Multi-objective Optimization Method and System for High-Speed Train Brake Disc Based on Machine Learning

Abstract

The present invention relates to the field of train braking, and discloses a multi-objective optimization method and system for a high-speed train brake disc based on machine learning to improve timeliness and resource utilization rate. The method includes: constructing and experimentally verifying a finite element parametric model of a high-speed train brake disc, where the finite element parametric model encapsulates the full process into code to achieve an automatic mapping of "parameter input - simulation output"; using an experimental design method to construct a dataset for machine learning based on the finite element parametric model, and automatically extracting input variables and output variables in the dataset by a batch processing program; then training, validating, and testing a target model for predicting the thermodynamic response index of the high-speed train brake disc structure according to the dataset; defining optimization objectives and constraint conditions for structural parameters, and obtaining the Pareto solution set of the optimization objective by embedding a non-dominated sorting genetic algorithm into the target model; and making an optimal decision on the Pareto solution set to obtain the optimal solution of the brake disc structural parameters.

Description

Technical Field

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

[0002] Structural optimization of C / C-SiC brake discs for high-speed trains is of great significance for extending service life, reducing maintenance costs and improving operational efficiency. The structural design of C / C-SiC brake discs involves multiple key structural parameters, such as the layout of heat dissipation ribs, friction layer thickness, and overall geometric shape, and there is a complex coupling relationship between 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 nonlinear effects between the various design variables, in order to achieve 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 time, and poor repeatability. It is also difficult to efficiently search for the global optimal solution in a high-dimensional design space, which limits its application in practical engineering. Therefore, it is particularly important to explore more advanced optimization methods.

[0003] Traditional research methods primarily rely on finite element simulation, experimental testing, and classical optimization algorithms. While experimental methods can provide intuitive performance data, they are costly and limited by experimental conditions, making them incapable of fully covering complex operating conditions. While finite element methods can simulate the effects of multi-physics coupling, they require high computational resources and the optimization process is time-consuming. Furthermore, traditional optimization algorithms (such as genetic algorithms and particle swarm optimization) often face challenges such as slow convergence and susceptibility to local optimality when dealing with high-dimensional, nonlinear problems, making them unable to meet the precision and efficiency requirements of modern high-speed train brake disc design.

[0004] The structural parameters of brake discs have a decisive influence on their performance. For example, disc thickness directly affects heat capacity and heat dissipation efficiency; the number, shape, and layout of heat dissipation ribs significantly influence thermal stress distribution and airflow organization. In-depth research on the intrinsic relationship between these parameters and thermodynamic response characteristics is crucial for design optimization. Currently, the mainstream research method still relies on a combination of finite element simulation and experiments, but this approach is not only time-consuming and costly, but also difficult to adapt to the needs of rapid design iteration. Therefore, it is urgent to introduce more efficient and intelligent optimization methods to achieve multi-objective structural optimization of C / C-SiC brake discs for high-speed vehicles. 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 to improve timeliness and resource utilization.

[0006] To achieve the above objectives, the present invention discloses a multi-objective optimization method for high-speed train brake discs based on machine learning, which includes:

[0007] 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 coded form, realizing an automated mapping of "parameter input - simulation output".

[0008] 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 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.

[0009] 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.

[0010] Step S4: Make an optimal decision for the Pareto solution set to obtain the optimal solution of the brake disc structural parameters.

[0011] Preferably, the brake disc is a C / C-SiC brake disc.

[0012] Preferably, the structural parameters 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.

[0013] Preferably, constructing the finite element parametric model includes:

[0014] (1) Import the ABAQUS core module;

[0015] (2) Define the key parameters of the finite element model through class functions;

[0016] (3) Establish a brake disc geometric model using the defined function;

[0017] (4) Combine the various components of the brake disc into a complete model, including: creating an instance through the Assembly module in ABAQUS, 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;

[0018] (5) Create material properties through the Material module and assign them to the brake disc components;

[0019] (6) Set the analysis step in the Step module, and specify the output frequencies of field variables and historical variables;

[0020] (7) Set the mechanical behavior between components in the Interaction module to define the interaction relationship;

[0021] (8) Apply loads and define boundary conditions in the Load module;

[0022] (9) Discretize the geometric model in the Mesh module, define the element type, mesh density, and perform mesh quality checks to ensure convergence;

[0023] (10) In the Job module, create the solution settings for the model and construct a Bat batch file using the Python language to solve at least two models simultaneously.

[0024] Preferably, in step S2, the sampling strategy of the DOE method adopts the Latin hypercube method.

[0025] Preferably, in step S2, the input variables and output variables in the dataset are automatically extracted by a batch processing program, including:

[0026] Read the temperature data of all nodes in a traversal manner to 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;

[0027] 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 comparison method of element information and integration point information to accurately output the stress corresponding to the maximum stress integration point;

[0028] Read the deformation data of all nodes in a traversal manner to 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.

[0029] Preferably, the target model is an MLP-ANN model.

[0030] Preferably, in the process of making the optimal decision for the Pareto solution set, step S4 includes:

[0031] Step S41: Determine the target decision variables, worst and best decision objectives corresponding to the CBW (Cloud Best-Worst) decision criterion;

[0032] 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 hyper entropies He of each scale;

[0033] Step S43: Determine the priority preference value of the optimal decision goal relative to other decision goals;

[0034] In the process of decision analysis, assume that the opinions of each expert have equal weight in the final decision; based on this assumption, construct a preference vector to represent the priority of each decision goal relative to the optimal decision goal; assume that m experts rate n decision goals, and the rating of the m-th expert on the i-th decision goal can be expressed as:

[0035] ;

[0036] ;

[0037] In the formula, represents the preference vector of all experts on the optimal decision goal relative to other criteria; is the cloud model vector of all experts on the optimal decision goal relative to the i-th decision goal; 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 goal relative to the i-th decision goal; represents the entropy of all experts on the optimal decision goal relative to the i-th decision goal; represents the hyper entropy of all experts on the optimal decision goal relative to the i-th decision goal; represents the expectation of the m-th expert on the optimal decision goal relative to the i-th decision goal; represents the entropy of the m-th expert on the optimal decision goal relative to the i-th decision goal; represents the hyper entropy of the m-th expert on the optimal decision goal relative to the i-th decision goal;

[0038] Step S44: Determine the priority preference value of the worst decision goal relative to other decision goals;

[0039] In the process of evaluating the worst decision relative to other goals, also assume that the opinions of each expert have equal weight in the final decision. Based on this assumption, construct a preference vector to represent the priority of each decision goal relative to the worst decision goal. The specific calculation formula is as follows:

[0040] ;

[0041] ;

[0042] In the formula, represents the preference vector of the m-th expert for the worst decision target relative to other criteria; represents the cloud model vector of the m-th expert for the worst decision target relative to the i-th decision target; represents the expectation of the m-th expert for the worst decision target relative to the i-th decision target; represents the entropy of the m-th expert for the worst decision target relative to the i-th decision target; represents the hyperentropy of the m-th expert for the worst decision target relative to the i-th decision target;

[0043] ;

[0044] ;

[0045] 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;

[0046] Step S45, find the optimal weight;

[0047] 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:

[0048] ;

[0049] In the formula, represents the weight value of the i-th decision target;

[0050] 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 , , They respectively represent the weight matrix of the optimal decision, the weight matrix of the i-th decision, and the weight matrix of the worst decision. Considering the non-negativity and cumulative sum conditions of the weights, the problem is transformed into the following model:

[0051] ;

[0052] ;

[0053] ;

[0054]

[0055] ;

[0056] 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; represents the hyper-entropy of all experts for the weight of the optimal decision target; represents the hyper-entropy of all experts for the weight of the i-th decision target; represents the expectation of all experts for the weight of the worst decision target; represents the entropy of all experts for the weight of the worst decision target; represents the hyper-entropy of all experts for the weight of the worst decision target;

[0057] Step S46. Determine the gain matrix and the gain weight matrix;

[0058] Based on the positive and negative correlations existing between decision targets, corresponding weights must be assigned with positive and negative correlation coefficients to determine the weights of decision targets. The positive and negative correlations are respectively defined as positive and negative gains:

[0059] ;

[0060] Among them, is the gain coefficient corresponding to the i-th decision target. If it is positive, it is represented as , and if it is negative, it is represented as ;

[0061] Therefore, according to the defined gain matrix, the gain weight matrix of the decision target is obtained as follows:

[0062] ;

[0063] Among them, represents the gain weight corresponding to the i-th decision objective;

[0064] Step S47: Multiply the Pareto solution set by the transpose matrix of the gain weight matrix to obtain the corresponding decision objective matrix; then, by calculating the sum of each row of the decision objective matrix, find the Pareto solution with the largest sum result as the optimal solution; the calculation formula is:

[0065] ;

[0066] In the formula, is the decision objective matrix; represents the Pareto solution set; represents the -th solution of the Pareto solution set, ; represents the i-th decision objective; the superscript represents the transpose.

[0067] 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.

[0068] The present invention has the following beneficial effects:

[0069] 1. The DOE method is adopted to construct a dataset for machine learning based on a finite element parametric model. Among them, the finite element parametric model greatly improves the efficiency compared with the traditional manual item-by-item control method, and automatically extracts the input variables and output variables in the dataset through a batch processing program, providing accurate and efficient dataset support for quickly constructing a target model for predicting the thermodynamic response index of the high-speed train brake disc structure.

[0070] 2. Based on the target model for predicting the thermodynamic response index 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, and the mode of the network can be changed to a prediction model, then the stress, displacement, and temperature can be directly predicted, which can greatly increase the rate of product upgrade and iteration and increase the product line characteristics (applicable to the development of brake discs for different speeds, energy levels, and different trains).

[0071] 3. The target model for predicting the thermodynamic response index of the high-speed train brake disc structure can be used for transfer learning. When training the original network with a small sample of data of a new structure / new material of the brake disc with a similar mechanism, the original network can directly call the weights trained previously, and then use the small sample data for retraining, which can be applied to the brake discs of new materials and new structures, improving the utilization rate of resources.

[0072] 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 index 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.

[0073] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The accompanying drawings that form 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:

[0075] Figure 1 is a schematic flowchart of the method disclosed in Embodiment 1 of the present invention.

[0076] Figure 2 is a schematic data processing flowchart of 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.

[0077] Figure 3 is a schematic diagram of the temperature-time curve of the thermocouple measurement point disclosed in Embodiment 1 of the present invention.

[0078] Figure 4 is a comparison diagram of experiment and simulation disclosed in Embodiment 1 of the present invention.

[0079] Figure 5 is a schematic flowchart of the method run by 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 DESCRIPTION OF THE EMBODIMENTS

[0080] 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.

[0081] Embodiment 1

[0082] This embodiment discloses a multi-objective optimization method for high-speed train brake discs 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 surrogate models, 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 objectives is obtained, and the CBW weight decision algorithm is used to make the optimal decision on the Pareto solution set to obtain the optimal solution of the structural parameters of the C / C-SiC brake disc.

[0083] In this embodiment, compared with the traditional finite element modeling method that relies on the interactive geometric modeling of three-dimensional software (repeated model construction is required for parameter adjustment), manually defining material properties and boundary conditions item by item, manually configuring grid strategies and solution parameters through the graphical interface, etc., which are time-consuming operations, parametric modeling encapsulates the entire process of geometric parameter driving, 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 the design of experiments (DOE) of the C / C-SiC brake disc to construct a large-scale data set. By eliminating human errors through standardized modeling logic, relying on the parallel computing ability to batch generate large-scale simulation data sets, it provides a high-quality data basis for machine learning model training, significantly improving the accuracy and efficiency of multi-objective optimization. The main steps of the finite element parametric modeling program for the C / C-SiC brake disc are as follows:

[0084] (1) Import the ABAQUS core module.

[0085] When performing finite element parametric modeling of C / C-SiC brake discs using the Python language in ABAQUS, it is first necessary to use the import statement to import the required modules. This is a basic requirement for Python programming and a prerequisite for accessing specific functions in ABAQUS. To access a specific object in ABAQUS, the module to which the object belongs must be imported first.

[0086] (2)Define the key parameters of the finite element model through class functions (class).

[0087] 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 enables the definition of methods within the class to achieve associated calculations between parameters.

[0088] (3)Use def() to define a function to establish the geometric model of the brake disc.

[0089] 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, causing the model to not be created correctly 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 achieved through code to ensure that the model size and shape can be dynamically adjusted according to the input parameters.

[0090] In other words, parametric modeling can be regarded as a secondary development of ABAQUS using the Python language. Usually, the.rpy file of the ABAQUS graphical user interface is utilized, but the default ".rpy file" uses the masking method for indexing. The mask contains mask encodings and is not universal, so this kind of code cannot be directly used; therefore, it should be avoided during 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 faces in the brake disc component. Among them, the findAt function creates point, surface, and cell sets through coordinate points and has the characteristics of parameterization, which is convenient for control.

[0091] (4)Complete the assembly of the model.

[0092] Combine the components of the brake disc into a complete model according to their actual working conditions. In ABAQUS, create an instance through the Assembly module, use the rotation or translation function to adjust the position, and fix the relative movement through constraints. It is necessary to verify that the geometry of the assembly has no interference and the degrees of freedom are reasonable.

[0093] (5)Assign material properties to the C / C-SiC brake disc.

[0094] 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.

[0095] (6)Set the analysis step.

[0096] 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.

[0097] Among them, the time step size refers to the total time it takes 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.

[0098] 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.

[0099] The initial increment is the first time step size at the beginning of the analysis. It determines the starting step size of the calculation. If the initial step size is too large, it may cause non-convergence in the first step. To improve the convergence of the model, the initial increment should be small, and its value can be set to 0.005.

[0100] (7)Define the interaction relationship.

[0101] Set the mechanical behavior between components in the Interaction module; including the definition of contact pairs and constraint types.

[0102] (8)Apply loads and define boundary conditions.

[0103] Apply external excitations in the Load module, and define the load type, boundary conditions, loading method, etc.

[0104] (9)Mesh generation.

[0105] Discretize the geometric model in the Mesh module, define the element type, mesh density, and perform mesh quality inspection to ensure convergence.

[0106] (10) Create a Job.

[0107] The creation of a Job for a single model, i.e., the solution settings of the model are completed. To submit and run multiple Jobs on a large scale, a Bat batch file is constructed using the Python language, and the parallel computing ability is utilized to batch generate simulation data, providing a large-scale dataset for subsequent analysis.

[0108] After that, based on the boundary conditions set by the finite element simulation, a full-scale bench emergency braking experiment can be carried out. By using the method of experimental-simulation comparison and verification, the accuracy of the finite element model is verified by analyzing the temperature-time curves in the experimental and simulation results.

[0109] Before constructing a data-driven model of the structural parameters and thermodynamic response indexes of the 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 excellently 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 indexes of the brake disc, the experimental design faces challenges such as strong coupling, large nonlinearity, and high computational intensity. 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 process of constructing 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 indexes (the highest temperature T, the maximum stress S, and the maximum axial deformation U) are used as output variables. Through the secondary development of the finite element software, the input variables (design parameters) and output variables (thermodynamic response indexes) 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 indexes in the DOE calculation data is as follows:

[0110] (1) Extraction of the highest 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 such as cumbersome operations 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.

[0111] 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 implemented by establishing an access path to 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) is 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.

[0112] 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.

[0113] After determining the information for finding the corresponding nodes, the next step is to obtain the temperature field data of these nodes to extract the maximum temperature data of the brake disc. The extraction process of the node maximum temperature data can be summarized as the following steps: First, all the temperature field data in a specific analysis step need to be output; then, the temperature data of all nodes are read in a traversal manner to find the maximum temperature value, and the corresponding node number is recorded; finally, the extreme value comparison method is used to find the node coordinate information corresponding to the highest temperature, and the temperature value corresponding to the highest temperature node is accurately output.

[0114] (2) Extraction of the maximum stress data of the brake disc: In 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 needs to be adopted to read the stress integration point data of the brake disc. For this purpose, in the process of extracting data, the initial minimum distance is first set to infinity, then all the element information is traversed, and the Euclidean norm is used to continuously calculate the distance between the given node information and the centroid integration point of each element. Finally, the element information closest to the given node is obtained by continuous iteration and update assignment. This method lays the foundation for reading the stress data of specific nodes. Through this accurate positioning method, the stress data of each key node can be accurately extracted, thus ensuring the accuracy and reliability of subsequent analysis.

[0115] After obtaining the stress integration point information in the simulation data of the C / C-SiC brake disc, the next step is to extract the data of the maximum stress point. 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, and 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.

[0116] 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, on the other hand, is used to represent the geometric elements obtained by discretizing differential equations. The hexahedron formed by connecting nodes is the basic element for discretizing differential equations. And 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.

[0117] (3) Extraction of the maximum axial deformation data of the brake disc: The deformation reading process of the C / C-SiC brake disc has significant similarities with the temperature reading process, 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 this node. In the specific implementation process, the find_close_node function can be called. By calling this function, an accurate correspondence relationship can be established between the spatial coordinates and the specific deformation data, thus greatly improving the accuracy and efficiency of the entire data extraction process.

[0118] During the simulation process of the C / C-SiC brake disc, the method for extracting the maximum axial deformation data of nodes is similar to the method for obtaining the maximum stress value. The specific extraction process can be summarized into 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 extreme value comparison method to find the node coordinate information corresponding to the maximum axial deformation, and accurately output the value corresponding to the maximum axial deformation node.

[0119] 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 dimension difference and accelerate the model convergence. Based on the normalized dataset, four machine learning models, namely MLP-ANN (Multi-Layer Perception-Artificial Neural Network), KNN, XGBoost, and CNN, are 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 high-speed train C / C-SiC brake disc.

[0120] Based on the comparative analysis among different models, in this embodiment, a 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:

[0121] 。

[0122] In the above formula, 、 and are the heat dissipation rib angle parameters (the inner diameter angle of the heat dissipation rib, the inner angle of the heat dissipation rib cut, the outer angle of the heat dissipation rib cut, the number of heat dissipation ribs ( ), and the friction layer thickness ( ) as design variables, and the highest temperature (T), the maximum stress (S), and the maximum axial deformation (U) of the C / C-SiC brake disc structure are the objective functions. The parameters of the supporting NSGA-II algorithm are shown in Table 1.

[0123] Table 1: Parameters of the NSGA-II algorithm:

[0124]

[0125] In this embodiment, the above MLP-ANN model is embedded in 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.

[0126] In this embodiment, after obtaining the Pareto solution set of the optimization objective based on the multi-objective optimization result of the machine learning-based NSGA-II algorithm, the CBW weight decision algorithm can be used to perform the 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:

[0127] (1) Determine the objective decision variables corresponding to the CBW decision criterion.

[0128] This patent takes T, S, and U of the C / C-SiC brake disc of high-speed trains as the objectives of multi-objective optimization.

[0129] (2) Determine the worst and best decision-making objectives.

[0130] 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-making objective, and U as the worst decision-making objective.

[0131] (3) Determine the scale combination of the decision-making algorithm.

[0132] The cloud model theory is incorporated into the Best-Worst (BW) method to construct a new weight decision-making algorithm (Cloud Best-Worst, CBW). Based on the basic theory of the cloud model, nine scale combinations (A1 to A9) 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.

[0133] Table 2: CBW preference values

[0134]

[0135] (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:

[0136] ;

[0137] .

[0138] 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; Denote the entropy of all experts' optimal decision goal relative to the $i$-th decision goal; Denote the hyperentropy of all experts' optimal decision goal relative to the $i$-th decision goal; Denote the expectation of the $m$-th expert's optimal decision goal relative to the $i$-th decision goal; Denote the entropy of the $m$-th expert's optimal decision goal relative to the $i$-th decision goal; Denote the hyperentropy of the $m$-th expert's optimal decision goal relative to the $i$-th decision goal.

[0139] (5) Determine the priority preference value of the worst decision goal relative to other decision goals.

[0140] 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:

[0141] ;

[0142] .

[0143] In the formula, Denote the preference vector of the $m$-th expert for the worst decision goal relative to other criteria; Denote the cloud model vector of the $m$-th expert for the worst decision goal relative to the $i$-th decision goal; Denote the expectation of the $m$-th expert for the worst decision goal relative to the $i$-th decision goal; Denote the entropy of the $m$-th expert for the worst decision goal relative to the $i$-th decision goal; Denote the hyperentropy of the $m$-th expert for the worst decision goal relative to the $i$-th decision goal.

[0144] ;

[0145] .

[0146] In the formula, Denote the preference vector of all experts for the worst decision goal relative to other criteria; Is the cloud model vector of all experts for the worst decision goal relative to the $i$-th decision goal; Denote the expectation of all experts for the worst decision goal relative to the $i$-th decision goal; Denote the entropy of all experts for the worst decision goal relative to the $i$-th decision goal; Denote the hyperentropy of all experts for the worst decision goal relative to the $i$-th decision goal.

[0147] (6) Find the optimal weight.

[0148] In the CBW weight decision algorithm, the basic idea of the BW method is adopted. Assuming that each decision objective has a corresponding weight value, the weight matrix of the decision objective can be expressed as: ; represents the weight value of the i-th decision objective.

[0149] To ensure that for any i, the optimal weight and one of them satisfies and conditions, where is the weight value of the optimal decision objective, is the weight value of the worst decision objective; 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:

[0150] ;

[0151] ; <�

[0152] ;

[0153]

[0154] .

[0155] In the formula, represents the expectation of all experts for the weight of the optimal decision objective; represents the expectation of all experts for the weight of the i-th decision objective; represents the entropy of all experts for the weight of the optimal decision objective; <� represents the entropy of all experts for the weight of the i-th decision objective; represents the hyper-entropy of all experts for the weight of the optimal decision objective; represents the hyper-entropy of all experts for the weight of the i-th decision objective; represents the expectation of all experts for the weight of the worst decision objective; represents the entropy of all experts for the weight of the worst decision objective; represents the hyper-entropy of all experts for the weight of the worst decision objective.

[0156] (7) Determine the gain matrix and the gain weight matrix.

[0157] Based on the existence of positive and negative correlations between decision-making objectives, corresponding weights must be assigned to the positive and negative correlation coefficients to determine the weights of the decision-making objectives. The positive and negative correlations are respectively defined as positive and negative gains:

[0158] ;

[0159] Among them, is the gain coefficient corresponding to the i-th decision-making objective. When it is positive, it is represented as , and when it is negative, it is represented as .

[0160] Therefore, according to the defined gain matrix, the gain weight matrix of the decision-making objective is obtained as follows:

[0161] .

[0162] Among them, represents the gain weight corresponding to the i-th decision-making objective.

[0163] (8) By multiplying the Pareto solution set by the transpose matrix of the gain weight matrix, the corresponding decision-making objective matrix is obtained; then, by calculating the sum of each row of the decision-making objective matrix, the Pareto solution with the largest sum result is found as the optimal solution; the calculation formula is:

[0164] ;

[0165] In the formula, is the decision-making objective 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.

[0166] To further illustrate the efficiency of the optimization process of 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:

[0167] ;

[0168] Among them, The total computing time required for the computational DOE of the machine learning MLP-ANN model The time required for MLP-ANN training The time required for each sample calculation after the model training is successful The number of samples for DOE

[0169] Furthermore: ; where The total computing time required for the computational DOE of the finite element model The time required for each sample calculation of the finite element model

[0170] Also: ; where The time ratio required for the computational DOE of the machine learning MLP-ANN model and the finite element model

[0171] From the comparison experiment results, it can be seen that when n = 80, TML and TFE are 402 hours and 80 hours respectively, and TIFE is 502.5%, the time required by MLP-ANN is greater than the computational time of the finite element model. When n = 1100, TML and TFE are 402.02 hours and 1100 hours respectively, and TIFE is 10.1%, the time required by MLP-ANN is less than the computational time of the finite element model. When n is small, the computational time of MLP-ANN will be longer than that of FEM. As the number of n increases, the computational time of MLP-ANN basically remains unchanged, while the computational time of the finite element model increases significantly, and TIFE will show an exponential decline. Therefore, it can be found that when the number of samples sampled during the optimization process is large, using the MLP-ANN model can greatly reduce the computational 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.

[0172] To observe the thermodynamic response index characteristics of the C / C-SiC brake disc during the emergency braking process of high-speed trains, a 400 km / h emergency braking test was carried out on the C / C-SiC brake disc on a full-scale railway brake test bench. The test adopted a two-gradient loading strategy: applying a 18 kN pre-tightening force brake in the high-speed range of 300 km / h - 400 km / h to suppress the thermoelastic instability phenomenon, and switching to a 32 kN main braking force mode until stopping after the speed dropped to 300 km / h. To eliminate the interference of the contact heterogeneity at the friction pair interface on the test data, before the test, according to the standard regulations, 20 - 30 running-in brakes 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% and achieve uniform friction.

[0173] To accurately obtain the temperature change during the braking process of the brake disc, in this embodiment, a contact thermocouple temperature measurement technology is adopted to monitor the temperature of the friction surface with high precision. In the central area of the double friction surfaces of the brake disc, 6 embedded thermocouples are symmetrically buried at intervals of 120° (the embedding depth is 1 mm), among which 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 and measurement blind areas, the embedded thermocouple can accurately obtain the real temperature data inside the structure, effectively avoiding the influence of dust splash and oxide layer formation during the braking process on non-contact temperature measurement, and providing high-reliability experimental data support for the study of the thermal-mechanical coupling effect of the brake disc.

[0174] In order to verify the thermodynamic response characteristics of the C / C-SiC brake disc 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 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 the experimental temperature curve 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 numerous factors affecting temperature change in the actual working conditions, such as test installation error, material inhomogeneity, detection error of the temperature measurement sensor, 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.

[0175] Embodiment 2

[0176] Corresponding to the above embodiment, 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, the following Figure 5 method steps shown are implemented:

[0177] 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 whole process code of geometric parameter drive, material association, load application, mesh generation and calculation submission, realizing the automatic mapping of "parameter input - simulation output".

[0178] Step S2: Use the DOE 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 by 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, the maximum stress, and the 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 according to the dataset.

[0179] Step S3: Define the optimization objective and the constraint conditions of the structural parameters, and obtain the Pareto solution set of the optimization objective by using the non-dominated sorting genetic algorithm embedded in the target model; the optimization objective is that the maximum temperature, the maximum stress, and the maximum axial deformation all take the minimum values.

[0180] Step S4: Make an optimal decision on the Pareto solution set to obtain the optimal solution of the brake disc structural parameters.

[0181] Preferably, the brake disc is a C / C-SiC brake disc. The structural parameters used as input variables include: the angle parameter of the heat dissipation ribs, the number of heat dissipation ribs, and the friction layer thickness. 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.

[0182] 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:

[0183] 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 item-by-item control method, and automatically extracts the input variables and output variables in the dataset by 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.

[0184] 2. Based on the target model for predicting the thermodynamic response indicators 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, and the mode of the network can be changed to a prediction model, then the 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 suitable for different speeds, energy levels, and different trains).

[0185] 3. The target model for predicting the thermodynamic response index of the high-speed train brake disc structure can be used for transfer learning. When using the small sample data of the new structure / new material of the brake disc with similar mechanism to train the original network, the original network can directly call the weights trained previously, and then use the small sample data for retraining, which can be used for the brake discs of new materials and new structures, improving the utilization rate of resources.

[0186] 4. The present invention adopts a method combining non-dominated sorting genetic algorithm and machine learning to conduct 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 the 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 index 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.

[0187] 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 can 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 the brake disc of a high-speed train based on machine learning, characterized in that, Including: 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 form, realizing the automatic mapping of "parameter input - simulation output". Step S2: Use the experimental design 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 the 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. Among them, in Step S2, automatically extracting the input variables and output variables in the dataset using a batch processing program includes: Reading the temperature data of all nodes in a traversal manner to find the maximum temperature value and recording the corresponding node number. Then, using the extreme value comparison method to find the node coordinate information corresponding to the maximum temperature, and outputting the temperature value corresponding to the maximum temperature node. Reading the maximum equivalent stress values of all stress integration points in a traversal manner and outputting the corresponding stress integration point element numbers. Using the extreme value comparison method to find the stress integration point coordinates and element node information corresponding to the maximum stress. Finally, using the comparison method of element information and integration point information to output the stress corresponding to the maximum stress integration point. Reading the deformation data of all nodes in a traversal manner to find the maximum temperature value and recording the corresponding node number. Finally, using the extreme value comparison method to find the node coordinate information corresponding to the maximum axial deformation, and outputting the temperature value corresponding to the maximum axial deformation node.

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

3. The multi-objective optimization method for the brake disc of a high-speed train based on machine learning according to claim 2, wherein The structural parameters as input variables include: the angle parameter 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 the brake disc of a high-speed train based on machine learning according to any one of claims 1 to 3, characterized in that Constructing the finite element parametric model includes: (1) Importing the ABAQUS core module; (2) Defining the key parameters of the finite element model through class functions; (3) Establishing the brake disc geometric model using the defined function; (4) Combining 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 geometry of the assembly has no interference and the degrees of freedom are reasonable; (5) Creating material properties through the Material module and assigning them to the brake disc components; (6) Setting the analysis step in the Step module and specifying 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, 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.

5. The multi-objective optimization method for the brake disc of a high-speed train 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, The target model is an MLP-ANN model.

7. The multi-objective optimization method for the brake disc of a high-speed train 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: Determine the target decision variables, worst and best decision objectives corresponding to the CBW 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 method, and calculate the eigenvalue expectations Ex, entropy En, and hyperentropy He of each scale; Step S43: Determine the priority preference value of the optimal decision objective relative to other decision objectives; In the decision analysis process, assume that the opinions of each expert have equal weight in the final decision; based on this assumption, construct a preference vector to represent the priority of each decision objective relative to the optimal decision objective; assume that m experts score n decision objectives, and the score of the mth expert for the ith decision objective is expressed as: ； ； In the formula, represents the preference vector of all experts for the optimal decision-making goal relative to other criteria; is the cloud model vector of all experts for the optimal decision-making goal relative to the i-th decision-making goal; 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 goal relative to the i-th decision-making goal; represents the entropy of all experts for the optimal decision-making goal relative to the i-th decision-making goal; represents the hyperentropy of all experts for the optimal decision-making goal relative to the i-th decision-making goal; represents the expectation of the m-th expert for the optimal decision-making goal relative to the i-th decision-making goal; represents the entropy of the m-th expert for the optimal decision-making goal relative to the i-th decision-making goal; represents the hyperentropy of the m-th expert for the optimal decision-making goal relative to the i-th decision-making goal; Step S44: Determine the priority preference value of the worst decision objective relative to other decision objectives; In the process of evaluating the worst decision relative to other objectives, also assume that the opinions of each expert have equal weight in the final decision, and based on this assumption, construct a preference vector to represent the priority of each decision objective relative to the worst decision objective. The specific calculation formula is as follows: ； ； wherein, represents the preference vector of the m-th expert for the worst decision target relative to other criteria; represents the cloud model vector of the m-th expert for the worst decision target relative to the i-th decision target; represents the expectation of the m-th expert for the worst decision target relative to the i-th decision target; represents the entropy of the m-th expert for the worst decision target relative to the i-th decision target; represents the hyperentropy of the m-th 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-making goal relative to other criteria; is the cloud model vector of all experts for the worst decision-making goal relative to the i-th decision-making goal; represents the expectation of all experts for the worst decision-making goal relative to the i-th decision-making goal; represents the entropy of all experts for the worst decision-making goal relative to the i-th decision-making goal; represents the hyper-entropy of all experts for the worst decision-making goal relative to the i-th decision-making goal; 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 objective has a corresponding weight value, the weight matrix of the decision objective is expressed as: ； In the formula, represents the weight value of the i-th decision-making objective; To ensure that for any i, the optimal weight and one of them satisfies and conditions, where is the weight value of the optimal decision objective, is the weight value of the worst decision objective; 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 weights, the problem is transformed into the following model: ； ； ； ； In the formula, represents the expectation of all experts for the weight of the optimal decision-making objective; represents the expectation of all experts for the weight of the i-th decision-making objective; represents the entropy of all experts for the weight of the optimal decision-making objective; represents the entropy of all experts for the weight of the i-th decision-making objective; represents the hyper-entropy of all experts for the weight of the optimal decision-making objective; represents the hyper-entropy of all experts for the weight of the i-th decision-making objective; represents the expectation of all experts for the weight of the worst decision-making objective; represents the entropy of all experts for the weight of the worst decision-making objective; represents the hyper-entropy of all experts for the weight of the worst decision-making objective; Step S46, determine the gain matrix and the gain weight matrix; Based on the positive and negative correlations existing between decision objectives, define the positive and negative correlations as positive and negative gains respectively: ； Among them, is the gain coefficient corresponding to the i-th decision objective, and is regularly expressed as , and is negative when expressed as ; Therefore, according to the defined gain matrix, the gain weight matrix of the decision-making objective is obtained as follows: ； Among them, represents the gain weight corresponding to the i-th decision objective; Step S47: Multiply the Pareto solution set by the transpose matrix of the gain weight matrix to obtain the corresponding decision objective matrix; then, find the Pareto solution with the largest sum of each row of the decision objective matrix as the optimal solution; the calculation formula is: ； In the formula, is the decision-making objective 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.

8. 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 on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 7 above.

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