High-speed train brake disc multi-objective optimization method and system based on machine learning

Abstract

The invention relates to the field of train braking, and discloses a high-speed train brake disc multi-objective optimization method and system based on machine learning so as to improve the timeliness and the resource utilization rate. The method comprises the steps that a finite element parameterization model of the high-speed train brake disc is constructed and verified through a test, the finite element parameterization model packages a whole process in a code mode, and automatic mapping of parameter input-simulation output is achieved; adopting an experimental design method to construct a data set for machine learning based on a finite element parameterized model, and automatically extracting an input variable and an output variable in the data set by a batch processing program; training, verifying and testing a target model for predicting the thermodynamic response index of the high-speed train brake disc structure according to the data set; defining an optimization target and constraint conditions of the structure parameters, and obtaining a Pareto solution set of the optimization target by a non-dominated sorting genetic algorithm of an embedded target model; and performing optimal decision on the Pareto solution set to obtain an optimal solution of the structural parameters of the brake disc.

Description

Technical Field

[0001] The present invention relates to the technical field of optimizing the braking performance of trains, and particularly to a multi-objective optimization method and system for high-speed train brake discs based on machine learning. Background Art

[0002] The structural optimization of high-speed train C / C-SiC brake discs is of great significance for extending service life, reducing maintenance costs, and improving operation efficiency. The structural design of C / C-SiC brake discs involves multiple key structural parameters, such as the layout of heat dissipation ribs, the thickness of the friction layer, and the overall geometric shape, etc. There are complex coupling relationships among these parameters. During the optimization process, it is necessary to comprehensively consider the interaction between the thermal field and the mechanical field, as well as the non-linear effects among various design variables, in order to achieve the collaborative optimization of multiple objectives such as braking performance, thermal management efficiency, and lightweight. However, traditional optimization methods have problems such as high computational cost, long cycle, poor repeatability, etc., and it is difficult to efficiently search for the global optimal solution in the high-dimensional design space, which limits their application in practical engineering. Therefore, it is particularly important to explore more advanced optimization methods.

[0003] Traditional research methods mainly rely on finite element simulation, experimental testing, and classical optimization algorithms. Although the experimental method can provide intuitive performance data, its cost is high and it is limited by experimental conditions, making it difficult to comprehensively cover complex working conditions; the finite element method can simulate the multi-physical field coupling effect, but it requires high computational resources and the optimization process takes a long time. In addition, traditional optimization algorithms (such as genetic algorithms, particle swarm algorithms, etc.) often face challenges such as slow convergence speed and easy to fall into local optimum when dealing with high-dimensional and non-linear problems, and it is difficult to meet the accuracy and efficiency requirements of modern high-speed train brake disc design.

[0004] The structural parameters of the brake disc have a decisive influence on its performance. For example, the brake disc thickness directly affects the heat capacity and heat dissipation efficiency; the number, shape, and layout of the heat dissipation ribs have a significant impact on the thermal stress distribution and air flow organization. In-depth study of the internal relationship between these parameters and the thermodynamic response characteristics is crucial for the optimization design. At present, the mainstream research method is still mainly the combination of finite element simulation and experiment, but this method is not only time-consuming but also costly, and it is difficult to meet the design requirements of rapid iteration. Therefore, it is urgent to introduce more efficient and intelligent optimization methods to achieve the multi-objective structural optimization of high-speed train C / C-SiC brake discs. Summary of the Invention

[0005] The purpose of the present invention is to disclose a multi-objective optimization method and system for high-speed train brake discs based on machine learning, so as to improve the timeliness and resource utilization rate.

[0006] To achieve the above object, the multi-objective optimization method for high-speed train brake discs based on machine learning disclosed by the present invention includes: Step S1: Construct and experimentally verify the finite element parametric model of the high-speed train brake disc. The finite element parametric model encapsulates the entire process of geometric parameter driving, material association, load application, mesh generation, and calculation submission into coded programs, realizing the automatic mapping of "parameter input - simulation output". Step S2: Use the DOE (Design of Experiments) method to construct a dataset for machine learning based on the finite element parametric model, and automatically extract the input variables and output variables in the dataset using a batch processing program. The input variables are structural parameters, and the output variables are thermodynamic response indicators. The thermodynamic response indicators include the maximum temperature, maximum stress, and maximum axial deformation. Then, train, validate, and test a target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure based on the dataset. Step S3: Define the optimization objective and the constraint conditions of the structural parameters, and obtain the Pareto solution set of the optimization objective using the non-dominated sorting genetic algorithm embedded in the target model. The optimization objective is to minimize the maximum temperature, maximum stress, and maximum axial deformation. Step S4: Make an optimal decision on the Pareto solution set to obtain the optimal solution of the brake disc structural parameters.

[0007] Preferably, the brake disc is a C / C-SiC brake disc.

[0008] Preferably, the structural parameters used as input variables include: the angular parameter of the cooling fins, the number of cooling fins, and the thickness of the friction layer.

[0009] Preferably, constructing the finite element parametric model includes: (1) Import the ABAQUS core module; (2) Define the key parameters of the finite element model through class functions; (3) Establish the brake disc geometric model using the defined functions; (4) Combine the various components of the brake disc into a complete model, including: creating instances in ABAQUS through the Assembly module, adjusting the position using the rotation or translation function, fixing the relative motion through constraints, and verifying that the geometry of the assembly has no interference and the degrees of freedom are reasonable; (5) Create material properties through the Material module and assign them to the brake disc components; (6) Set the analysis step in the Step module and specify the output frequencies of the field variables and history variables; (7) Set the mechanical behavior between components in the Interaction module to define the interaction relationship; (8) Apply loads and define boundary conditions in the Load module. (9) Discretize the geometric model in the Mesh module, define the element type and mesh density, and perform mesh quality checks to ensure convergence; (10) In the Job module, create the solution settings for the model and build a Bat batch file using the Python language to solve at least two models simultaneously.

[0010] Preferably, in step S2, the sampling strategy of the DOE method adopts the Latin hypercube method.

[0011] Preferably, in step S2, the input variables and output variables in the dataset are automatically extracted by a batch processing program, including: Read the temperature data of all nodes in a traversal manner and find the maximum temperature value, and record the corresponding node number; then use the extreme value comparison method to find the node coordinate information corresponding to the maximum temperature, and accurately output the temperature value corresponding to the maximum temperature node; Read the maximum equivalent stress values of all stress integration points in a traversal manner, and output the corresponding stress integration point element numbers. Use the extreme value comparison method to find the stress integration point coordinates and element node information corresponding to the maximum stress; finally, use the method of comparing the element information and the integration point information to accurately output the stress corresponding to the maximum stress integration point; Read the deformation data of all nodes in a traversal manner and find the maximum temperature value, and record the corresponding node number; finally, use the extreme value comparison method to find the node coordinate information corresponding to the maximum axial deformation, and accurately output the temperature value corresponding to the maximum axial deformation node.

[0012] Preferably, the target model is an MLP-ANN model.

[0013] Preferably, in the process of making the optimal decision for the Pareto solution set, step S4 includes: Step S41: Determine the target decision variables, worst and best decision objectives corresponding to the CBW (Cloud Best-Worst) decision criterion; Step S42: Determine that the decision algorithm scale combination is the CBW algorithm constructed by adding the cloud model theory to the BW (Best-Worst) method, and calculate the eigenvalue expectations Ex, entropies En, and hyperentropies He of each scale; Step S43: Determine the priority preference value of the optimal decision objective relative to other decision objectives; In the process of decision-making analysis, it is assumed that the opinions of each expert have equal weight in the final decision; based on this assumption, a preference vector is constructed to represent the priority of each decision-making objective relative to the optimal decision-making objective; suppose there are m experts scoring n decision-making objectives, and the score of the m-th expert for the i-th decision-making objective can be expressed as: ; ; In the formula, represents the preference vector of all experts for the optimal decision-making objective relative to other criteria; is the cloud model vector of all experts for the optimal decision-making objective relative to the i-th decision-making objective; m is the ordinal number of the corresponding expert; M is the total number of experts; represents the expectation of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the entropy of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the hyperentropy of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the expectation of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective; represents the entropy of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective; represents the hyperentropy of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective; Step S44: Determine the priority preference value of the worst decision-making objective relative to other decision-making objectives; In the process of evaluating the worst decision relative to other objectives, it is also assumed that the opinions of each expert have equal weight in the final decision. Based on this assumption, a preference vector is constructed to represent the priority of each decision-making objective relative to the worst decision-making objective. The specific calculation formula is as follows: ; ; In the formula, represents the preference vector of the m-th expert for the worst decision-making objective relative to other criteria; represents the cloud model vector of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; represents the expectation of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; represents the entropy of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; represents the hyperentropy of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; ; ; In the formula, represents the preference vector of all experts for the worst decision target relative to other criteria; is the cloud model vector of all experts for the worst decision target relative to the i-th decision target; represents the expectation of all experts for the worst decision target relative to the i-th decision target; represents the entropy of all experts for the worst decision target relative to the i-th decision target; represents the hyperentropy of all experts for the worst decision target relative to the i-th decision target; Step S45, find the optimal weight; In the CBW weight decision algorithm, the basic idea of the BW method is adopted. Assuming that each decision target has a corresponding weight value, the weight matrix of the decision target can be expressed as: ; In the formula, represents the weight value of the i-th decision target; To ensure that for any i of the optimal weight, and one of them satisfies and conditions, where is the weight value of the optimal decision target, is the weight value of the worst decision target; so that and the absolute value difference between them reaches the maximum, where , , represent the weight matrix of the optimal decision, the weight matrix of the i-th decision, and the weight matrix of the worst decision respectively; considering the non-negativity and cumulative sum conditions of the weight, the problem is transformed into the following model: ; ; ;

[0014] ; In the formula, represents the expectation of all experts for the weight of the optimal decision target; represents the expectation of all experts for the weight of the i-th decision target; represents the entropy of all experts for the weight of the optimal decision target; represents the entropy of all experts for the weight of the i-th decision target; Denote the hyperentropy of all experts' weights for the optimal decision-making goal; Denote the hyperentropy of all experts' weights for the i-th decision-making goal; Denote the expectation of all experts' weights for the worst decision-making goal; Denote the entropy of all experts' weights for the worst decision-making goal; Denote the hyperentropy of all experts' weights for the worst decision-making goal; Step S46: Determine the gain matrix and the gain weight matrix; Based on the positive and negative correlations among decision-making goals, corresponding weights must be assigned to the positive and negative correlation coefficients to determine the weights of decision-making goals. Define the positive and negative correlations as positive and negative gains respectively: ; where, is the gain coefficient corresponding to the i-th decision-making goal. When it is positive, it is denoted as , and when it is negative, it is denoted as ; Therefore, according to the defined gain matrix, obtain the gain weight matrix of decision-making goals as follows: ; where, denotes the gain weight corresponding to the i-th decision-making goal; Step S47: Multiply the Pareto solution set by the transpose matrix of the gain weight matrix to obtain the corresponding decision-making goal matrix; then, by calculating the sum of each row of the decision-making goal matrix, find the Pareto solution with the largest sum result as the optimal solution; the calculation formula is: ; In the formula, is the decision-making goal matrix; denotes the Pareto solution set; denotes the -th solution of the Pareto solution set, ; denotes the i-th decision-making goal; the superscript denotes the transpose.

[0015] To achieve the above object, the present invention also discloses a multi-objective optimization system for high-speed train brake discs based on machine learning, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above method is implemented.

[0016] The present invention has the following beneficial effects: 1. The DOE method is adopted to construct a dataset for machine learning based on a finite element parametric model. Compared with the traditional manual one-by-one manipulation method, the finite element parametric model greatly improves the efficiency, and batch processing programs are used to automatically extract the input variables and output variables in the dataset, providing accurate and efficient dataset support for quickly constructing a target model for predicting the thermodynamic response indexes of the high-speed train brake disc structure.

[0017] 2. Based on the target model for predicting the thermodynamic response indexes of the high-speed train brake disc structure of the present invention, as long as new structural parameters are given, the trained weights of the network can be directly called, the mode of the network can be changed to a prediction model, and stress, displacement and temperature can be directly predicted, which can greatly increase the rate of product upgrade and iteration and increase the product pedigree (for the development of brake discs applicable to different speeds, energy levels and different trains).

[0018] 3. The target model for predicting the thermodynamic response indexes of the high-speed train brake disc structure can be used for transfer learning. In the process of training the original network with small sample data of new structures / new materials of brake discs with similar mechanisms, the original network can directly call the weights trained previously, and then use the small sample data to train again, which can be used for brake discs of new materials and new structures, improving the utilization rate of resources.

[0019] 4. The present invention adopts a method combining non-dominated sorting genetic algorithm and machine learning to perform multi-objective structural optimization on the high-speed train brake disc. As an efficient multi-objective optimization algorithm, the non-dominated sorting genetic algorithm can effectively search for the Pareto optimal solution set in a complex multi-objective space through fast non-dominated sorting and crowding degree calculation, and is especially suitable for solving high-dimensional and non-linear engineering optimization problems. The target model for predicting the thermodynamic response indexes of the high-speed train brake disc structure is embedded in the non-dominated sorting genetic algorithm of the present invention, which not only retains the advantages of strong global search ability and uniform solution set distribution of the non-dominated sorting genetic algorithm, but also realizes a significant improvement in calculation efficiency through the data-driven characteristics of machine learning. When dealing with large-scale data, the calculation time can be significantly reduced.

[0020] The present invention will be further described in detail below with reference to the accompanying drawings. Description of the Drawings

[0021] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 It is a schematic flow chart of the method disclosed in Embodiment 1 of the present invention.

[0022] Figure 2It is a schematic diagram of the data processing flow for embedding the MLP-ANN model as a surrogate model into the non-dominated sorting genetic algorithm to obtain the Pareto solution set of the optimization objective disclosed in Embodiment 1 of the present invention.

[0023] Figure 3 It is a schematic diagram of the temperature-time curve of the thermocouple measurement point disclosed in Embodiment 1 of the present invention.

[0024] Figure 4 It is a comparison diagram of experiment and simulation disclosed in Embodiment 1 of the present invention.

[0025] Figure 5 It is a schematic diagram of the method flow for the operation of the multi-objective optimization system of the high-speed train brake disc based on machine learning disclosed in Embodiment 2 of the present invention. Detailed implementation manners

[0026] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways defined and covered by the claims.

[0027] Embodiment 1 This embodiment discloses a multi-objective optimization method for a high-speed train brake disc based on machine learning. As Figure 1 shown, first, a finite element parametric model of the C / C-SiC brake disc is constructed using the Python scripting language. Relying on a full-scale railway brake test bench, an emergency braking test of the C / C-SiC brake disc of a 400 km / h high-speed train is carried out to verify the accuracy of the finite element model. Secondly, the design of experiments (DOE) method is used to sample the data of the C / C-SiC brake disc finite element model to generate a data set for machine learning. Then, four machine learning models, namely the hybrid multi-layer perceptron and artificial neural network (MLP-ANN), extreme gradient boosting algorithm (XGBoost), K-nearest neighbor algorithm (KNN), and convolutional neural network (CNN), are introduced to predict the thermodynamics response indexes of the C / C-SiC brake disc structure. By comparing the prediction accuracies of the four machine learning models, the optimal prediction model is selected as MLP-ANN. Next, the hybrid multi-layer perceptron and artificial neural network (MLP-ANN) are used as a surrogate model, and combined with the non-dominated sorting genetic algorithm (NSGA-II) to perform multi-objective structural optimization on the C / C-SiC brake disc. Finally, based on the multi-objective optimization results, the Pareto solution set of the optimization objective is obtained, and the CBW weight decision algorithm is used to perform the optimal decision on the Pareto solution set to obtain the optimal solution of the structural parameters of the C / C-SiC brake disc.

[0028] In this embodiment, compared with the traditional finite element modeling method that relies on the interactive geometric modeling of 3D software (repeated model construction is required for parameter adjustment), manually defining material properties and boundary conditions item by item, manually configuring mesh strategies and solution parameters in the graphical interface, etc., which are time-consuming operations, parametric modeling encapsulates the entire process of geometric parameter drive, material association, load application, mesh generation, and calculation submission into code, realizing the automated mapping of "parameter input - simulation output". This provides strong support for constructing a large-scale dataset for the design of experiments (DOE) of C / C-SiC brake discs. By standardizing the modeling logic to eliminate human errors, relying on the parallel computing ability to batch generate a large number of regular simulation datasets, providing a high-quality data basis for machine learning model training, and significantly improving the accuracy and efficiency of multi-objective optimization. The main steps of the finite element parametric modeling program for C / C-SiC brake discs are as follows: (1) Import the ABAQUS core module.

[0029] When using the Python language for finite element parametric modeling of C / C-SiC brake discs in ABAQUS, it is necessary to first use the import statement to import the required modules. This is a basic requirement of Python programming and a prerequisite for accessing specific functions of ABAQUS. To access a specific object in ABAQUS, the module to which the object belongs must be imported first.

[0030] (2) Define the key parameters of the finite element model through class functions (class).

[0031] By defining a dedicated class to encapsulate the key parameters of the finite element model, the organization and readability of the code can be improved, facilitating the rapid creation and modification of models of different sizes. The use of classes allows for the repeated definition of parameters in different models and also allows for the definition of methods in the class to achieve associated calculations between parameters.

[0032] (3) Use def() to define a function to establish the geometric model of the brake disc.

[0033] This function mainly involves creating a constraint sketch and determining the plane and direction of the sketch. When dealing with complex models, masks often appear, resulting in the inability to correctly create the model once the structural parameters are changed. To solve this problem, relevant functions are used to globally search for the faces and edges at the specified coordinates and output the corresponding indices. The parameter definition of the geometric model is realized through code to ensure that the model size and shape can be dynamically adjusted according to the input parameters.

[0034] In other words, parametric modeling can be regarded as a secondary development of ABAQUS using the Python language. Usually, the.rpy files of the ABAQUS graphical user interface are utilized, but the default ".rpy files" are indexed in a masked manner. The mask contains mask codes and lacks generality, so this kind of code cannot be directly used; therefore, it should be avoided when performing parametric modeling. Thus, in order to obtain code that can be directly used in this embodiment, that is, the model can still be correctly established after changing the structural parameters, findAt(), find_round_edge_index, and find_round_face_inde can be used to replace the mask to complete the indexing of objects such as points, lines, and surfaces in the brake disc component. Among them, the findAt function creates sets of point, surface, and cell in the way of coordinate points, with the characteristics of parameterization and is convenient for control.

[0035] (4) Complete the assembly of the model.

[0036] Combine each component of the brake disc into a complete model according to the actual working condition positions. Create instances through the Assembly module in ABAQUS, use the rotation or translation function to adjust the positions, and fix the relative motion through constraints. It is necessary to verify that there is no geometric interference in the assembly and the degrees of freedom are reasonable.

[0037] (5) Assign material properties to the C / C-SiC brake disc.

[0038] Associate material properties such as the density, elastic parameters (elastic modulus, Poisson's ratio), and thermophysical parameters (thermal conductivity, specific heat capacity, coefficient of thermal expansion) of the C / C-SiC composite material with the geometric model to achieve automatic assignment of material parameters.

[0039] (6) Set the analysis step.

[0040] Define the analysis (temperature-displacement coupling) in the Step module, and set key parameters such as the time step size, maximum number of increment steps, and initial increment. Specify the output frequencies of field variables and history variables.

[0041] Among them, the time step size refers to the total time spent for the finite element model of the brake disc to achieve braking and stop under emergency braking conditions such as 400 / km. For example: when the brake disc is emergently braked from 400 km / h to 0 km / h, the braking time used is 122.02 s, so the time step size is set to 122.02 s.

[0042] The function of the maximum number of increment steps is to limit the maximum number of increment steps allowed in an analysis step. If this value is reached but the analysis is not completed, the program will report an error and terminate. Therefore, this parameter can be set to 0.1 in the model.

[0043] The initial increment is the first time step at the start of the analysis. It determines the starting step size of the calculation. An overly large initial step size may cause non-convergence in the first step. To improve the model's convergence, the initial increment should be small, and its value can be set to 0.005.

[0044] (7)Define the interaction relationship.

[0045] Set the mechanical behavior between components in the Interaction module; including the definition of contact pairs and constraint types.

[0046] (8)Apply loads and define boundary conditions.

[0047] Apply external excitation in the Load module and define load types, boundary conditions, loading methods, etc.

[0048] (9)Mesh generation.

[0049] Discretize the geometric model in the Mesh module, define element types, mesh density, and perform mesh quality checks to ensure convergence.

[0050] (10)Create a Job.

[0051] Create a Job for a single model, which means completing the solution settings of the model. To submit and run multiple Jobs on a large scale, use the Python language to build a Bat batch file, utilize the parallel computing ability, and batch generate simulation data to provide a large-scale data set for subsequent analysis.

[0052] After that, based on the boundary conditions set by the finite element simulation, a full-scale bench emergency braking experiment can be carried out. Adopt the method of experimental-simulation comparison and verification. By analyzing the temperature-time curves in the experimental and simulation results, verify the accuracy of the finite element model.

[0053] Before constructing a data-driven model of the structural parameters and thermodynamic response indicators of a C / C-SiC brake disc, it is necessary to generate a finite element simulation dataset using the DOE method. Since different DOE sampling strategies directly affect the data feature distribution, sample representativeness, and model generalization ability. The Latin Hypercube method performs well in studying nonlinear models, can simultaneously examine the influence of multiple features on the model performance, and provides a higher-quality sample set. Considering the complex dynamic behavior of high-dimensional coupling, uncertainty, and multi-scale effects between the structural parameters and thermodynamic response indicators of the brake disc, the experimental design faces challenges such as strong coupling, large nonlinearity, and computational intensiveness. Based on these considerations, this patent selects the Latin Hypercube method to sample the brake disc structure, and a total of 500 groups of sample points are generated. During the construction of the dataset, the heat dissipation rib angle parameter, the number of heat dissipation ribs, and the friction layer thickness of the C / C-SiC brake disc are used as input variables, and the thermodynamic response indicators (maximum temperature T, maximum stress S, maximum axial deformation U) are used as output variables. Through the secondary development of finite element software, the input variables (design parameters) and output variables (thermodynamic response indicators) of the DOE calculation data are automatically extracted to construct a dataset for multi-objective optimization. The specific implementation method for obtaining the thermodynamic response indicators in the DOE calculation data is as follows: (1) Extraction of the maximum temperature data of the brake disc: The DOE simulation data of the C / C-SiC brake disc is mainly generated using the ABAQUS software. Since the simulation data is relatively large, the methods such as the field output report, field variable X-Y data, and query values built into the ABAQUS software have problems of cumbersome operation and low efficiency, and are not suitable for the extraction of large-scale simulation data. To solve this problem, a batch processing program is developed for data extraction and management. The underlying language of the ABAQUS software is mainly based on the Python language, which provides convenience for directly using Python for data extraction and summary.

[0054] The simulation result data Odb file contains two types of information: model data (such as node, element, node set, and element set information) and result data. The data extraction program can be realized by establishing the access path of the Odb object. When extracting the temperature of the C / C-SiC brake disc, a specific process needs to be followed. First, the corresponding nodes need to be found; then, the information of these nodes is extracted and the corresponding output data is obtained. The Euclidean distance method (L2 norm) can be used to calculate the distance between the target coordinate and each node coordinate, and finally the node label and coordinate with the closest distance are returned.

[0055] In this embodiment, the brake disc geometry is divided into hexahedral elements, and the nodes are the connection points between the elements, which determine the spatial distribution of the mesh. The surface temperature field of the brake disc is obtained by interpolating the node temperatures.

[0056] After determining the information for finding the corresponding nodes, the next step is to obtain the temperature field data of these nodes in order to extract the maximum temperature data of the brake disc. The process of extracting the maximum temperature data of the nodes can be summarized into the following steps: First, it is necessary to output all the temperature field data in a specific analysis step; then, read the temperature data of all nodes in a traversal manner and find the maximum temperature value, and record the corresponding node number; finally, use the method of extreme value comparison to find the node coordinate information corresponding to the highest temperature, and accurately output the temperature value corresponding to the highest temperature node.

[0057] (2) Extraction of the maximum stress data of the brake disc: During the data extraction process, a special challenge is faced: the stress in the ABAQUS calculation results is mainly calculated by the integration point method. This means that simply using the Cartesian coordinates of the nodes to read the data may lead to errors in node identification. Therefore, in the process of reading the stress of the brake disc, a special method is needed to read the stress integration point data of the brake disc. For this purpose, in the process of data extraction, first set the initial minimum distance to infinity, then traverse all the element information, and continuously calculate the distance between the given node information and the centroid integration point of each element using the Euclidean norm. Finally, obtain the element information closest to the given node by continuously iterating and updating the assignment. This method lays the foundation for reading the stress data of specific nodes. Through this precise positioning method, the stress data of each key node can be accurately extracted, thus ensuring the accuracy and reliability of subsequent analysis.

[0058] After obtaining the stress integration point information in the C / C-SiC brake disc simulation data, the next step is to extract the maximum stress point data. The specific extraction process can be summarized into the following steps: First, it is necessary to output all the stress field data in a specific analysis step; then, read the maximum equivalent stress values of all stress integration points in a traversal manner, and output the corresponding stress integration point element numbers. Use the method of extreme value comparison to find the stress integration point coordinates and element node information corresponding to the maximum stress; finally, use the method of comparing the element information and the integration point information to accurately output the stress corresponding to the maximum stress integration point.

[0059] Generally, node information is used to represent geometric discrete points. The brake disc geometry is discretized into a finite number of discrete points. Nodes are the vertices of the mesh and also the "sampling points" for numerical calculations. Each node bears displacement and temperature. Element information is used to represent the geometric elements after the discretization of the differential equation. The hexahedron formed by connecting nodes is the basic element for the discretization of the differential equation. And the integration point information is the key point of numerical integration, which is the discrete point inside the element and is used to calculate the element stiffness matrix and stress.

[0060] (3)Extraction of the maximum axial deformation data of the brake disc: The process of reading the deformation of the C / C-SiC brake disc is significantly similar to the process of reading the temperature, and both follow the following basic steps: First, locate the target and determine the node information corresponding to the given coordinates; then, based on the obtained node information coordinates, traverse the corresponding deformation field data; finally, extract and output the specific data corresponding to the node. In the specific implementation process, the find_close_node function can be called. By calling this function, an accurate correspondence between the spatial coordinates and the specific deformation data can be established, thus greatly improving the accuracy and efficiency of the entire data extraction process.

[0061] During the simulation process of the C / C-SiC brake disc, the method for extracting the maximum axial deformation data of the nodes is similar to the method for obtaining the maximum stress value. The specific extraction process can be summarized as the following steps: First, it is necessary to output all the deformation field data in a specific analysis step; then, read the deformation data of all nodes in a traversal manner and find the maximum axial deformation value, and record the corresponding node number; finally, use the method of extreme value comparison to find the node coordinate information corresponding to the maximum axial deformation, and accurately output the value corresponding to the node with the maximum axial deformation.

[0062] After that, the inputs and outputs of the data-driven model can be randomly divided into a training set and a test set, and the input data and output data are normalized to eliminate the dimensional difference and accelerate the model convergence. Based on the normalized data set. Four machine learning models, namely MLP-ANN (Multi-Layer Perception-Artificial Neural Network), KNN, XGBoost, and CNN, are respectively used to predict the thermodynamic response indexes of the C / C-SiC brake disc, and the prediction accuracies of different models are compared and analyzed. The machine learning model with the highest prediction accuracy is used as the final prediction model for the thermodynamic response indexes of the C / C-SiC brake disc of high-speed trains.

[0063] Based on the comparative analysis between different models, in this embodiment, the multi-MLP-ANN model is used as a surrogate model to replace the traditional computationally intensive finite element simulation, so as to significantly improve the optimization efficiency. The mathematical model of an optimization problem is as follows: .

[0064] In the above formula, , and are the angle parameters of the heat dissipation ribs (the inner diameter angle of the heat dissipation rib, the inner angle of the heat dissipation rib notch, the outer angle of the heat dissipation rib notch, the number of heat dissipation ribs ( ), and the thickness of the friction layer ( Taking the maximum temperature (T), maximum stress (S), and maximum axial deformation (U) of the C / C-SiC brake disc structure as design variables, the objective function is set. The parameters of the accompanying NSGA-II algorithm are shown in Table 1.

[0065] Table 1: Parameters of the NSGA-II algorithm:

[0066] In this embodiment, the above MLP-ANN model is embedded into the non-dominated sorting genetic algorithm to obtain the Pareto solution set of the optimization objective, and the corresponding data processing flow is as Figure 2 shown.

[0067] In this embodiment, after obtaining the Pareto solution set of the optimization objective based on the multi-objective optimization results of the machine learning-based NSGA-II algorithm, the CBW weight decision algorithm can be used to make an optimal decision on the optimized Pareto solution set to obtain the optimal solution of the C / C-SiC brake disc structure parameters. The specific method is as follows: (1) Determine the objective decision variables corresponding to the CBW decision criterion.

[0068] This patent takes T, S, and U of the high-speed train C / C-SiC brake disc as the objectives of multi-objective optimization.

[0069] (2) Determine the worst and best decision objectives.

[0070] When the train brakes, about 95% of the braking kinetic energy is converted into heat energy through friction. The temperature field affects the entire brake disc volume through heat conduction, and its gradient distribution (temperature difference between the surface and the interior) directly affects the distribution of the thermal stress field and the deformation field. Therefore, T is selected as the best decision objective, and U is the worst decision objective.

[0071] (3) Determine the scale combination of the decision algorithm.

[0072] The cloud model theory is added to the Best-Worst (BW) method to construct a new weight decision algorithm (Cloud Best-Worst, CBW). Based on the basic theory of the cloud model, 9 scale combinations (A 1 to A 9 ) of the corresponding CBW are developed, as shown in Table 2. By calculating the characteristic values Ex (expectation), En (entropy), and He (hyper-entropy) of each scale, the distribution and its uncertainty of the data can be better understood and analyzed. Specifically, Ex represents the central tendency of the data, reflecting the average level of the data; En reflects the degree of uncertainty of the data, indicating the volatility of the data; and He describes the dispersion degree of the entropy, revealing the diversity of the data distribution.

[0073] Table 2: CBW preference values

[0074] (4) In the process of decision-making analysis, it is assumed that the opinions of each expert have equal weight in the final decision; based on this assumption, a preference vector is constructed to represent the priority of each decision-making objective relative to the optimal decision-making objective; suppose there are m experts scoring n decision-making objectives, and the score of the m-th expert for the i-th decision-making objective can be expressed as: ; .

[0075] In the formula, represents the preference vector of all experts for the optimal decision-making objective relative to other criteria; is the cloud model vector of all experts for the optimal decision-making objective relative to the i-th decision-making objective; m is the ordinal number of the corresponding expert; M is the total number of experts; represents the expectation of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the entropy of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the hyperentropy of all experts for the optimal decision-making objective relative to the i-th decision-making objective; represents the expectation of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective; represents the entropy of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective; represents the hyperentropy of the m-th expert for the optimal decision-making objective relative to the i-th decision-making objective.

[0076] (5) Determine the priority preference value of the worst decision-making objective relative to other decision-making objectives.

[0077] In the process of evaluating the worst decision relative to other objectives, it is also assumed that the opinions of each expert have equal weight in the final decision. Based on this assumption, a preference vector is constructed to represent the priority of each decision-making objective relative to the worst decision-making objective. The specific calculation formula is as follows: ; .

[0078] In the formula, represents the preference vector of the m-th expert for the worst decision-making objective relative to other criteria; represents the cloud model vector of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; represents the expectation of the m-th expert for the worst decision-making objective relative to the i-th decision-making objective; Denote the entropy of the worst decision target relative to the \(i\)-th decision target by the \(m\)-th expert; Denote the hyper-entropy of the worst decision target relative to the \(i\)-th decision target by the \(m\)-th expert.

[0079] ; .

[0080] In the formula, Denote the preference vector of all experts for the worst decision target relative to other criteria; Is the cloud model vector of all experts for the worst decision target relative to the \(i\)-th decision target; Denote the expectation of all experts for the worst decision target relative to the \(i\)-th decision target; Denote the entropy of all experts for the worst decision target relative to the \(i\)-th decision target; Denote the hyper-entropy of all experts for the worst decision target relative to the \(i\)-th decision target.

[0081] (6) Find the optimal weight.

[0082] In the CBW weight decision algorithm, the basic idea of the BW method is adopted. Assume that each decision target has a corresponding weight value, then the weight matrix of the decision target Can be expressed as: ; Denote the weight value of the \(i\)-th decision target.

[0083] To ensure that for any \(i\) of the optimal weight, And One of them satisfies And The conditions, where, Is the weight value of the optimal decision target, Is the weight value of the worst decision target; so that And The absolute value difference between them reaches the maximum, where, , , Represent the weight matrix of the optimal decision, the weight matrix of the \(i\)-th decision, and the weight matrix of the worst decision respectively; considering the non-negativity and cumulative sum conditions of the weight, the problem is transformed into the following model: ; ; ;

[0084] .

[0085] In the formula, represents the expectation of all experts for the weight of the optimal decision-making goal; represents the expectation of all experts for the weight of the i-th decision-making goal; represents the entropy of all experts for the weight of the optimal decision-making goal; represents the entropy of all experts for the weight of the i-th decision-making goal; represents the hyper-entropy of all experts for the weight of the optimal decision-making goal; represents the hyper-entropy of all experts for the weight of the i-th decision-making goal; represents the expectation of all experts for the weight of the worst decision-making goal; represents the entropy of all experts for the weight of the worst decision-making goal; represents the hyper-entropy of all experts for the weight of the worst decision-making goal.

[0086] (7) Determine the gain matrix and the gain weight matrix.

[0087] Based on the positive and negative correlations between decision-making goals, corresponding weights must be assigned with positive and negative correlation coefficients to determine the weights of decision-making goals. The positive and negative correlations are defined as positive and negative gains respectively: ; Among them, is the gain coefficient corresponding to the i-th decision-making goal. When it is positive, it is expressed as , and when it is negative, it is expressed as .

[0088] Therefore, according to the defined gain matrix, the gain weight matrix of the decision-making goal is obtained as follows: .

[0089] Among them, represents the gain weight corresponding to the i-th decision-making goal.

[0090] (8) By multiplying the Pareto solution set by the transpose matrix of the gain weight matrix, the corresponding decision-making goal matrix is obtained; then, by calculating the sum of each row of the decision-making goal matrix, the Pareto solution with the largest sum result is found as the optimal solution; the calculation formula is: ; In the formula, is the decision-making goal matrix; represents the Pareto solution set; represents the -th solution of the Pareto solution set, ; represents the \(i\)th decision-making objective; the superscript represents the transpose.

[0091] To further illustrate the efficiency of the optimization process in this embodiment, the MLP-ANN model and the finite element model (FEM) are respectively used to compare the calculation time of the optimization process. The calculation times of the optimization processes of MLP-ANN and FEM are as follows: ; where is the total calculation time required for the machine learning MLP-ANN model to calculate the DOE, is the time required for MLP-ANN training, is the time required for each sample calculation after the model training is successful, is the number of samples of the DOE.

[0092] Furthermore: ; where is the total calculation time required for the finite element model to calculate the DOE, is the time required for each sample calculation of the finite element model.

[0093] Also: ; where is the ratio of the time required for the machine learning MLP-ANN model and the finite element model to calculate the DOE.

[0094] From the results of the comparative experiments, it can be seen that when \(n = 80\), \(T_{ML}\) and \(T_{FE}\) are 402 hours and 80 hours respectively, \(T_{IFE}\) is 502.5%, and the time required by MLP-ANN is greater than the calculation time of the finite element model. When \(n = 1100\), \(T_{ML}\) and \(T_{FE}\) are 402.02 hours and 1100 hours respectively, \(T_{IFE}\) is 10.1%, and the time required by MLP-ANN is less than the calculation time of the finite element model. When \(n\) is small, the calculation time of MLP-ANN will be longer than that of FEM. As the number of \(n\) increases, the calculation of MLP-ANN basically remains unchanged, while the calculation time of the finite element model increases significantly, and \(T_{IFE}\) will show an exponential decrease. Therefore, it can be found that when the number of samples sampled in the optimization process is large, using the MLP-ANN model can greatly reduce the calculation time. The MLP-ANN model can enable the optimization process to achieve big data empowerment and bring the structural optimization of C / C-SiC brake discs into a new field.

[0095] To observe the thermodynamic response index characteristics of C / C-SiC brake discs during the emergency braking process of high-speed trains, an emergency braking test of C / C-SiC brake discs was carried out on a full-scale railway brake test bench at a speed of 400 km / h. The test adopted a two-gradient loading strategy: apply a braking force with a pre-tightening force of 18 kN in the high-speed range of 300 km / h - 400 km / h to suppress the thermoelastic instability phenomenon, and switch to the main braking force mode of 32 kN until the vehicle stops after the speed drops to 300 km / h. To eliminate the interference of the contact heterogeneity of the friction pair interface on the test data, before the test, in accordance with the standard regulations, 20 - 30 running-in brakings were carried out under the conditions of 120 km / h and 32 kN to ensure that the effective contact area of the friction pair ≥ 85%, achieving uniform friction. To accurately obtain the temperature change of the brake disc during braking, in this embodiment, a contact thermocouple temperature measurement technology is used to monitor the temperature of the friction surface with high precision. Six embedded thermocouples (embedded depth 1 mm) are symmetrically buried at intervals of 120° in the central area of the double friction surfaces of the brake disc. Among them, 2 are arranged at the average radius position, and 4 are located in the heat dissipation sensitive area 40 mm outside the average radius. Compared with the infrared thermal imaging technology, which is easily restricted by surface emissivity, environmental interference, measurement blind spots, etc., the embedded thermocouple can accurately obtain the real temperature data inside the structure, effectively avoiding the influence of dust splashing and oxide layer formation during the braking process on non-contact temperature measurement, providing high-reliability experimental data support for studying the thermo-mechanical coupling effect of the brake disc.

[0096] To verify the thermodynamic response characteristics of C / C-SiC brake discs and the correctness of the finite element modeling method, a bench braking test was carried out using a full-scale railway brake test bench. At the same time, the finite element simulation results can be further verified by the experimental results. During the braking test, the temperature changes of six temperature measurement points on the brake disc were recorded in real time, as Figure 3 shown. The peak temperatures recorded by different thermocouples are different, reflecting the differences in the test positions, that is, the thermal characteristics of different parts of the brake disc are different. Figure 4 It is the comparison curve of the test and finite element simulation of the highest temperature of the brake disc changing with time. The results show that the change trend of the finite element simulation and experimental temperature curves of the C / C-SiC brake disc is consistent, and the highest temperature is 913.94 °C, and the relative error with the test result is only 1.16%. Considering the many factors affecting the temperature change in the actual working conditions, such as test installation errors, material inhomogeneity, detection errors of temperature measurement sensors, etc., it is reasonable to have a certain difference, which can verify the accuracy and reliability of the numerical simulation and can be used for subsequent research.

[0097] Example 2 Corresponding to the above embodiments, this embodiment discloses a multi-objective optimization system for high-speed train brake discs based on machine learning, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements Figure 5 the following method steps shown: Step S1: Construct and experimentally verify a finite element parametric model of a high-speed train brake disc. The finite element parametric model encapsulates the entire process of geometric parameter driving, material association, load application, mesh generation, and calculation submission into code, realizing an automated mapping of "parameter input - simulation output".

[0098] Step S2: Use the DOE method to construct a dataset for machine learning based on the finite element parametric model, and automatically extract input variables and output variables from the dataset using a batch processing program; the input variables are structural parameters, and the output variables are thermodynamic response indicators; the thermodynamic response indicators include the maximum temperature, maximum stress, and maximum axial deformation; then train, validate, and test a target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure based on the dataset.

[0099] Step S3: Define the optimization objectives and the constraint conditions of the structural parameters, and obtain the Pareto solution set of the optimization objectives using the non-dominated sorting genetic algorithm embedded in the target model; the optimization objectives are to minimize the maximum temperature, maximum stress, and maximum axial deformation.

[0100] Step S4: Make an optimal decision on the Pareto solution set to obtain the optimal solution of the brake disc structural parameters.

[0101] Preferably, the brake disc is a C / C-SiC brake disc. The structural parameters used as input variables include: the angular parameter of the heat dissipation ribs, the number of heat dissipation ribs, and the thickness of the friction layer. The target model can be an MLP-ANN model. The specific implementation of each step refers to the above embodiments and will not be elaborated here.

[0102] In summary, the multi-objective optimization method and system for high-speed train brake discs based on machine learning disclosed in the embodiments of the present invention have at least the following beneficial effects: 1. Use the DOE method to construct a dataset for machine learning based on the finite element parametric model. Among them, the finite element parametric model greatly improves the efficiency compared with the traditional manual operation method item by item, and automatically extracts input variables and output variables from the dataset using a batch processing program, providing accurate and efficient dataset support for quickly constructing a target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure.

[0103] 2. For the target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure based on the present invention, as long as new structural parameters are given, the pre-trained weights of the network can be directly called, and the mode of the network can be changed to a prediction model, so that stress, displacement and temperature can be directly predicted, which can greatly increase the rate of product upgrade and iteration and increase the product lineage (for the development of brake discs applicable to different speeds, energy levels and different trains).

[0104] 3. The target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure can be used for transfer learning. During the process of training the original network with small sample data of new structures / new materials of brake discs with similar mechanisms, the original network can directly call the weights trained previously, and then use the small sample data for retraining, so that it can be used for brake discs of new materials and new structures, improving the utilization rate of resources.

[0105] 4. The present invention adopts a method combining non-dominated sorting genetic algorithm and machine learning to perform multi-objective structural optimization on the high-speed train brake disc. As an efficient multi-objective optimization algorithm, the non-dominated sorting genetic algorithm can effectively search for the Pareto optimal solution set in a complex multi-objective space through fast non-dominated sorting and crowding degree calculation, and is particularly suitable for solving high-dimensional and non-linear engineering optimization problems. The target model for predicting the thermodynamic response indicators of the high-speed train brake disc structure is embedded in the non-dominated sorting genetic algorithm of the present invention, which not only retains the advantages of strong global search ability and uniform solution set distribution of the non-dominated sorting genetic algorithm, but also realizes a significant improvement in computational efficiency through the data-driven characteristics of machine learning. When dealing with large-scale data, it can significantly reduce the calculation time.

[0106] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization method for high-speed train brake discs based on machine learning, characterized in that: include: Step S1, constructing and experimentally verifying a finite element parametric model of a high-speed train brake disc, wherein the finite element parametric model encapsulates the entire process of geometric parameter driving, material association, load application, meshing and calculation submission in a coded manner, thereby realizing an automated mapping of "parameter input-simulation output"; Step S2, using an experimental design method to construct a data set for machine learning based on the finite element parameterized model, and automatically extracting input variables and output variables in the data set by a batch processing program; the input variables are structural parameters, and the output variables are thermodynamic response indicators; the thermodynamic response indicators include maximum temperature, maximum stress and maximum axial deformation; then training, verifying and testing a target model for predicting thermodynamic response indicators of a high-speed train brake disc structure according to the data set; Step S3, defining the optimization target and the constraints of the structural parameters, and obtaining the Pareto solution set of the optimization target by using a non-dominated sorting genetic algorithm embedded in the target model; the optimization target is to minimize the maximum temperature, the maximum stress and the maximum axial deformation; Step S4: Optimizing the Pareto solution set to obtain optimal solutions for the brake disc structural parameters.

2. The multi-objective optimization method for high-speed train brake discs based on machine learning according to claim 1 is characterized in that: The brake disc is a C / C-SiC brake disc.

3. The multi-objective optimization method for high-speed train brake discs based on machine learning according to claim 2 is characterized in that: The structural parameters used as input variables include: the angle parameters of the heat dissipation ribs, the number of heat dissipation ribs and the thickness of the friction layer.

4. The multi-objective optimization method for high-speed train brake discs based on machine learning according to any one of claims 1 to 3, characterized in that: Constructing a finite element parametric model includes: (1) Import the ABAQUS core module; (2) Define the key parameters of the finite element model through class functions; (3) Use the defined function to establish the brake disc geometric model; (4) Assemble the components of the brake disc into a complete model, including: creating an instance in ABAQUS through the Assembly module, adjusting the position using the rotation or translation function, fixing the relative motion through constraints, and verifying that the assembly geometry has no interference and the degrees of freedom are reasonable; (5) Create material properties through the Material module and assign them to the brake disc component; (6) Set the analysis step in the Step module and specify the output frequency of field variables and historical variables; (7) Set the mechanical behavior between components in the Interaction module to define the interaction relationship; (8) Apply loads and define boundary conditions in the Load module; (9) Discretize the geometric model in the Mesh module, define the element type and mesh density, and perform mesh quality checks to ensure convergence; (10) In the Job module, create the model solution settings and use Python language to build a Bat batch file to solve at least two models simultaneously.

5. The multi-objective optimization method for high-speed train brake discs based on machine learning according to any one of claims 1 to 3, characterized in that: In step S2, the sampling strategy of the experimental design method adopts the Latin hypercube method.

6. The multi-objective optimization method for high-speed train brake discs based on machine learning according to any one of claims 1 to 3, characterized in that: In step S2, the batch processing procedure is used to automatically extract input variables and output variables from the data set, including: The temperature data of all nodes are read in a traversal manner to find the maximum temperature value and record the corresponding node number; then the node coordinate information corresponding to the maximum temperature is found by using the extreme value comparison method, and the temperature value corresponding to the maximum temperature node is output; The maximum equivalent stress value of all stress integration points is read in a traversal manner, and the corresponding stress integration point unit number is output. The stress integration point coordinates and unit node information corresponding to the maximum stress are found by using extreme value comparison. Finally, the stress corresponding to the maximum stress integration point is output by comparing the unit information and the integration point information. The deformation data of all nodes are read in a traversal manner to find the maximum temperature value and record the corresponding node number; finally, the node coordinate information corresponding to the maximum axial deformation is found by using the extreme value comparison method, and the temperature value corresponding to the node with the maximum axial deformation is output.

7. The multi-objective optimization method for high-speed train brake discs based on machine learning according to any one of claims 1 to 3, characterized in that: The target model is an MLP-ANN model.

8. The multi-objective optimization method for high-speed train brake discs based on machine learning according to any one of claims 1 to 3, characterized in that: In the process of making the optimal decision for the Pareto solution set, step S4 includes: Step S41, determining the target decision variable, the worst decision target and the best decision target corresponding to the CBW decision criterion; Step S42, determining the decision algorithm scale combination as the CBW algorithm constructed by adding the cloud model theory to the BW method, and calculating the eigenvalue expectation Ex, entropy En and super entropy He of each scale; Step S43, determining the priority preference value of the optimal decision target relative to other decision targets; In the decision analysis process, it is assumed that the opinions of each expert have equal weight in the final decision. Based on this assumption, a preference vector is constructed to represent the priority of each decision target relative to the optimal decision target. Suppose m experts score n decision targets, and the score of the mth expert on the i-th decision target is expressed as: ； ； In the formula, represents the preference vector of all experts on the optimal decision-making target relative to other criteria; is the cloud model vector of the optimal decision target of all experts relative to the i-th decision target; m is the ordinal number of the corresponding expert; M is the total number of experts; represents the expectation of all experts on the optimal decision-making target relative to the i-th decision-making target; represents the entropy of all experts’ optimal decision objectives relative to the i-th decision objective; represents the super entropy of all experts for the optimal decision target relative to the i-th decision target; represents the expectation of the mth expert on the optimal decision target relative to the i-th decision target; It represents the entropy of the optimal decision target of the mth expert relative to the i-th decision target; It represents the super entropy of the optimal decision target of the mth expert relative to the i-th decision target; Step S44, determining the priority preference value of the worst decision target relative to other decision targets; In the process of evaluating the worst decision relative to other goals, it is also assumed that the opinions of each expert have equal weight in the final decision. Based on this assumption, a preference vector is constructed to represent the priority of each decision goal relative to the worst decision goal. The specific calculation formula is as follows: ； ； In the formula, represents the preference vector of the mth expert for the worst decision target relative to other criteria; Represents the cloud model vector of the mth expert’s worst decision target relative to the i-th decision target; represents the expectation of the mth expert on the worst decision target relative to the i-th decision target; It represents the entropy of the mth expert's worst decision target relative to the i-th decision target; It represents the super entropy of the mth expert for the worst decision target relative to the i-th decision target; ； ； In the formula, represents the preference vector of all experts for the worst decision goal relative to other criteria; is the cloud model vector of the worst decision target for all experts relative to the i-th decision target; represents the expectation of all experts on the worst decision target relative to the i-th decision target; Represents the entropy of the worst decision target of all experts relative to the i-th decision target; represents the super entropy of all experts for the worst decision target relative to the i-th decision target; Step S45, finding the optimal weight; In the CBW weighted decision algorithm, the basic idea of ​​the BW method is adopted. Assuming that each decision target has a corresponding weight value, the weight matrix of the decision target is It is expressed as: ； In the formula, Represents the weight value of the i-th decision target; To ensure the optimal weight at any i, and One of the satisfaction and The conditions, among which, is the weight value of the optimal decision target, is the weight value of the worst decision target; so that and The absolute value difference between them reaches the maximum, among which, , , They represent the weight matrix of the optimal decision, the weight matrix of the i-th decision, and the weight matrix of the worst decision respectively; considering the non-negativity and cumulative sum conditions of the weights, the problem is transformed into the following model: ； ； ； ； In the formula, represents the expectation of all experts on the optimal decision-making objective weight; represents the expectation of all experts on the weight of the i-th decision target; represents the entropy of all experts’ weights on the optimal decision target; represents the entropy of all experts’ weights on the i-th decision target; represents the super entropy of all experts’ weights on the optimal decision target; represents the super entropy of all experts’ weights on the i-th decision target; represents the expectation of the worst decision objective weights of all experts; represents the entropy of the weights of the worst decision targets by all experts; represents the super entropy of the weights of the worst decision targets by all experts; Step S46: Determine the gain matrix and gain weight matrix; Based on the positive and negative correlations between decision targets, the positive and negative correlations are defined as positive and negative gains, respectively: ； in, is the gain coefficient corresponding to the i-th decision target, which is expressed as , which is negative is represented by ; Therefore, according to the defined gain matrix, the gain weight matrix of the decision target is obtained as follows: ； in, represents the gain weight corresponding to the i-th decision target; Step S47, by multiplying the Pareto solution set with the transposed matrix of the gain weight matrix, the corresponding decision target matrix is ​​obtained; then, by calculating the sum of each row of the decision target matrix, the Pareto solution with the largest sum is found as the optimal solution; the calculation formula is: ； In the formula, is the decision target matrix; represents the Pareto solution set; represents the first A solution, ; represents the i-th decision goal; superscript Indicates transpose.

9. A multi-objective optimization system for high-speed train brake discs based on machine learning, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method according to any one of claims 1 to 8 is implemented.

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