical models for different configurations of VCSs are difficult to derive, calibrate, and update over time. For example, it is difficult to formulate analytical models for multi-zone vapor compression systems (MZ-VCSs) that include at least one compressor connected to multiple heat exchangers located in one or more indoor zones. In other words, the complexity of MZ-VCSs may preclude the use of corresponding analytical models.

[0037] In the absence of an accurate model of the dynamic system (e.g., VCS), some control methods use operating data generated by the dynamic system in real time to construct a control policy that stabilizes the dynamics of the dynamic system. Designing a control policy using operating data in this way is called data-driven control. There are two types of data-driven control methods: indirect and direct. Indirect methods include building a surrogate model of the dynamic system and leveraging the surrogate model to design a controller. Direct methods include directly building a control policy based on operating data without building an intermediate model. A disadvantage of indirect methods is that they may require a large amount of data at the model building stage. Conversely, direct methods require less data, but even state-of-the-art direct control methods have difficulty handling the state and input constraints necessary to maintain safe operation of a closed-loop control system such as a VCS.

[0038] To that end, it is an objective of some embodiments to provide an indirect data-driven control method for closed-loop control of a VCS. Such a closed-loop control method may not suffer from the complexity of model-based control methods and direct data-driven control methods. However, to provide such indirect data-driven control, it is necessary to generate a surrogate model that can efficiently manage the operation of the VCS.

[0039] Some embodiments are based on the recognition that there are several obstacles in constructing a surrogate model for controlling the VCS. For example, constructing the surrogate model requires exploring a large and practically infinite continuous space of values ​​of the control inputs to the actuators of the VCS. To address this challenge, some embodiments replace the surrogate model 110 of the control inputs to the actuators of the VCS with a surrogate model 120 of the setpoints of the different actuators that the VCS control needs to achieve and / or track. In this way, the optimization of the VCS control is decoupled from the actual control, and the space of setpoints can be sampled without jeopardizing the continuous control of the different actuators of the VCS.

[0040] The surrogate model 102 provides a mapping between various combinations of setpoints 102a of different actuators of the VCS and the corresponding operating costs 102b of the VCS. As used herein, a "setpoint" refers to a desired value of a variable of the VCS. The term setpoint applies to any particular value of a particular set of control signals, thermodynamic parameters, and environmental parameters. For example, the term "setpoint" may refer to a particular state of a component of the VCS. The different actuators of the VCS may include one or more of an actuator controlling a position of an expansion valve of the VCS, an indoor fan of the VCS, an outdoor fan of the VCS, and a damper actuator, etc. According to an embodiment, the operating costs corresponding to the setpoint combinations are the power consumption of the VCS operating according to the setpoint combinations. Additionally, the surrogate model 102 may be used to control the operation of the VCS.

[0041] FIG. 1B is a schematic diagram illustrating the principle used by some embodiments to control the operation of a vapor compression system (VCS) 110 using a surrogate model 102. Some embodiments are based on the recognition that various search techniques, such as gradient descent, can be used on the surrogate model 102 to select an optimal combination of setpoints that reduces the operating cost of the VCS 110. However, decoupling the control from the actual VCS control slows down the dynamic response of the VCS 110, which creates other challenges. For example, the surrogate model 102 needs to map the setpoints and the operating cost of the VCS in a steady state. However, it takes time (e.g., 15 minutes) for the VCS 110 to reach a steady state corresponding to the setpoints. Also, if the optimization and control of the setpoints are decoupled, an additional feedback controller needs to be used to iteratively change the state of the actuators to the setpoints, which then requires additional time to stabilize the output of the VCS.

[0042] Therefore, separating the optimization of setpoints from the actual VCS control causes inherent problems, namely, a lot of time is consumed to wait for the steady state of VCS operation, and a large number of samples of pairs of setpoint combinations and corresponding operating costs are required to build the surrogate model 102. Therefore, an objective of some embodiments is to estimate the operating cost of the VCS in a transient time without waiting for the steady state of VCS operation, and to reduce the number of samples required to build the surrogate model 102.

[0043] According to one embodiment, this objective can be achieved by constructing a probabilistic surrogate model using Bayesian optimization of combinations of setpoints and their corresponding estimated operating costs. The probabilistic surrogate model provides a mapping between various combinations of setpoints for different actuators of the VCS 110 and a probability distribution of the corresponding operating costs. The surrogate model 102 corresponds to the probabilistic surrogate model. The probabilistic nature of the surrogate model 102 includes (1) uncertainties that can be used to estimate the operating costs of the VCS without waiting for a steady state of VCS operation, since transient measurements include uncertainties that can be incorporated into the probabilistic surrogate model, and (2) uncertainties that can be used to guide the surrogate model construction process to account for such uncertainties in order to reduce the number of samples required to construct the surrogate model 102.

[0044] In one embodiment, the operating costs corresponding to the setpoint combinations are estimated after operating the VCS 110 according to the setpoint combinations for a predetermined period of time (e.g., 5 minutes) that is insufficient for the VCS 110 to reach a steady state. In some embodiments, at least a portion of the operating costs are estimated during a transient state of the VCS 110 operating according to the corresponding setpoint combinations.

[0045] According to one embodiment, the probabilistic surrogate model can be constructed using a probabilistic machine learning algorithm (e.g., Gaussian process regression) that maps combinations of set points to a probability distribution of corresponding estimated operating costs, such that at least the first second moment of the operating costs is defined in the probabilistic mapping. In one embodiment, at least the first second moment can include a mean value of the operating costs and a squared variance (also referred to as a confidence range) of the operating costs. For example, for a particular combination of set points, the surrogate model 102 provides not only a predicted value of the power consumption, but also a confidence range of the predicted power consumption (e.g., the predicted value of the power consumption is 1000 W, and the confidence range is 95% that the predicted power consumption lies between 960 W and 1040 W).

[0046] 1C is a diagram illustrating the average prediction and confidence range provided by the surrogate model 102 according to some embodiments. The points 120 represent the samples / observations. The curve 116 represents the average prediction and the shaded area 118 represents the confidence range.

[0047] Additionally, some embodiments aim to select the next setpoint (also referred to as "data point") combination that should be queried. As used herein, querying a setpoint (or data point) combination refers to evaluating an objective using the setpoint combination (e.g., operating the vapor compression system 110 according to the setpoint combination). Some embodiments use a first second moment acquisition function 104 of the operating cost to select the next setpoint combination to query.

[0048] 1D illustrates a curve 124 of the acquisition function 104 according to some embodiments. The acquisition function 104 uses the probabilistic mapping provided by the surrogate model 102 to select the next combination of set points (i.e., data points) to query. For example, if the surrogate model 102 provides that at a first data point (not previously queried), the power consumption may be at least 900 W with a confidence range of 85%, and at a second data point (also not previously queried), the power consumption may be at least 990 W with a confidence range of 95%, then the first data point should be queried before querying the second data point, even though the first data point is in a low confidence range, since 900 W is likely to be the optimal power consumption of the vapor compression system 110. Thus, the acquisition function 104 is used as a guide to determine which data point to sample / query next.

[0049] In one embodiment, the acquisition function 104 is maximized to select the optimal combination of set points 106 that are most likely to be the global minimum 122 of the surrogate model 102 to query and optimize the operation of the VCS 110. The construction of such a surrogate model and its utilization is part of Bayesian optimization 114. In other words, the Bayesian optimization 114 includes a surrogate model 102 that uses Gaussian process regression to provide a probabilistic mapping, and an acquisition function 104 that utilizes the probabilistic mapping provided by the surrogate model 102 to direct the query of the resulting set points.

[0050] The optimal combination of the selected setpoints 106 is applied to a feedback controller 108 associated with the VCS 110. The feedback controller 108 is configured to determine a control command corresponding to the optimal combination of the selected setpoints 106. Furthermore, the feedback controller 108 modifies the state of the actuators of the VCS 110 according to the optimal combination of the selected setpoints 106 by controlling the operation of the VCS 110 based on the control command. Specifically, in one embodiment, the feedback controller 108 measures the output (or process variable) of the VCS 110. The measurement is applied to the feedback controller 108 as a feedback signal 130. The feedback controller 108 calculates the difference between the optimal combination of the selected setpoints 106 and the feedback signal 130 as an error signal. The feedback controller 108 uses control parameters such as a proportional gain, an integral term, and / or a derivative term. By applying the control parameters to the error signal, the VCS 110 can determine an input for driving the process variable or the VCS output according to the optimal combination of the selected setpoints 106. The feedback controller 108 is one or a combination of a PI controller, a PID controller, an MPC controller, or a robust controller.

[0051] Further, the vapor compression system 110 provides a performance output 112 (e.g., power consumption) of the optimal combination of the selected setpoints 106. Further, the optimal combination of the selected setpoints 106 and the corresponding performance output 112 are used to update the surrogate model 102 using Bayesian optimization. As a result, an updated surrogate model is obtained. Further, by applying the same acquisition function 104 to the updated surrogate model, a new optimal combination of setpoints for controlling the VCS 110 is selected and the surrogate model 120 is updated. In a similar manner, the surrogate model 102 is updated at each iteration. Such an iterative process is performed online, i.e., during real-time operation of the vapor compression system 110, until a termination condition is met. The termination condition may be a number of iterations. The number of iterations may be arbitrary or may be defined by a user.

[0052] Iterative updates of the surrogate model 102 result in an accurate surrogate model. At each iteration, the surrogate model 102 is updated and used in combination with the acquisition function 104 to determine optimal settings, so that the surrogate model 102 in combination with the acquisition function 104 acts as a set-point optimizer.

[0053] 2 is a block diagram illustrating a controller 200 for controlling the operation of the vapor compression system 110, according to some embodiments. The controller 200 includes a number of interfaces, which can connect the controller 200 to other systems and devices. For example, a network interface controller (NIC) 214 is configured to connect the controller 200 to a network 216 via a bus 212. The controller 200 can receive sensor measurements 218 indicative of one or more of an indoor fan speed, an outdoor fan speed, an expansion valve position, a compressor speed, and a performance output 112 of the vapor compression system 110, etc., via a wireless or wired network 216. Additionally or alternatively, the sensor measurements 218 may be received via an input interface 202. The controller 200 can monitor the operation of the components of the vapor compression system 110 based on the sensor measurements.

[0054] The controller 200 includes a processor 204 configured to execute stored instructions and a memory 206 that stores instructions executable by the processor 204. The processor 204 may be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 206 may include a random access memory (RAM), a read-only memory (ROM), a flash memory, or any other suitable memory system. The processor 204 is connected to one or more input and output devices via a bus 212. In addition, the controller 200 includes a storage device 208 configured to store different modules that store instructions executable by the processor 204. The storage device 208 may be implemented using a hard drive, an optical drive, a thumb drive, a drive array, or any combination thereof.

[0055] The storage device 208 is configured to store the surrogate model 102, which provides a probabilistic mapping between various combinations of setpoints for different actuators of the VCS and their corresponding operating costs. The storage device 208 is configured to store the acquisition function 104. The acquisition function 104 is used to select the next combination of different operating parameters of the vapor compression system 110 to query / sample. In some embodiments, the acquisition function 104 is used to select the optimal combination of setpoints that is most likely to be a global minimum in the surrogate model 102.

[0056] In some embodiments, the processor 204 is configured to estimate the operating cost of the VCS 110 for each of the different combinations of setpoints by controlling the operation of the VCS 110 using different combinations of setpoints for different actuators of the VCS 110, and to calculate a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints for different actuators of the VCS 110 and their corresponding operating costs using Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs. The probabilistic surrogate model defines at least a first second moment of the operating costs in the probabilistic mapping. The processor 204 is further configured to select an optimal combination of setpoints that is most likely to be a global minimum in the surrogate model according to the acquisition function 104 of the first second moment of the operating costs. The processor 204 is further configured to modify the state of the actuators of the VCS 110 according to the corresponding setpoints in the selected optimal combination by transmitting the selected optimal combination of setpoints to the feedback controller 108 via the output interface 220. The feedback controller 108 is one or a combination of a PI controller, a PID controller, an MPC controller, or a robust controller.

[0057] In one embodiment, the processor 204 is further configured to estimate an operating cost for an optimal combination of the selected settings 106, and update the surrogate model 102 using Bayesian optimization with the optimal combination of the selected settings and the corresponding estimated operating cost. In some embodiments, the processor 204 is further configured to recursively update the surrogate model 102 with the newly selected optimal combination of the settings according to an acquisition function applied to the updated surrogate model until a termination condition is met.

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[0064] Alternatively, in some embodiments, the surrogate model 102 may be determined by neural process regression or other variants of Bayesian neural networks and / or machine learning.

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[0069] At block 404, the EI acquisition function for each random sample is maximized. At block 406, the sample maximum is selected as the data point to be queried.

[0070] To that end, the acquisition function (e.g., Equation (5)) provides the data points to be queried. By querying at the selected data points, the corresponding stationary power is obtained. Some embodiments are based on the recognition that the accuracy of the surrogate model 102 can be improved by updating / retraining the surrogate model 102 with the data points determined from the acquisition function. In particular, the hyper-parameter set is recalculated using the data samples and data points selected using the acquisition function.

[0071] Similarly, in the next iteration, the acquisition function (e.g., Equation (5)) can be used with the updated / retrained surrogate model 102 to select another data point to query. Furthermore, the updated / retrained surrogate model 102 can be updated / retrained again using the other selected data points. Such iterations of updating the surrogate model 102 are performed until a termination condition is met. After a suitable number of iterations, the surrogate model 102 learns the underlying function J.

[0072] Alternatively, in some implementations, an improved probability obtaining function or an upper confidence bound obtaining function can be used to select the next data point to query. Stride length adjustment based on gradient estimation

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[0074] Some embodiments are based on the recognition that adaptive gradient algorithms such as Adam, stochastic gradient descent, Adagrad, and RMSprop exploit not only the gradient but also the corresponding statistics to provide a robust estimation of the gradient. Also, the adaptive gradient algorithm includes a momentum-based mechanism to quickly identify the stride length to improve the convergence rate. The adaptive gradient algorithm is typically used to train neural networks. However, some embodiments are based on the recognition that the adaptive gradient algorithm can be used in extremum seeking control (ESC) to automatically adjust the stride length based on the smoothness of the function J in a local neighborhood. To that end, one embodiment aims to formulate Adam accelerated extremum seeking control by incorporating the Adam algorithm into extremum seeking control.

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[0085] FIG. 7A illustrates an exemplary convex function 700, according to some embodiments. In the convex function 700, a local minimum can be achieved by starting the ESC anywhere in the domain 702. FIG. 7B illustrates an exemplary non-convex function 704, according to some embodiments. In the non-convex function 704, which includes multiple local minima 710a and 710b, the determination of the global minimum depends on the domain in which the ESC is started. For example, if the ESC is started in the domain 706, the ESC determines the global minimum, i.e., the local minimum 710a. However, if the ESC is started in the domain 708, the ESC may only determine the local minimum 710b (i.e., the local minimum) and not the global minimum.

[0086] Some embodiments are based on the realization that when function J is a non-convex function, determining the global minimum involves identifying a good initial guess, i.e., starting the ESC in a region where function J is locally convex and contains the global minimum. Furthermore, a gradient estimate is used within the region to identify the global minimum. Without a good initial guess, the gradient-based algorithm may converge slowly and get stuck in a local minimum.

[0087] Some embodiments are based on the recognition that the surrogate model 102 can be used to initiate the ESC in regions (e.g., region 706) that are most likely to contain a global minimum. In particular, some embodiments are based on the recognition that the stochastic nature of the surrogate model 102 and its ability to estimate the operating costs of the transient state of the VCS being controlled may not adequately capture the dynamics of the VCS in selecting the optimal combination of set points. To that end, some embodiments warm start the ESC, which explores the VCS dynamics in a data-driven manner, with the optimal combination of set points selected according to the stochastic model. Advantageously, the ESC can optimize the control inputs without a model. However, the ESC can take several hours to converge to the optimal set points. Such slow convergence characteristics of the ESC present a barrier to a real-time optimization solution of the performance of a vapor compression system that can be overcome with a warm-up according to various embodiments.

[0088] 8 shows a flow chart of a Bayesian optimized warm start ESC according to some embodiments. The Bayesian optimized warm start ESC includes a Bayesian optimized warm start mechanism for providing an initial guess for the ESC.

[0089] In step 800, an initial set of set points is sampled (800) in an allowable space of set points. The initial set of set points, together with subsequent set points and corresponding steady-state power outputs, form a data set. In step 802, a surrogate model is determined based on the data set. In step 804, a next best set point is selected using an acquisition function. In some implementations, the obtained next best set point may correspond to a combination of parameters that is most likely to be a global minimum of the surrogate model. Steps 802 and 804 are described in detail in FIGS. 3 and 4.

[0090] In step 806, the obtained next best setting is applied to the ESC as an initial guess. Multi-Zone Vapor Compression System

[0091] Some embodiments are based on the recognition of the advantages of multi-zone vapor compression systems (MZ-VCS) for controlling residential and commercial facilities. In one embodiment, the VCS 110 may correspond to an MZ-VCS. The MZ-VCS includes at least one compressor connected to multiple heat exchangers arranged in one or more indoor zones. The MZ-VCS is described in detail below with reference to Figures 9A and 9B.

[0092] 9A and 9B are block diagrams illustrating a multi-zone vapor compression system (MZ-VCS) according to some embodiments. The MZ-VCS includes a compressor and a set of heat exchangers configured to control the environment of a set of zones. At least one heat exchanger is disposed in each zone. For example, in one embodiment of FIG. 9A, each zone 925 or 935 corresponds to a room in a building allowing the MZ-VCS to provide cooling or heating to multiple zones simultaneously. In an alternative embodiment shown in FIG. 9B, multiple heat exchangers are disposed in one room or zone 937 in a building, allowing the MZ-VCS to provide cooling or heating to different portions of the room.

[0093] In this disclosure, for clarity, a two zone MZ-VCS has been described, but it should be understood that any number of zones may be used, subject to the physical limitations of refrigerant line length, capacity, compressor pump power, and building codes. If the zone is an indoor zone, e.g., a room or portion of a room, then the heat exchanger is an indoor heat exchanger.

[0094] The compressor 910 receives the low pressure refrigerant in a vapor state and performs mechanical work, increasing the pressure and temperature of the refrigerant. Depending on the configuration of the four-way valve 909, the hot refrigerant can be routed to either the outdoor heat exchanger (in which case the system is operating in a cooling mode to transfer heat to the exterior environment and provide useful cooling) or the indoor heat exchanger (in which case the system is operating in a heating mode to transfer heat to one or more indoor zones and provide useful heating).

[0095] For clarity and simplicity of the ensuing discussion, we will generally consider the cooling mode, i.e., the compressor is connected to the rest of the vapor compression system as shown by the solid lines at the four-way valve 909. It should be understood that by appropriately substituting the condenser with an evaporator and the condensing temperature with an evaporating temperature, a similar discussion can be applied to a system operating in a heating mode.

[0096] In cooling mode, high temperature, high pressure refrigerant flows to an exterior heat exchanger 915 and an associated optional fan 916 blows air through the exterior heat exchanger 915. Heat is transferred from the refrigerant to the air, causing the refrigerant to condense from a vapor to a liquid.

[0097] The phase change process in which the vapor refrigerant condenses from a saturated vapor to a two-phase mixture of both liquid and vapor and to a saturated liquid is isothermal in an idealized description of the vapor compression cycle, i.e., the phase change process occurs at a constant temperature and therefore there is no apparent change in temperature. However, when additional heat is removed from the saturated liquid, the temperature of the saturated liquid decreases by an appropriate amount. In this case, the refrigerant is called a "subcooled" refrigerant. The subcooling temperature is the difference between the temperature of the subcooled refrigerant and the temperature of the saturated liquid refrigerant calculated at the same pressure.

[0098] Hot liquid refrigerant leaves the outdoor heat exchanger 915 and is split by a manifold 917 for distribution to the connected indoor zones 925, 935 or 937. Separate expansion valves 926, 936 are connected to the inlet manifold. These expansion valves are restrictive elements and significantly reduce the pressure of the refrigerant. Because the pressure is rapidly reduced without substantial heat exchange in the expansion valve, the temperature of the refrigerant is significantly reduced and is referred to as "adiabatic" in an idealized description of the vapor compression cycle. The refrigerant leaving the expansion valve is a low pressure, low temperature two-phase mixture of liquid and vapor.

[0099] The two-phase refrigerant enters the indoor heat exchangers 920, 930 and associated fans 921, 931 blow air through the heat exchangers 920, 930, respectively. Heat 922, 932, representing the heat load from the indoor space, is transferred from the zone to the refrigerant, causing it to evaporate from a two-phase mixture of liquid and vapor to a saturated vapor state.

[0100] The phase change process by which a refrigerant evaporates from a saturated vapor to a two-phase mixture of both liquid and vapor is isothermal in an idealized description of the vapor compression cycle, i.e., it occurs at a constant temperature and therefore without any apparent change in temperature. However, when additional heat is added to the saturated vapor, the temperature of the saturated vapor increases by an appropriate amount. In this case, the refrigerant is referred to as a "superheated" refrigerant. The superheat temperature is the difference between the temperature of the superheated refrigerant vapor and the saturated vapor temperature calculated at the same pressure.

[0101] The low pressure refrigerant vapor exiting the indoor heat exchanger joins a common flow path at the outlet manifold 918. Finally, the low pressure refrigerant vapor returns to the compressor 910 and the cycle repeats.

[0102] The primary actuators in the MZ-VCS include the compressor 910, the outdoor heat exchanger fan 916, the indoor heat exchanger fans 921, 931, and the expansion valves 926, 936. In some systems, the compressor speed may be fixed at one or more predetermined speeds or may be continuously varied. Similarly, the outdoor heat exchanger fan 916 may be fixed at a constant speed or may be continuously varied. In some configurations, the indoor heat exchanger fans 921, 931 may be determined by the MZ-VCS controller or its speed may be determined by the occupant when the occupant wishes to directly control the airflow in the room. The expansion valve is controlled by the controller 200, e.g., electronically controlled, to vary continuously from a fully closed position to a fully open position, including all possible intermediate positions. Some MZ-VCS implementations replace the electronically controlled expansion valve with a series combination of an on / off controlled solenoid valve and a separate variable opening valve to precisely control the flow rate.

[0103] The high and low refrigerant pressures are determined by thermodynamic conditions such as the combination of outdoor air temperature, indoor air temperature, compressor speed, and valve opening. Although each of the expansion valves 926 and 936 can be set to a different opening, the overall high and low pressures are determined by the combined pressure drop of the expansion valves placed in parallel in the refrigerant circuit. Also, because there is no pressure reducing element between the indoor heat exchangers 920, 930 and the outlet manifold 918, all of the heat exchangers operate at substantially the same pressure. Furthermore, due to the isothermal nature of phase change discussed above, all of the indoor heat exchangers are constrained to evaporate at the same temperature.

[0104] According to one embodiment, the heating or cooling capacity of the indoor heat exchangers 920 and 930 can be regulated by duty cycling each heat exchanger between "on" and "off" operating modes. When the inlet valve controlling the refrigerant flow is closed, or alternatively when the compressor 910 pumping the refrigerant through the system is stopped, the heat exchangers 920 and 930 are off and do not provide cooling or heating. When the inlet valve is open and the compressor 910 is running, the heat exchangers 920 and 930 are on and the heat exchangers 920 and 930 in the indoor zones 925 and 935 operate at full thermal capacity. The controller determines the mode switch based on the difference between the indoor zone temperature and the desired indoor zone temperature.

[0105] However, switching heat exchangers on and off, especially in an MZ-VCS where zone heat exchangers can be switched on and off independently of one another, has been found to be energetically inefficient and to reduce occupant comfort, resulting in continuous fluctuations in the system's output, e.g., zone temperatures and heat exchanger temperatures. Thus, a need exists for a control system and method for smoothly controlling the thermal capacity of heat exchangers, such as those in an MZ-VCS.

[0106] Some embodiments are based on the recognition that the probabilistic surrogate model 102 can be advantageously used to reduce the complexity of controlling the MZ-VCS. Specifically, in an MZ-VCS with a large number of settings, brute-force sampling of the settings can result in extra computational consumption and long adjustment times. The sampling efficiency is significantly reduced by using a Bayesian optimization algorithm that can balance exploration and exploitation via the probabilistic surrogate model 102. According to some embodiments, an MZ-VCS with a large number of settings requires a scalable probabilistic machine learning algorithm. In some embodiments, the scalable probabilistic machine learning algorithm can be based on a Bayesian deep neural network or a variational autoencoder. result

[0107] FIG. 10 shows performance results of standard time-varying ESC, Adam accelerated time-varying ESC, and Bayesian optimized warm-start ESC, according to some embodiments. To evaluate the performance, a system including a vapor compression cycle with a feedback controller is considered. The feedback controller is configured to regulate the cooling capacity to a set value by controlling the compressor speed. Such a system facilitates the study of optimization methods for the vapor compression cycle without requiring the slower and lower range thermal dynamics of the living space. Furthermore, by applying the optimization methods (e.g., standard time-varying ESC, Adam accelerated time-varying ESC, and Bayesian optimized warm-start ESC), the inputs of the system (e.g., expansion valve position, indoor fan speed (IFS), outdoor fan speed (OFS)) are adjusted to optimize the power consumption.

[0108] As a case study, a PI loop is selected to regulate the cooling capacity of a vapor compression cycle to 2 kW, and an optimization method is applied to determine the optimal values ​​of the expansion valve position and the fan speed. The PI gains are tuned offline (i.e., in advance). The PI gains are unknown to the setpoint regulating mechanism.

[0109] In the power plot 1000, 1002 represents the standard time-varying ESC, 1004 represents the Adam Acceleration Time-Varying ESC, and 906 represents the Bayesian Optimized Warm Start ESC (Hybrid). From the power plot 1000, it can be seen that the standard time-varying ESC 1002 and the Adam Acceleration Time-Varying ESC 1004 show slower convergence compared to the Bayesian Optimized Warm Start ESC 906. The Bayesian Optimized Warm Start ESC 906 converges to a steady cycle power of 0.335 kW within 3 hours, while the other algorithms require more than 10 hours to approach minimum cycle power.

[0110] According to one embodiment, the difference in steady cycle power is caused by the difference in the optimal LEV (linear expansion valve) position determined by the standard time-varying ESC 1002, the Adam acceleration time-varying ESC 1004, and the Bayesian optimization warm start ESC 906. The standard time-varying ESC 1002 and the Adam acceleration time-varying ESC 1004 converge to a steady LEV position of about 300 counts because they depend on the initial LEV position. Meanwhile, the Bayesian optimization warm start ESC 906 determines that a steady value of 260 counts results in significantly better energy efficiency. The Bayesian optimization warm start ESC 906 includes a search phase, and at the end of the search phase, the BO warm start results in a local set of effective tuning parameters. However, local gradient information can still be utilized online, so that the power consumption after the Bayesian optimization warm start can be further reduced. Furthermore, it can be seen from plots 1008 and 1010 that although the capacity setpoint was achieved through the setpoint adjustment procedure, the compressor frequency associated with the LEV position was not maintained at the intended 40 Hz, but rather gradually decreased to approximately 17 Hz.

[0111] Figure 11 shows performance results of standard time-varying ESC and Bayesian optimized warm-start ESC for a combined system, according to some embodiments. The combined system includes the same cycle as described in the description of Figure 10, but includes two feedback loops: one that regulates room temperature to a setpoint via control of compressor speed, and one that regulates the evaporator superheat temperature (CITE) to a setpoint of 5°C via control of expansion valve position. The combined system is run on a 27m 3 A cubic room model with a volume of 1.0 m and a 20 cm thick exterior wall with thermal properties of wood is connected, and the exterior and interior heat transfer coefficients are 1.5 Wm -2 and 3.5Wm -2The combined system is operated in a commercial office building that is operational during the day and vacant at night. The resulting sensible and latent loads for the space are set to 3200W and 800W between 8AM and 6PM, and 2000W and 100W at other times. The ambient temperature is assumed to vary sinusoidally between 24°C and 40°C over a 24-hour period, with a peak at 2PM.

[0112] Additionally, we consider two adjustable inputs: indoor fan speed (IFS) and outdoor fan speed (OFS). Both adjustable inputs are assumed to be bounded, e.g., the bounds of IFS are known to be [200,500] rpm and the bounds of OFS are known to be [500,900] rpm. Standard time-varying ESC and Bayesian optimized warm-start ESC assume that no a priori information is given about the temperature or thermal profile, but that the heat load can be measured at the current time.

[0113] The Bayesian optimized warm start ESC uses the first 18 hours to collect data for each load mode, i.e., when the thermal load is high and when the thermal load is low. For each load mode, a surrogate model of energy efficiency (e.g., surrogate model 102) and the corresponding optimal IFS-OFS pair are learned. After 18 hours, the Adam accelerated time-varying ESC takes over and gradient-based updates are used for both the IFS and the OFS. Performance results show that the standard time-varying ESC exhibits limited adaptability. For example, the IFS fluctuates in a narrow range of 290-310 rpm, and the OFS stagnates. Conversely, in the Bayesian optimized warm start ESC, the surrogate model can quickly reset the ESC position, improving energy efficiency. Also, the Bayesian optimized warm start ESC provides improvements over several days, e.g., the power output decline after 48 hours (approximately 60-70 hours) is more noticeable than after 24-48 hours.

[0114] 12 illustrates control of a heating, ventilation, and air conditioning (HVAC) system 1210 using the controller 200 according to some embodiments. An "HVAC" system refers to any heating, ventilation, and air conditioning (HVAC) system that implements a vapor compression cycle. HVAC systems 1210 encompass a very wide range of systems, ranging from systems that provide only outdoor air to the building occupants, to systems that control only the temperature of the building, or systems that control temperature and humidity.

[0115] HVAC system 1210 is configured to condition room 1200. Room 1200 is occupied by occupants 1202, 1204, 1206, and 1208. Arrows 1214 represent air supplied by HVAC system 1210 to condition room 1200. A controller (e.g., controller 200) determines an optimal combination of set points that minimizes power consumption of HVAC system 1210 based on a surrogate model (e.g., surrogate model 102).

[0116] The optimal combination of set points is then input to a feedback controller 1212 associated with the HVAC system 1210. The feedback controller 1212 generates control commands based on the optimal combination of set points. The feedback controller 1212 controls the HVAC system 1210 according to the control commands, thereby minimizing power consumption of the HVAC system 1210.

[0117] Optimization based on surrogate modeling (e.g., Bayesian optimization warm start ESC using surrogate model 102) offers crucial advantages. For example, machine learning methods allow building a surrogate model of the vapor compression system's input to the performance output, e.g., via Gaussian process regression, despite noise in the measurements. However, model-free approaches (e.g., ESC) estimate gradients directly from noisy data, which can lead to undesirable effects such as oscillations or divergence around the optimal input. Surrogate modeling also learns an input-output model once a termination criterion is achieved and stores it, e.g., on the cloud, to provide a good initial guess (warm start) for the inputs in subsequent operations. Moreover, convergence rates improve with surrogate modeling via smooth regressors, since smooth optimization methods such as linear and quadratic methods can be used directly on the surrogate model.

[0118] The above description provides exemplary embodiments only and is not intended to limit the scope, application, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes in the function and arrangement of elements are contemplated without departing from the spirit and scope of the subject matter set forth in the appended claims.

[0119] In the above description, specific details are described to provide a thorough understanding of the embodiments. However, those skilled in the art can understand that the embodiments can 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 diagrams so as not to obscure the embodiments in unnecessary detail. Also, well-known processes, structures, and techniques may be shown without unnecessary detail so as not to obscure the embodiments. Moreover, like reference numbers and names in the various drawings refer to like elements.

[0120] Also, each embodiment 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. Although a flowchart describes operations as a sequential process, many operations may be performed in parallel or simultaneously. Also, the order of operations may be changed. A process may be terminated when the operations of a process are completed, but the process may include additional steps not discussed or shown. Moreover, not all operations within a specifically described process need be included in every embodiment. A process may be a method, a function, a procedure, a subroutine, a subprogram, etc. When a process is a function, the termination of the function corresponds to the return of the function to the calling function or to the main function.

[0121] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, manually or automatically. The manual or automated implementation may be implemented, or at least assisted, by machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented by software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine-readable medium. A processor may perform the necessary tasks.

[0122] The various methods or steps outlined herein may be coded as software executable on one or more processors employing any one of a variety of operating systems or platforms. Moreover, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and 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 in various embodiments as desired.

[0123] The embodiments of the present disclosure may be embodied as methods, which are provided as examples. The operations performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed that perform operations in a different order than those performed sequentially in the exemplary embodiments, and that may include performing some operations simultaneously. Although the present disclosure has been described with reference to certain preferred embodiments, it should be understood that various other adaptations and modifications may be made within the spirit and scope of the present disclosure. Accordingly, the appended claims are intended to cover all such variations and modifications that are within the true spirit and scope of the present disclosure.

Claims

1. A control device for controlling operation of a vapor compression system (VCS), comprising: At least one processor; and a memory storing instructions that, when executed by the at least one processor, cause the controller to perform the following operations: The operation includes: controlling the operation of the vapor compression system using different combinations of set points of different actuators of the vapor compression system to estimate a cost of operating the vapor compression system for each of the different combinations of set points; and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints for different actuators of the vapor compression system and their corresponding estimated operating costs using a Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first two moments of the operating costs in the probabilistic mapping; The operation includes: selecting an optimal combination of settings that is most likely to be a global minimum in the probabilistic surrogate model according to a gain function of the first two moments of the operating cost; transmitting the selected optimal combination of set points to a feedback controller to vary states of the actuators of the vapor compression system according to corresponding set points in the selected optimal combination; implementing an extremum-seeking controller that perturbs inputs to the feedback controller starting from the optimal combination of selected set points, and adjusting the optimal combination of selected set points based on a gradient in the operating costs caused by the perturbations; The processor estimates the gradient of the operating cost caused by the perturbation by mapping perturbation values ​​of the optimal combination of the selected set points to values ​​of the operating cost on the stochastic surrogate model according to the acquisition function.

2. 2. The control device of claim 1, wherein the operating cost for a combination of set points is estimated after operating the vapor compression system according to the combination of set points for a predetermined time insufficient for the vapor compression system to reach a steady state.

3. The controller of claim 1 , wherein at least a portion of the operating costs are estimated during a transient condition of the vapor compression system operating according to the corresponding setpoint combinations.

4. 2. The control device of claim 1, wherein the processor is further configured to estimate the operating cost for an optimal combination of the selected set points and update the probabilistic surrogate model using the Bayesian optimization with the optimal combination of the selected set points and the corresponding estimated operating cost.

5. 5. The control device of claim 4, wherein the processor is further configured to recursively update the probabilistic surrogate model with an optimal combination of newly selected settings according to the acquisition function applied to the updated probabilistic surrogate model until a termination condition is met.

6. The control device of claim 1 , wherein the Bayesian optimization determines the probabilistic surrogate model using any one or a combination of Gaussian process regression, neural process regression, and machine learning.

7. The controller of claim 1 , wherein the Bayesian optimization includes an acquisition function that utilizes the probabilistic mapping provided by the probabilistic surrogate model to direct resulting set point queries.

8. 2. The control device of claim 1, wherein the vapor compression system is a multi-zone vapor compression system (MZ-VCS) including at least one compressor connected to multiple heat exchangers disposed in one or more indoor zones.

9. The control device of claim 1 , wherein the operating cost corresponding to the setpoint combination is a power consumption of the vapor compression system operating according to the setpoint combination.

10. The control device of claim 1 , wherein the feedback controller is any one or a combination of a PI controller, a PID controller, an MPC controller, or a robust controller.

11. 1. A method for controlling operation of a vapor compression system (VCS), comprising: controlling the operation of the vapor compression system using different combinations of set points of different actuators of the vapor compression system to estimate a cost of operating the vapor compression system for each of the different combinations of set points; and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints for different actuators of the vapor compression system and their corresponding estimated operating costs using a Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first two moments of the operating costs in the probabilistic mapping; The method comprises: selecting an optimal combination of settings that is most likely to be a global minimum in the probabilistic surrogate model according to a gain function of the first two moments of the operating cost; transmitting the selected optimal combination of set points to a feedback controller to vary states of the actuators of the vapor compression system according to corresponding set points in the selected optimal combination; implementing an extremum-seeking controller that perturbs inputs to the feedback controller starting from the optimal combination of selected set points, and adjusting the optimal combination of selected set points based on a gradient in the operating costs caused by the perturbations; and estimating the gradient of the operating cost caused by the perturbation by mapping perturbation values ​​of the optimal combination of the selected set points to values ​​of the operating cost on the probabilistic surrogate model according to the acquisition function.

12. 1. A non-transitory computer readable storage medium having embodied thereon a program executable by a processor to perform a method for controlling operation of a vapor compression system (VCS), the method comprising: controlling the operation of the vapor compression system using different combinations of set points of different actuators of the vapor compression system to estimate a cost of operating the vapor compression system for each of the different combinations of set points; and calculating a probabilistic surrogate model that provides a probabilistic mapping between various combinations of setpoints for different actuators of the vapor compression system and their corresponding estimated operating costs using a Bayesian optimization of the setpoint combinations and their corresponding estimated operating costs, the probabilistic surrogate model defining at least a first two moments of the operating costs in the probabilistic mapping; The method comprises: selecting an optimal combination of settings that is most likely to be a global minimum in the probabilistic surrogate model according to a gain function of the first two moments of the operating cost; transmitting the selected optimal combination of set points to a feedback controller to vary states of the actuators of the vapor compression system according to corresponding set points in the selected optimal combination; implementing an extremum-seeking controller that perturbs inputs to the feedback controller starting from the optimal combination of selected set points, and adjusting the optimal combination of selected set points based on a gradient in the operating costs caused by the perturbations; and estimating the gradient of the operating cost caused by the perturbation by mapping perturbation values ​​of the optimal combination of the selected set points to values ​​of the operating cost on the probabilistic surrogate model according to the acquisition function.

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