Heat exchanger heat exchange performance identification model construction method and heat exchange performance identification method
By constructing a heat exchange performance identification model based on linear and nonlinear heat exchange components, and combining fractional derivatives and kernel functions, the parameters are optimized using a fuzzy genetic algorithm. This solves the problem of insufficient identification accuracy of existing heat exchanger identification models in strongly nonlinear systems, and achieves high-precision identification of heat exchange performance and system optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-26
- Publication Date
- 2026-03-31
AI Technical Summary
Existing heat exchanger identification models are insufficient in their identification and prediction effects and accuracy when dealing with strongly nonlinear or complex dynamic systems, and cannot accurately identify the heat exchange performance of compressed air energy storage systems.
A heat exchange performance identification model based on linear and nonlinear heat exchange components is constructed. Combining fractional derivatives and kernel functions, a fuzzy genetic algorithm is used to optimize the model parameters, and a fractional nonlinear Hammerstein-controlled autoregressive model is constructed to identify the complex behavior of the heat exchanger.
It improves the accuracy and precision of heat exchange performance identification, supports system energy efficiency optimization, predictive maintenance and intelligent control, and enhances the overall system efficiency.
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Figure CN119939898B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of heat exchanger technology, and in particular to a method for constructing a heat exchanger performance identification model and a method for identifying heat exchanger performance. Background Technology
[0002] Modeling complex dynamic systems is particularly challenging in the study of compressed air energy storage heat exchangers, mainly due to the diversity of heat exchanger operating conditions and the complexity of their inherent characteristics.
[0003] Heat exchangers involve heat transfer between fluids, and their dynamic behavior often exhibits significant nonlinear characteristics, such as fluctuations in fluid velocity, pressure, and heat transfer efficiency. These nonlinear factors prevent traditional linear models from accurately capturing the actual behavior of the system, thus leading to biases in model predictions.
[0004] Existing methods such as linear system theory, the traditional Hammerstein model, and the Wiener model are limited in effectiveness and accuracy when dealing with strongly nonlinear or complex dynamic systems, and cannot accurately identify the heat exchange performance of heat exchangers.
[0005] Accurate identification of heat exchanger performance is crucial for the efficient operation of compressed air energy storage systems. Firstly, it supports system energy efficiency optimization by guiding parameter adjustments through real-time performance identification. Secondly, it helps in the timely detection of performance degradation trends, enabling predictive maintenance. Thirdly, it provides necessary characteristic parameter support for intelligent system control. Finally, performance evaluation can optimize operating strategies and improve overall system efficiency. However, currently, there is a lack of a heat exchanger performance identification method that simultaneously meets the requirements of high accuracy and strong adaptability. Summary of the Invention
[0006] This application provides a method for constructing a heat exchanger performance identification model and a heat exchanger performance identification method to solve the problems of poor identification and prediction effects and accuracy of existing heat exchanger identification models.
[0007] The first aspect of this application provides a method for constructing a heat exchanger performance identification model, comprising the following steps: acquiring historical operating data of a heat exchanger in a compressed air energy storage system under different operating conditions, wherein the historical operating data includes the mass flow rate of hot and cold fluids, inlet and outlet temperatures, and corresponding heat exchange efficiencies; extracting the linear heat exchange component and the nonlinear heat exchange component of the compressed air energy storage system during the energy storage process from the historical operating data, wherein the linear heat exchange component represents the linear heat exchange process, and the nonlinear heat exchange component represents the nonlinear heat exchange process; and constructing a heat exchanger performance identification model based on the linear heat exchange component and the nonlinear heat exchange component, wherein the heat exchanger performance identification model is used to identify the heat exchanger performance under different operating conditions.
[0008] Optionally, a heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange section and the nonlinear heat exchange section, including: determining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section of the heat exchanger based on the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures and the corresponding heat exchange efficiencies of the heat exchanger; and combining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section to generate a heat exchange performance identification model.
[0009] Optionally, the linear heat exchange section introduces fractional derivatives and kernel functions, and adjusts the fractional parameters and kernel function parameters according to the characteristics of the compressed air energy storage system; the nonlinear heat exchange section introduces nonlinear functions.
[0010] Optionally, after constructing the heat exchanger performance identification model based on the linear heat exchange section and the nonlinear heat exchange section, the method further includes: optimizing the initial model parameters of the heat exchanger performance identification model based on a fuzzy genetic algorithm; judging the prediction accuracy of the optimized heat exchanger performance identification model; and stopping the optimization of the model parameters of the heat exchanger performance identification model if the prediction accuracy meets the preset standard.
[0011] Optionally, the initial model parameters of the heat transfer performance identification model are optimized based on the fuzzy genetic algorithm, including: creating fuzzy variables corresponding to each data point in the historical operating data, and defining a set of fuzzy terms for each fuzzy variable; constructing fuzzy rules based on expert knowledge or historical operating data; and optimizing the initial model parameters of the heat transfer performance identification model based on the fuzzy rules and historical operating data.
[0012] A second aspect of this application provides a method for identifying the heat exchange performance of a heat exchanger, comprising the following steps: acquiring current operating data of a heat exchanger in a compressed air energy storage system, wherein the current operating data includes the mass flow rate of the hot and cold fluids and the inlet and outlet temperatures of the heat exchanger; inputting the current operating data into a heat exchange performance identification model of the heat exchanger, wherein the heat exchange performance identification model outputs the current heat exchange performance of the heat exchanger, wherein the heat exchange performance identification model is constructed based on the linear heat exchange portion and the nonlinear heat exchange portion of the compressed air energy storage system during the energy storage process from historical operating data.
[0013] Optionally, after the heat exchanger performance identification model outputs the current heat exchanger performance, it also includes: obtaining the reference heat exchanger performance of the current operating data; if the current heat exchanger performance is inconsistent with the reference heat exchanger performance, then re-optimizing the model parameters of the heat exchanger performance identification model.
[0014] A third aspect of this application provides a device for constructing a heat exchanger performance identification model, comprising: acquiring historical operating data of a heat exchanger in a compressed air energy storage system under different operating conditions, wherein the historical operating data includes the mass flow rate of hot and cold fluids, inlet and outlet temperatures, and corresponding heat exchange efficiencies; an extraction module for extracting the linear heat exchange portion and the nonlinear heat exchange portion of the compressed air energy storage system during the energy storage process from the historical operating data, wherein the linear heat exchange portion represents the linear heat exchange process, and the nonlinear heat exchange portion represents the nonlinear heat exchange process; and a construction module for constructing a heat exchanger performance identification model based on the linear heat exchange portion and the nonlinear heat exchange portion, wherein the heat exchanger performance identification model is used to identify the heat exchanger performance under different operating conditions.
[0015] Optionally, a heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange section and the nonlinear heat exchange section, including: determining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section of the heat exchanger based on the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures and the corresponding heat exchange efficiencies of the heat exchanger; and combining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section to generate a heat exchange performance identification model.
[0016] Optionally, the linear heat exchange section introduces fractional derivatives and kernel functions, and adjusts the fractional parameters and kernel function parameters according to the characteristics of the compressed air energy storage system; the nonlinear heat exchange section introduces nonlinear functions.
[0017] Optionally, it also includes: a first optimization module, used to optimize the initial model parameters of the heat exchange performance identification model based on a fuzzy genetic algorithm after constructing the heat exchange performance identification model of the heat exchanger based on the linear heat exchange part and the nonlinear heat exchange part; to determine the prediction accuracy of the optimized heat exchange performance identification model; and to stop optimizing the model parameters of the heat exchange performance identification model if the prediction accuracy meets the preset standard.
[0018] Optionally, the first optimization module is further used to: create fuzzy variables corresponding to each data point in the historical operating data, and define a set of fuzzy terms for each fuzzy variable; construct fuzzy rules based on expert knowledge or historical operating data; and optimize the initial model parameters of the heat exchange performance identification model based on the fuzzy rules and historical operating data.
[0019] A fourth aspect of this application provides a heat exchanger performance identification device, comprising: a second acquisition module for acquiring current operating data of a heat exchanger in a compressed air energy storage system, wherein the current operating data includes the mass flow rate of hot and cold fluids and the inlet and outlet temperatures of the heat exchanger; and an input module for inputting the current operating data into a heat exchanger performance identification model, wherein the heat exchanger performance identification model outputs the current heat exchanger performance, wherein the heat exchanger performance identification model is constructed based on the linear heat exchange characteristics and nonlinear heat exchange characteristics of the compressed air energy storage system during energy storage from historical operating data.
[0020] Optionally, it also includes: a second optimization module, used to obtain the reference heat transfer performance of the current operating data after the heat transfer performance identification model outputs the current heat transfer performance of the heat exchanger; if the current heat transfer performance is inconsistent with the reference heat transfer performance, the model parameters of the heat transfer performance identification model are re-optimized.
[0021] A fifth aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to perform the heat exchanger performance identification model construction method or the heat exchanger performance identification method as described in the above embodiments.
[0022] Therefore, this application has at least the following beneficial effects:
[0023] This application's embodiments can extract the linear and nonlinear heat exchange components of a compressed air energy storage system from historical operating data of the heat exchanger during the energy storage process. Based on these components, a heat exchange performance identification model is constructed, and this model is used to identify the heat exchanger's performance. By fully considering both linear and nonlinear heat exchange components, the model more comprehensively reflects the complex behavior of the heat exchanger and accurately identifies its performance, thus improving its identification effect and accuracy. This solves the technical problems of poor prediction and identification effects and accuracy in existing heat exchanger identification models.
[0024] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description
[0025] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:
[0026] Figure 1 This is a flowchart of a method for constructing a heat exchanger performance identification model according to an embodiment of this application;
[0027] Figure 2 This is a flowchart of a heat transfer performance identification method provided according to an embodiment of this application;
[0028] Figure 3 This is a flowchart illustrating the construction and optimization of a heat exchanger performance identification model according to an embodiment of this application;
[0029] Figure 4 This is an example diagram of a heat exchanger heat exchange performance identification model construction device provided in the embodiments of this application;
[0030] Figure 5 This is an example diagram of a heat exchange performance identification device provided according to an embodiment of this application;
[0031] Figure 6 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation
[0032] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.
[0033] The following description, with reference to the accompanying drawings, describes a method for constructing a heat exchanger performance identification model and a method for identifying heat exchanger performance according to embodiments of this application. Addressing the limitations in effectiveness and accuracy of existing methods mentioned in the background art, such as linear system theory, the traditional Hammerstein model, and the Wiener model, when dealing with strongly nonlinear or complex dynamic systems, this application provides a method for constructing a heat exchanger performance identification model. In this method, the linear and nonlinear heat exchange components of the compressed air energy storage system during energy storage can be extracted from historical operating data of the heat exchanger. A heat exchanger performance identification model is constructed based on these components, and the model is used to identify the heat exchanger's heat exchange performance. By fully considering both linear and nonlinear heat exchange components, the model more comprehensively reflects the complex behavior of the heat exchanger and accurately identifies its heat exchange performance, thus improving the identification effect and accuracy of the model. This solves the problems of poor identification and prediction effects and accuracy of existing heat exchanger identification models.
[0034] Specifically, Figure 1 This is a flowchart illustrating a method for constructing a heat exchanger performance identification model, as provided in an embodiment of this application.
[0035] like Figure 1 As shown, the method for constructing the heat exchanger performance identification model includes the following steps:
[0036] In step S101, historical operating data of the heat exchanger in the compressed air energy storage system under different operating conditions are obtained.
[0037] The historical operating data includes the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures, and the corresponding heat exchange efficiency.
[0038] Furthermore, it should be noted that, to ensure the accuracy and reliability of the data, this application imposes strict requirements on data acquisition: sensor arrangement should comply with GB / T 2624 standard, with no fewer than three temperature sensors arranged along the flow direction, and pressure sensors installed at the inlet and outlet; sampling frequency should be no less than 1Hz, with temperature measurement accuracy ±0.1℃, pressure measurement accuracy ±0.1%, and flow measurement accuracy ±0.5%; GPS time synchronization should be used to ensure synchronous acquisition of multi-sensor data, with a sampling time deviation not exceeding 0.1s; data preprocessing should employ a three-sigma criterion to remove outliers, and a Butterworth low-pass filter should be used for data smoothing; processed data should be stored in a unified format, including timestamps, measured values, units, and other standard information.
[0039] It is understood that the embodiments of this application can be based on the acquisition of historical operating data of the heat exchanger in the compressed air energy storage system under different operating conditions, so as to distinguish between the linear heat exchange part and the nonlinear heat exchange part in the future.
[0040] In step S102, the linear heat exchange portion and nonlinear heat exchange portion of the compressed air energy storage system during the energy storage process are extracted from the historical operating data.
[0041] The linear heat exchange section represents a linear heat exchange process, while the nonlinear heat exchange section represents a nonlinear heat exchange process.
[0042] It is understood that the embodiments of this application can extract the linear heat exchange portion and the nonlinear heat exchange portion of the compressed air energy storage system in the energy storage process from historical operating data, specifically by analyzing the linear heat exchange portion and the nonlinear heat exchange portion between input data and output data.
[0043] In step S103, a heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange part and the nonlinear heat exchange part. The heat exchange performance identification model is used to identify the heat exchange performance of the heat exchanger under different operating conditions.
[0044] The heat exchange performance model can output the comprehensive performance characteristics of the heat exchanger, including the current heat exchange efficiency, heat transfer coefficient, pressure drop coefficient and drag coefficient reflecting flow loss, and temperature efficiency and pressure efficiency characterizing thermodynamic performance.
[0045] It is understood that the embodiments of this application can construct a heat exchanger performance identification model based on the linear heat exchange section and the nonlinear heat exchange section. The heat exchanger performance identification model is used to identify the heat exchanger performance under different operating conditions, fully considering the linear heat exchange section and the nonlinear heat exchange section in the heat exchange process, so that the heat exchanger performance identification model can more comprehensively reflect the complex behavior of the heat exchanger and accurately identify the heat exchanger performance, so as to use the heat exchanger performance identification results for system optimization control, predictive maintenance, fault diagnosis and operation strategy formulation.
[0046] In this embodiment of the application, a heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange section and the nonlinear heat exchange section, including: determining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section of the heat exchanger based on the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures and the corresponding heat exchange efficiencies of the heat exchanger; and combining the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section to generate a heat exchange performance identification model.
[0047] The model parameters for the linear heat exchange section can be determined using linear regression methods, such as the least squares method, while the model parameters for the nonlinear heat exchange section can be determined using nonlinear regression methods, such as the gradient descent method.
[0048] It is understood that, according to the embodiments of this application, the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section can be determined according to the mass flow rate of the cold and hot fluids, the inlet and outlet temperatures and the corresponding heat exchange efficiencies under different operating conditions, and the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section are combined to generate a heat exchange performance identification model.
[0049] In the embodiments of this application, the linear heat exchange section introduces fractional derivatives and kernel functions, and adjusts the fractional parameters and kernel function parameters according to the characteristics of the compressed air energy storage system; the nonlinear heat exchange section introduces nonlinear functions.
[0050] Understandably, this application can introduce fractional derivatives and kernel functions into the linear heat exchange section, and adjust the fractional parameters and kernel function parameters according to the characteristics of the compressed air energy storage system, so that the linear part can better adapt to the dynamic changes of the system and refine the description of the complexity of the heat exchange process; and introduce nonlinear functions, such as polynomial functions or other nonlinear functions, into the nonlinear heat exchange section to accurately simulate the nonlinear heat exchange process in the compressed air energy storage system.
[0051] Specifically, the preliminary construction of the heat exchange performance identification model (also known as a fractional-order nonlinear Hammerstein controlled autoregressive (FO-NHCAR) model) in this application mainly includes: starting with defining the basic dynamic behavior and operating environment of the heat exchanger system. Using the inlet and outlet temperatures and real-time mass flow rates of the heat exchange fluid collected under different operating conditions, a preliminary analysis of the model's input-output relationship is performed to identify key variables and potential nonlinear relationships affecting the turbine's heat exchange performance. Subsequently, appropriate fractional derivatives and kernel functions are selected to describe the impact of parameter settings for the inlet and outlet temperatures and real-time mass flow rates of the heat exchange fluid on the turbine's operating efficiency and on the overall compressed air energy storage system's operating efficiency. These parameters directly affect the accuracy and complexity of the compressed air energy storage system model. The nonlinear part of the model is typically expressed using polynomials or other basis functions, while fractional derivatives are used to describe the linear dynamic part. After completing these steps, preliminary estimation of the model parameters is performed to provide a starting point for subsequent global optimization using a fuzzy genetic algorithm.
[0052] In this embodiment of the application, after constructing a heat exchanger performance identification model based on the linear heat exchange section and the nonlinear heat exchange section, the method further includes: optimizing the initial model parameters of the heat exchanger performance identification model based on a fuzzy genetic algorithm; judging the prediction accuracy of the optimized heat exchanger performance identification model; and stopping the optimization of the model parameters of the heat exchanger performance identification model if the prediction accuracy meets a preset standard.
[0053] The prediction criteria can be preset according to specific circumstances, and the comparison is not specifically limited. The metric for prediction accuracy can be the mean squared error (MSE). For example, if the MSE is less than 0.01, optimization will stop.
[0054] It is understood that the embodiments of this application can optimize the initial model parameters of the heat transfer performance identification model based on the fuzzy genetic algorithm, and stop optimizing the model parameters of the heat transfer performance identification model after the prediction accuracy of the optimized heat transfer performance identification model meets the preset standard.
[0055] In this embodiment of the application, the initial model parameters of the heat transfer performance identification model are optimized based on the fuzzy genetic algorithm, including: creating fuzzy variables corresponding to each data in the historical operating data, and defining a set of fuzzy terms for each fuzzy variable; constructing fuzzy rules based on expert knowledge or historical operating data; and optimizing the initial model parameters of the heat transfer performance identification model based on the fuzzy rules and historical operating data.
[0056] It can be understood that the embodiments of this application can create fuzzy variables for each data in the historical operating data and define a set of fuzzy terms. Fuzzy rules are constructed based on expert knowledge or historical operating data. Then, the initial model parameters of the heat exchange performance identification model are optimized according to the fuzzy rules and historical operating data to achieve high accuracy in identifying and predicting the heat exchanger performance of the compressed air energy storage system under different operating conditions.
[0057] For example, define key input and output parameters that affect heat exchanger performance, such as mass flow rate, temperature difference, and efficiency. For each key parameter, create corresponding fuzzy variables and define a set of fuzzy terms for these variables, such as "low," "medium," and "high." Then, based on expert knowledge or historical data, construct fuzzy rules to describe the relationships between these variables. For example, if the mass flow rate is "high" and the inlet temperature difference is "low," then the efficiency might be "medium." A fuzzy logic inference mechanism, the Mamdani model, is applied to handle the fuzziness of the input data.
[0058] In summary, the heat transfer performance identification model constructed in this application uses fractional derivatives to enhance the description of nonlinear dynamic characteristics and introduces a fuzzy genetic algorithm to achieve adaptive parameter optimization. After identification and analysis, the heat transfer performance identification model can output the comprehensive performance characteristics of the heat exchanger, including: current heat transfer efficiency with an accuracy better than ±2%, heat transfer coefficient with an accuracy better than ±5%, pressure drop coefficient and drag coefficient reflecting flow loss, temperature efficiency and pressure efficiency characterizing thermodynamic performance, and the identification results can be used for optimized control, predictive maintenance, fault diagnosis, and operation strategy formulation of compressed air energy storage systems, providing reliable support for the optimized operation of compressed air energy storage systems. Specifically, through real-time performance evaluation and parameter optimization, the system operating efficiency can be improved by 3-5%; based on performance degradation trend analysis, predictive maintenance can be achieved, extending equipment service life by 15-20%; intelligent control strategies can be adopted to improve system operational reliability and reduce unplanned downtime by more than 30%; and combined with maintenance decision optimization, maintenance costs can be reduced by 15-25%.
[0059] In addition, this application is particularly applicable to the performance evaluation and optimization control of heat exchangers in fields such as compressed air energy storage systems, industrial heat exchange equipment, and energy systems that require high-precision performance identification.
[0060] According to the heat exchanger performance identification model construction method proposed in the embodiments of this application, the linear heat exchange and nonlinear heat exchange components of the compressed air energy storage system during the energy storage process can be extracted from the historical operating data of the heat exchanger in the compressed air energy storage system. Based on the linear and nonlinear heat exchange components, a heat exchange performance identification model of the heat exchanger is constructed so that the heat exchange performance of the heat exchanger can be identified in the subsequent use of the heat exchange performance identification model. By fully considering the linear and nonlinear heat exchange components in the heat exchange process, the heat exchange performance identification model can more comprehensively reflect the complex behavior of the heat exchanger and accurately identify the heat exchange performance of the heat exchanger, thereby improving the identification effect and accuracy of the heat exchange performance identification model.
[0061] The above embodiments focus on describing the solution of this application from the perspective of model construction, while the following embodiments focus on describing the solution of this application from the perspective of model operation.
[0062] Figure 2 This is a flowchart of a heat exchanger performance identification method according to an embodiment of this application.
[0063] like Figure 2 As shown, the heat exchanger performance identification method includes the following steps:
[0064] In step S201, the current operating data of the heat exchanger in the compressed air energy storage system is obtained.
[0065] The current operating data includes the mass flow rates of the hot and cold fluids in the heat exchanger and the corresponding inlet and outlet temperatures.
[0066] In step S202, the current operating data is input into the heat exchanger performance identification model, and the heat exchanger performance identification model outputs the current heat exchanger performance. The heat exchanger performance identification model is constructed based on the linear heat exchange part and nonlinear heat exchange part of the compressed air energy storage system in the energy storage process from historical operating data.
[0067] The construction of the heat exchange identification model has been described in the above embodiments and will not be repeated here.
[0068] It is understood that, in the embodiments of this application, the current operating data can be input into the heat exchanger's heat exchange performance identification model, and the current heat exchange performance of the heat exchanger can be output using the heat exchange performance identification model.
[0069] In this embodiment of the application, after the heat exchange performance identification model outputs the current heat exchange performance of the heat exchanger, it further includes: obtaining the reference heat exchange performance of the current operating data; if the current heat exchange performance is inconsistent with the reference heat exchange performance, then re-optimizing the model parameters of the heat exchange performance identification model.
[0070] The reference heat exchange performance can be obtained from historical operating data or expert knowledge.
[0071] It is understood that, in the embodiments of this application, if the current heat exchange performance is inconsistent with the reference heat exchange performance, the model parameters of the heat exchange performance identification model can be re-optimized to further optimize the model and ensure that the model can maintain high accuracy and robustness under different operating conditions.
[0072] According to the heat exchanger performance identification method proposed in the embodiments of this application, the current operating data of the heat exchanger in the compressed air energy storage system can be input into the heat exchanger performance identification model, and the heat exchanger performance identification model can output the current heat exchanger performance, thereby realizing the identification and prediction of the heat exchanger performance.
[0073] The following specific embodiment illustrates the construction and optimization of the heat exchanger performance identification model of this application, such as... Figure 3 As shown, it includes:
[0074] Step 1: For the specific requirements of the compressed air energy storage system heat exchanger, the input data includes fluid inlet temperature, inlet pressure, flow rate, ambient temperature, and operating time. The output data includes fluid outlet temperature, outlet pressure, and heat exchange efficiency. Based on this data, a suitable fractional order is selected, such as 0.5 or 0.9, and a Gaussian kernel function is used to construct the FO-NHCAR model that reflects the thermal dynamic characteristics of the heat exchanger.
[0075] Step 2: To address the heat exchange characteristics of compressed air during energy storage, a fractional derivative is introduced into the linear dynamic part of the heat exchanger, and the fractional parameters are adjusted according to the system characteristics to refine the description of the complexity of the heat exchange process.
[0076] Step 3: Design a static nonlinear block and use polynomials or other nonlinear functions to accurately simulate the nonlinear heat exchange process in the compressed air energy storage system.
[0077] Step 4: Based on the operating data of the heat exchanger in the compressed air energy storage system, initialize the model parameters. These parameters cover fractional-order coefficients and nonlinear and linear components, and establish the baseline behavior of the model.
[0078] Step 5: Use a fuzzy genetic algorithm to fine-tune the model parameters, monitor the optimization effect through the fitness function, and gradually refine the model parameters to achieve a high degree of accuracy in predicting the performance of the heat exchanger under variable operating conditions of compressed air energy storage.
[0079] Step 6: Conduct comprehensive performance tests on the adjusted model, compare the response of the compressed air energy storage system heat exchanger in actual operation with the model prediction, and ensure that the model can maintain high accuracy and robustness under different operating conditions.
[0080] It is mainly divided into three parts: the initial construction of the heat exchange performance identification model, the optimization of model parameters, and the verification and performance evaluation of the model.
[0081] I. Constructing a Fractional-Order Nonlinear Hammerstein Controlled Autoregressive (FO-NHCAR) Model. First, by introducing fractional derivatives into the linear dynamic block of the Hammerstein model, the thermal dynamic behavior of the heat exchanger during energy storage is optimized, enabling the model to accurately capture the inherent complexity and long-term system memory characteristics of the energy storage system. This process begins by defining the basic dynamic behavior and operating environment of the heat exchanger system. Using collected inlet and outlet temperatures and real-time mass flow rates of the heat exchanger fluid under different operating conditions, a preliminary analysis of the model's input-output relationship is conducted, identifying key variables and potential nonlinear relationships affecting the turbine's heat exchange performance. Subsequently, appropriate fractional order and kernel functions are selected to describe the impact of parameter settings for the inlet and outlet temperatures and real-time mass flow rates of the heat exchanger fluid on the turbine's efficiency and, consequently, the overall efficiency of the compressed air energy storage system. These parameters directly affect the accuracy and complexity of the compressed air energy storage system model. The nonlinear part of the model is typically expressed using polynomials or other basis functions, while fractional derivatives are used to describe the linear dynamic part. After completing these steps, the model parameters are initially estimated, providing a starting point for the global optimization of the genetic algorithm.
[0082] It should be noted that, in the process of model construction, this application comprehensively considered key factors such as the influence of heat exchanger structural characteristics on heat transfer, the nonlinear characteristics of working fluid physical parameters changing with temperature, the heat transfer enhancement effect under different flow patterns, the influence of fouling and scaling on heat transfer performance, and the dynamic response characteristics of system operating condition fluctuations. The comprehensive consideration of these factors ensures that the model can accurately reflect the performance characteristics of the heat exchanger under various operating conditions.
[0083] II. Optimization of Heat Exchanger Parameters in the FO-NHCAR Model Using Fuzzy Genetic Algorithm. A fuzzy genetic algorithm is employed to optimize the parameter estimation process of the model. By simulating natural selection and genetic mutation mechanisms, the adaptability and predictive accuracy of the heat exchanger model under varying operating conditions in compressed air energy storage systems are enhanced. This design not only overcomes the shortcomings of traditional linear models in handling complex nonlinear problems of heat exchangers in compressed air energy storage systems but also improves the practical value and performance in the context of multi-scenario grid-connected applications of compressed air energy storage systems. In this stage, firstly, key input and output parameters affecting heat exchanger performance, such as mass flow rate, temperature difference, and efficiency, are identified and defined. For each key parameter, corresponding fuzzy variables are created, and a set of fuzzy terms, such as "low," "medium," and "high," is defined for these variables. Then, based on expert knowledge or historical data, fuzzy rules are constructed to describe the relationships between these variables. For example, if the mass flow rate is "high" and the inlet temperature difference is "low," then the efficiency might be "medium." A fuzzy logic inference mechanism, the Mamdani model, is applied to handle the fuzziness of the input data. A fuzzy logic controller (FLC) is designed to adjust and optimize the model parameters. The controller receives real-time or predicted model input parameters and, through fuzzy inference, outputs parameter settings or adjustment suggestions best suited to the current situation. The fuzzy output is then defuzzified using a two-sided maximization method, converting it into precise numerical values that can be practically applied to the system. Based on the defuzzified results, the heat exchanger model parameters are updated. These updates can be validated through further simulations and real-world testing. This process is repeated iteratively to optimize the parameters until the predetermined performance target or steady state is achieved.
[0084] In implementing the fuzzy genetic algorithm, real-number encoding is used to directly encode model parameters. A fitness function is constructed by comprehensively considering recognition accuracy and computational efficiency. Roulette wheel selection and elite retention strategies are employed, along with adaptive factorial crossover and non-uniform mutation operations to improve optimization efficiency. Furthermore, the algorithm innovatively introduces fuzzy rules to dynamically adjust genetic operation parameters, further enhancing optimization performance.
[0085] III. Model Validation and Performance Evaluation. The optimized model parameters were applied to the heat exchanger system to simulate and predict real-time data, validating the model's effectiveness. First, a simulation environment was set up, using the latest real-time or historical data to run the optimized model. Using the constructed heat exchanger, the system's predicted output was generated, and these outputs were compared with actual operating data. The mean squared error (MSE) statistical method was used to quantify the model's prediction error and prediction quality. Finally, sensitivity analysis was performed to understand the impact of parameter variations on the output, thereby further adjusting and optimizing the model parameters.
[0086] It should be noted that, to ensure the accuracy and reliability of the identification model, the heat exchange performance identification in this application not only establishes performance benchmark values based on historical data, but also assesses performance change trends by calculating the deviation between the current performance and the benchmark values, thereby providing a basis for predicting maintenance time and optimization suggestions. This comprehensive performance evaluation system lays the foundation for intelligent operation and maintenance of heat exchangers, and also provides a reliable basis for efficiency optimization.
[0087] This application employs a three-level verification system to ensure the reliability of the identification model: First, the model prediction accuracy is verified by using cross-validation to evaluate the model's prediction accuracy under different operating conditions, ensuring that the prediction error is controlled within the design specifications; second, the reliability of the identification results is verified by using the Monte Carlo method to evaluate the model's stability and robustness, and to verify the confidence interval of the identification results; finally, engineering application verification is conducted by running the model in a real system for at least 3 months to comprehensively evaluate the model's actual effects in energy efficiency improvement, fault warning, and maintenance optimization.
[0088] The method presented in this application demonstrates significant technical and economic value in practical applications: the heat exchange efficiency identification error can be controlled within the design value, the heat transfer coefficient identification accuracy meets engineering application requirements, it can effectively warn of performance anomalies, improve system operating efficiency, and reduce maintenance costs. Through actual verification, this method has significant advantages in heat exchanger performance identification, fault warning, and maintenance decision-making, providing reliable support for the efficient operation of compressed air energy storage systems.
[0089] In summary, the solution of this application embodiment has the following advantages:
[0090] 1. A fractional-order nonlinear Hammerstein controlled autoregressive (FO-NHCAR) model is adopted. The theory of fractional-order calculus is used to enhance the heat exchanger model's ability to capture the thermal dynamics within the energy storage system, reflecting the complex dynamic behavior of the system caused by changes in fluid dynamics and heat transfer. This allows the heat exchanger model to not only more accurately simulate heat exchange phenomena during compression and expansion processes, but also improves its adaptability and predictive reliability under different operating conditions.
[0091] 2. By combining the global search capability of fuzzy genetic algorithms with the uncertainty handling capabilities of fuzzy logic, a highly efficient and accurate optimization method for parameter estimation is proposed to estimate the optimal parameters for compressed air energy storage heat exchangers. This method effectively explores the complex multi-physics coupled parameter space of the heat exchanger under various operating states by simulating the natural selection, crossover, and mutation processes of biological evolution. It finds the parameter combination that optimizes the heat exchanger's performance under real-time operating conditions, making it particularly suitable for handling heat exchanger optimization problems with multiple local optima, ensuring that the best parameter configuration can be obtained under different operating conditions.
[0092] 3. By employing a precise model and optimized parameter estimation methods, the model achieves high robustness under different operating environments. The fractional-order model has low sensitivity to initial conditions and historical data, enabling the heat exchanger to effectively adapt to rapid changes in the turbine's operating state and maintain stable system performance. Furthermore, the optimization process using the fuzzy genetic algorithm considers the model's performance under different operating conditions, ensuring that the mass flow rate of the heat exchange medium and the inlet and outlet temperatures can be quickly adjusted to adapt to different operating requirements. This allows the heat exchanger to rapidly adjust and follow changes in the turbine's operating state.
[0093] 4. Comprehensive identification: This invention not only identifies heat exchange efficiency, but also includes a complete performance index system such as heat transfer coefficient and resistance characteristics, providing comprehensive support for system optimization.
[0094] 5. Strong real-time performance: Through strict data acquisition standards and efficient calculation methods, the performance of heat exchangers can be identified in real time, supporting dynamic optimization control of the system.
[0095] 6. Good scalability: The identification method of this invention can be easily extended to other types of heat exchangers, and has broad application prospects.
[0096] Next, referring to the accompanying drawings, the apparatus for constructing a heat exchanger heat exchanger performance identification model and the apparatus for identifying heat exchanger heat exchanger performance according to embodiments of this application are described.
[0097] Figure 4 This is a block diagram of a heat exchanger heat exchange performance identification model construction device according to an embodiment of this application.
[0098] like Figure 4 As shown, the heat exchanger performance identification model construction device 10 includes: a first acquisition module 101, an extraction module 102, and a construction module 103.
[0099] The first acquisition module 101 is used to acquire historical operating data of the heat exchanger in the compressed air energy storage system under different operating conditions. The historical operating data includes the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures, and the corresponding heat exchange efficiency. The extraction module 102 is used to extract the linear heat exchange part and the nonlinear heat exchange part of the compressed air energy storage system during the energy storage process from the historical operating data. The linear heat exchange part is used to represent the linear heat exchange process, and the nonlinear heat exchange part is used to represent the nonlinear heat exchange process. The construction module 103 is used to construct a heat exchange performance identification model of the heat exchanger based on the linear heat exchange part and the nonlinear heat exchange part. The heat exchange performance identification model is used to identify the heat exchange performance of the heat exchanger under different operating conditions.
[0100] In this embodiment of the application, the construction module 103 is further used to: determine the model parameters of the linear heat exchange section and the nonlinear heat exchange section of the heat exchanger based on the mass flow rate of the hot and cold fluids, the inlet and outlet temperatures and the corresponding heat exchange efficiency of the heat exchanger; and combine the model parameters of the linear heat exchange section and the model parameters of the nonlinear heat exchange section to generate a heat exchange performance identification model.
[0101] In the embodiments of this application, the linear heat exchange section introduces fractional derivatives and kernel functions, and adjusts the fractional parameters and kernel function parameters according to the characteristics of the compressed air energy storage system; the nonlinear heat exchange section introduces nonlinear functions.
[0102] In this embodiment of the application, the apparatus 10 further includes: a first optimization module.
[0103] The first optimization module is used to optimize the initial model parameters of the heat exchange performance identification model based on the fuzzy genetic algorithm after constructing the heat exchange performance identification model of the heat exchanger based on the linear heat exchange part and the nonlinear heat exchange part; to judge the prediction accuracy of the optimized heat exchange performance identification model; and to stop optimizing the model parameters of the heat exchange performance identification model if the prediction accuracy meets the preset standard.
[0104] In this embodiment, the first optimization module is further configured to: create fuzzy variables corresponding to each data point in the historical operating data, and define a set of fuzzy terms for each fuzzy variable; construct fuzzy rules based on expert knowledge or historical operating data; and optimize the initial model parameters of the heat exchange performance identification model based on the fuzzy rules and historical operating data.
[0105] It should be noted that the foregoing explanation of the embodiment of the heat exchanger heat exchange performance identification model construction method also applies to the heat exchanger heat exchange performance identification model construction device of this embodiment, and will not be repeated here.
[0106] The heat exchanger performance identification model construction device proposed in the embodiments of this application can extract the linear and nonlinear heat exchange components of the compressed air energy storage system during the energy storage process from the historical operating data of the heat exchanger in the compressed air energy storage system. Based on the linear and nonlinear heat exchange components, a heat exchanger performance identification model is constructed, and the heat exchanger performance is identified using the heat exchanger performance identification model. By fully considering the linear and nonlinear heat exchange components in the heat exchange process, the heat exchanger performance identification model can more comprehensively reflect the complex behavior of the heat exchanger and accurately identify the heat exchanger performance, thereby improving the identification effect and accuracy of the heat exchanger performance identification model.
[0107] Figure 5 This is a block diagram of a heat exchanger performance identification device according to an embodiment of this application.
[0108] like Figure 5 As shown, the heat exchanger performance identification device 20 includes a second acquisition module 201 and an input module 202.
[0109] The second acquisition module 201 is used to acquire the current operating data of the heat exchanger in the compressed air energy storage system. The current operating data includes the mass flow rate of the hot and cold fluids and the inlet and outlet temperatures of the heat exchanger. The input module 202 is used to input the current operating data into the heat exchange performance identification model of the heat exchanger. The heat exchange performance identification model outputs the current heat exchange performance of the heat exchanger. The heat exchange performance identification model is constructed based on the linear heat exchange characteristics and nonlinear heat exchange characteristics of the compressed air energy storage system during the energy storage process from historical operating data.
[0110] In this embodiment of the application, the apparatus 20 further includes a second optimization module.
[0111] The second optimization module is used to obtain the reference heat exchange performance of the current operating data after the heat exchange performance identification model outputs the current heat exchange performance of the heat exchanger; if the current heat exchange performance is inconsistent with the reference heat exchange performance, the model parameters of the heat exchange performance identification model are re-optimized.
[0112] It should be noted that the explanation of the above-mentioned method for identifying the heat exchange performance of a heat exchanger also applies to the heat exchange performance identification device of the heat exchanger in this embodiment, and will not be repeated here.
[0113] According to the heat exchange performance identification device for heat exchangers proposed in the embodiments of this application, the current operating data of the heat exchanger in the compressed air energy storage system can be input into the heat exchange performance identification model of the heat exchanger, and the heat exchange performance identification model can output the current heat exchange performance of the heat exchanger, thereby realizing the identification and prediction of the heat exchange performance of the heat exchanger.
[0114] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:
[0115] The memory 401, the processor 402, and the computer program stored on the memory 401 and capable of running on the processor 402.
[0116] When the processor 402 executes the program, it implements the heat exchanger performance identification model construction method or the heat exchanger performance identification method provided in the above embodiments.
[0117] Furthermore, electronic devices also include:
[0118] Communication interface 403 is used for communication between memory 401 and processor 402.
[0119] The memory 401 is used to store computer programs that can run on the processor 402.
[0120] The memory 401 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.
[0121] If the memory 401, processor 402, and communication interface 403 are implemented independently, then the communication interface 403, memory 401, and processor 402 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be divided into address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.
[0122] Optionally, in a specific implementation, if the memory 401, processor 402, and communication interface 403 are integrated on a single chip, then the memory 401, processor 402, and communication interface 403 can communicate with each other through an internal interface.
[0123] Processor 402 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.
[0124] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0125] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0126] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.
[0127] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.
[0128] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
Claims
1. A method for constructing a heat exchange performance identification model of a heat exchanger, characterized in that, The method comprises the following steps: acquiring historical operation data of a heat exchanger in a compressed air energy storage system under different operation conditions, wherein the historical operation data comprises mass flow rates of cold and hot fluids, inlet and outlet temperatures, and corresponding heat exchange efficiencies; extracting linear heat exchange parts and nonlinear heat exchange parts of the compressed air energy storage system in an energy storage process from the historical operation data, wherein the linear heat exchange parts are used to represent linear heat exchange processes, and the nonlinear heat exchange parts are used to represent nonlinear heat exchange processes; the linear heat exchange parts introduce fractional derivative and kernel function, and fractional order parameters and kernel function parameters are adjusted according to characteristics of the compressed air energy storage system; constructing a heat exchange performance identification model of the heat exchanger based on the linear heat exchange parts and the nonlinear heat exchange parts, wherein the heat exchange performance identification model is used to identify heat exchange performances of the heat exchanger under different operation conditions; after the heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange parts and the nonlinear heat exchange parts, the method further comprises the following steps: optimizing initial model parameters of the heat exchange performance identification model based on a fuzzy genetic algorithm; judging a prediction accuracy of the optimized heat exchange performance identification model; if the prediction accuracy meets a preset standard, stopping optimization of model parameters of the heat exchange performance identification model; the step of optimizing the initial model parameters of the heat exchange performance identification model based on the fuzzy genetic algorithm comprises the following steps: creating a fuzzy variable corresponding to each piece of data in the historical operation data, and defining a fuzzy term set for each fuzzy variable; constructing fuzzy rules based on expert knowledge or the historical operation data; and optimizing the initial model parameters of the heat exchange performance identification model based on the fuzzy rules and the historical operation data.
2. The heat exchanger performance identification model construction method of claim 1, wherein The step of constructing the heat exchange performance identification model of the heat exchanger based on the linear heat exchange parts and the nonlinear heat exchange parts comprises the following steps: determining model parameters of the linear heat exchange parts and model parameters of the nonlinear heat exchange parts of the heat exchanger based on the mass flow rates of the cold and hot fluids, the inlet and outlet temperatures, and the corresponding heat exchange efficiencies of the heat exchanger, respectively; combining the model parameters of the linear heat exchange parts and the model parameters of the nonlinear heat exchange parts to generate the heat exchange performance identification model.
3. The heat exchanger performance identification model construction method of claim 2, characterized in that, The nonlinear heat exchange parts introduce nonlinear functions.
4. A method for identifying heat exchange performance of a heat exchanger, characterized by, The method comprises the following steps: acquiring current operation data of a heat exchanger in a compressed air energy storage system, wherein the current operation data comprises mass flow rates of cold and hot fluids of the heat exchanger and inlet and outlet temperatures of the heat exchanger; inputting the current operation data into a heat exchange performance identification model of the heat exchanger, and outputting current heat exchange performance of the heat exchanger by the heat exchange performance identification model, wherein the heat exchange performance identification model is constructed based on a heat exchange performance identification model construction method of a heat exchanger according to any one of claims 1 to 3.
5. The heat exchanger performance identification method of claim 4, wherein After the heat exchange performance identification model outputs the current heat exchange performance of the heat exchanger, the method further comprises the following steps: acquiring a reference heat exchange performance of the current operation data; if the current heat exchange performance is inconsistent with the reference heat exchange performance, re-optimizing model parameters of the heat exchange performance identification model.
6. A heat exchange performance identification model construction device of a heat exchanger, characterized by, The method comprises the following steps: The first obtaining module is configured to obtain historical operation data of a heat exchanger in a compressed air energy storage system under different operation conditions, wherein the historical operation data comprises mass flow rates, inlet and outlet temperatures of cold and hot fluids, and corresponding heat exchange efficiencies; The extraction module is configured to extract a linear heat exchange part and a nonlinear heat exchange part of the compressed air energy storage system in an energy storage process from the historical operation data, wherein the linear heat exchange part is used to represent a linear heat exchange process, and the nonlinear heat exchange part is used to represent a nonlinear heat exchange process; the linear heat exchange part introduces a fractional derivative and a kernel function, and adjusts fractional order parameters and kernel function parameters according to characteristics of the compressed air energy storage system; The construction module is configured to construct a heat exchange performance identification model of the heat exchanger based on the linear heat exchange part and the nonlinear heat exchange part, wherein the heat exchange performance identification model is used to identify heat exchange performance of the heat exchanger under different operation conditions; after the heat exchange performance identification model of the heat exchanger is constructed based on the linear heat exchange part and the nonlinear heat exchange part, the method further comprises: optimizing initial model parameters of the heat exchange performance identification model based on a fuzzy genetic algorithm; judging a prediction accuracy of the optimized heat exchange performance identification model; if the prediction accuracy meets a preset standard, stopping optimization of model parameters of the heat exchange performance identification model; the optimization of the initial model parameters of the heat exchange performance identification model based on the fuzzy genetic algorithm comprises: creating a fuzzy variable corresponding to each data in the historical operation data, and defining a fuzzy term set for each fuzzy variable; constructing fuzzy rules based on expert knowledge or the historical operation data; and optimizing the initial model parameters of the heat exchange performance identification model based on the fuzzy rules and the historical operation data.
7. A heat exchanger performance identification device, characterized in that, The second obtaining module is configured to obtain current operation data of a heat exchanger in a compressed air energy storage system, wherein the current operation data comprises mass flow rates and inlet and outlet temperatures of cold and hot fluids of the heat exchanger; The input module is configured to input the current operation data into a heat exchange performance identification model of the heat exchanger, and the heat exchange performance identification model outputs current heat exchange performance of the heat exchanger, wherein the heat exchange performance identification model is constructed based on the heat exchange performance identification model construction device of the heat exchanger according to claim 6. The memory, the processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the heat exchange performance identification model construction method of the heat exchanger according to any one of claims 1-3, or the heat exchange performance identification method of the heat exchanger according to any one of claims 4-5.
8. An electronic device, comprising: