Improved water chilling unit performance prediction method based on physical information neural network

Abstract

The invention provides a water chilling unit performance prediction method based on an improved physical information neural network. The method comprises the following steps: step 10, constructing a neural network model; step 20, selecting to obtain a neuron variable, and embedding the neuron variable into the neural network model as a physical neuron to obtain a physical neuron embedded physical information neural network model; step 30, introducing a loss function into the physical neuron embedded physical information neural network model; 40, carrying out data balance processing on the original data set, and screening to obtain a training set; step 50, utilizing the training set to train the physical neuron embedded physical information neural network model to obtain a water chilling unit performance prediction model; and step 60, predicting the performance of the water chilling unit by using the water chilling unit performance prediction model. According to the improved water chilling unit performance prediction method based on the physical information neural network, high-precision prediction of the performance of the water chilling unit is achieved, and the generalization ability and the model interpretability are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of integrated physics knowledge data-driven building energy management. Specifically, it relates to a method for predicting the performance of a chiller based on an improved physics-informed neural network. Background Art

[0002] As a key component in the building energy system, the accuracy of chiller performance prediction is of great significance for reducing building energy consumption. With the development of artificial intelligence technology, data-driven modeling methods have gradually become the mainstream of chiller performance prediction. Among them, physics-informed neural networks have shown good prospects in improving the generalization ability and physical consistency of chiller performance prediction models due to the integration of data-driven and physical constraints. However, existing physics-informed neural networks mainly rely on imposing physical residual penalties in the loss function as soft constraints, which are difficult to ensure that the model strictly follows the complex physical laws of chillers. At the same time, there is a competitive relationship between multiple physical loss terms, which easily leads to instability in the training process and affects the convergence effect of the model. In addition, this type of method usually only constrains the physical relationship between input and output variables, and it is difficult to effectively capture the complex coupling mechanism between multiple physical variables inside the chiller. More importantly, the structure of the physics-informed neural network still retains the "black box" characteristic, and its internal parameters lack clear physical meanings. Affected by the above factors, existing physics-informed neural networks still face challenges such as insufficient generalization ability and poor interpretability, and it is difficult to accurately predict the performance of chillers under operating conditions beyond the training data distribution. This will not only lead to problems such as reduced energy efficiency and lagged load response in some operating conditions, but may also cause operation strategy failures, frequent equipment starts and stops, and even fault alarms, thereby increasing energy waste and maintenance costs and affecting the stability and reliability of the building energy system. At the same time, the model lacks the ability to reveal the internal physical mechanism of performance changes, making chiller fault identification and performance optimization more complex and reducing users' trust in the model prediction results. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for predicting the performance of a chiller based on an improved physics-informed neural network, realizing high-precision prediction of chiller performance and improving the generalization ability.

[0004] To solve the above technical problem, the present invention adopts the following technical solutions: The present invention provides a method for predicting the performance of a chiller based on an improved physics-informed neural network, including the following steps: Step 10, constructing a neural network model according to the relationships between various physical variables in the chiller; Step 20: Select neuron variables from all the physical variables of the chiller, and embed the neuron variables as physical neurons into the neural network model to obtain a physical neuron-embedded physical information neural network model; Step 30: Construct control equations between neuron variables, and introduce a loss function into the physical neuron-embedded physical information neural network model; Step 40: Use the k-means clustering algorithm to balance the data of the original dataset, and screen to obtain a training set; Step 50: Use the training set to train the physical neuron-embedded physical information neural network model to obtain a chiller performance prediction model; Step 60: Use the chiller performance prediction model to predict the performance of the chiller.

[0005] As a further improvement of the present invention, the input variables of the neural network model include chilled water supply temperature, chilled water return temperature, chilled water flow rate, cooling water supply temperature, cooling water return temperature, and cooling water flow rate, and the output variable is the coefficient of performance.

[0006] As a further improvement of the present invention, the selection of the neuron variables should follow the following principles: originating from thermodynamics, heat transfer, or system characteristics, representing the operating state of the system, and having clear physical meanings; being intermediate physical process variables between input variables and output variables; and being calculable through known physical equations.

[0007] As a further improvement of the present invention, the neuron variables include chiller refrigerating capacity, chiller condensing heat load, chilled water flow ratio, cooling water flow ratio, cooling load ratio, condensing heat load ratio, evaporator heat transfer coefficient, condenser heat transfer coefficient, evaporation temperature, condensation temperature, dimensionless temperature difference between the two heat exchangers, ideal coefficient of performance, and thermodynamic perfection degree.

[0008] As a further improvement of the present invention, in Step 20, the embedding of the neuron variables as physical neurons into the neural network model specifically includes: if there is no mutual influence relationship between neuron variables, the corresponding physical neurons do not form connections; if there is a mutual influence relationship between neuron variables, direct or indirect connections are constructed between the corresponding physical neurons.

[0009] As a further improvement of the present invention, in Step 20, if the relationship between neuron variables can be quantitatively described, the direct connection relationship between the corresponding physical neurons is constructed using Equation (1): Equation (1) In the formula, represents the neuron variable corresponding to the physical neuron of the current layer, respectively represent the neuron variables corresponding to the physical neurons in the previous layer, respectively represent the weights of the physical neurons in the previous layer, represents and the functional relationship between represents the bias of the physical neuron in the current layer.

[0010] As a further improvement of the present invention, in step 20, if the relationship between neuron variables cannot be quantitatively described, artificial neurons are introduced between the corresponding physical neurons, and the indirect connection relationship between the corresponding physical neurons is constructed using Equation (2): Equation (2) In the formula, represents and the activation function between

[0011] As a further improvement of the present invention, step 30 specifically includes: Step 301, construct the control equations between neuron variables, such as Equations (3) to (5): Equation (3) Equation (4) Equation (5) In the formula, represents the thermal perfection degree obtained from the control equation composed of the cooling load ratio and the dimensionless temperature difference between the two heat exchangers, represents the heat transfer coefficient of the evaporator obtained from the control equation composed of the cooling load ratio and the chilled water flow ratio, represents the heat transfer coefficient of the condenser obtained from the control equation composed of the condensation heat load ratio and the cooling water flow ratio, represents the cooling load ratio, represents the dimensionless temperature difference between the two heat exchangers, represents the chilled water flow ratio, represents the condensation heat load ratio, represents the cooling water flow ratio, and A, B, C, D, E, F, a, b, c, d, e, f, g, h, i, j, k, and l all represent constants; Step 302, construct the physical loss terms, such as Equations (6) to (8): Equation (6) Equation (7) Equation (8) In the formula, Represents the physical loss of thermal perfection, Represents the thermal perfection obtained from the j-th control equation composed of the cooling load ratio and the dimensionless temperature difference between the two apparatuses in the sample array, Represents the thermal perfection obtained from the forward propagation of the neural network for the j-th in the sample array, Represents the weighting coefficient of the physical loss term, Represents the total number of the sample array, Represents the physical loss of the evaporator heat transfer coefficient, Represents the evaporator heat transfer coefficient obtained from the j-th control equation composed of the cooling load ratio and the chilled water flow rate ratio in the sample array, Represents the evaporator heat transfer coefficient obtained from the forward propagation of the neural network for the j-th in the sample array, Represents the physical loss of the condenser heat transfer coefficient, Represents the condenser heat transfer coefficient obtained from the j-th control equation composed of the condensation heat load ratio and the cooling water flow rate ratio in the sample array, Represents the condenser heat transfer coefficient obtained from the forward propagation of the neural network for the j-th in the sample array; Step 303, construct a loss function, as shown in Equation (9): Equation (9) In the formula, Represents the total loss of the neural network backpropagation, Represents the observed loss obtained from the forward propagation calculation of the neural network.

[0012] As a further improvement of the present invention, the specific steps of step 40 include: Step 401, perform normalization processing on the data in the original dataset to obtain a normalized dataset; Step 402, use the silhouette coefficient method to determine the clustering value, and randomly select data from the normalized dataset as the initial centroids; Step 403, calculate the Euclidean distance from each data in the normalized dataset to each centroid, and assign each data to the nearest cluster; the centroids are iteratively updated until convergence to obtain the clustering result; Step 404, map the data in all clusters to the original data form, and randomly select sample data from each cluster for aggregation to obtain a training set.

[0013] As a further improvement of the present invention, the specific steps of step 50 include: The data in the original dataset that is not in the training set is composed into a validation set. The training set is used to train the physical neuron embedded physical information neural network, and the validation set is used to test the performance of the trained physical neuron embedded physical information neural network model; Calculate the coefficient of determination of the validation set. If the coefficient of determination is greater than 0.9, the trained physical neuron embedded physical information neural network is used as the performance prediction model of the chiller; otherwise, continue training.

[0014] Compared with the prior art, the technical solution of the present invention has the following beneficial effects: An improved physical information neural network based chiller performance prediction method provided by the present invention first performs balance processing on the data to form a training set with uniform feature distribution. Since the data collected during the actual operation of the chiller has the characteristic of uneven working condition distribution, usually, the amount of data under certain features is rich, while the data under certain features is relatively scarce or even missing, resulting in the model being more inclined to learn the rich features of the data, which affects the model's learning ability of the performance law of the full working condition. The present invention provides conditions for the model to achieve balanced learning of various features; subsequently, physical neurons are introduced and embedded into the neural network architecture, which enables some physical variables in the chiller to be explicitly controlled by known thermodynamic laws and empirical formulas, reduces the number of trainable parameters of the model, and improves the stability of training. At the same time, due to the embedding of physical neurons, the neural network architecture combines the intermediate physical process mechanism, can directly express the energy transfer and component coupling mechanism inside the chiller, and enhances the physical transparency and interpretability of the performance prediction model, providing support for the reliable application of the model in actual scenarios such as fault diagnosis and abnormal working condition prediction. In addition, on the basis of this network architecture, a physical constraint loss term is further introduced. This type of loss term is not only used to constrain the relationship between the input and output variables of the chiller, but also can be used to constrain the physical consistency relationship between the key intermediate variables inside the system, so as to realize a more comprehensive and detailed utilization of the physical information of the chiller. Under the combined action of the physical neuron embedding and the physical loss term, the model can more accurately capture the thermal coupling and energy transfer mechanism between the components of the chiller, significantly enhances the modeling ability of the equipment behavior under complex operating conditions, effectively maintains physical consistency, and improves the generalization prediction ability of the model under non - typical working conditions such as variable load operation and seasonal switching. Description of the Drawings

[0015] Figure 1 It is a flowchart of the improved physical information neural network based chiller performance prediction method provided by the present invention; Figure 2 It is a schematic diagram of the intermediate variable recurrence relationship between the input variables and output variables in the method of the present invention; Figure 3It is the architecture diagram of the physical neuron embedded in the physical information neural network in the method of the present invention; Figure 4 It is the structural schematic diagram of the physical neuron embedded in the physical information neural network model in the method of the present invention; Figure 5 It is the input data distribution diagram of the training set, validation set and test set in Example 1, Comparative Example 1 and Comparative Example 2; Figure 6 (a) It is the COP performance prediction ability diagram of Example 1 using the validation set data; Figure 6 (b) It is the COP performance prediction ability diagram of Example 1 using the test set data; Figure 6 (c) It is the COP performance prediction ability diagram of Comparative Example 1 using the validation set data; Figure 6 (d) It is the COP performance prediction ability diagram of Comparative Example 1 using the test set data; Figure 6 (e) It is the COP performance prediction ability diagram of Comparative Example 2 using the validation set data; Figure 6 (f) It is the COP performance prediction ability diagram of Comparative Example 2 using the test set data; Figure 7 It is the schematic diagram of the physical neuron embedded in the physical information neural network in Example 1 using its interpretability for equipment fault diagnosis. Detailed implementation manners

[0016] The technical solutions of the present invention will be described in detail below.

[0017] The embodiment of the present invention provides an improved physical information neural network-based chiller performance prediction method, as Figure 1 shown, including the following steps: Step 10, according to the relationship between the physical variables in the chiller, construct a neural network model; the neural network model adopts a physical information neural network; Step 20, select neuron variables from all the physical variables of the chiller, and embed the neuron variables into the neural network model as physical neurons to obtain a physical neuron embedded physical information neural network model; Step 30, construct a control equation between the neuron variables, and introduce a loss function into the physical neuron embedded physical information neural network model; Step 40, use the k-means clustering algorithm to perform data balancing processing on the original data set, and screen to obtain a training set; Step 50, use the training set to train the physical neuron embedded physical information neural network model to obtain a chiller performance prediction model; Step 60, use the chiller performance prediction model to predict the chiller performance.

[0018] In engineering applications, the chilled water supply temperature, chilled water return temperature, chilled water flow rate, cooling water inlet temperature, cooling water outlet temperature, cooling water flow rate, evaporation temperature, condensation temperature, and chiller operating power of a chiller can usually be monitored. The performance of a chiller is usually evaluated by the coefficient of performance (COP), which is the ratio of the cooling capacity of the chiller to the chiller operating power. Usually, the COP of a chiller is affected by six variables: chilled water supply temperature, chilled water return temperature, chilled water flow rate, cooling water inlet temperature, cooling water outlet temperature, and cooling water flow rate. Therefore, when establishing a neural network model for a chiller, the chilled water supply temperature, chilled water return temperature, chilled water flow rate, cooling water supply temperature, cooling water return temperature, and cooling water flow rate are used as the input variables of the neural network model, and the COP is used as the output variable of the neural network model.

[0019] As a preferred example, when selecting neuron variables from all the physical variables of a chiller, the following principles should be followed: 1) They originate from thermodynamics, heat transfer, or system characteristics, represent the operating state of the system, and have clear physical meanings; 2) They must be intermediate physical process variables between the input and output variables, and can form a recursive physical relationship chain from the input to the output to ensure the gradual transfer of physical information from the input to the output; 3) They can be calculated through known physical equations to ensure physical consistency and computational feasibility. According to the above principles, the selected neuron variables include cooling capacity, condensation heat load, chilled water flow ratio, cooling water flow ratio, cooling load ratio, condensation heat load ratio, evaporator heat transfer coefficient, condenser heat transfer coefficient, evaporation temperature, condensation temperature, dimensionless temperature difference between the two heat exchangers, ideal coefficient of performance, and thermodynamic perfection degree.

[0020] Specifically, the cooling capacity can be calculated from the chilled water supply temperature , chilled water return temperature , and chilled water flow rate as shown in Equation (11). The condensation heat load can be calculated from the cooling water supply temperature , cooling water return temperature , and cooling water flow rate as shown in Equation (12). The chilled water flow ratio can be calculated from the chilled water flow rate as shown in Equation (13). The cooling water flow ratio can be calculated from the cooling water flow rate as shown in Equation (14). The cooling load ratio can be calculated from the cooling capacity as shown in Equation (15). The condensation heat load ratio can be calculated from the condensation heat load as shown in Equation (16). In a chiller, the heat transfer coefficients of the evaporator and condenser are usually affected by the refrigerant-side flow rate and the water-side flow rate. Generally, the greater the cooling load ratio or condensation heat load ratio of the chiller, the greater the refrigerant-side flow rate. Therefore, the cooling load ratio and condensation heat load ratio can be used to characterize the refrigerant-side flow rate. Thus, the heat transfer coefficient of the evaporator can be regarded as a function of the cooling load ratio of the chiller and the chilled water flow ratio. Similarly, the heat transfer coefficient of the condenser can be regarded as a function of the condensation heat load ratio and the cooling water flow ratio. The evaporation temperature can be calculated from the chilled water flow rate , the chilled water supply temperature , the refrigerating capacity and the heat transfer coefficient of the evaporator as shown in Equation (17). The condensation temperature can be calculated from the cooling water flow rate , the cooling water supply temperature , the condensation heat load and the heat transfer coefficient of the condenser as shown in Equation (18). The dimensionless temperature difference between the two heat exchangers can be calculated from the evaporation temperature and the condensation temperature as shown in Equation (19). The thermal perfection degree can be regarded as the efficiency of the compressor inside the chiller. From the efficiency curve of the compressor, it can be seen that the compressor efficiency is related to the refrigerant flow ratio and the relative compression ratio. The cooling load ratio of the chiller can characterize the refrigerant flow ratio, and the dimensionless temperature difference between the two heat exchangers can characterize the relative compression ratio. Therefore, the thermal perfection degree can be regarded as a function of the cooling load ratio of the chiller and the dimensionless temperature difference between the two heat exchangers. The ideal coefficient of performance can be calculated from the evaporation temperature and the condensation temperature as shown in Equation (20). The COP can be calculated from the thermal perfection degree and the ideal coefficient of performance as shown in Equation (21).

[0021] Equation (11) Equation (12) Equation (13) Equation (14) Equation (15) Equation (16) Formula (17) Formula (18) Formula (19) Formula (20) Formula (21) Where, Represents the specific heat capacity of water, the unit is kJ / (kg·℃); Indicates the density of water in kg / m 3 ; Indicates the chilled water supply temperature in °C; Indicates the chilled water return temperature in °C; Indicates the chilled water flow rate in m 3 / s; Indicates the cooling water return temperature in °C; Indicates the cooling water supply temperature in °C; Indicates cooling water flow rate, unit is m 3 / s; Indicates cooling capacity in kW; Indicates the condensing heat load in kW; Indicates the rated cooling capacity in kW; Indicates cooling load rate; Indicates the condensing heat load rate; Indicates the maximum value of condensing heat load, take 1.3 times of represents the chilled water flow ratio, Indicates the maximum flow rate of chilled water, represents the cooling water flow ratio, Indicates the maximum flow rate of cooling water. The maximum flow rates of chilled water and cooling water are both 1.5 times their respective nominal values. represents the evaporation temperature, Indicates the condensation temperature in K; represents the evaporator heat transfer coefficient, Indicates the condenser heat transfer coefficient, the unit is kJ / K; represents the dimensionless temperature difference between the two devices; represents the ideal performance coefficient; Indicates thermal perfection.

[0022] Therefore, the recursive relationship between the intermediate variables of the above input variables and output variables can be summarized as follows: Figure 2 As shown in , the neuron variables selected as physical neurons are shown in Table 1.

[0023] Table 1 Neuron variables

[0024] As a preferred example, in step 20, the neuron variables are embedded as physical neurons into the neural network model, specifically including: if there is no mutual influence relationship between the neuron variables, then the corresponding physical neurons do not form connections; if there is a mutual influence relationship between the neuron variables, then direct connections or indirect connections are constructed between the corresponding physical neurons.

[0025] Specifically, when there is an explicit physical equation between the neuron variables that can quantitatively describe their mutual relationship, a direct connection method is used to construct the relationship between the corresponding physical neurons. These connections can occur between adjacent neural network layers or span multiple neural network levels, depending specifically on their physical control equations. Additionally, set the weight w = 1 and bias b = 0 of the previous layer of physical neurons and keep the two constant during the training process. If the explicit physical equation between these neuron variables is Equation (22), then use Equation (1) to construct the direct connection relationship between the corresponding physical neurons, that is, in the forward propagation process, the physical neurons first substitute the values from the previous layer into the custom function determined by the physical control equation (i.e., Equation (1)) for independent processing. Subsequently, sum all the values processed by the custom function to obtain the output value of the current layer of physical neurons.

[0026] Equation (22) Equation (1) In the formula, represents the neuron variable corresponding to the current layer of physical neurons,[[]] respectively represent the neuron variables corresponding to the previous layer of physical neurons,[[]] respectively represent the weights of each physical neuron in the previous layer,[[]] represents[[]] and[[]] the functional relationship between,[[]] represents the bias of the current layer of physical neurons.

[0027] When there is a mutual influence relationship between the neuron variables, but there is a lack of an explicit physical control equation to describe the situation, then artificial neurons are introduced between the corresponding physical neurons to achieve indirect connections between the physical neurons. This structure enables the neural network to autonomously learn implicit dependency relationships through training and retains appropriate guidance for known physical laws. The calculation of the values in the corresponding physical neurons and artificial neurons in this case is shown in Equation (2): Equation (2) representation and The activation function therebetween. Preferably, the activation function is tanh.

[0028] Preferably, there are 2 layers of artificial neurons introduced between the physically connected neurons, and the number of artificial neurons in each layer is 5.

[0029] Therefore, according to the variable relationships of the physical equations defined by the formulas (11) to (21) existing in the known chiller, and the variable relationships that have an impact on each other but lack a clear physical control equation description, finally, a physical neuron embedded physical information neural network architecture as shown in Figure 3 is formed.

[0030] As a preferred example, step 30 specifically includes: Step 301, constructing the control equations between neuron variables, such as equations (3) to (5): Equation (3) Equation (4) Equation (5) In the equations, represents the thermodynamic perfection degree obtained from the control equation composed of the cooling load ratio and the dimensionless temperature difference between the two heat exchangers, represents the evaporator heat transfer coefficient obtained from the control equation composed of the cooling load ratio and the chilled water flow ratio, represents the condenser heat transfer coefficient obtained from the control equation composed of the condensation heat load ratio and the cooling water flow ratio, represents the cooling load ratio, represents the dimensionless temperature difference between the two heat exchangers, represents the chilled water flow ratio, represents the condensation heat load ratio, represents the cooling water flow ratio, and A, B, C, D, E, F, a, b, c, d, e, f, g, h, i, j, k, and l all represent constants.

[0031] Step 302, constructing the physical loss terms, such as equations (6) to (8): Equation (6) Equation (7) Equation (8) In the equations, represents the physical loss of the thermodynamic perfection degree, represents the thermodynamic perfection degree obtained from the control equation composed of the cooling load ratio and the dimensionless temperature difference between the two heat exchangers for the jth in the sample array, represents the thermal perfection degree obtained by the forward propagation of the neural network for the j-th in the sample array, represents the weighting coefficient of the physical loss term. Preferably, this value is taken as 1. represents the total number of the sample array, represents the physical loss of the evaporator heat transfer coefficient, represents the evaporator heat transfer coefficient obtained by the control equation composed of the cooling load ratio and the chilled water flow ratio for the j-th in the sample array, represents the evaporator heat transfer coefficient obtained by the forward propagation of the neural network for the j-th in the sample array, represents the physical loss of the condenser heat transfer coefficient, represents the condenser heat transfer coefficient obtained by the control equation composed of the condensation heat load ratio and the cooling water flow ratio for the j-th in the sample array, represents the condenser heat transfer coefficient obtained by the forward propagation of the neural network for the j-th in the sample array.

[0032] Step 303, construct a loss function, as shown in Equation (9): Equation (9) In the formula, represents the total loss of the neural network during backpropagation, represents the observed loss obtained by the forward propagation calculation of the neural network.

[0033] In the method of the present invention, some intermediate variables with clear physical meanings are explicitly embedded in the neural network structure as physical neurons, enabling them to undertake specific physical calculation functions during the forward propagation process of the model, thereby organically integrating the complex thermal process mechanism inside the chiller into the model structure. This design not only reduces the number of trainable parameters and the dependence on large-scale training data, but also improves the model's ability to express the coupling relationship of key components. At the same time, during the construction of the loss function, a physical residual term related to the above physical variables is introduced, and the energy conservation, thermal balance, and empirical formulas during the operation of the chiller are incorporated into the optimization objective as explicit constraints, realizing physical consistency control throughout the process from input to output. Thanks to the synergistic effect of physical neurons and physical loss terms, the model can effectively suppress the non-physical deviation of intermediate variables, improve the stability of the training process, enhance the generalization prediction ability for unseen working conditions, and make the internal reasoning process have clear physical meanings, thus significantly improving the interpretability and engineering usability of the model.

[0034] As a preferred example, step 40 specifically includes: Step 401, normalize the data in the original dataset using Equation (23) to obtain a normalized dataset.

[0035] Equation (23) In the formula,[[]]END]] represents the original data; represents the normalized data of; represents the th data.

[0036] Step 402, use the silhouette coefficient method to determine the clustering value. Specifically, use Equation (24) to calculate the silhouette coefficients for different values: Equation (24) In the formula,[[]]END]] represents the average distance between the data and all other data within the same cluster; represents the minimum average distance between the data and the data in any other cluster; the silhouette coefficient ranges from -1 to 1. The higher the value, the better the clustering structure. The final silhouette is obtained by averaging the of all data points.

[0037] Randomly select data from the normalized dataset as the initial centroids.

[0038] Step 403, use Equation (25) to calculate the Euclidean distance from each data in the normalized dataset to each centroid: Equation (25) In the formula,[[]]END]] represents the centroid of the cluster,[[]]END]] represents the index of the clustering feature.

[0039] Assign each data to the nearest cluster. The centroids are iteratively updated until convergence to obtain the clustering result; Step 404, map the data in all clusters to the original data form by retrieving the corresponding rows from the original dataset. Randomly select sample data from each cluster, and aggregate the sample data from all clusters to obtain the training set.

[0040] The method of the present invention performs balancing processing on the original data using the above process, which can significantly improve the representativeness and coverage of training samples on the basis of fully retaining the characteristic distribution structure of the original data. By means of the normalization operation, the dimensional influence between different features is eliminated, making the subsequent clustering analysis more objective and reliable; the silhouette coefficient method is introduced to dynamically determine the number of clusters, which helps to obtain a more reasonable data grouping structure and ensure that the division boundary of samples in the feature space is clear and the internal similarity is high. The sample extraction mechanism based on the cluster center can avoid the overfitting phenomenon caused by uneven data distribution during the model training process, and effectively improve the learning ability and generalization ability of the model under different working conditions and different feature combinations. Especially in equipment such as chillers with complex working conditions and highly variable operating states, constructing a training set through the clustering balance sampling strategy helps to enhance the modeling ability of the model for scarce feature intervals such as marginal working conditions and low-frequency operating states, thereby improving the accuracy and robustness of the overall performance prediction, and providing a prerequisite guarantee for the subsequent balanced and comprehensive learning of the model under various working conditions.

[0041] As a preferred example, step 50 specifically includes: Taking the training data as the training set and the remaining unselected data in the original data as the validation set, training the physical neuron embedded physical information neural network using the training set, and testing the performance of the trained physical neuron embedded physical information neural network model using the validation set.

[0042] Calculating the coefficient of determination of the validation set using Equation (10): Equation (10) In the formula, represents the coefficient of determination, represents the observed value (i.e., the actual value), represents the predicted value of the physical neuron embedded physical information neural network model, represents the average value of the observed values in the array, represents the total number of samples.

[0043] If the coefficient of determination is greater than 0.9, the trained physical neuron embedded physical information neural network is used as the chiller performance prediction model; otherwise, continue training.

[0044] The following provides an example and two comparative examples.

[0045] The prediction objects in Example 1, Comparative Example 1, and Comparative Example 2 are the same chiller, and the rated cooling capacity of this chiller is 440 kW, the rated power is 69.6 kW, the rated chilled water flow rate is 76 m 3 / s, and the rated cooling water flow rate is 95 m 3 / s. The chiller is controlled to operate with a cooling load ratio between 0.4 and 0.8, and the chilled water supply temperature is maintained in the range of 5 - 8°C.

[0046] In Example 1, the method of the present invention is adopted. In Comparative Example 1, a prediction method based on a physics-informed neural network is adopted. In Comparative Example 2, a prediction method based on a multi-layer feedforward neural network is adopted. The model descriptions in Comparative Example 1 and Comparative Example 2 are shown in Table 2.

[0047] Table 2 Benchmark models adopted in two comparative examples

[0048] The original data sets adopted in Example 1, Comparative Example 1, and Comparative Example 2 are the same. The cooling load ratios in the data are all in the range of 0.4 - 0.8, and the chilled water supply temperatures are all in the range of 5 - 8°C. The training sets are all processed by step 40 of the method of the present invention ( taking the value 8, taking the value 10), and the validation sets are composed of the data remaining in the original data set after removing the training sets. The test sets are data outside the original data set, and the cooling load ratios in the data are outside the range of 0.4 - 0.8, and the chilled water supply temperatures are outside the range of 5 - 8°C. Figure 5 The input data distribution diagrams of the training set, validation set, and test set are given. Since there are 6-dimensional data in total for the input and it cannot be visualized on the graph, the principal component analysis method is used to reduce the 6-dimensional data to 3 dimensions for visualization.

[0049] Table 3 shows the calculation results of the root mean square error of the models in Example 1, Comparative Example 1, and Comparative Example 2 on the validation data and test data. Figure 6 It is a comparison chart of the generalization abilities of Example 1, Comparative Example 1, and Comparative Example 2.

[0050] Table 3 Comparison of root mean square error of models (100 times)

[0051] The method of the present invention introduces physical neurons and embeds them into the neural network, and at the same time constructs a physical loss term. Under the combined action of the two, the physical consistency is better maintained. From Figure 6As can be seen from Table 3, the physical neurons embedded in the physical information neural network model show a smaller root mean square error both on the verification data and the test data. Compared with the existing physical information neural network and multi-layer feedforward neural network, the prediction accuracy has been greatly improved, and the prediction relative error is basically within ±10%. On the test data, the root mean square errors of the physical information neural network and the multi-layer feedforward neural network are both extremely large, and accurate prediction cannot be achieved. The prediction error of the method of the present invention on the test set is similar to the prediction error on the verification set, which fully demonstrates that compared with the existing methods, the method of the present invention has a significant improvement in the generalization ability of model prediction. At the same time, from the difference between the maximum and minimum values, the difference of the method of the present invention is smaller than that of the other two existing methods, which fully demonstrates that the method of the present invention has good robustness.

[0052] Figure 7 The schematic diagram of the embodiment 1 showing the physical neurons embedded in the physical information neural network and using its interpretability for equipment fault diagnosis. Figure 7 It can be seen from the figure that when a fault occurs, the measured COP is significantly lower than the COP predicted in Example 1. This can be traced back to the physical neurons embedded in the physical information neural network model. T ev and T cn , where it is observed that, under fault conditions, the measured T ev is significantly lower than the predicted value, while the actual T cn The COP is slightly lower than the predicted value. These two factors contribute to the decrease in COP. Therefore, the significant difference between the measured and predicted values indicates a fault. These observations, combined with expert knowledge in the field, indicate the probability of a refrigerant leak. This further demonstrates that the method presented in this paper is more interpretable than existing data-driven methods, enabling analysis of energy efficiency degradation and the cause of the fault based on the output structure and the process mechanism of the neural network structure.

[0053] Compared with the existing technology, the method of the present invention has better generalization ability, robustness and interpretability, fully demonstrating the significant advancement of the method of the present invention.

[0054] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art will appreciate that the present invention is not limited to the specific embodiments described above. The specific embodiments and descriptions in the specification are intended only to further illustrate the principles of the present invention. The basic principles, main features, and advantages of the present invention are shown and described above without departing from the spirit and scope of the present invention. Those skilled in the art will appreciate that various changes and modifications may be made, and such changes and modifications are intended to fall within the scope of the invention as claimed.

Claims

1. An improved method for predicting the performance of a chiller using a physics-informed neural network, characterized in that, It includes the following steps: Step 10: Construct a neural network model according to the relationships among various physical variables in the chiller. Step 20: Select neuron variables from all the physical variables of the chiller, and embed the neuron variables as physical neurons into the neural network model to obtain a physical neuron-embedded physical information neural network model. Step 30: Construct control equations among the neuron variables, and introduce a loss function into the physical neuron-embedded physical information neural network model. Step 40: Use the k-means clustering algorithm to perform data balancing processing on the original dataset, and screen to obtain a training set. Step 50: Use the training set to train the physical neuron-embedded physical information neural network model to obtain a chiller performance prediction model. Step 60: Use the chiller performance prediction model to predict the performance of the chiller.

2. The performance prediction method of the chiller using the improved physical information neural network according to claim 1, characterized in that The input variables of the neural network model include chilled water supply temperature, chilled water return temperature, chilled water flow rate, cooling water supply temperature, cooling water return temperature, and cooling water flow rate, and the output variable is the coefficient of performance.

3. The performance prediction method of the chiller based on the improved physical information neural network according to claim 1, characterized in that The selection of the neuron variables should follow the following principles: originating from thermodynamics, heat transfer, or system characteristics, representing the operating state of the system, having clear physical meanings; being intermediate physical process variables between the input variables and the output variables; and being calculable through known physical equations.

4. The method for predicting the performance of a chiller using the improved physical information neural network according to claim 1, characterized in that, The neuron variables include chiller refrigerating capacity, chiller condensation heat load, chilled water flow ratio, cooling water flow ratio, cooling load ratio, condensation heat load ratio, evaporator heat transfer coefficient, condenser heat transfer coefficient, evaporation temperature, condensation temperature, dimensionless temperature difference between the two heat exchangers, ideal coefficient of performance, and thermodynamic perfection degree.

5. The method for predicting the performance of a chiller using the improved physical information neural network according to claim 1, characterized in that, In Step 20, the embedding of the neuron variables as physical neurons into the neural network model specifically includes: if there is no mutual influence relationship among the neuron variables, the corresponding physical neurons do not form connections; if there is a mutual influence relationship among the neuron variables, direct connections or indirect connections are constructed between the corresponding physical neurons.

6. The method for predicting the performance of a chiller using the improved physical information neural network according to claim 5, characterized in that, In Step 20, if the relationship between the neuron variables can be quantitatively described, the direct connection relationship between the corresponding physical neurons is constructed using Equation (1): Formula (1) In the formula, represents the neuron variable corresponding to the physical neuron of the current layer, respectively represent the neuron variables corresponding to the physical neurons of the previous layer, respectively represent the weights of the physical neurons of the previous layer, represents and the functional relationship between them, represents the bias of the physical neuron of the current layer.

7. The method for predicting the performance of a chiller using the improved physical information neural network according to claim 5, characterized in that, In Step 20, if the relationship between the neuron variables cannot be quantitatively described, artificial neurons are added between the corresponding physical neurons, and the indirect connection relationship between the corresponding physical neurons is constructed using Equation (2): Formula (2) In the formula, represents the activation function between and 8. The performance prediction method of the chiller based on the improved physical information neural network according to claim 5, characterized in that Step 30 specifically includes: Step 301: Construct control equations among the neuron variables, such as Equations (3) to (5): Formula (3) Formula (4) Formula (5) Wherein, represents the thermodynamic perfection degree obtained from the control equation composed of the cooling load ratio and the dimensionless temperature difference between the two heat exchangers; represents the evaporator heat transfer coefficient obtained from the control equation composed of the cooling load ratio and the chilled water flow ratio; represents the condenser heat transfer coefficient obtained from the control equation composed of the condensation heat load ratio and the cooling water flow ratio; represents the cooling load ratio; represents the dimensionless temperature difference between the two heat exchangers; represents the chilled water flow ratio; represents the condensation heat load ratio; represents the cooling water flow ratio. A, B, C, D, E, F, a, b, c, d, e, f, g, h, i, j, k, and l all represent constants; Step 302: Construct physical loss terms, such as Equations (6) to (8): Formula (6) Formula (7) Formula (8) In the formula, represents the physical loss of the thermal perfection degree, represents the thermal perfection degree obtained from the control equation composed of the cold load ratio and the dimensionless temperature difference between the two heat exchangers for the j-th in the sample array, represents the thermal perfection degree obtained from the forward propagation of the neural network for the j-th in the sample array, represents the weighting coefficient of the physical loss term, represents the total number of the sample array, represents the physical loss of the evaporator heat transfer coefficient, represents the evaporator heat transfer coefficient obtained from the control equation composed of the cold load ratio and the chilled water flow ratio for the j-th in the sample array, represents the evaporator heat transfer coefficient obtained from the forward propagation of the neural network for the j-th in the sample array, represents the physical loss of the condenser heat transfer coefficient, represents the condenser heat transfer coefficient obtained from the control equation composed of the condensation heat load ratio and the cooling water flow ratio for the j-th in the sample array, represents the condenser heat transfer coefficient obtained from the forward propagation of the neural network for the j-th in the sample array; Step 303: Construct a loss function, such as Equation (9): Formula (9) In the formula, represents the total loss of the neural network during backpropagation, represents the observed loss obtained from the forward propagation calculation of the neural network.

9. The method for predicting the performance of a chiller using the improved physical information neural network according to claim 1, wherein Step 40 specifically includes: Step 401: Normalize the data in the original dataset to obtain a normalized dataset. Step 402, determine the clustering value, randomly select data as the initial centroid from the normalized dataset; Step 403: Calculate the Euclidean distance from each data in the normalized dataset to each centroid, and assign each data to the nearest cluster; the centroids are iteratively updated until convergence to obtain a clustering result. Step 404, map the data in all clusters to the original data form, and randomly extract sample data from each cluster for aggregation to obtain a training set.

10. The performance prediction method of the chiller based on the improved physical information neural network according to claim 1, characterized in that, Step 50 specifically includes: The data in the original dataset that is not in the training set is used to form the validation set. The training set is used to train the physical neuron embedded physical information neural network, and the validation set is used to test the performance of the trained physical neuron embedded physical information neural network model; Calculate the coefficient of determination of the validation set. If the coefficient of determination is greater than 0.9, the trained physical neuron embedded physical information neural network is used as the chiller performance prediction model; otherwise, continue training.

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