CN115809608A - A parameter identification and optimization method for mining heavy-duty solid tires - Google Patents

Abstract

The invention discloses a parameter identification and optimization method for mining heavy-duty solid tires, including: 1. performing test operations on the tires according to the test of mine-used heavy-duty solid tires to obtain test data; 2. based on the test data, The mine heavy-duty solid MF tire model is optimized for the first time, and the first objective function value is obtained, and the mining heavy-duty MF solid tire model is obtained. 3. The parameters in the mining heavy-duty MF solid tire model are initially identified by Gauss-Newton iteration method , 4. Through the hybrid optimization algorithm, the parameters obtained by the initial identification are quickly optimized and deeply optimized to obtain parameters with higher accuracy and precision. The invention can efficiently and quickly identify the parameters in the mine heavy-duty MF solid tire model, is easy to implement, has good adaptability and high identification accuracy, and is suitable for the typical mine road environment and the dynamics and stability research of heavy-duty transport vehicles.

Description

A parameter identification and optimization method for mining heavy-duty solid tires

technical field

The invention belongs to the technical field of vehicles, in particular to a parameter identification and optimization method for mining heavy-duty solid tires.

Background technique

With the rapid development of ground vehicle technology and computer information technology, whether it is for traditional vehicles or new energy vehicles, vehicle design tends to be more efficient and informatized, and the application of information technology, especially computer simulation technology, in the automotive industry is extremely important. It greatly facilitates the design and development of products, improves the quality of products, and provides effective help to manufacturers and related scientific research institutions. Among them, vehicle simulation analysis technology can realize the early prediction and analysis of product performance and manufacturability, thereby shortening the production time. Product design and manufacturing cycles reduce product development costs and improve the ability of the R&D design system to quickly respond to market changes.

Under the call of the state for energy conservation and emission reduction, coal mines have the objective requirements of reducing staff and increasing efficiency, improving coal mine safety and reducing the incidence of accidents. There is an urgent need to develop clean, efficient and intelligent coal machinery equipment to achieve mechanization and reduce manpower. With the rapid expansion of the mining vehicle industry and the substantial increase in market inventory, it is difficult to achieve a reasonable configuration of the overall performance and parameters of mining vehicles due to explosion-proof transformation, and the speed of underground driving is complicated due to complex road conditions, coupled with poor ventilation conditions. Compared with ground vehicles with design capabilities, there are obvious pain points of low efficiency, poor safety, and poor adaptability to working conditions. It is urgent to learn from ground vehicle technology and computer information technology, especially vehicle simulation technology, to improve power performance.

Heavy-duty solid rubber tires for mining vehicles are components that directly contact the ground, and their mechanical properties directly affect vehicle dynamics and ride comfort characteristics. Conventional pneumatic tire models have certain differences, and have the characteristics of solid rubber, low damping, thick patterns, and large flattening ratio. Therefore, when using the pneumatic tire model and empirical parameters in the traditional method for dynamic modeling and simulation calculation of mining vehicles, it is likely to produce large model mismatch errors, and it is impossible to accurately describe the actual motion state of mining heavy-duty vehicles , and the precise control of its behavior has become a key problem that has long restricted the research on the dynamics and stability of mining vehicles, and has not been fundamentally resolved. Therefore, considering the important influence of tire-road contact mechanical properties on vehicle lateral stability regulation, the non-linear rolling-sliding contact mechanical properties of heavy-duty traction solid rubber tires of mining vehicles on road cement pavement are studied, and the tire material, geometric It is particularly important to accurately identify the model parameters of heavy-duty solid or filled tires based on structural characteristics, and to establish a solution model suitable for the typical mine road environment and heavy-duty transport vehicle tire forces.

Establish a reasonable tire dynamics model to analyze the impact of the longitudinal force, lateral force, vertical load and aligning moment on the vehicle's dynamic performance, handling stability, braking stability, ride comfort and driving safety It is an important part of vehicle simulation technology and plays a key role in product development and vehicle performance analysis, so the accuracy of the tire model directly affects the key technology research of vehicle products. At present, the research on this technology of mining vehicles mainly adopts the method of transplanting related technologies on the ground. The dynamics of ground vehicles generally adopts the empirical model formula obtained based on test data in the aspect of analyzing tire cornering performance, which is composed of trigonometric functions. Combination fitting is obtained, which can completely express the joint action conditions of longitudinal force, righting moment, overturning moment and drag distance respectively and longitudinal force and lateral force on the tire. However, the formula itself has the characteristics of many parameters and high nonlinearity, and it is difficult to identify the parameters. The algorithm adopted has a slow convergence speed and poor real-time performance. In addition, the structural particularity of the mining vehicle itself and the complex and changeable driving conditions make parameter identification even more difficult. It is urgent to improve the level of vehicle simulation technology in researching and evaluating the identification accuracy of tire model parameters.

To sum up, how to establish a parameter identification and optimization method for mining tires is a technical problem to be solved urgently by those skilled in the art.

Contents of the invention

The present invention aims to solve the shortcomings of the above-mentioned prior art, and proposes a parameter identification and optimization method for mining heavy-duty solid tires, in order to efficiently and quickly identify the parameters in the mining heavy-duty MF solid tire model. parameters, and achieve the effects of high calculation efficiency, strong global solution ability, and high precision, which can fundamentally improve the dynamic performance of the vehicle.

The present invention adopts following technical scheme in order to achieve the above-mentioned purpose of the invention:

A kind of parameter identification and optimization method for mining heavy-duty solid tires of the present invention is characterized in that it is carried out according to the following steps:

Step 1. Carry out the test operation on the tire according to the mine heavy-duty solid tire test, obtain the test data, and use the test data to construct the mine heavy-duty solid MF tire model;

Step 1.1, define the current number of tests as s, and initialize s=1;

其中，

表示第s次测试下的任意第i组试验数据，且

表示第i组试验数据x_i中的第j个特征量，并将第i组试验数据

中第j个特征量

的拟合值记作

的试验值记作

m表示特征量的总数；Step 1.2, carry out the s-th test on the tire sample of the heavy-duty rubber solid traction of the mining vehicle through the six-component force test bench, and obtain the n-group test data under the s-th test

in,

represents any i-th test data under the s-th test, and

Indicates the jth feature quantity in the i-th group of experimental data x _i , and the i-th group of experimental data

The jth feature quantity in

The fitting value of is denoted as

The test value of

m represents the total number of feature quantities;

Step 1.3, using formula (1) to establish the objective function Z ^s of the semi-empirical tire model during the s-th test:

Step 1.4, after assigning s+1 to s, judge whether s>Smax is true, if true, execute step 2, otherwise, return to step 1.2 and execute sequentially, where Smax represents the maximum number of trials;

Step 2, sort the objective function values during the Smax times of testing in ascending order, and obtain the sorted first objective function value as the initial value of the semi-empirical tire model, thereby obtaining the mine heavy-duty MF solid tire model;

Step 3, will identify the parameters in the mine heavy-duty MF solid tire model by Gauss-Newton iteration method:

Step 3.1, carrying out Taylor series expansion on the mine heavy-duty MF solid tire model, and deleting the second-order and above partial derivative items to obtain a nonlinear regression tire model;

Step 3.2, define the current number of iterations as v, and initialize v=1;

Step 3.3, using the least squares method to estimate the nonlinear regression tire model for the vth time, and obtain the correction factor for the vth estimation;

Step 3.4, calculate the residual sum of squares SSR ^v of the correction factor estimated for the vth time;

Step 3.5, identify the coefficients to be regressed:

时，停止迭代，并将得到第v次估计的修正因子代入所述非线性回归轮胎模型中，得到修正后的矿用重载MF实心轮胎模型；否则，将v+1赋值给v后，返回步骤3.3顺序执行；For a given allowable error rate k, when

, stop the iteration, and substitute the correction factor estimated for the vth time into the nonlinear regression tire model to obtain the revised mine heavy-duty MF solid tire model; otherwise, after assigning v+1 to v, return Step 3.3 is executed sequentially;

Step 4. Generate an initial population according to the parameter values to be identified in the revised mine heavy-duty MF solid tire model;

Step 4.1, set the population size as U, define the current generation of the population as g; and initialize g=1;

从而得到第g代种群集合记为

All the parameter values to be identified in the revised mine heavy-duty MF solid tire model are taken as the u-th chromosome in the g-th generation population

Thus, the population set of the gth generation is obtained and denoted as

的适应度值

并将第u个染色体

中适应度值最高的两个基因进行交叉操作后，得到第u个染色体

的两个新基因，用于替换第u个染色体

中适应度值最高的两个基因，从而得到更新后的第u个染色体

进而得到更新后的第g代种群A′^g；Step 4.2, calculate according to formula (1) to obtain the uth chromosome in the gth generation population A ^g

fitness value

and put the uth chromosome

After the two genes with the highest fitness value are crossed over, the uth chromosome is obtained

Two new genes of , used to replace the u-th chromosome

The two genes with the highest fitness values in , so as to get the updated uth chromosome

And then get the updated g generation population A′ ^g ;

的两个新基因作为模拟退火算子的初始最优解并进行退火操作：Step 4.3, the u-th chromosome

The two new genes of are used as the initial optimal solution of the simulated annealing operator and are annealed:

Step 4.3.1, define the current number of cycles of the annealing operation as k, and initialize k=0;

Let the temperature T _k of the k-th cycle randomly generate the state ω _k of the current k-th cycle as the optimal solution of the k-th cycle;

Step 4.3.2, set the temperature T _k+1 of the k+1th cycle = αT _k ; where α represents the cooling factor, 0<α<1;

Step 4.3.3. After assigning k+1 to k, obtain the state ω _k of the k-th cycle according to T _k , and use it as the optimal solution ω _k of the k-th cycle;

Step 4.3.4. Let the increment of the k-th cycle be ΔZ _k =Z(ω _k )-Z(ω _k-1 ), where Z represents the objective function of the semi-empirical tire model; ω _k-1 represents the k-th -1 cycle status;

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

否则，执行步骤4.3.5；If ΔZ _k ≤ 0, replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, perform step 4.3.5;

则将第k次循环的最优解ω_k替换第u个染色体

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

否则，第k-1次循环的最优解ω_k-1替换第u个染色体

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

其中，ε表示系数；r_k表示第k次循环的随机数，且r_k∈[0,1]；Step 4.3.5, if

Then replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, the optimal solution ω _k-1 of the k-1th cycle replaces the u-th chromosome

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Among them, ε represents the coefficient; r _k represents the random number of the kth cycle, and r _k ∈ [0,1];

进行变异操作，得到新的染色体

若第g+1代的第j个增量

则将新的染色体

加入第g+1代种群A^g+1，并得到更新后的第g+1代种群A′^g+1，否则，在[0，1]之间产生第g+1代的第j个随机数

若

则将新的染色体

加入第g+1代种群A^g+1，并得到更新后的第g+1代种群A′^g+1，否则，将第j条染色体

仍然保持在第g+1代种群A^g+1中，其中，t_j表示第j个退温函数；Step 4.4, according to the mutation probability P _m, any jth chromosome in the g+1th generation population A ^g+1

Perform mutation operations to obtain new chromosomes

If the jth increment of the g+1th generation

the new chromosome

Join the g+1th generation population A ^g+1 , and get the updated g+1th generation population A′ ^g+1 , otherwise, generate the jth random number

like

the new chromosome

Join the g+1th generation population A ^g+1 , and get the updated g+1th generation population A′ ^g+1 , otherwise, the jth chromosome

Still remain in the g+1th generation population A ^g+1 , where t _j represents the jth cooling function;

的适应度值

判第u个染色体

中适应度值高的两个基因作为模拟退火算子的初始最优解并进行退火操作：Step 4.5. Calculate the uth chromosome in the updated g+1th generation population A' ^g+1 according to formula (1)

fitness value

judge the uth chromosome

The two genes with high fitness values are used as the initial optimal solution of the simulated annealing operator and annealed:

Step 4.5.1, initializing the current number of cycles of the annealing operation k=0;

Let the temperature T _k ′ of the k-th cycle randomly generate the state ω _k ′ of the current k-th cycle as the optimal solution of the k-th cycle;

Step 4.5.2, let the temperature T _k ′ _{+ 1} of the k+1th cycle = αT _k ′; where α represents the cooling factor, 0<α<1;

Step 4.5.3, after assigning k+1 to k, obtain the state ω _k ′ of the k-th cycle according to T _k ′, and use it as the optimal solution ω _k ′ of the k-th cycle;

Step 4.5.4. Let the increment of the kth cycle be ΔZ _k ′=Z(ω _k ′)-Z(ω _k ′ _-1 ), where ω _k ′ _-1 represents the state of the k-1th cycle ;

中适应度值高的两个基因并得到第g+2代种群A^g+2的第u个染色体

否则，执行步骤4.5.5；If ΔZ _k ′≤0, replace the uth chromosome with the optimal solution ω _k ′ of the kth cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, go to step 4.5.5;

则将第k次循环的最优解ω_k′替换第u个染色体

中适应度值高的两个基因并得到第g+2代种群A^g+2的第u个染色体

否则，第k-1次循环的最优解ω_k′_-1替换第u个染色体

中适应度值高的两个基因并得到第g+2代种群A^{g +2}的第u个染色体

其中，r_k′表示第k次循环的随机数，且r_k′∈[0,1]；Step 4.5.5, if

Then replace the u-th chromosome with the optimal solution ω _k ′ of the k-th cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, the optimal solution ω _k ′ _-1 of the k-1th cycle replaces the uth chromosome

Two genes with high fitness value and get the uth chromosome of the g+2 generation population A ^{g +2}

Among them, r _k ′ represents the random number of the kth cycle, and r _k ′∈[0,1];

Step 4.6. After assigning g+2 to g, judge whether g>gmax is established. If it is established, it means that the gmax generation population is obtained, and the chromosome with the highest fitness is selected as the corrected mine heavy-duty MF solid tire model. The optimal identification parameter value, otherwise, return to step 4.2 and execute sequentially.

An electronic device according to the present invention, comprising a memory and a processor, is characterized in that the memory is used to store a program that supports the processor to execute the parameter identification and optimization method, and the processor is configured to execute the program in the memory stored program.

The present invention is a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the parameter identification and optimization method when the computer program is run by a processor.

Compared with the prior art, the method of the present invention is applicable to the typical mine road surface environment and heavy-duty transportation conditions, according to the mine-used heavy-duty solid tire test, the tires are tested and collected to obtain test data, and then based on semi-empirical The tire model establishes an optimization model and evaluation index, and brings the identified parameters into the tire model. Under the same conditions, the square root of the difference between the calculation result and the actual test value is the smallest, and the corresponding solution is optimal, that is, it is hoped that the smaller objective function value corresponds to The fitness value of the solution is high. First, the Gauss-Newton method is used to expand the function to be identified by Taylor, ignoring the second-order and above-order partial derivatives, and iteratively obtains the nonlinear regression tire model, and the least square method is used to estimate the nonlinear regression tire model to identify the coefficients to be regressed, and the correction is obtained The final heavy-duty MF solid tire model for mines; through the genetic algorithm and simulated annealing algorithm, the initial identification parameters are deeply optimized, and the optimal solution in each generation population is searched again with the simulated annealing algorithm to enhance the search ability of the algorithm, and through The simulated annealing algorithm maintains the diversity of the population and prevents the population from converging on a certain local area. This method can realize the adaptive adjustment, final identification and optimization of the parameters in the common tire empirical formula. The obtained parameter identification value is used to calculate and analyze the force of the tire under complex working conditions, and guide the design of the whole vehicle. An important part of analytical techniques. This method has strong purpose, very fast convergence speed, and high solution accuracy. The specific advantages are:

1. The present invention proposes to identify the objective function to establish an optimization model and an evaluation index, combine the Gauss-Newton iterative method, the genetic algorithm and the adaptive simulated annealing algorithm, first select the Gauss-Newton iterative method to first identify the main parameters of the test sampling data, and then The genetic algorithm optimizes and re-identifies the initial identification results, and the optimal solution in each generation population is searched again with the simulated annealing algorithm to enhance the search ability of the algorithm. Finally, the adaptive simulated annealing algorithm is used to jump out of the local optimal solution and find the global optimal solution , maintain the diversity of the population, have strong search ability, short running time and high solution accuracy, and are easy to implement. In view of the strong nonlinear characteristics caused by the large vertical load range of mining vehicle tires, the fixed parameter settings and optimization strategies of traditional algorithms are difficult to solve. To adapt to the situation, the method of the present invention can obtain relevant test data through the six-component force testing equipment, identify the tire model parameters under complex working conditions, and further conduct real vehicle experiments on the traction characteristics of the whole vehicle under different load conditions, and the test results It shows that compared with the pure genetic algorithm in terms of algorithm performance, the accuracy of the identification model is greatly improved, and it solves the pain points of the heavy-duty traction solid tire model of mining vehicles, which has many parameters and is highly nonlinear, which makes accurate modeling difficult. The calculation efficiency and High calculation speed. It provides the best identification algorithm for establishing a solution model suitable for the typical mine road environment and the tire force of heavy-duty transport vehicles.

2. The advantage of the mixed optimization algorithm adopted in the present invention is: in view of the important impact of tire road contact mechanical characteristics on the regulation and control of vehicle lateral stability, this algorithm is by studying the nonlinearity of the heavy-duty traction solid rubber tire of the mine vehicle on the road cement road surface. Rolling-sliding contact mechanical properties, accurately identify the model parameters of heavy-duty solid or filled tires based on tire materials and geometric structure characteristics, and establish a solution model suitable for typical mine road environments and heavy-duty transport vehicle tire forces. Compared with the genetic algorithm, the algorithm has a greater improvement in the global optimization and rapid convergence ability of the longitudinal force parameter identification in the pure longitudinal sliding mode under a certain working condition of the solid tire model of the heavy-duty traction of the mining vehicle, and converges to the global optimal The success rate reaches 70%, an increase of more than 50% compared with the genetic algorithm, the average algebra of convergence to the global optimum is reduced by more than 35%, the total time of convergence to the global optimum has increased by 6%, and the average time of convergence to the global optimum It is reduced by more than 30%; the evaluation index of the objective function of longitudinal force identification under the pure longitudinal sliding condition is increased by more than 10% compared with the single genetic algorithm.

The method of the present invention is based on the PAC2002 magic formula basic model, on the basis of correcting and proposing the mathematical model of the compound working condition of heavy-duty traction solid tires of mine vehicles, a hybrid optimization algorithm is proposed for parameter identification, and the results are verified, which shows that the proposed hybrid optimization algorithm The recognition stability is better, and the recognition accuracy is also higher. The deviation between the tire longitudinal traction calculated according to the identification parameters and the real vehicle test results is no more than 4%, which verifies the validity of the identification model. In order to accurately describe the actual state of motion of heavy-duty mine vehicles and precisely control their behavior The foundation has been laid and the key problems that have long restricted the study of mine vehicle dynamics and stability have been overcome.

Description of drawings

Fig. 1 is the flowchart of parameter identification of hybrid optimization algorithm of the present invention;

Fig. 2 is an evolution curve diagram of the hybrid optimization algorithm of the present invention.

Detailed ways

In this embodiment, as shown in Figure 1, a parameter identification and optimization method for mining heavy-duty solid tires is carried out in the following steps:

Step 1. Carry out the test operation on the tire according to the mine heavy-duty solid tire test, obtain the test data, and use the test data to construct the mine heavy-duty solid MF tire model;

Carry out tests on the corresponding mechanical properties of tires under different working conditions, and collect various data in the tire model under each working condition through the detection and collection of sensors in the test, including independent variables and dependent variables, such as lateral force, righting moment or longitudinal force, and the side slip angle or longitudinal slip rate of the tire corresponding to different working conditions.

Step 1.1, define the current number of tests as s, and initialize s=1;

其中，

表示第s次测试下的任意第i组试验数据，且

表示第i组试验数据x_i中的第j个特征量，并将第i组试验数据

中第j个特征量

的拟合值记作

的试验值记作

m表示特征量的总数；Step 1.2, carry out the s-th test on the tire sample of the heavy-duty rubber solid traction of the mining vehicle through the six-component force test bench, and obtain the n-group test data under the s-th test

in,

represents any i-th test data under the s-th test, and

Indicates the jth feature quantity in the i-th group of experimental data x _i , and the i-th group of experimental data

The jth feature quantity in

The fitting value of is denoted as

The test value of

m represents the total number of feature quantities;

Step 1.3, using formula (1) to establish the objective function Z ^s of the semi-empirical tire model during the s-th test:

Step 1.4: After assigning s+1 to s, judge whether s>Smax is true, if true, execute step 2, otherwise, return to step 1.2 and execute sequentially, where Smax represents the maximum number of trials.

Step 2. Sorting the objective function values in ascending order for the Smax times of testing, and obtaining the first objective function value after sorting as the initial value of the semi-empirical tire model, thereby obtaining the heavy-duty MF solid tire model for mine use.

Step 3. The parameters in the mining heavy-duty MF solid tire model will be identified by the Gauss-Newton iterative method:

The Gauss-Newton iterative method is used to first identify the main parameters in the objective function, mainly to perform nonlinear least squares estimation and iterative correction on the data sampled in step 1, so that the regression coefficient is continuously approaching the best regression coefficient of the nonlinear regression model , and finally the residual sum of squares of the original model is minimized, and the parameter values in the objective function are obtained from the initial identification.

The Gauss-Newton iterative method identifies parameter values through five parts: initial value selection, Taylor series expansion, estimated correction factor, accuracy test, and repeated iterations. After selecting or calculating the iterative initial value, the Taylor series is used to The expansion formula approximately replaces the nonlinear regression model, and then through multiple iterations, the regression coefficient is revised multiple times, so that the regression coefficient is continuously approaching the optimal regression coefficient of the nonlinear regression model, and finally the residual sum of squares of the original model is minimized. The biggest feature of the Gauss-Newton method is that it overcomes the large model error problem caused by linear approximation for parameter estimation when the nonlinear strength of the model is high, and the solution accuracy is high; at the same time, it is in principle the same as the linear least squares Approximation, the formula is simple in structure and has fast convergence ability, so it is very convenient to apply, and it is still a widely used nonlinear least squares estimation method. The general steps of the Gauss-Newton method are:

Step 3.1, carrying out Taylor series expansion on the mine heavy-duty MF solid tire model, and deleting the second-order and above partial derivative items to obtain a nonlinear regression tire model;

(1) There are three ways to select the initial value, one is to select the initial value based on previous experience, the other is to use the segment method to obtain the initial value; the third is to use linear transformation for the nonlinear regression model that can be linearized , and then implement the least square method to find the initial value.

(2) Taylor series expansion, let the nonlinear regression model be:

为方程输出值，误差项ε_i～N(0,σ²)，设

为待回归系数r＝(r₀,r₁,…,r_p-1)^T的初始值，将公式(2)的f(x_i,r)在g⁰点附近作泰勒展开，并略去非线性回归模型的二阶及二阶以上的偏导数项，得：In formula (2), r is the coefficient to be regressed, x _i is the parameter to be identified,

is the output value of the equation, the error term ε _i ～N(0,σ ² ), let

To be the initial value of regression coefficient r=(r ₀ ,r ₁ ,…,r _p-1 ) ^T , make Taylor expansion of f( _xi ,r) in formula (2) around point g ⁰ , and omit The partial derivative terms of the second order and above the second order of the nonlinear regression model, get:

Substituting formula (3) into formula (2), then:

Transition:

make

but:

Expressing the above formula in matrix form is:

Y ⁽⁰⁾ ≈ D ⁽⁰⁾ b ⁽⁰⁾ +ε (4)

In formula (4):

Step 3.2, define the current number of iterations as v, and initialize v=1;

Step 3.3, use the least squares method to estimate the correction factor for the vth nonlinear regression tire model of formula (4), then the correction factor b ^(v) of the vth iteration:

b ^(v) = (D ^(v)T D ^(v) ) ^-1 D ^(v)T Y ^(v ) (5)

v+1 iteration value: g ^(v+1) = g ^(v) + b ^(v) ;

In formula (5), D ^(v) is the calculation factor of the vth iteration under compound working conditions, and Y ^(v) is the output matrix of the equation;

Step 3.4, calculate the residual sum of squares SSR ^v of the correction factor estimated for the vth time;

Step 3.5, identify the coefficients to be regressed:

时，停止迭代；并将得到第v次估计的修正因子代入非线性回归轮胎模型中，得到修正后的矿用重载MF实心轮胎模型；否则，将v+1赋值给v后，返回步骤3.3顺序执行。For a given allowable error rate k, when

When , stop the iteration; and substitute the estimated correction factor of the vth time into the nonlinear regression tire model to obtain the revised mining heavy-duty MF solid tire model; otherwise, after assigning v+1 to v, return to step 3.3 Execute sequentially.

Step 4. Generate an initial population based on the parameter values obtained from the initial optimization identification of the revised mining heavy-duty MF solid tire model; use the genetic algorithm to calculate the initial value, and optimize the fitness value through the initial parameter values identified in step 3. According to the genetic algorithm After continuous crossover, mutation, and optimization of genetic operators, a scientific and reasonable formula parameter value close to the optimal solution is found in the global scope.

Based on the global probability search algorithm of natural selection and Mendelian law of inheritance, according to the research problem, determine the objective function formula (1), and then initialize the population randomly, the individual in the population represents a possible solution of the research problem, and the individual is carried out The preferred way is to select individuals with high fitness values. The fitness value is calculated according to the objective function formula (1). Multiple selected excellent individuals constitute a new next-generation population, and then through crossover and mutation Operation to increase the diversity of this new population, and repeating this process, can make the population continuously evolve and produce a better next-generation population.

Select the real code to encode the value of the parameter to be identified, set the upper and lower limits of the parameter to be identified, and initialize the population. Usually, the group size Np=10-200. In this embodiment, the group size Np=200 when performing parameter identification on the longitudinal force and cornering force.

Through the mechanism of survival of the fittest, the individuals with poor fitness value are eliminated, and the surviving individuals are selected according to the level of fitness and according to certain rules, and reproduced to form new groups. The higher the fitness, the better the solution, and the lower the fitness, the worse the quality of the solution. The selection operation of the present invention uses a proportional selection method to select excellent individuals.

Through crossover and mutation operations, the next generation population is generated. Crossover is to randomly select two individuals (parents), and exchange genes at one or more points to generate two new individuals. Mutation is a mutation at one or more points in a gene. If the crossover probability Pc is too small, it is difficult to search forward, and if it is too large, it will easily destroy some excellent individuals. Usually, Pc=0.25～1.00. In this paper, single-point crossover is selected, and the crossover probability Pc=0.65. If the mutation probability Pm is too small, it is difficult to generate a new gene structure, and if it is too large, the genetic algorithm will become a random search. Usually, Pm=0.001-0.1. In this embodiment, the mutation probability is selected as Pm=0.07.

The offspring repeat the above operations to carry out a new round of genetic evolution process. Based on the characteristics of the fast calculation speed of the fitness function of this method, in this embodiment, the maximum number of genetic generations is set to 10,000 generations. as shown in picture 2;

Judging whether the population meets the termination condition, if so, the algorithm ends, and an approximate optimal solution is obtained. Next, the adaptive simulated annealing algorithm is used to improve the calculation efficiency, and further local optimization is performed. The optimal solution is output through random value iteration, and it is judged whether the objective function reaches Evaluation index requirements.

The simulated annealing algorithm is an extension of the local search algorithm, which is mainly used in combinatorial optimization problems. It is derived from the principle of metal annealing. The metal is heated to a certain temperature and then allowed to cool slowly. When cooling, the interior of the metal particles gradually tends to be orderly. When the temperature drops to a certain level, the internal energy is minimized. Based on this characteristic, the simulated annealing algorithm starts from a certain higher temperature, and with the continuous decrease of the temperature parameter, combines the probability map jump feature to randomly search for the global optimal solution in the solution space, that is, it can jump out of the local optimal solution probabilistically. The solution eventually tends to the global optimum, and the local search ability is strong, and the running time is short.

Based on the simulated annealing algorithm, the adaptive simulated annealing algorithm (ASA) has been improved in the quenching method, re-annealing method and cooling method. Compared with the simulated annealing algorithm, it has better calculation efficiency and overall Solving ability.

Specific steps are as follows:

Step 4.1, set the population size as U, define the current generation of the population as g; and initialize g=1;

从而得到第g代种群集合记为

All the parameter values to be identified in the revised mine heavy-duty MF solid tire model are taken as the u-th chromosome in the g-th generation population

Thus, the population set of the gth generation is obtained and denoted as

的适应度值

并将第u个染色体

中适应度值最高的两个基因进行交叉操作后，得到第u个染色体

的两个新基因，用于替换第u个染色体

中适应度值最高的两个基因，从而得到更新后的第u个染色体

进而得到更新后的第g代种群A′^g。Step 4.2, calculate according to formula (1) to obtain the uth chromosome in the gth generation population A ^g

fitness value

and put the uth chromosome

After the two genes with the highest fitness value are crossed over, the uth chromosome is obtained

Two new genes of , used to replace the u-th chromosome

The two genes with the highest fitness values in , so as to get the updated u-th chromosome

Then the updated g-th generation population A' ^g is obtained.

的两个新基因作为模拟退火算子的初始最优解并进行退火操作：Step 4.3, the u-th chromosome

The two new genes of are used as the initial optimal solution of the simulated annealing operator and are annealed:

Step 4.3.1, define the current number of cycles of the annealing operation as k, and initialize k=0;

Let the temperature T _k of the k-th cycle randomly generate the state ω _k of the current k-th cycle as the optimal solution of the k-th cycle;

Step 4.3.2, set the temperature T _k+1 of the k+1th cycle = αT _k ; where α represents the cooling factor, 0<α<1;

Step 4.3.3. After assigning k+1 to k, obtain the state ω _k of the k-th cycle according to T _k , and use it as the optimal solution ω _k of the k-th cycle;

Step 4.3.4. Let the increment of the k-th cycle be ΔZ _k =Z(ω _k )-Z(ω _k-1 ), where Z represents the objective function of the semi-empirical tire model; ω _k-1 represents the k-th -1 cycle status;

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

否则，执行步骤4.3.5；If ΔZ _k ≤ 0, replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, perform step 4.3.5;

则将第k次循环的最优解ω_k替换第u个染色体

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

否则，第k-1次循环的最优解ω_k-1替换第u个染色体

的两个新基因并得到第g+1代种群A^g+1的第u个染色体

其中，ε表示系数；r_k表示第k次循环的随机数，且r_k∈[0,1]。Step 4.3.5, if

Then replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, the optimal solution ω _k-1 of the k-1th cycle replaces the u-th chromosome

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Among them, ε represents the coefficient; r _k represents the random number of the kth cycle, and r _k ∈ [0,1].

Step 4.4. According to the mutation probability P _m , insert the new individual into the parent population to obtain a new population. The new population generated after the cloning gene mutation operation is not used as the next generation population, but the new individual should be obtained with a certain Insert the generation gap (GAP=0.95) into the parent population to obtain the temporary population tempop, use the MetropoliS sampling standard to discriminate the chromosomes in the temporary population tempop, and determine whether it can enter the next generation population, the specific operation is as follows:

进行变异操作，得到新的染色体

若第g+1代的第j个增量

则将新的染色体

加入第g+1代种群A^g+1，并得到更新后的第g+1代种群A′^g+1，否则，在[0，1]之间产生第g+1代的第j个随机数

若

则将新的染色体

加入第g+1代种群A^g+1，并得到更新后的第g+1代种群A′^g+1，否则，将第j条染色体

仍然保持在第g+1代种群A^g+1中，其中，t_j表示退温函数。For any jth chromosome in the g+1th generation population A ^g+1

Perform mutation operations to obtain new chromosomes

If the jth increment of the g+1th generation

the new chromosome

Join the g+1th generation population A ^g+1 , and get the updated g+1th generation population A′ ^g+1 , otherwise, generate the jth random number

like

the new chromosome

Join the g+1th generation population A ^g+1 , and get the updated g+1th generation population A′ ^g+1 , otherwise, the jth chromosome

Still remain in the g+1th generation population A ^g+1 , where t _j represents the cooling function.

的适应度值

判第u个染色体

中适应度值高的两个基因作为模拟退火算子的初始最优解并进行退火操作：Step 4.5. Calculate the uth chromosome in the updated g+1th generation population A' ^g+1 according to formula (1)

fitness value

judge the uth chromosome

The two genes with high fitness values are used as the initial optimal solution of the simulated annealing operator and annealed:

Step 4.5.1, initializing the current number of cycles of the annealing operation k=0;

Let the temperature T _k ′ of the k-th cycle randomly generate the state ω _k ′ of the current k-th cycle as the optimal solution of the k-th cycle;

Step 4.5.2, let the temperature T _k ′ _{+ 1} of the k+1th cycle = αT _k ′; where α represents the cooling factor, 0<α<1;

Step 4.5.3, after assigning k+1 to k, obtain the state ω _k ′ of the k-th cycle according to T _k ′, and use it as the optimal solution ω _k ′ of the k-th cycle;

Step 4.5.4. Let the increment of the kth cycle be ΔZ _k ′=Z(ω _k ′)-Z(ω _k ′ _-1 ), where ω _k ′ _-1 represents the state of the k-1th cycle ;

中适应度值高的两个基因并得到第g+2代种群A^g+2的第u个染色体

否则，执行步骤4.5.5；If ΔZ _k ′≤0, replace the uth chromosome with the optimal solution ω _k ′ of the kth cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, go to step 4.5.5;

则将第k次循环的最优解ω_k′替换第u个染色体

中适应度值高的两个基因并得到第g+2代种群A^g+2的第u个染色体

否则，第k-1次循环的最优解ω_k′_-1替换第u个染色体

中适应度值高的两个基因并得到第g+2代种群A^{g +2}的第u个染色体

进入下一代种群，其中，r_k′表示第k次循环的随机数，且r_k′∈[0,1]。Step 4.5.5, if

Then replace the u-th chromosome with the optimal solution ω _k ′ of the k-th cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, the optimal solution ω _k ′ _-1 of the k-1th cycle replaces the uth chromosome

Two genes with high fitness value and get the uth chromosome of the g+2 generation population A ^{g +2}

Enter the next generation population, where r _k ′ represents the random number of the kth cycle, and r _k ′∈[0,1].

Step 4.6. Calculate the chromosome fitness value in the new generation population, find out the maximum fitness value Z(i) _max , and judge whether the termination condition of the number of iterations GEN=MAXGEN=100 is satisfied, that is, judge Z(i) _max , Z(i- 1) Whether _max , ..., Z(iq) _max are the same, if yes, the calculation will be terminated, the specific steps are as follows:

After assigning g+2 to g, judge whether g>gmax is established. If it is established, it means that the gmax generation population is obtained, and the chromosome with the highest fitness is selected as the optimal identification of the revised mining heavy-duty MF solid tire model parameter value, otherwise, return to step 4.2 and execute sequentially.

In this embodiment, an electronic device includes a memory and a processor, the memory is used to store a program that supports the processor to execute the above parameter identification and optimization method, and the processor is configured to execute the program stored in the memory program.

In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and when the computer program is run by a processor, the steps of the above parameter identification and optimization method are executed.

Claims (3)

1. A parameter identification and optimization method for mining heavy-duty solid tires is characterized in that it is carried out in the following steps: Step 1. Carry out the test operation on the tire according to the mine heavy-duty solid tire test, obtain the test data, and use the test data to construct the mine heavy-duty solid MF tire model; Step 1.1, define the current number of tests as s, and initialize s=1; Step 1.2, carry out the s-th test on the tire sample of the heavy-duty rubber solid traction of the mining vehicle through the six-component force test bench, and obtain the n-group test data under the s-th test

in,

represents any i-th test data under the s-th test, and

Indicates the jth feature quantity in the i-th group of experimental data x _i , and the i-th group of experimental data

The jth feature quantity in

The fitting value of is denoted as

The test value of

m represents the total number of feature quantities; Step 1.3, using formula (1) to establish the objective function Z ^s of the semi-empirical tire model during the s-th test:

Step 1.4, after assigning s+1 to s, judge whether s>Smax is true, if true, execute step 2, otherwise, return to step 1.2 and execute sequentially, where Smax represents the maximum number of trials; Step 2, sort the objective function values during the Smax times of testing in ascending order, and obtain the sorted first objective function value as the initial value of the semi-empirical tire model, thereby obtaining the mine heavy-duty MF solid tire model; Step 3, will identify the parameters in the mine heavy-duty MF solid tire model by Gauss-Newton iteration method: Step 3.1, carrying out Taylor series expansion on the mine heavy-duty MF solid tire model, and deleting the second-order and above partial derivative items to obtain a nonlinear regression tire model; Step 3.2, define the current number of iterations as v, and initialize v=1; Step 3.3, using the least squares method to estimate the nonlinear regression tire model for the vth time, and obtain the correction factor estimated for the vth time; Step 3.4, calculate the residual sum of squares SSR ^v of the correction factor estimated for the vth time; Step 3.5, identify the coefficients to be regressed: For a given allowable error rate k, when

, stop the iteration, and substitute the correction factor estimated for the vth time into the nonlinear regression tire model to obtain the revised mine heavy-duty MF solid tire model; otherwise, after assigning v+1 to v, return Step 3.3 is executed sequentially; Step 4. Generate an initial population according to the parameter values to be identified in the revised mine heavy-duty MF solid tire model; Step 4.1, set the population size as U, define the current generation of the population as g; and initialize g=1; All the parameter values to be identified in the revised mine heavy-duty MF solid tire model are taken as the u-th chromosome in the g-th generation population

Thus, the population set of the gth generation is obtained and denoted as

Step 4.2, calculate according to formula (1) to obtain the uth chromosome in the gth generation population A ^g

fitness value

and put the uth chromosome

After the two genes with the highest fitness value are crossed over, the uth chromosome is obtained

Two new genes of , used to replace the u-th chromosome

The two genes with the highest fitness values in , so as to get the updated uth chromosome

And then get the updated g generation population A′ ^g ; Step 4.3, the u-th chromosome

The two new genes of are used as the initial optimal solution of the simulated annealing operator and are annealed: Step 4.3.1, define the current number of cycles of the annealing operation as k, and initialize k=0; Let the temperature T _k of the k-th cycle randomly generate the state ω _k of the current k-th cycle as the optimal solution of the k-th cycle; Step 4.3.2, set the temperature T _k+1 of the k+1th cycle = αT _k ; where α represents the cooling factor, 0<α<1; Step 4.3.3. After assigning k+1 to k, obtain the state ω _k of the k-th cycle according to T _k , and use it as the optimal solution ω _k of the k-th cycle; Step 4.3.4. Let the increment of the k-th cycle be ΔZ _k =Z(ω _k )-Z(ω _k-1 ), where Z represents the objective function of the semi-empirical tire model; ω _k-1 represents the k-th -1 cycle status; If ΔZ _k ≤ 0, replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, perform step 4.3.5; Step 4.3.5, if

Then replace the u-th chromosome with the optimal solution ω _k of the k-th cycle

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Otherwise, the optimal solution ω _k-1 of the k-1th cycle replaces the u-th chromosome

and get the uth chromosome of population A ^{g+1 of g+} 1th generation

Among them, ε represents the coefficient; r _k represents the random number of the kth cycle, and r _k ∈ [0,1]; Step 4.4, according to the mutation probability P _m, any jth chromosome in the g+1th generation population A ^g+1

Perform mutation operations to obtain new chromosomes

If the jth increment of the g+1th generation

the new chromosome

Join the g+1th generation population A ^g+1 , and get the updated g+1th generation population A′ ^g+1 , otherwise, generate the jth random number

like

the new chromosome

Join the g+1th generation population A ^{g +1} , and get the updated g+1th generation population A′ ^g+1 , otherwise, the jth chromosome

Still remain in the g+1th generation population A ^{g +1} , where t _j represents the jth cooling function; Step 4.5. Calculate the uth chromosome in the updated g+1th generation population A' ^g+1 according to formula (1)

fitness value

judge the uth chromosome

The two genes with high fitness values are used as the initial optimal solution of the simulated annealing operator and annealed: Step 4.5.1, initializing the current number of cycles of the annealing operation k=0; Let the temperature T _k ′ of the k-th cycle, randomly generate the state ω _k ′ of the current k-th cycle as the optimal solution of the k-th cycle; Step 4.5.2, let the temperature T _k ′ _{+ 1} of the k+1th cycle = αT _k ′; where α represents the cooling factor, 0<α<1; Step 4.5.3, after assigning k+1 to k, obtain the state ω _k ′ of the k-th cycle according to T _k ′, and use it as the optimal solution ω _k ′ of the k-th cycle; Step 4.5.4. Let the increment of the kth cycle be ΔZ _k ′=Z(ω _k ′)-Z(ω _k ′ _-1 ), where ω _k ′ _-1 represents the state of the k-1th cycle ; If ΔZ _k ′≤0, replace the uth chromosome with the optimal solution ω _k ′ of the kth cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, go to step 4.5.5; Step 4.5.5, if

Then replace the u-th chromosome with the optimal solution ω _k ′ of the k-th cycle

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Otherwise, the optimal solution ω _k ′ _-1 of the k-1th cycle replaces the uth chromosome

Two genes with high fitness value and get the uth chromosome of the g+2th generation population A ^g+2

Among them, r _k ′ represents the random number of the kth cycle, and r _k ′∈[0,1]; Step 4.6. After assigning g+2 to g, judge whether g>gmax is established. If it is established, it means that the gmax generation population is obtained, and the chromosome with the highest fitness is selected as the corrected mine heavy-duty MF solid tire model. The optimal identification parameter value, otherwise, return to step 4.2 and execute sequentially. 2. An electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor to perform the parameter identification and optimization method according to claim 1, and the processor is configured to execute programs stored in the memory. 3. A computer-readable storage medium, with a computer program stored on the computer-readable storage medium, wherein the computer program executes the steps of the parameter identification and optimization method according to claim 1 when the computer program is run by a processor.

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