CN116384258A - A wheel-tire integrated wheel impact dynamics simulation method - Google Patents

Abstract

The invention discloses a hub-tire integrated wheel impact dynamics simulation method, and belongs to the field of machine learning and cloud computing. According to the invention, a basic equation obtained by combining field knowledge and priori knowledge is used as an initial solution of the optimizing part, and an equation learning neural network is introduced to automatically explore a solution space of a constitutive equation of a material to generate more fitting terms which are not involved in the basic equation, so that the constitutive equations of the two materials are added into an initial population of a genetic algorithm, the optimizing efficiency of the optimal solution of a constitutive model of a hub material can be ensured, and meanwhile, the problem of sinking into a local optimal solution is avoided. According to the invention, the hub-tire integrated wheel impact dynamics simulation is further arranged on the cloud service platform, so that a user is allowed to call and integrate resources on the cloud platform. The user only needs to connect the cloud service platform, uploads or online imports the hub model and simulation parameters which need to be subjected to impact test simulation, and can carry out simulation calculation according to the steps, so that the simulation difficulty is greatly reduced.

Description

A hub-tire integrated wheel impact dynamics simulation method

Technical Field

The present invention belongs to the field of machine learning and cloud computing, and in particular relates to a method for realizing wheel hub-tire integration simulation through a neural network.

Background Art

As a key bearing structure during the driving process of a car, the wheel hub’s lightweight degree and mechanical properties directly affect the stability, safety and economy of the car. In order to meet the market demand and performance of the wheel hub, save costs and improve product competitiveness, high-strength and lightweight wheel hubs have become the development goal of the industry. Among them, impact resistance is one of the important indicators for measuring wheel hub strength. In order to simulate the scenario when the wheel hits the curb laterally or runs over obstacles such as gravel during driving, consider the ability of the wheel to resist lateral and longitudinal impacts, and verify and control the quality of the wheels. Different countries have given different wheel impact test standards. The commonly used domestic standards are GB/T 15704-2012 "Road vehicles Light alloy wheel impact test method" and QC/T 991-2015 "Passenger car light alloy wheel 90° impact test method". Commonly used foreign standards include ISO 7141:2022 Road vehicles — Light alloy wheels — Lateral impact test and SAE J175_202107 Wheels - Lateral Impact Test Procedure - Road Vehicles. The test principle is to use a hammer of a specific shape to impact different positions of the wheel at different angles to test the impact resistance of the wheel.

The impact test of the wheel needs to be carried out on a specific impact testing machine, and the test object must be a representative finished wheel that has gone through a complete process route and can be used for vehicles. If the impact performance of the wheel is unqualified, a large amount of mold opening cost and processing cost will be lost. Therefore, in order to reduce the test cost and shorten the R&D cycle, it is very necessary to perform dynamic simulation of the impact test of the wheel in the early stage of product development. Accurate and efficient wheel impact dynamics simulation can quickly feedback the mechanical properties of the wheel hub without testing. Based on the simulation output results, product development engineers can quickly perform structural analysis and optimization of the wheel hub until the impact resistance of the wheel hub meets the requirements.

Traditional wheel impact simulation methods generally simplify dynamic problems into static problems, convert the impact force of the hammer into equivalent static load acting on the wheel hub, and often ignore the tire model. The energy absorbed by the rubber tire is compensated by deducting part of the hammer energy. Although these simplifications improve the simulation efficiency, they are bound to bring about the problem of excessive errors. With the deepening of research, more and more studies have taken the tire model into consideration, established a wheel-tire coupled wheel impact dynamics simulation model, and used the display analysis method for dynamic calculation, which improved the accuracy and simulation precision of the simulation. The existing wheel impact dynamics simulation method solves the problem of large simulation errors in traditional methods. The shortcomings are that the scope of application is narrow, and the finite element model needs to be re-established when equipping tires of different specifications and models and analyzing wheel impact tests at different angles. The operation is cumbersome, and the calculation time is long and the cost is high. It cannot meet the convenient and efficient use needs of wheel developers. Users need to maintain the hardware and software facilities by themselves, and the user experience is poor. Cloud computing is a scalable and convenient network access. It uses virtualization technology to provide computer resources according to the computer environment scale required by users to realize the sharing of computing resources. However, how to transfer traditional wheel impact dynamics simulation to the cloud has brought new technical problems that need to be solved.

Summary of the invention

The purpose of the present invention is to solve the defects of large error and complicated operation of wheel impact dynamics simulation in the prior art, and to provide a wheel hub-tire integrated wheel impact dynamics simulation method.

The specific technical solutions adopted by the present invention are as follows:

A hub-tire integrated wheel impact dynamics simulation method, comprising:

S1. Obtain a sample data set by sampling the material mechanical test data of the wheel hub;

S2. Using the sample data set to train the equation learning neural network multiple times, the equation learning neural network fits the material constitutive equation to obtain multiple machine learning fitting equations; at the same time, using the sample data set to fit the existing material constitutive equation obtained according to domain knowledge and prior knowledge to obtain a basic equation;

S3. Encode each basic equation, the machine learning fitting equation, and the randomly generated random expression into a binary tree consisting of terminal symbols and operators; use all the encoded binary trees as the initial population of the genetic algorithm and perform an initial crossover operation, and update the individuals obtained after the initial crossover operation to the original initial population;

S4. Based on the updated initial population and the fitness function constructed by combining the equation fitting degree and the equation complexity, the population iteration is optimized by a genetic algorithm for multiple objectives, and during the iteration process, the basic equation fitted by the sample data set is regularly added to the latest offspring population to guide the evolution direction of the genetic algorithm. After the genetic algorithm iterates to the termination condition, the optimal solution is output as the optimal constitutive equation of the hub material.

S5. Import the hub model and tire model of the target wheel, the wheel impact test standard, and the simulation parameters including the optimal constitutive equation of the hub material into the dynamics simulation system, perform finite element simulation by calling the solver, and output the simulation result of the target wheel under impact.

Preferably, the dynamics simulation system is installed on a cloud service platform, and the cloud service platform has a built-in standard library, model library and software resource library;

The standard library has built-in different wheel impact test standards for users to choose from;

The model library includes one or more of a hub model sub-library, a tire model sub-library, a wheel assembly model sub-library, a bench model sub-library, and a material model sub-library. The models in each sub-library are used to provide a direct call function when the user does not upload the corresponding model.

The software resource library has one or more dynamics simulation software built in for users to call.

Preferably, the cloud service platform is further provided with a pre-processing module, which includes a user data sub-module and a model generation sub-module; the user data sub-module is used for the user to upload or select the hub model and tire model of the target wheel, the wheel impact test standard and simulation parameters, wherein the optimal constitutive equation of the hub material in the simulation parameters is fitted online or offline; the model generation sub-module is used to generate the calculation files required by the dynamic simulation system according to the data in the user data sub-module.

Preferably, the cloud service platform is further provided with a computing module, which includes a preprocessing submodule and a solving submodule. The preprocessing submodule is used to allocate corresponding cloud computing resources according to the simulation calculation amount of the dynamic simulation system, and the solving submodule is used to perform finite element simulation through a solver based on the cloud computing resources allocated by the preprocessing submodule.

Preferably, the cloud service platform is further provided with a result output module for storing the relevant data of the dynamics simulation in the cloud in the form of cloud storage, and outputting the simulation results in the output form set by the user.

Preferably, the existing material constitutive equations used to fit the basic equations include the Johnson-Cook yield model, Cowper-Symonds yield model, Swift hardening model and Voce hardening model determined based on domain knowledge, as well as multiple custom material constitutive equations determined based on prior knowledge.

Preferably, the sample data set is divided into a first sample data set and a second sample data set; the basic equations as the initial population and the machine learning fitting equations are trained or fitted by the first sample data set, and the basic equations added to the offspring population in the iteration process are fitted by the second sample data set;

The sampling range of the first sample data set in the material mechanics test data is the yield platform or the vicinity of 0.2% equivalent plastic strain, as well as the necking stage and the yield strengthening stage, and the sampling interval of the yield strengthening stage is greater than that of other stages;

The sampling range of the second sample data set in the material mechanics test data is near the yield platform or 0.2% equivalent plastic strain, and the necking stage; and the sampling interval of the second sample data set is smaller than the sampling interval of the first sample data set.

Preferably, the genetic algorithm needs to pre-set initialization parameters before executing the iterative process, including a terminal symbol set and a function symbol set, a genetic operator, a maximum number of evolutions, a population size and a coding form; wherein the terminal symbols in the terminal symbol set include all independent variables and real constants involved in the basic equations and the machine learning fitting equations; the function symbol set includes all operators involved in the basic equations and the machine learning fitting equations; the coding form is a binary tree structure; in the genetic operator, the crossover operator only performs a crossover operation on the structure containing independent variables in the binary tree, and the mutation operator is used to perform a local search for the real constants of the new individual while changing the operator.

Preferably, the fitness function includes mean absolute relative error, root mean square error, fit coefficient and equation complexity, wherein the fit coefficient is the difference between 1 and the coefficient of determination, and the equation complexity is the sum of the complexities of all operators in the equation; the genetic algorithm comprehensively performs multi-objective optimization in the decision space based on the four fitness functions.

Preferably, the optimal solution of the genetic algorithm selects a compromise solution with the smallest fitting coefficient in the Pareto non-dominated solution set.

Compared with the prior art, the present invention has the following beneficial effects:

1) The present invention uses the basic equations obtained by combining domain knowledge and prior knowledge as the initial solution for optimization, and introduces an equation learning neural network to autonomously explore the solution space of the material constitutive equation to generate more fitting items not involved in the basic equation. Setting the above two types of material constitutive equations to construct the initial population of the genetic algorithm can ensure the optimization efficiency of the optimal solution of the hub material constitutive model while avoiding falling into the local optimal solution.

2) The present invention further places the wheel hub-tire integrated wheel impact dynamics simulation on the cloud service platform, allowing users to dynamically integrate the resources on the cloud platform through cloud computing. Users do not need to install complex dynamics simulation software modules, nor do they need to configure the operating environment and hardware facilities such as servers and storage by themselves. As long as they connect to the cloud service platform and import the wheel hub model and related simulation parameters that need to be simulated for the impact test, they can perform simulation calculations step by step, realizing the on-demand allocation and efficient use of computing resources.

3) The present invention enables users to quickly conduct analysis and research on specific problems and needs, realize efficient and accurate simulation calculation of wheel impact dynamics, and solve the defects of existing wheel impact dynamics simulation methods such as complex parameter settings, large workload, and time-consuming calculations. For front-line engineers such as wheel manufacturers, they can directly call relevant resources on the cloud platform to carry out wheel impact dynamics simulation analysis more efficiently. Moreover, thanks to the complete resource library and model library and powerful computing power on the cloud service platform, the present invention can realize serialized simulation calculation of wheel impact dynamics for different models and different needs, and help enterprises formulate corresponding wheel impact performance evaluation standards.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the steps of a hub-tire integrated wheel impact dynamics simulation method;

FIG2 is a fitting flow chart of the optimal constitutive equation of the hub material;

FIG3 is a schematic diagram of a hub-tire integrated wheel impact dynamics simulation system based on a cloud service platform.

DETAILED DESCRIPTION

In order to make the above-mentioned purpose, features and advantages of the present invention more obvious and easy to understand, the specific implementation mode of the present invention is described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present invention can be combined accordingly without conflicting with each other.

In the description of the present invention, it should be understood that the terms "first" and "second" are only used for the purpose of distinguishing descriptions, and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

The present invention provides a hub-tire integrated wheel impact dynamics simulation method, which can perform impact dynamics simulation on the hub-tire integrated wheel. The hub-tire integrated wheel mentioned in the present invention refers to a wheel formed by the integrated assembly of the hub and the tire, that is, the hub and the tire in the assembled state are considered at the same time during the simulation in the present invention, so that the impact form is closer to the actual operating condition of the tire. The specific implementation method of the hub-tire integrated wheel impact dynamics simulation method is described in detail below.

As shown in FIG1 , in a preferred implementation of the present invention, the above-mentioned hub-tire integrated wheel impact dynamics simulation method includes the following steps S1 to S5 . The specific implementation process is described in detail below.

S1. A sample data set is obtained by sampling the material mechanical test data of the wheel hub.

（三个参数分别表示流动应力、等效塑性应变、等效塑性应变率）数据，换算公式为领域内公知常识，不再赘述。It should be noted that the material mechanics test data of the wheel hub can be obtained according to the material mechanics test scheme in the conventional impact test method. Generally speaking, the material mechanics test used is a uniaxial tensile test at different tensile rates, and the original test data is converted into the corresponding

The data (the three parameters represent flow stress, equivalent plastic strain, and equivalent plastic strain rate, respectively) and the conversion formula are common knowledge in the field and will not be repeated here.

The sample data set obtained by sampling in the present invention is used to fit the material constitutive equation of the hub. After obtaining the material mechanics test data, a corresponding sampling method can be selected based on the data characteristics. In the embodiment of the present invention, a non-uniform sampling method is preferably used.

S2. The equation learning (EQL) neural network is trained multiple times using the above sample data set, and the material constitutive equation is fitted by the equation learning neural network to obtain multiple machine learning fitting equations. At the same time, the existing material constitutive equations obtained based on domain knowledge and prior knowledge are fitted using the above sample data set to obtain the basic equation.

It should be noted that the material constitutive equations in the present invention include two categories, wherein the machine learning fitting equations are obtained by fitting the equation learning neural network, and the basic equations are obtained by fitting the existing material constitutive equations. However, the above-mentioned machine learning fitting equations and basic equations are equations after regression fitting, and the parameters to be fitted therein already have specific fitting values. In an embodiment of the present invention, the existing material constitutive equations used to fit the basic equations include some classic material constitutive equations in the field determined according to the field knowledge, including but not limited to the Johnson-Cook yield model, the Cowper-Symonds yield model, the Swift hardening model and the Voce hardening model, and may also include multiple custom material constitutive equations determined according to prior knowledge. The so-called custom material constitutive equations are possible custom material constitutive equations derived from the trend of the test curve according to prior knowledge, and the parameters of these equations are unknown but the expression form is known. The prior knowledge here can be relevant literature, predecessors' experience, or equations that are fitted and optimized according to experimental data, that is, the above-mentioned custom material constitutive equations can be equations proposed in relevant literature, or equations corrected according to experience, or self-constructed equations. There is no restriction on the form of the specific custom material constitutive equation. In theory, the richer and more accurate the custom material constitutive equation is, the more initial information guidance can be provided for the subsequent genetic algorithm optimization.

The wheel impact test is a dynamic mechanics problem, involving the strain hardening and strain rate hardening effects of the material, which is often accompanied by large plastic deformation and fracture failure behavior. In order to better describe the stress-strain relationship of the hub material and enable the wheel impact dynamics simulation to accurately reflect the local deformation of the hub and the occurrence of cracks or fractures in the actual impact test, it is very important to accurately describe the material constitutive model of the hub (if the failure fracture situation needs to be simulated, the failure model needs to be added). The reason for setting the above two types of material constitutive equations in the present invention is to ensure the optimization efficiency of the optimal solution of the hub material constitutive model while avoiding falling into the local optimal solution. Because the basic equations are obtained based on domain knowledge and prior knowledge, their fitting performance has been verified, and these material constitutive equations can be used as the initial solution for optimization to ensure the efficiency of optimization. However, if the basic equations are fully adopted, the possibility of variation is insufficient during the genetic algorithm optimization process, and it is difficult to introduce some fitting items that are not in the basic equations. Therefore, the present invention further introduces the equation learning EQL neural network to autonomously explore the solution space of the fitting equation and generate more fitting items that are not involved in the basic equations.

The equation learning neural network used in the present invention is a neural network that can be used to fit equations. Its implementation belongs to the prior art. For details, please refer to the prior art document: "Martius G, Lampert C H. Extrapolation and learning equations [J]. 2016." In addition to this document, EQL neural networks have been widely reported in other documents. The following is a brief introduction to facilitate understanding of the principle of using this neural network.

The EQL neural network is essentially a fully connected layer neural network, consisting of an input layer, two hidden layers, and an output layer. Its forward reasoning process can be expressed as:

分别是第1和第2全连接层的权重矩阵，

是第2层到输出层的权重矩阵，

是输入数据，即等效塑性应变和等效塑性应变率（

）的矩阵形式，

是神经网络的输出，即一个具体函数形式的材料本构方程。EQL神经网络与传统全连接神经网络不同的地方在于激活函数

。具体而言，与传统机器学习常见的

等函数不同，EQL神经网络的激活函数

采用了备选数学函数和运算符自定义激活函数，以得到最终的具体函式输出。其中备选数学函数和运算符包括但不限于单位、平方、三次、指数、对数、乘法等。允许在每一层中复制激活函数，即在

的多个组件可以使用相同的激活函数，目的是降低系统对随机初始化的敏感性，创造更平滑的优化环境。In the formula,

are the weight matrices of the 1st and 2nd fully connected layers, respectively.

is the weight matrix from layer 2 to the output layer,

is the input data, namely the equivalent plastic strain and the equivalent plastic strain rate (

),

is the output of the neural network, that is, a material constitutive equation in a specific functional form. The difference between the EQL neural network and the traditional fully connected neural network is the activation function

Specifically, unlike traditional machine learning

Different functions, activation functions of EQL neural network

The activation function is customized using alternative mathematical functions and operators to obtain the final specific function output. The alternative mathematical functions and operators include but are not limited to unit, square, cubic, exponential, logarithm, multiplication, etc. It is allowed to copy the activation function in each layer, that is,

Multiple components of a network can use the same activation function to reduce the system's sensitivity to random initialization and create a smoother optimization environment.

正则化项来确保神经网络的潜在稀疏性，使神经网络尽可能拟合出简单的解。In addition, the EQL neural network is introduced into the loss function during training

The regularization term is used to ensure the potential sparsity of the neural network, so that the neural network can fit a simple solution as much as possible.

是权重，

是一个常值，设定为0.01。In the formula,

is the weight,

is a constant value set to 0.01.

The mean square error loss function that finally introduces the regularization term is expressed as follows:

为第一样本数据集的容量，

为真实值，即流动应力

的试验数据换算值，

为预测值，即通过神经网络拟合的方程对应自变量

的输出值，

为超参数，用来平衡正则项的惩罚力度。EQL神经网络通过最小化上述引入正则项的均方误差损失函数，即可实现网络训练，训练后最终得到的是一个方程式，而不是传统神经网络的黑盒模型。作为本发明的一个实施例，神经网络训练可以分初始阶段、中间阶段、后期阶段、终了阶段，在初始阶段，

设置为一个较小的值0.01，网络自由演化计算潜在参数；在中间阶段，增大

值来增强网络的稀疏性；在后期阶段，设定一个阈值

，将低于该阈值的权重进行归零；在终了阶段，

设置为0，即去掉

正则项，以微调网络模型的权重。

is the capacity of the first sample data set,

is the true value, i.e., flow stress

The experimental data conversion value of

is the predicted value, that is, the equation fitted by the neural network corresponds to the independent variable

The output value of

is a hyperparameter used to balance the penalty of the regularization term. The EQL neural network can achieve network training by minimizing the mean square error loss function introduced with the regularization term. What is finally obtained after training is an equation, rather than a black box model of a traditional neural network. As an embodiment of the present invention, the neural network training can be divided into an initial stage, an intermediate stage, a later stage, and a final stage. In the initial stage,

Set to a small value of 0.01, the network is free to evolve to calculate the potential parameters; in the intermediate stage, increase

value to enhance the sparsity of the network; in the later stage, a threshold is set

, the weights below the threshold are reset to zero; at the end stage,

Set to 0 to remove

Regularization term to fine-tune the weights of the network model.

，这些机器学习拟合方程式可与其他基础方程式一起作为初始种群通过进化算法进行优化，达到对方程的精细化修正效果，使之更好地拟合试验数据，准确描述材料特性，提高仿真准确度。Since the EQL neural network system is sensitive to random initialization, each training will produce different results and it is easy to fall into local minima. Therefore, we train N times to obtain N EQL fitting machine learning equations.

,These machine learning fitting equations can be used as the initial population together with other basic equations through evolutionary algorithms to achieve a refined correction effect on the equations, so that they can better fit the experimental data, accurately describe the material properties, and improve the simulation accuracy.

S3. Encode each basic equation, the machine learning fitting equation and the randomly generated random expression into a binary tree consisting of terminal symbols and operators; use all the encoded binary trees as the initial population of the genetic algorithm and perform an initial crossover operation, and update the individuals obtained after the initial crossover operation to the original initial population.

）和实常量，运算符是方程中涉及的运算符合（例如

），终结符和运算符组合得到材料本构方程的表达式。将方程式编码为二叉树形式的具体方式属于现有技术，对此不再赘述。It should be noted that the above terminators include the independent variables involved in the material constitutive equation (e.g.

) and real constants, and operators are the sum of the operators involved in the equation (e.g.

), the terminal symbol and the operator are combined to obtain the expression of the material constitutive equation. The specific method of encoding the equation into a binary tree form belongs to the prior art and will not be described in detail.

It should be noted that the genetic algorithm used in the present invention can be selected according to actual conditions, and the NSGA-III genetic algorithm is preferably used because the NSGA-III genetic algorithm can be well combined with the EQL neural network for composite regression to fit the material constitutive equation.

It should be noted that the random expression in the initial population before the execution of the above-mentioned initial crossover operation can be randomly generated by the genetic algorithm through operator recursion. Compared with the traditional genetic algorithm, the present invention is different in that a special initial crossover operation is performed before executing the genetic algorithm. The population individuals obtained by this initial crossover operation that are different from the original equation are added to the original initial population, together with the original basic equation, the machine learning fitting equation, and the binary tree of the random expression as a new initial population participating in the iteration of the genetic algorithm. The purpose of doing this is because these equations in the original initial population are all fitted, and directly using them as the initial population can easily cause the genetic algorithm to directly fall into the local optimal solution and fail to find the global optimal solution.

S4. Based on the updated initial population and the fitness function constructed by combining the equation fitting degree and the equation complexity, the population iteration is optimized by multi-objective through the genetic algorithm, and during the iteration process, the basic equation fitted by the sample data set is regularly added to the latest offspring population to guide the evolution direction of the genetic algorithm. After the genetic algorithm iterates to the termination condition, the optimal solution is output as the optimal constitutive equation of the hub material.

It should be noted that before the genetic algorithm performs the iterative process, the initialization parameters need to be set in advance, and the specific parameters can be processed according to the relevant parameter settings of the genetic algorithm. In the embodiment of the present invention, since the optimization object of the genetic algorithm is the material constitutive equation, the initialization parameters that need to be set include the terminal symbol set and the function symbol set, the genetic operator, the maximum number of evolutions, the population number and the encoding form. The terminal symbols in the above-mentioned terminal symbol set include all the independent variables and real constants involved in the basic equations and the machine learning fitting equations; the above-mentioned function symbol set contains all the operators involved in the basic equations and the machine learning fitting equations; the above-mentioned encoding form is a binary tree structure; in the above-mentioned genetic operator, the crossover operator only performs a crossover operation on the structure containing independent variables in the binary tree, and the mutation operator is used to perform a local search for the real constants of the new individual and change the operator at the same time; the above-mentioned maximum number of evolutions is used to control the maximum number of iterations of the algorithm to avoid falling into an infinite loop when it cannot converge; the above-mentioned population number should be greater than the original initial population number, so as to leave a certain space for the aforementioned initial crossover operation and enrich the population diversity.

It should be noted that the specific function form and type of the above fitness function can be selected according to actual needs. In an embodiment of the present invention, the fitness function may include the mean absolute relative error, the root mean square error, the fit coefficient and the equation complexity, wherein the fit coefficient is the difference obtained by subtracting the determination coefficient R ² from 1, and the equation complexity is the sum of the complexity of all operators in the equation. Different operators can set corresponding complexity values according to the actual operation complexity; the genetic algorithm comprehensively performs multi-objective optimization in the decision space based on the four fitness functions. Under the multi-objective optimization framework, the optimal solution of the final genetic algorithm selects a compromise solution with the smallest fit coefficient in the Pareto non-dominated solution set. The entire compromise solution solution process can be shown in Figure 2.

It should also be noted that the sample data set obtained by sampling in the present invention is used to fit the material constitutive equation of the hub. In theory, as long as the sample data set can accurately fit the material constitutive equation, its specific sampling interval and sample quantity can be unrestricted. However, since the sample data set is required for fitting in both S2 and S4, in one embodiment of the present invention, considering the functional requirements of the sample data for fitting the constitutive equations of different materials, the sampled sample data set can also be divided into two different data sets, respectively recorded as the first sample data set and the second sample data set. The sampling range of the first sample data set in the above-mentioned material mechanics test data is near the yield platform or 0.2% equivalent plastic strain, as well as the necking stage and the yield strengthening stage, and the sampling interval of the yield strengthening stage is greater than that of other stages. The sampling range of the second sample data set in the above-mentioned material mechanics test data is near the yield platform or 0.2% equivalent plastic strain, as well as the necking stage; and the sampling interval of the second sample data set is smaller than the sampling interval of the above-mentioned first sample data set. Based on the above-mentioned first sample data set and second sample data set, the basic equation as the initial population and the machine learning fitting equation are trained or fitted by the first sample data set, and the basic equation adding the offspring population in the iterative process is fitted by the second sample data set.

S5. Import the hub model and tire model of the target wheel, the wheel impact test standard and the simulation parameters including the optimal constitutive equation of the hub material into the dynamics simulation system, perform finite element simulation by calling the solver, and output the simulation result of the target wheel under impact.

It should be noted that, in addition to the optimal constitutive equation of the hub material, the above simulation parameters should also include other necessary simulation parameters set in the dynamic simulation system. In the embodiment of the present invention, the simulation parameters include but are not limited to material data, wheel impact dynamics model structural parameters, loads and constraints, grid data, solver, pre-output data settings, etc.

In addition, the solver used in the present invention can be selected according to the actual dynamics simulation system, including but not limited to finite element software solvers such as ANSYS, ABAQUS, LS-DYNA, etc.

In the dynamic simulation process of the present invention, the hub model and tire model in the target wheel are assembled and then simulated, so that the simulation result is consistent with the actual wheel working condition. The hub model and tire model can be designed in advance in the three-dimensional modeling software and then imported. Of course, if there is an existing three-dimensional model file, it can also be directly called. In addition, the wheel impact test standard includes multiple wheel impact test standards from different countries and regions, and one of them can be selected according to actual needs.

It can be seen that the wheel hub-tire integrated wheel impact dynamics simulation method described in S1 to S5 of the present invention, through the combination of genetic algorithm and EQL neural network to perform composite regression fitting of material constitutive equations, can allow users to quickly carry out analysis and research on specific problems and needs, and realize efficient and accurate serialized simulation calculation of wheel impact dynamics. In order to better demonstrate the specific implementation form of the present invention, the specific implementation cases of the wheel hub-tire integrated wheel impact dynamics simulation method described in S1 to S5 are demonstrated through two embodiments below.

Example 1

In this embodiment, the NSGA-III genetic algorithm is combined with the EQL neural network to perform composite regression fitting of the optimal constitutive equation of the hub material, and the hub-tire integrated wheel impact dynamics simulation is performed based on the optimal constitutive equation of the hub material. The specific steps of the hub-tire integrated wheel impact dynamics simulation method are as follows:

Step 1: Initial sample collection:

数据。Carry out material mechanics tests on the wheel hub in advance, and collect material mechanics test data of the wheel hub. A non-uniform sampling method based on data characteristics is adopted: dense sampling with a sampling interval of 10 is performed near the yield platform or 0.2% equivalent plastic strain of the material mechanics test data and in the necking stage, in order to better capture the yield characteristics and strength limit of the material; sparse sampling with a sampling interval of 100 is performed in the yield strengthening stage, and the original test data after sampling is converted to obtain a first sample data set with a reasonable capacity; at the same time, local samples are collected with a sampling interval of 5 near the yield platform or 0.2% plastic strain of the material mechanics test data and in the necking stage, and similarly, they are converted as the second sample data set. The material mechanics test in this embodiment is a uniaxial tensile test of the wheel hub at different tensile rates, and the original test data is obtained through the conversion formula

data.

Step 2: Algorithm initialization settings:

）和实常量，函数集包括一些运算符（

），终结符和运算符组合得到表达式。其中，除法运算有相应的保护机制，在分母中加上一个微小量保证运算意义。编码形式为二叉树结构。交叉算子只对二叉树中含自变量的结构进行操作，变异算子一来对新个体的常数值进行局部搜索，二来改变运算符，丰富多样性。交叉概率为0.8，变异概率为0.05。Set the terminal symbol set and function symbol set, genetic operator, maximum number of evolutions, population number, encoding form, etc. Set the initial number of evolutions to 0, the maximum number of evolutions to M, and the population number to N. The terminal symbol includes the independent variables involved in the material constitutive equation (

) and real constants, the function set includes some operators (

), the terminal symbol and the operator are combined to get the expression. Among them, the division operation has a corresponding protection mechanism, and a small amount is added to the denominator to ensure the meaning of the operation. The encoding form is a binary tree structure. The crossover operator only operates on the structure containing independent variables in the binary tree. The mutation operator first performs a local search for the constant value of the new individual, and secondly changes the operator to enrich the diversity. The crossover probability is 0.8 and the mutation probability is 0.05.

Step 3: Generate the initial population:

最接近1的妥协解作为最终解，可以达到对现有的材料本构方程进行精细化修正使之更好地拟合试验数据和预测材料性能的效果。The composite regression method in this embodiment refers to the method of combining numerical regression with symbolic regression. Specifically, the material constitutive equation with known parameters and specific expressions is obtained by numerical regression of the equations of some existing models in the field and possible custom equations inferred from the trend of the test curve based on prior knowledge, and then the equation obtained by training the neural network based on equation learning (EQL) is added. These individuals are combined with the expressions randomly generated by the genetic algorithm through operator recursion to form an initial population. The direction of the symbolic regression fitting of the genetic algorithm is guided by the equations obtained by numerical regression and the equations obtained by neural network training. The NSGA-Ⅲ algorithm is used to achieve multi-objective optimization in the symbolic regression process, and the Pareto solution set of the material constitutive equation is obtained, and finally a determination coefficient is selected.

The compromise solution closest to 1 is taken as the final solution, which can achieve the effect of fine-tuning the existing material constitutive equation to better fit the test data and predict material properties.

In this embodiment, common material flow models and dynamic mechanical constitutive models include Johnson-Cook yield model, Cowper-Symonds yield model, Swift hardening model, and Voce hardening model. The wheel impact test is carried out at room temperature, and the temperature rise during the impact process is very small, so the effect of temperature on material properties can be ignored. Ignoring the temperature term, the material constitutive equations of the above four models and some four custom material constitutive equations inferred based on prior knowledge (the last four of the following eight equations) are shown as follows:

表示流动应力，不同下角标对应不同模型的流动应力，是待拟合方程的输出；

分别表示等效塑性应变和等效塑性应变率，是待拟合方程的输入；

分别表示静态屈服强度和静态屈服强度点对应的等效塑性应变，这两个物理量通过材料力学试验数据可以直接得到；

为参考应变率，是自定义值；

为材料本构方程的待拟合参数。In the formula,

represents flow stress, different subscripts correspond to flow stress of different models, and is the output of the equation to be fitted;

They represent the equivalent plastic strain and equivalent plastic strain rate, respectively, and are the inputs of the equation to be fitted;

They represent the static yield strength and the equivalent plastic strain corresponding to the static yield strength point, respectively. These two physical quantities can be directly obtained through material mechanics test data;

is the reference strain rate, which is a custom value;

are the parameters to be fitted in the material constitutive equation.

。另外，由于EQL神经网络系统对随机初始化具有一定的敏感性，每次训练都得到不同的结果，且容易陷入局部极小值，因此本实施例中将EQL神经网络在第一样本数据集上训练20次，得到20个EQL拟合方程

，并与其他初始种群一起通过进化算法优化，达到对方程的精细化修正效果，使之更好地拟合试验数据。因此将

、

、通过遗传算子递归随机生成一系列随机表达式

均编码成二叉树形式后共同构成初始种群，初始种群的数量小于预设的初始种群数N，以便于留出一定的空间进行后续的初始交叉操作，丰富初始种群多样性。通过数值回归和神经网络训练得到的这些方程可引导遗传算法符号回归拟合的方向，避免遗传算法在符号回归过程中的盲目性。传统的遗传算法拟合时初始种群中只有随机生成的表达式，存在不易收敛、进化盲目的缺点。In this embodiment, the four classical material constitutive equations and four custom material constitutive equations defined above are used as basic equations, and the first sample data set is used to perform numerical regression fitting on the basic equations using the least squares method. Specifically, the Lsqcurvefit function and the Levenberg-marquardt algorithm in Matlab are used to obtain the material constitutive equations with eight known parameters.

In addition, since the EQL neural network system is sensitive to random initialization, each training will produce different results and it is easy to fall into a local minimum. Therefore, in this embodiment, the EQL neural network is trained 20 times on the first sample data set to obtain 20 EQL fitting equations.

, and together with other initial populations, through the evolutionary algorithm optimization, the equation is refined and modified to better fit the experimental data.

,

, recursively generate a series of random expressions through genetic operators

After being encoded into a binary tree form, they together constitute the initial population. The number of the initial population is less than the preset initial population number N, so as to leave a certain space for subsequent initial crossover operations and enrich the diversity of the initial population. These equations obtained through numerical regression and neural network training can guide the direction of the genetic algorithm symbolic regression fitting and avoid the blindness of the genetic algorithm in the symbolic regression process. When the traditional genetic algorithm is fitted, there are only randomly generated expressions in the initial population, which has the disadvantages of being difficult to converge and evolving blindly.

Step 4: Initial crossover operation:

After the initial population is generated, an initial crossover operation needs to be performed before the genetic algorithm iteration to generate new population individuals. The purpose of the pre-crossover is to prevent the competitive advantage of the individuals generated by the numerical regression from being too large and directly eliminating the random expressions randomly generated by the genetic algorithm. The diversity of the population is guaranteed by the pre-crossover operation. Therefore, in this embodiment, the parent population before the initial crossover needs to be copied to the next generation, and together with the individuals generated after the crossover, the offspring population is formed. This offspring population replaces the original initial population as the actual initial population in the iterative process of the genetic algorithm. The number of the initial population is finally N.

Step 5: Calculate individual fitness:

）、均方根误差（

）、决定系数（

）、方程复杂度（

）综合评价个体适应度，目的是得到形式尽量简单且拟合度好的材料本构方程。其中，方程复杂度公式通过综合考虑自变量、常量、不同运算符的出现次数得到。将

四个运算符的复杂度加权为其他运算符的三倍，对方程的指数项复杂度做了进一步限定。各函数形式如下：Determine the fitness function and calculate the fitness of each individual in the population. Use the mean absolute relative error (

), Root Mean Square Error (

), coefficient of determination (

), equation complexity (

) Comprehensively evaluate individual fitness, the purpose is to obtain a material constitutive equation with the simplest form and good fit. Among them, the equation complexity formula is obtained by comprehensively considering the number of occurrences of independent variables, constants, and different operators.

The complexity of the four operators is weighted three times that of other operators, which further limits the complexity of the exponential term of the equation. The function forms are as follows:

为拟合得到的材料本构方程的预测值，

为实际试验采集的样本数据值，

为第一样本数据集的容量，

表示方程编码的二叉树从根节点到叶节点的最长路径下的所有节点数量，

表示前述所有节点中

运算符节点数量，

表示方程中包含的指数项的最高次幂。In the formula,

is the predicted value of the material constitutive equation obtained by fitting,

is the sample data value collected from the actual experiment,

is the capacity of the first sample data set,

represents the number of all nodes under the longest path from the root node to the leaf node of the binary tree encoded by the equation,

Indicates that among all the above nodes

The number of operator nodes,

Represents the highest power of the exponential terms contained in the equation.

和

越接近0，

越接近1，

越小，表示个体适应度越好。为了方便描述优化模型，定义拟合度系数

。多目标优化数学模型可表示为：

and

The closer to 0,

The closer it is to 1,

The smaller it is, the better the individual fitness is. In order to facilitate the description of the optimization model, the fitness coefficient is defined

The multi-objective optimization mathematical model can be expressed as:

为决策向量，

为决策空间，此处即为每个材料本构方程个体组成的种群；

为目标向量，所在空间为目标空间。优化的目标是获得最小的目标空间。In the formula,

is the decision vector,

is the decision space, which is the population composed of individuals of the constitutive equation of each material;

is the target vector, and the space it is in is the target space. The optimization goal is to obtain the smallest target space.

Step 6: Selection, crossover and mutation:

During the iteration of the genetic algorithm, the parent population is merged with the offspring population, and the merged population is fast non-dominated sorted and sorted based on the reference point. N individuals are selected from the sorted population, and crossover and mutation operations are performed on these individuals. All the new individuals obtained are added to the offspring population, and the fitness is recalculated.

Step 7: Expand the offspring population every 50 evolutions:

The second sample data set is numerically regressed using the basic equation and added to the offspring population to further guide the direction of the genetic algorithm symbolic regression fitting. The purpose is to make the final material constitutive equation better fit the local yield characteristics and strength limit of the material.

Step 8: Termination judgment:

Determine whether the maximum number of evolutions is reached or other termination conditions are met. If so, end the algorithm and output the Pareto non-dominated solution set. If not, return to step 3 and continue executing the algorithm.

Step 9: Optimal solution selection

最小的一个解作为多目标复合回归拟合的妥协解，得到最终的轮毂材料本构最优方程

。Select from the Pareto non-dominated solution set

The smallest solution is used as a compromise solution for multi-objective composite regression fitting to obtain the final optimal constitutive equation of the hub material.

.

Step 9: Dynamics simulation

The hub model and tire model of the target wheel to be simulated, the wheel impact test standard and the simulation parameters including the optimal constitutive equation of the hub material are imported into the dynamic simulation system, and the finite element simulation is performed by calling the solver to output the simulation result of the target wheel under impact.

In this embodiment, the wheel impact test standards include but are not limited to GB/T 15704-2012 "Road Vehicle Light Alloy Wheel Impact Test Method", QC/T 991-2015 "Passenger Car Light Alloy Wheel 90° Impact Test Method", ISO71412022 Road vehicles — Light alloy wheels — Lateral impact test, SAE J175_202107 Wheels - Lateral Impact Test Procedure - Road Vehicles, etc. Users can select the corresponding reference standard according to their wheel impact simulation needs. The dynamics simulation system can be implemented using finite element software with powerful dynamics simulation functions such as ANSYS, ABAQUS, LS-DYNA, etc. on the local side, and the corresponding solvers include but are not limited to finite element software solvers such as ANSYS, ABAQUS, LS-DYNA, etc. The simulation parameters that need to be input include material data of tires and wheels, structural parameters of wheel impact dynamics model, loads and constraints, mesh data, solvers, pre-output data settings, etc.

It can be seen that when performing the above-mentioned wheel hub-tire integrated wheel impact dynamics simulation, the user needs to input a large amount of data and set a large number of parameters, such as simulation parameters such as tire specifications and models, impact angle parameters, wheel hub and tire three-dimensional models, and wheel hub and tire material models. They all need to be manually set or constructed on the local computer. The process of using NSGA-Ⅲ genetic algorithm combined with EQL neural network for composite regression fitting of the optimal constitutive equation of the wheel hub material also requires a large amount of computing resources, so it takes a lot of time and energy. And it is particularly noted that users with wheel impact dynamics simulation requirements are mostly wheel hub manufacturers and wheel hub design engineers. They generally cannot directly obtain the material data of the tire. Therefore, when this part of the data is missing, it is often difficult to complete the wheel hub-tire integrated wheel impact dynamics simulation of the present invention. Therefore, in another embodiment of the present invention, based on the wheel hub-tire integrated wheel impact dynamics simulation method in Example 1, it is further cloud-based, and a corresponding dynamics simulation system is constructed on the cloud platform to achieve a wheel hub-tire integrated wheel impact dynamics simulation method that can be conveniently and quickly used and has low cost. In actual use, users only need to call the corresponding module according to actual needs, realize the customization of wheel assembly of different specifications and models, impact angle parameters, etc., and accurately simulate the test conditions, so that users can quickly analyze and study specific problems and needs, and realize efficient and accurate simulation calculation of wheel hub-tire integrated wheel impact dynamics. The implementation form of the above-mentioned cloud platform-based wheel hub-tire integrated wheel impact dynamics simulation method is demonstrated through Example 2.

Example 2

In this embodiment, the wheel hub-tire integrated wheel impact dynamics simulation system is established on a cloud service platform. As shown in Figure 3, the modules on the cloud service platform include a pre-processing module, a calculation module, a result output module, a standard library, a model library, and a software resource library. The pre-processing module includes a user data submodule and a model generation submodule; the calculation module includes a pre-processing submodule and a solution submodule; the result output module includes a storage submodule and an analysis submodule. The steps for users to perform wheel hub-tire integrated wheel impact dynamics simulation through the cloud service platform are as follows:

1): The user enters personal or corporate account information to log in to the cloud service platform. The cloud deploys an agent, which sends user information to the system. After identity authentication and permission configuration, the user enters the platform's hub-tire integrated wheel impact dynamics simulation system and uses the corresponding cloud computing services.

2): Enter the pre-processing module of the wheel hub-tire integrated wheel impact dynamics simulation system, input the reference wheel impact test standard in the user data sub-module, import the wheel hub model, upload the relevant simulation parameters, and the system automatically establishes the wheel hub-tire integrated impact dynamics simulation model through the self-programming program of the model generation sub-module and generates a calculation file.

3): Enter the calculation module, preprocess the calculation file in the preprocessing submodule, analyze the relationship between the number of CPU cores, memory resources, calculation time and cost required for the calculation, and provide different calculation service solutions. Users can choose the corresponding calculation service according to their needs.

4): The cloud service platform automatically deploys the task data and command stream generated by the above steps to the backend cloud server through the corresponding code or instructions, and calls the corresponding solver resources. Users only need to click "Run" in the solving sub-module to realize cloud computing of wheel-tire integrated impact dynamics simulation.

5): After the simulation calculation is completed, enter the result output module. The entire calculation file, calculation process data and result data are saved in the storage submodule in the form of cloud storage. Users can access and download them at any time, or enter the analysis submodule for online data processing and analysis.

The above cloud service platform solves the problem of confidentiality of data and calculations by deploying a trusted execution environment (TEE) in the cloud. The specific implementation form of each functional module in the above cloud service platform is described in detail below.

In the above-mentioned cloud service platform, the user data submodule also integrates an intelligent fitting system and a stretching simulation system, among which: the intelligent fitting system provides a composite regression method, which integrates regression algorithms such as the least squares method, genetic algorithm, and EQL neural network, and fits the constitutive equations of wheel and tire materials through the composite regression method; and the stretching simulation system automatically completes the specimen stretching simulation through the constitutive equation of the wheel material obtained by the intelligent fitting system, and obtains data such as equivalent fracture strain and stress triaxiality that are difficult to directly obtain in actual stretching tests. These data are then returned to the intelligent fitting system to fit the material failure model of the wheel.

In the above cloud service platform, the standard library provides multiple wheel impact test standards from different countries and regions. The wheel impact test standards include but are not limited to GB/T 15704-2012 "Road Vehicles Light Alloy Wheels Impact Test Method", QC/T 991-2015 "Passenger Car Light Alloy Wheel 90° Impact Test Method", ISO 71412022 Roadvehicles — Light alloy wheels — Lateral impact test, SAE J175_202107 Wheels- Lateral Impact Test Procedure - Road Vehicles, etc. Users can select the corresponding reference standard according to their wheel impact simulation needs and enter the corresponding standard code in the pre-processing module of the cloud service platform.

In the above cloud service platform, the model library includes but is not limited to the wheel hub model library, tire model library, wheel assembly model library, bench model library, and material model library. The wheel hub model library and tire model library include models voluntarily shared by different users and models acquired by the platform from users; the wheel assembly model library includes a variety of wheel hub-tire integrated models with corresponding specifications and models and a good assembly relationship; the bench model library includes the wheel impact test bench model (including wheel support seat and hammer) pre-established by the cloud service platform according to various wheel impact test standards; the material model library includes but is not limited to the density, Young's modulus, Poisson's ratio and other data of common materials, as well as special material models and model parameters such as Mooney-Rivlin, Yeoh, and Johnson-Cook.

In the above cloud service platform, the software resource library provides finite element software services with powerful dynamic simulation functions, including but not limited to ANSYS, ABAQUS, LS-DYNA, etc. Users do not need to download and install the software by themselves, as long as they log in to the cloud service platform, they can enjoy the latest software solver resources in the cloud.

In the above cloud service platform, the wheel hub model in step 2) is a wheel hub 3D model file designed in advance by the user in the 3D modeling software.

In the above cloud service platform, the simulation parameters related to step 2) include but are not limited to material data, wheel impact dynamics model structural parameters, loads and constraints, mesh data, solvers, pre-output data settings, etc. The material data include but are not limited to the density, Young's modulus, Poisson's ratio, mechanical properties test data, selected material models, etc. of the hub material and each component material of the tire; the wheel impact dynamics model structural parameters include hammer shape, drop height, impact angle, etc.; the impact angle is the angle between the axis of the wheel and the direction of the hammer falling, that is, the angle between the axis of the wheel and the vertical direction; the loads and constraints include but are not limited to tire inflation pressure, hammer mass, local gravity acceleration, contact form and friction coefficient between the hub and the tire, wheel hub mounting plate bolt torque, contact form and friction coefficient between the hammer and the impacted wheel, etc.; mesh data include but are not limited to mesh division method and mesh size, etc.; solvers include but are not limited to finite element software solvers such as ANSYS, ABAQUS, LS-DYNA, etc.; pre-output data settings include but are not limited to stress, strain, acceleration, displacement, energy, etc.

One thing that needs to be explained is that among the above-mentioned simulation parameters, some data (for example: hammer shape, hammer mass, drop height, impact angle, etc.) have specified values in the relevant wheel impact test standards. When the standard is selected, this part of the data is automatically generated. After the user uploads the simulation parameters, the cloud system automatically analyzes the rationality and conflict of all data and generates a data analysis report. The user modifies the data according to personal needs and determines whether to cover the conflicting data. Finally, the data is confirmed and the cloud service platform automatically completes the material data fitting and the establishment of the impact dynamics simulation model.

One thing that needs to be explained is that in step 2), users can upload their own specific simulation parameters or use the model library data provided by the wheel-tire integrated wheel impact dynamics simulation system of the cloud service platform. For example, when uploading material data, users with wheel impact dynamics simulation requirements are mostly wheel manufacturers and wheel design engineers, who generally cannot directly obtain tire material data. Most users only need to upload their own developed wheel model and mechanical test data of the wheel material sample, and the tire selection calls the tire model of the corresponding specification model in the tire model library to complete the expected wheel impact dynamics simulation analysis. The cloud service platform integrates an intelligent fitting system, which automatically fits the material constitutive equation and failure equation for simulation based on the material constitutive model and failure model selected by the user and the test data provided by the user. The test data includes but is not limited to uniaxial tensile test data of smooth round rods or flat plate samples at different tensile rates, uniaxial tensile test data of notched round rods or flat plate samples, uniaxial compression test data, and pure shear test data. For users who want to simply and quickly analyze whether the impact resistance of the wheel hub meets the initial requirements without pursuing extremely high simulation accuracy, they only need to upload the wheel hub model and select a reference impact test standard. All simulation parameters can be obtained from the model library. The system automatically establishes a wheel hub-tire integrated impact dynamics simulation model through the self-programming program of the model generation submodule. This greatly saves the modeling time of finite element simulation, improves simulation efficiency, and has guiding significance for the development and design of the wheel hub.

。输入标准代号GB/T 15704-2012之后，云服务平台自动匹配台架模型库的冲击试验台架模型，并生成相关仿真参数：冲锤形状为长方体，棱边倒圆5mm；冲击角度

；下落高度230mm；轮胎充气压力200kPa。另外，用户还需要上传的仿真参数如下：For example, in this embodiment, after the user enters the pre-processing module of the wheel hub-tire integrated wheel impact dynamics simulation system, he can enter the reference wheel impact test standard code GB/T 15704-2012 in the user data submodule, import the user's pre-designed wheel hub three-dimensional model, upload the relevant simulation parameters, and the system automatically establishes the wheel hub-tire integrated wheel impact dynamics simulation model through the self-programming program of the model generation submodule, and generates a calculation file. GB/T 15704-2012 "Road Vehicle Light Alloy Wheel Impact Test Method" can evaluate the performance of light alloy wheels axially (laterally) impacting the curb. The impact angle specified by the standard is

After entering the standard code GB/T 15704-2012, the cloud service platform automatically matches the impact test bench model in the bench model library and generates relevant simulation parameters: the shape of the hammer is a rectangular parallelepiped with 5mm rounded edges; the impact angle

; Drop height 230mm; Tire inflation pressure 200kPa. In addition, the simulation parameters that users need to upload are as follows:

Material data: density of hub material, Young's modulus, Poisson's ratio, material mechanical test data of hub specimen, material constitutive model selected for fitting

Load and constraint conditions: Hammer mass (calculated by the following formula, the maximum static load of the hub is 800kg)

Where: m is the mass of the hammer, in kilograms (kg);

W is the maximum static load of the hub specified by the user, in kilograms (kg).

The wheel hub mounting plate bolt torque is 110N·m; the local gravity acceleration is 9.79m/s ² ; the contact forms of the hammer, tire and wheel hub are all friction contacts, the contact friction coefficient between the tire and the wheel hub is 0.5, the contact friction coefficient between the hammer and the tire is 0.5, and the contact friction coefficient between the hammer and the wheel hub is 0.2.

Mesh data: Due to the complex shape and structure of the wheel hub, it is difficult to divide it into hexahedral meshes. Therefore, free division is adopted to directly divide it into tetrahedral meshes with a mesh size of 5mm; the tire mesh adopts the arbitrary Lagrange Euler method with a mesh size of 6mm; the hammer adopts the mapped hexahedral mesh with a mesh size of 10mm; the wheel support seat adopts the free division form with a mesh size of 10mm.

Solver: Select ABAQUS/Explicit solver

Pre-output data settings include but are not limited to Mises stress, equivalent plastic strain, equivalent strain energy density, displacement, acceleration, stiffness degradation, damage initiation criterion, state, etc.

The model library data used is as follows:

By entering the tire specification model in the user data submodule, the corresponding tire model can be obtained from the tire model library.

The tire model consists of tread, sidewall, shoulder, tread base, steel belt, carcass cord, inner liner, apex rubber, rim liner, and bead wire, in which the steel belt and carcass cord are embedded in the rubber tire as embedded layers. The rubber material adopts the incompressible Mooney-Rivlin hyperelastic material model (the model expression is as follows), and the embedded layer adopts ordinary steel material, which is given density, Young's modulus and Poisson's ratio material properties.

为材料力学性能常数，I₁，I₂为右柯西-格林变形张量的第一，第二基本不变量。Where: W is the strain energy function,

is the material mechanical property constant, I ₁ and I ₂ are the first and second fundamental invariants of the right Cauchy-Green deformation tensor.

In addition, the present embodiment can also provide an automatic meshing function to conveniently and quickly divide the hub-tire integrated wheel impact dynamics simulation model into high-quality discrete meshes. Preferably, the automatic meshing function can adopt a free meshing method to directly divide the entire wheel impact dynamics model into tetrahedral meshes; preferably, the automatic meshing function can also adopt a mapping meshing method to generate a mapping mesh by selecting appropriate unit properties and mapping methods; preferably, the automatic meshing function can also adopt any Lagrangian Euler method to achieve mesh redrawing by moving nodes during the calculation process, which is suitable for simulation scenarios with large deformation of rubber tires.

The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims (10)

1. A method of hub-tire integrated wheel impact dynamics simulation comprising:

s1, sampling material mechanics test data of a hub to obtain a sample data set;

s2, training the equation learning neural network for a plurality of times by using the sample data set, and fitting a constitutive equation of the material by the equation learning neural network to obtain a plurality of machine learning fitting equations; simultaneously, fitting an existing material constitutive equation obtained according to field knowledge and priori knowledge by using the sample data set to obtain a basic equation;

s3, each basic equation, the machine learning fitting equation and the randomly generated random expression are respectively encoded into a binary tree form consisting of a terminator and an operator; taking all binary trees obtained by coding as an initial population of a genetic algorithm, performing initial cross operation, and updating individuals obtained after the initial cross operation into the original initial population;

S4, carrying out multi-objective optimization on population iteration through a genetic algorithm based on the updated initial population and an fitness function constructed by combining equation fitting degree and equation complexity, and periodically adding a basic equation fitted by the sample data set into the latest offspring population to guide the evolution direction of the genetic algorithm in the iteration process, and outputting an optimal solution after the genetic algorithm is iterated to a final condition to serve as a hub material constitutive optimal equation;

s5, the hub model and the tire model of the target wheel, the wheel impact test standard and simulation parameters including the optimal equation of the hub material structure are led into a dynamic simulation system, finite element simulation is carried out by calling a solver, and a simulation result of the target wheel under impact is output.

2. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the dynamics simulation system is carried on a cloud service platform, and a standard library, a model library and a software resource library are built in the cloud service platform;

different wheel impact test standards for users to select are built in the standard library;

the model library comprises one or more of a hub model sub-library, a tire model sub-library, a wheel assembly model sub-library, a bench model sub-library and a material model sub-library, and the model in each sub-library is used for providing a direct calling function when a user does not upload a corresponding model;

And one or more dynamic simulation software for user call is built in the software resource library.

3. The hub-tire integrated wheel impact dynamics simulation method according to claim 2, wherein a preprocessing module is further arranged in the cloud service platform, and the preprocessing module comprises a user data sub-module and a model generation sub-module; the user data sub-module is used for uploading or selecting a hub model and a tire model of a target wheel, a wheel impact test standard and simulation parameters by a user, wherein a hub material constitutive optimal equation in the simulation parameters is fitted in an online or offline mode; the model generation sub-module is used for generating a calculation file required by the dynamic simulation system according to the data in the user data sub-module.

4. The hub-tire integrated wheel impact dynamics simulation method according to claim 3, wherein a calculation module is further arranged in the cloud service platform, the calculation module comprises a preprocessing sub-module and a solving sub-module, the preprocessing sub-module is used for allocating corresponding cloud computing resources according to simulation calculation amount of the dynamics simulation system, and the solving sub-module is used for carrying out finite element simulation through a solver according to the cloud computing resources allocated by the preprocessing sub-module.

5. The hub-tire integrated wheel impact dynamics simulation method according to claim 4, wherein a result output module is further arranged in the cloud service platform, and is used for storing relevant data of dynamics simulation in a cloud storage mode in the cloud, and outputting simulation results according to an output mode set by a user.

6. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the existing material constitutive equations used to fit to form the base equation include a Johnson-Cook yield model, a Cowper-Symonds yield model, a Swift hardening model, and a Voce hardening model determined from domain knowledge, and a plurality of custom material constitutive equations determined from prior knowledge.

7. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the sample data set is divided into a first sample data set and a second sample data set; the basic equation serving as the initial population and the machine learning fitting equation are trained or fitted by the first sample data set, and the basic equation added with the offspring population in the iteration process is fitted by the second sample data set;

The sampling range of the first sample data set in the material mechanical test data is near a yield platform or 0.2% equivalent plastic strain, and a necking stage and a yield strengthening stage, wherein the sampling interval of the yield strengthening stage is larger than that of other stages;

the sampling range of the second sample data set in the material mechanics test data is near the yield platform or 0.2% equivalent plastic strain, and a necking stage; and the sampling intervals of the second sample data set are each smaller than the sampling intervals of the first sample data set.

8. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the genetic algorithm needs to preset initialization parameters before performing the iterative process, including a terminal symbol set and a function symbol set, a genetic operator, a maximum evolution number, a population number and a coding form; wherein the terminals in the terminal set include all of the independent variables and real constants involved in the base equation and the machine learning fit equation; the function symbol set comprises all basic equations and operators involved in the machine learning fit equation; the coding form is a binary tree structure; and in the genetic operators, the crossover operator only carries out crossover operation on the structure containing the independent variable in the binary tree, and the mutation operator is used for carrying out local search on the real constant of the new individual and simultaneously changing the operator.

9. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the fitness function comprises an average absolute relative error, a root mean square error, a fitness coefficient and an equation complexity, wherein the fitness coefficient is a difference obtained by subtracting the decision coefficient from 1, and the equation complexity is a sum of respective complexities of all operators in the equation; the genetic algorithm comprehensively performs multi-objective optimization in a decision space based on four fitness functions.

10. The hub-tire integrated wheel impact dynamics simulation method according to claim 1, wherein the optimal solution of the genetic algorithm selects one compromise solution with the smallest coefficient of fit among pareto non-dominant solutions.

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