High-speed train bogie dynamic performance game optimization method

Abstract

The invention relates to a high-speed train bogie dynamic performance game optimization method, which comprises the following steps: S1, constructing a high-speed train dynamic simulation agent model, namely constructing a dynamic simulation model and training the agent model; s2, constructing an uncertainty quantitative model, wherein the uncertainty quantitative model comprises uncertainty representation and uncertainty propagation; s3, constructing a game model, including game pattern construction, strategy set division and utility function construction; and S4, solving the game model. By the adoption of the method, random changes in the running process of the high-speed train can be taken into consideration, and meanwhile overall optimization of the dynamic performance is guaranteed.

Description

Technical Field

[0001] The invention relates to a method for optimizing dynamics performance, and in particular to a method for optimizing the dynamics performance of a high-speed train bogie through game theory. Background Art

[0002] As a running device that supports, pulls and brakes the car body and can rotate relative to the car body, the bogie is a core component that determines the safety and quality of train operation and restricts speed increase. Among them, dynamic performance design is the core of bogie design. Different suspension parameter matching settings directly affect the vehicle's operating performance. Strict requirements make the matching between suspension parameters more difficult. At the same time, the suspension parameters have random uncertainties during train operation, such as random fluctuations in parameters caused by manufacturing errors, rubber aging, temperature changes, etc. The increase in speed makes the random changes in suspension parameters have a more drastic impact on dynamic performance, which makes the parameter matching results lack adaptability, poor dynamic performance, and even endangers driving safety. In the past, it was a deterministic optimization design, which was difficult to meet the requirements of dynamic performance robustness under the influence of random factors. The optimization of the dynamic performance of high-speed train bogies considering the influence of random factors can reduce the impact of random changes in suspension parameters on dynamic performance, which is of great significance for bogie design and development.

[0003] At present, the research on the dynamic performance of high-speed train bogies pays more and more attention to the influence of random factors on the bogies. The Monte Carlo method is used to obtain the distribution characteristics of dynamic indicators, which reflects the vehicle dynamic performance more realistically and comprehensively. However, the Monte Carlo method takes parameters according to probability distribution, combines them into thousands of working conditions, and obtains the distribution of dynamic performance indicators. Obviously, the high computational cost of the above method for nonlinear rail vehicle numerical simulation models when designing suspension parameters is unacceptable. In the process of optimizing the dynamic performance indicators of bogies, most of the current studies only consider the optimality of a single performance indicator, ignoring the overall optimality that needs to be achieved under the mutual influence of performance indicators. Summary of the invention

[0004] The purpose of the present invention is to propose a bogie suspension parameter design method in view of the above-mentioned technical development and existing deficiencies, which can take into account the random changes during the operation of high-speed trains while ensuring the overall optimization of dynamic performance.

[0005] A high-speed train bogie dynamics performance game optimization method, comprising steps S1-S4:

[0006] Step S1: constructing a high-speed train dynamics simulation agent model, including dynamics simulation model construction and agent model training;

[0007] Step S2: construct an uncertainty quantification model, including uncertainty representation and uncertainty propagation;

[0008] Step S3: constructing a game model, including game pattern construction, strategy set division and utility function construction;

[0009] Step S4: solving the game model.

[0010] Step S1 specifically includes the following steps S11-S16:

[0011] Step S11: constructing a dynamics simulation model;

[0012] Step S12: Determine design variables, constraint intervals and optimization objectives;

[0013] Step S13: sampling simulation;

[0014] Step S14: dividing the proxy model samples;

[0015] Step S15: training the agent model;

[0016] Step S16: Verify the accuracy of the proxy model.

[0017] Step S11: constructing a dynamics simulation model;

[0018] Step S12: Determine design variables, constraint intervals and optimization targets; including S121-S123:

[0019] S121: Determine design variables and select suspension parameters that need to be optimized;

[0020] S122: Determine the constraint interval and clarify the optional range of the suspension parameters;

[0021] S123: Determine the optimization target and the kinetic index to be optimized;

[0022] Step S13: Sampling simulation; including S131-S133:

[0023] S131: Based on the design variables and constraint intervals determined in S12, a certain number of design variable combination sample values ​​are extracted using Latin hypercube sampling;

[0024] S132: inputting the extracted sample values ​​into the simulation model to calculate the dynamic performance index;

[0025] S133: combining the design variables and the corresponding dynamics performance indicators to form sample values ​​for constructing a dynamics proxy model;

[0026] Step S14: Divide the proxy model samples

[0027] The random sample partitioning rule is used to randomly divide the data set into training set and test set;

[0028] Step S15: training the agent model;

[0029] Based on the above division of sample training set and test set, the training set is used to train the proxy model;

[0030] Step S16: Verify the accuracy of the proxy model.

[0031] Step S2 includes:

[0032] Step S21: uncertainty characterization analysis;

[0033] Step S22: uncertainty propagation analysis, constructing a chaotic polynomial model.

[0034] In step S21, a probability method is used to characterize the random uncertainty and clarify the random variation range of the suspension parameters.

[0035] Step S22 includes steps S221 to S226:

[0036] Step S221: Initialize the sample set;

[0037] Step S222: setting the order expansion range;

[0038] Step S223: low-order interaction truncation, using the following low-order interaction truncation:

[0039] A(M,p,q)≡{α∈N M :||α|| q ≤p,0<q≤1} (2)

[0040] Where A(M,p,q) is the candidate chaotic polynomial basis set under specific input and order, M is the dimension of input, N is the design variable space, α is the input vector, p is the chaotic polynomial order, ||·|| q is the q-norm; when q is 1, it is the standard cutoff; when q < 1, high-order interaction terms will be eliminated, and the smaller q is, the more will be eliminated;

[0041] Step S224: minimum angle regression, further obtaining a sparser chaotic polynomial basis set based on the minimum angle regression;

[0042] Step S225: Calculate the chaotic polynomial coefficients using the least squares method, substitute the samples and the corresponding function response values ​​into the right and left ends of the chaotic polynomial model, and obtain ψb=Y, where:

[0043]

[0044] In the formula, Φ is a polynomial, M is the dimension of the input, p is the order of the chaotic polynomial, ψ is the polynomial matrix, s is the vector dimension, and ξ is a standard random variable;

[0045]

[0046] In the formula, b is the coefficient matrix, Y is the output matrix, g is the response value, x is the input vector, and s is the vector dimension;

[0047] According to the least quadratic regression method, the chaotic polynomial coefficients are obtained:

[0048] b = (ψ T ψ) -1 ψ T Y (5)

[0049] In the formula, b is the coefficient matrix, Y is the output matrix, and ψ is the polynomial matrix;

[0050] Step S226: Use the leave-one-out method to perform a posteriori cross error estimation:

[0051]

[0052] In the formula, k is the number of original models established by the leave-one-out method, g(x i ) is x i The original model response output at point is the proxy model output, g PCE (x i ) The chaotic polynomial agent constructed in x i The output value at is the mean of the response values ​​of k chaotic polynomial proxy models; in the construction of the chaotic polynomial model cycle, according to the smallest ε Loocv Obtain the best chaotic polynomial expansion order;

[0053] Based on the obtained chaotic polynomial coefficients, the statistical information of random output is obtained; the response mean is equal to the coefficient of the chaotic polynomial constant term, and the variance σ c Equal to the sum of squares of the remaining coefficients of the chaotic polynomial constant term:

[0054]

[0055] In the formula, μ c and E[Y] is the response mean, σ c 2 and Var[Y] is the response variance, α i is the expansion coefficient; Φ i (X) is the standardized orthogonal polynomial basis; P is the highest order of the orthogonal polynomial.

[0056] Step S3 includes:

[0057] Step S31: constructing a game pattern;

[0058] Step S32: dividing the strategy set;

[0059] Step S33: Utility function construction.

[0060] In step S31, the stability and security indicators are used as leaders, and the stability indicators are used as followers to construct a game pattern;

[0061] Step S32 includes steps S321 to S3210:

[0062] Step S321: clarifying the system output to be analyzed and the parameters that may affect the output;

[0063] Step S322: Select a local or global sensitivity analysis method;

[0064] Step S323: Generate a sample combination of parameters by a sampling method, for evaluating the response of the output to the parameter change;

[0065] Step S324: Calculate the sensitivity coefficient of each parameter to the output;

[0066] Step S325: clustering the sensitivity analysis results using fuzzy C-means clustering;

[0067] Step S326: Initializing parameters, including selecting the number of clusters, setting the fuzzy coefficient, initializing the membership matrix and setting the error threshold;

[0068] Step S327: Calculate cluster centers;

[0069] Step S328: Update the membership matrix;

[0070] Step S329: Check convergence conditions;

[0071] Step S3210: output the result;

[0072] In step S33, the lateral acceleration of the bottom end of the bogie frame (y1) is used as the evaluation index of the snaking motion stability, the derailment coefficient (y2), the wheel weight reduction rate (y3), the wheel axle lateral force (y4), and the wheel-rail vertical force (y5) are used as the evaluation indexes of the curve passing performance, and the vertical stability (y6) and the lateral stability (y7) are used as the evaluation indexes of the stability. The construction of the utility function refers to converting the dynamic evaluation index into the goal of each game player. First, the dynamic evaluation index is converted into the satisfaction s by formula (8): i ; The stability only uses the lateral acceleration of the bottom end of the frame (y 1 ) is used as the evaluation index, and its comprehensive index is formula (9);

[0073]

[0074] In the formula, yi is the kinetic index, y min and max are the minimum and maximum values ​​of the corresponding kinetic indicators of the samples; s i is the satisfaction value of the corresponding dynamics index;

[0075] μ 1 =s 1 (9)

[0076] In the formula, μ 1 is the stability index satisfaction value, s 1 is the lateral acceleration satisfaction value at the bottom of the frame;

[0077] The curve passes through the comprehensive safety performance index composed of four satisfaction levels, and its comprehensive satisfaction value is constructed using the AHP method:

[0078] μ 2 =0.57s 2 +0.21s 3 +0.11s 4 +0.11s 5 (10)

[0079] In the formula, μ 2 is the safety index satisfaction value, s 2 is the derailment coefficient satisfaction value, s 3 is the wheel load reduction rate satisfaction value, s 4 is the satisfaction value of the axle lateral force, s 5 is the satisfaction value of wheel-rail vertical force;

[0080] The stability adopts Sperling as the evaluation index, among which the lateral and longitudinal stability have the same importance, so the comprehensive performance index of stability is as follows:

[0081] μ 3 =0.5s 6 +0.5s 7 (11)

[0082] In the formula, μ 3 is the stability index satisfaction value, s 6 is the vertical stability satisfaction value, s 7 is the satisfaction value of lateral stability;

[0083] The mean value of the comprehensive dynamic evaluation index (M μi ) and standard deviation (S μi ) weighted sum to calculate the comprehensive evaluation index robustness metric (R i );

[0084] R i =0.5Mμi +0.5S μi (12)

[0085] In the formula, R i is the robustness measure of the comprehensive evaluation index, M μi is the mean value of the comprehensive evaluation index of dynamics, S μi is the standard deviation of the comprehensive evaluation index of dynamics.

[0086] Step S4 includes:

[0087] Step S41: constructing a game model;

[0088] Step S42: Obtaining a master-slave balance.

[0089] Step S41: construct a game model; assume that there are N leaders and M followers in the game; the master-slave game is expressed as the following multi-objective optimization problem:

[0090]

[0091] In the formula, x v represents the strategy of the vth leader, y s Denotes the sth follower strategy; X v is the vth leader’s strategy sentence, Y s is the strategy set of the sth follower; F v is the utility function of the vth participant in the upper layer, f s is the utility function of the sth participant in the lower layer;

[0092] Step S42: Find the master-slave equilibrium; the specific steps are S421-S425, where (1≤n≤N, 1≤m≤M) represents all the game participants in the solution process:

[0093] S421: Setting the convergence index ε;

[0094] S422: Initialize the number of cycles i = 0, and randomly generate an initial strategy μ in the strategy set i ={x n i ,y m i};

[0095] S423: Leader Optimization, μ i ={x n i ,y m i} is the initial design variable, keeping y m i is a constant, by adjusting x n iTo optimize F, a sub-Nash game is played among multiple participants of the leader to obtain the optimized strategy combination {x n i +1 ,y m i};

[0096] S424: Optimization of followers, with {x n i+1 ,y m i} is the design variable, keeping x n i+1 is a constant, by adjusting y m i To optimize f, that is, to play a sub-Nash game among multiple participants of the followers under the result of the leader, and obtain the optimized strategy combination {x n i+1 ,y m i+1};

[0097] S425: Convergence judgment, such as ||μ i -μ i+1 ||≤ε, the loop terminates, μ i+1 ={x n i+1 ,y m i+1} is the desired master-slave game equilibrium; otherwise, set i=i+1 and return to S423.

[0098] Compared with the prior art, the present invention has the following beneficial effects:

[0099] (1) The inventors have found in practice that considering the random changes of suspension parameters in the design can more comprehensively reflect the changes in dynamic performance and obtain more robust dynamic performance. On this basis, it is proposed to adopt an uncertainty quantification method to obtain the random change characteristics of high-speed train dynamics by analyzing the random changes of bogie suspension parameters.

[0100] (2) The inventors have found in practice that it is difficult for designers in the prior art to clearly define the random variation characteristics of the suspension parameters during actual operation. The present invention combines the actual operation forms of the suspension parameters, mainly considering their temperature variation characteristics, and summarizes the general random variation characteristics of the suspension parameters.

[0101] (3) The inventors found in practice that the existing uncertainty quantification methods in the prior art are aimed at uncertainty analysis, that is, the suspension parameter settings have been clearly defined for dynamic performance index analysis, which cannot adapt to the high time cost caused by the large number of simulation requirements in the optimization process. In response to this, the present invention proposes an uncertainty quantification method suitable for suspension parameter optimization design to improve the calculation time and accuracy.

[0102] (4) The inventors have found in practice that in existing optimization methods, genetic algorithms are usually used for multi-objective optimization. However, in the problem of suspension parameter optimization, there is a conflict between the suspension parameters and the dynamic performance indicators. The traditional genetic algorithm cannot take into account such conflicting relationships. Therefore, the present invention proposes a dynamic performance game optimization method to improve the comprehensive performance of the optimization results.

[0103] (5) The inventors found in practice that in the existing game solving methods, it is necessary to construct three elements of the game model: participants, strategy space and strategy set. It is found that this can produce a one-to-one correspondence with the design variables, design space and constraints in multi-objective optimization. To this end, the inventors proposed a high-speed train suspension parameter uncertainty game optimization modeling method to construct a high-speed train dynamics robustness game model.

[0104] (6) The inventors have found in practice that in solving traditional game models, it is still necessary to update and iterate the population, which requires thousands of simulation calculations. For this reason, the inventors use proxy model technology to replace expensive simulation calculations. The calculation results can serve the construction of uncertainty quantification models, increase the number of iterations and improve optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 The flowchart for adaptive sparse chaotic polynomial uncertainty quantification is shown in Figure 1.

[0106] Figure 2 Flowchart for solving the master-slave game,

[0107] Figure 3 is the change diagram of the game utility function,

[0108] Figure 4 To compare the distribution of kinetic indicators before and after optimization. DETAILED DESCRIPTION

[0109] To make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be described clearly and completely in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them.

[0110] Therefore, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the invention claimed for protection, but merely represents some embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0111] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features and technical solutions in the embodiments may be combined with each other.

[0112] A high-speed train bogie dynamics performance game optimization method, comprising steps S1-S4:

[0113] Step S1: constructing a high-speed train dynamics simulation agent model, including dynamics simulation model construction and agent model training.

[0114] Step S2: Construct an uncertainty quantification model, including uncertainty characterization and uncertainty propagation.

[0115] Step S3: Construct a game model, including game pattern construction, strategy set division and utility function construction.

[0116] Step S4: solving the game model.

[0117] Preferably, step S1 specifically includes the following steps S11-S16:

[0118] Step S11: construct a dynamics simulation model.

[0119] Step S12: Determine the design variables, constraint intervals and optimization objectives.

[0120] Step S13: Sampling simulation.

[0121] Step S14: Divide the proxy model samples.

[0122] Step S15: training the agent model.

[0123] Step S16: Verify the accuracy of the proxy model.

[0124] Step S11: construct a dynamic simulation model. Including S111-S112:

[0125] S111: According to the actual operation of the high-speed train, basic parameters are set to construct a high-speed train dynamics model. The basic parameters at least include: track gauge, weight, and moment of inertia.

[0126] S112: Setting typical line operating parameters, which at least include: running speed, track unevenness, curve radius, and superelevation.

[0127] Step S12: Determine the design variables, constraint intervals and optimization objectives. Including S121-S123:

[0128] S121: Determine the design variables, that is, select the suspension parameters that need to be optimized.

[0129] S122: Determine the constraint interval, that is, clarify the optional range of the suspension parameters.

[0130] S123: Determine the optimization target, that is, determine the kinetic index to be optimized.

[0131] Step S13: Sampling simulation. Including S131-S133:

[0132] S131: Based on the design variables and constraint intervals determined in S12, a certain number of design variable combination sample values ​​are extracted using Latin hypercube sampling:

[0133] (1) Divide the interval: Divide the value range of each variable into n equal intervals.

[0134] (2) Random sampling: randomly select a sample point in each interval.

[0135] (3) Combined samples: Combine sample points of different dimensions into n n-dimensional points.

[0136] (4) Random permutation: The generated sample points are randomly arranged to ensure the independence of the samples.

[0137] S132: Input the extracted sample values ​​into the simulation model to calculate the dynamic performance index.

[0138] S133: Combining the design variables and the corresponding dynamics performance indicators to form sample values ​​for constructing a dynamics proxy model.

[0139] Step S14: Divide the proxy model samples

[0140] The data set is randomly divided into a training set and a test set using a random sample division rule. Preferably, the data set is divided in proportion, where: 80% training and 20% test.

[0141] Step S15: training the agent model.

[0142] Based on the above division of sample training set and test set, several proxy models are trained using the training set. Preferably, the proxy model is selected from one of radial basis, kriging, and artificial neural network.

[0143] Step S16: Verify the accuracy of the proxy model. Including S161-S162:

[0144] Step S161: Use the test set in the sample to verify the accuracy of the aforementioned proxy models, and use error analysis to evaluate the accuracy of the proxy models, which includes at least the following methods:

[0145] Root Mean Square Error (RMSE): measures the difference between the predicted value and the true value.

[0146] Coefficient of determination (R 2 ): Indicates the model's ability to explain the data. The closer the value is to 1, the higher the model accuracy.

[0147] Residual analysis: Check the deviation between the model prediction value and the true value, and analyze whether there is a systematic error. Step S162: Select the most accurate proxy model to replace the simulation model for subsequent optimization.

[0148] Step S2: constructing an uncertainty quantification model. Step S2 includes:

[0149] Step S21: uncertainty characterization analysis;

[0150] Step S22: uncertainty propagation analysis, i.e. building a chaotic polynomial model.

[0151] Step S21: uncertainty characterization analysis.

[0152] Considering the random effects of the suspension parameters of high-speed trains, a probability method is used to characterize the random uncertainty and clarify the random variation range of the suspension parameters. Preferably, a normal distribution is used to fit the probability distribution of the suspension parameter variation to obtain the coefficient of variation of the suspension parameter distribution.

[0153] Step S22: uncertainty propagation analysis, i.e. building a chaotic polynomial model.

[0154] Uncertainty propagation is the study of estimating output uncertainty information under specific input uncertainty information. Compared with traditional Monte Carlo simulation, the chaotic polynomial method can obtain similar accuracy to MCS with the support of a small number of samples, and can more easily obtain the mean and variance of the response in the optimization cycle. The non-embedded chaotic polynomial method regards uncertainty propagation as a black box, and the random variables are represented as a set of orthogonal polynomial weighted sums, focusing only on the mapping relationship between input and output. Construct a chaotic polynomial proxy model of output response to realize uncertainty propagation, thereby serving uncertainty optimization.

[0155] Preferably, the following chaotic polynomial is constructed: response function y=g(x)(x=[x 1 ,…,x i ,…,x d ]), the output response is expressed as a p-order truncated chaotic polynomial model under the chaotic polynomial theory.

[0156]

[0157] Where b i is the chaotic polynomial coefficient; Φ i is an orthogonal polynomial; p is the order of the polynomial model (generally greater than 3); ξ is a standard random variable ξ=[ξ 1 ,…,ξ i ,…,ξ d ],ξ i With the original variable x i According to the probability distribution type of the original variable, the original variable x is converted into i Mapped to a standard random variable distribution suitable for chaotic polynomial expansion.

[0158] The construction of the above traditional chaotic polynomial model mainly involves two aspects: polynomial selection and order determination, among which:

[0159] Polynomial selection: that is, you need to select a suitable polynomial basis according to the input distribution type.

[0160] Order determination: The order is determined manually based on experience or by performing incremental tests (gradually increasing the order to build the model and perform precision analysis).

[0161] In order to solve the problem of dimensionality disaster caused by the above-mentioned excessively high input dimension and polynomial order, the inventors proposed a modeling method of adaptive sparse chaotic polynomials, which optimized the steps of polynomial selection and order determination, avoided the problem of dimensionality disaster in dimensional construction model, and accelerated the efficiency of model construction.

[0162] Preferably, step S22 includes steps S221 to S226.

[0163] Step S221: Initialize the sample set;

[0164] Step S222: setting the order expansion range;

[0165] Step S223: low-order interaction truncation, using the following low-order interaction truncation:

[0166] A(M,p,q)≡{α∈N M :||α|| q ≤p,0<q≤1} (2)

[0167] Where A(M,p,q) is the candidate chaotic polynomial basis set under specific input and order, M is the dimension of input, N is the design variable space, α is the input vector, p is the chaotic polynomial order, ||·|| qis the q-norm. When q is 1, it is the standard cutoff; when q < 1, high-order interaction terms will be eliminated, and the smaller q is, the more will be eliminated.

[0168] Step S224: Minimum angle regression, based on which a sparser chaotic polynomial basis set is further obtained. Minimum angle regression can select the corresponding orthogonal polynomial basis according to the probability distribution of the random parameter, use an algorithm to select the polynomial basis function with the greatest correlation with the response variable, and construct a sparse polynomial chaotic expansion.

[0169] Step S225: Calculate the chaotic polynomial coefficients using the least squares method, substitute the sample and the corresponding function response value into the right and left ends of the chaotic polynomial model (Formula (3)) respectively, and obtain ψb=Y, where:

[0170]

[0171] Where Φ is a polynomial, M is the dimension of the input, p is the order of the chaotic polynomial, ψ is the polynomial matrix, s is the vector dimension, and ξ is a standard random variable.

[0172]

[0173] Where b is the coefficient matrix, Y is the output matrix, g is the response value, x is the input vector, and s is the vector dimension.

[0174] According to the least quadratic regression method, the chaotic polynomial coefficients can be obtained:

[0175] b = (ψ T ψ) -1 ψ T Y (5)

[0176] Where b is the coefficient matrix, Y is the output matrix, and ψ is the polynomial matrix.

[0177] Step S226: Use the leave-one-out method to perform a posteriori cross error estimation:

[0178]

[0179] In the formula, k is the number of original models established by the leave-one-out method, g(x i ) is x i The original model response output at point is the proxy model output, g PCE (x i ) The chaotic polynomial agent constructed in x i The output value at is the mean of the response values ​​of the k chaotic polynomial proxy models. In the construction of the chaotic polynomial model cycle, the smallest ε Loocv Obtain the optimal chaotic polynomial expansion order.

[0180] Based on the previously obtained chaotic polynomial coefficients (the coefficients include the constant term coefficients and the remaining coefficients except the constant term), the statistical information of the random output can be quickly and conveniently obtained. As shown in formula (7), the response mean is equal to the chaotic polynomial constant term coefficient, and the variance σ c Equal to the sum of squares of the remaining coefficients of the chaotic polynomial constant term:

[0181]

[0182] In the formula, μ c and E[Y] is the response mean, σ c 2 and Var[Y] is the response variance, α i is the expansion coefficient; Φ i (X) is the standardized orthogonal polynomial basis; P is the highest order of the orthogonal polynomial.

[0183] Step S3: Construct a game model, including game pattern construction, strategy set division and utility function construction.

[0184] Step S31: Construct a game pattern. The game pattern includes at least three elements: game subject, strategy set and utility function. There is the following mapping relationship between it and the dynamic optimization design: construct three game subjects corresponding to three bogie dynamic performance indicators (stability, safety and stability); each game subject strategy corresponds to the distribution mean under the random fluctuation of the bogie suspension parameters; the robustness measurement under the game strategy set is the utility function of the corresponding game subject. During the operation of high-speed trains, the running lines are mostly straight lines. While ensuring the stability of high-speed trains in straight lines and the performance of curve driving, we are committed to improving the running stability of trains. Therefore, the present invention takes stability and safety indicators as leaders and stability indicators as followers to construct a game pattern.

[0185] Step S32: strategy set division. In the game subject strategy, the strategy set in the present invention does not correspond to the number of game participants. The solution is to set each goal as the game party, convert the design variable set into the strategy set of each party, and use the strategy set division method combining sensitivity analysis and fuzzy clustering to achieve it. The strategy set division method combining sensitivity analysis and fuzzy clustering is as follows: Steps S321-S3210:

[0186] Step S321: clarifying the system output to be analyzed and the parameters that may affect the output. Preferably, the system output is a dynamics index, and the parameters that may affect the output are suspension parameters.

[0187] Step S322: Select a local or global sensitivity analysis method according to the nature of the problem. Preferably, for complex multi-parameter systems, global sensitivity analysis is more applicable;

[0188] Step S323: Generate a sample combination of parameters by a sampling method (such as Latin hypercube sampling) for evaluating the response of the output to the parameter change;

[0189] Step S324: Calculate the sensitivity coefficient of each parameter to the output. Commonly used indicators include relative sensitivity coefficient, partial derivative, etc.

[0190] Step S325: clustering the sensitivity analysis results using fuzzy C-means clustering;

[0191] Step S326: Initialize parameters, including selecting the number of clusters, setting the fuzzy coefficient, initializing the membership matrix and setting the error threshold.

[0192] Step S327: Calculate cluster centers;

[0193] Step S328: Update the membership matrix;

[0194] Step S329: Check convergence conditions;

[0195] Step S3210: Output the result.

[0196] Step S33: Utility function construction, using the lateral acceleration of the bottom end of the bogie frame (y1) as the evaluation index of the snaking motion stability, the derailment coefficient (y2), wheel weight reduction rate (y3), wheel axle lateral force (y4), wheel-rail vertical force (y5) as the evaluation index of the curve passing performance, and the vertical stability (y6) and lateral stability (y7) as the evaluation index of stability. Utility function construction refers to converting the dynamic evaluation index into the goal of each game player. First, the dynamic evaluation index is converted into the satisfaction s by formula (8): i The stability is only based on the lateral acceleration of the bottom end of the frame (y 1 ) is used as the evaluation index, and its comprehensive index is formula (9).

[0197]

[0198] In the formula, y i is the kinetic index, y min and max They are the minimum and maximum values ​​of the corresponding dynamic indicators of the samples. i is the corresponding dynamic index satisfaction value.

[0199] μ 1 =s 1 (9)

[0200] In the formula, μ 1 is the stability index satisfaction value, s 1 is the lateral acceleration satisfaction value at the bottom of the frame.

[0201] The curve passes through the comprehensive safety performance index composed of four satisfaction levels, and its comprehensive satisfaction value is constructed using the AHP method:

[0202] μ 2 =0.57s 2 +0.21s 3 +0.11s 4 +0.11s 5 (10)

[0203] In the formula, μ 2 is the safety index satisfaction value, s 2 is the derailment coefficient satisfaction value, s 3 is the wheel load reduction rate satisfaction value, s 4 is the satisfaction value of the axle lateral force, s 5 is the satisfaction value of wheel-rail vertical force.

[0204] The stability adopts Sperling as the evaluation index, among which the lateral and longitudinal stability have the same importance, so the comprehensive performance index of stability is as follows:

[0205] μ 3 =0.5s 6 +0.5s 7 (11)

[0206] In the formula, μ 3 is the stability index satisfaction value, s 6 is the vertical stability satisfaction value, s 7 is the lateral stability satisfaction value.

[0207] The random changes in suspension parameters will make the dynamic evaluation index show randomness. The mean value represents the overall performance of the dynamic performance, and the standard deviation represents the anti-interference ability of the dynamic performance. Game optimization design needs to take both goals into consideration at the same time, so the mean value of the dynamic comprehensive evaluation index (M μi ) and standard deviation (S μi ) weighted sum to calculate the comprehensive evaluation index robustness metric (R i ).

[0208] R i =0.5M μi +0.5S μi (12)

[0209] In the formula, R i is the robustness measure of the comprehensive evaluation index, M μi is the mean value of the comprehensive evaluation index of dynamics, S μi is the standard deviation of the comprehensive evaluation index of dynamics.

[0210] Step S4: solving the game model.

[0211] Step S41: Construct a game model. The game model of two leaders and one follower constructed by the present invention is that the leaders make decisions first, and they conduct non-cooperative Nash games and reach Nash equilibrium. Then the followers make decisions after observing the Nash equilibrium of the leaders. Finally, when the leaders' benefits cannot be improved, the master-slave game equilibrium is reached. The definition and solution steps are given below: Assume that there are N leaders and M followers in the game; the master-slave game can be expressed as the following multi-objective optimization problem:

[0212]

[0213] In the formula, x v represents the strategy of the vth leader, y s Denotes the sth follower strategy; X v is the vth leader’s strategy sentence, Y s is the strategy set of the sth follower; F v is the utility function of the vth participant in the upper layer, f s is the utility function of the sth participant in the lower layer.

[0214] Step S42: Find the master-slave equilibrium. The specific steps are as follows S421-S425, where (1≤n≤N, 1≤m≤M) (N is the number of leaders, M is the number of followers) represents all the game participants in the solution process:

[0215] S421: Setting the convergence index ε;

[0216] S422: Initialize the number of cycles i = 0, and randomly generate an initial strategy μ in the strategy set i ={x n i ,y m i};

[0217] S423: Leader Optimization, μ i ={x n i ,y m i} is the initial design variable, keeping y m i is a constant, by adjusting x n i To optimize F, a sub-Nash game is played among multiple participants of the leader to obtain the optimized strategy combination {x n i+1 ,y m i};

[0218] S424: Optimization of followers, with {x n i+1 ,y m i} is the design variable, keeping x n i+1 is a constant, by adjusting y m i To optimize f, that is, to play a sub-Nash game among multiple participants of the followers under the result of the leader, and obtain the optimized strategy combination {x n i+1 ,y m i+1};

[0219] S425: Convergence judgment, such as ||μ i -μ i+1 ||≤ε, the loop terminates, μ i+1 ={x n i+1 ,y m i+1 Otherwise, set i=i+1 and return to S423.

[0220] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described in the present invention. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the above specific implementation methods. Therefore, any modification or equivalent replacement of the present invention; and all technical solutions and improvements thereof that do not depart from the spirit and scope of the invention are included in the scope of the claims of the present invention.

Claims

1. A high-speed train bogie dynamics performance game optimization method, characterized by: The method comprises steps S1-S4: Step S1: constructing a high-speed train dynamics simulation agent model, including dynamics simulation model construction and agent model training; Step S2: construct an uncertainty quantification model, including uncertainty representation and uncertainty propagation; Step S3: constructing a game model, including game pattern construction, strategy set division and utility function construction; Step S4: solving the game model.

2. A high-speed train bogie dynamics performance game optimization method according to claim 1, characterized in that: Step S1 specifically The process comprises the following steps S11-S16: Step S11: constructing a dynamics simulation model; Step S12: Determine design variables, constraint intervals and optimization objectives; Step S13: sampling simulation; Step S14: dividing the proxy model samples; Step S15: training the agent model; Step S16: Verify the accuracy of the proxy model.

3. A high-speed train bogie dynamics performance game optimization method as claimed in claim 2, characterized in that: Step S11: constructing a dynamics simulation model; Step S12: Determine design variables, constraint intervals and optimization targets; including S121-S123: S121: Determine design variables and select suspension parameters that need to be optimized; S122: Determine the constraint interval and clarify the optional range of the suspension parameters; S123: Determine the optimization target and the kinetic index to be optimized; Step S13: Sampling simulation; including S131-S133: S131: Based on the design variables and constraint intervals determined in S12, a certain number of design variable combination sample values ​​are extracted using Latin hypercube sampling; S132: inputting the extracted sample values ​​into the simulation model to calculate the dynamic performance index; S133: combining the design variables and the corresponding dynamics performance indicators to form sample values ​​for constructing a dynamics proxy model; Step S14: Divide the proxy model samples The random sample partitioning rule is used to randomly divide the data set into training set and test set; Step S15: training the agent model; Based on the above division of sample training set and test set, the training set is used to train the proxy model; Step S16: Verify the accuracy of the proxy model.

4. A high-speed train bogie dynamics performance game optimization method as claimed in claim 3, characterized in that: Step S2 includes: Step S21: uncertainty characterization analysis; Step S22: uncertainty propagation analysis, constructing a chaotic polynomial model.

5. A high-speed train bogie dynamics performance game optimization method as claimed in claim 4, characterized in that: In step S21, a probability method is used to characterize the random uncertainty and clarify the random variation range of the suspension parameters.

6. A high-speed train bogie dynamics performance game optimization method as claimed in claim 5, characterized in that: Step S22 includes steps S221 to S226: Step S221: Initialize the sample set; Step S222: setting the order expansion range; Step S223: low-order interaction truncation, using the following low-order interaction truncation: A(M,p,q)≡{α∈N M :||α|| q ≤p,0<q≤1} (2) Where A(M,p,q) is the candidate chaotic polynomial basis set under specific input and order, M is the dimension of input, N is the design variable space, α is the input vector, p is the chaotic polynomial order, ||·|| q is the q-norm; when q is 1, it is the standard cutoff; when q < 1, high-order interaction terms will be eliminated, and the smaller q is, the more will be eliminated; Step S224: minimum angle regression, further obtaining a sparser chaotic polynomial basis set based on the minimum angle regression; Step S225: Calculate the chaotic polynomial coefficients using the least squares method, substitute the samples and the corresponding function response values ​​into the right and left ends of the chaotic polynomial model, and obtain ψb=Y, where: In the formula, Φ is a polynomial, M is the dimension of the input, p is the order of the chaotic polynomial, ψ is the polynomial matrix, s is the vector dimension, and ξ is a standard random variable; In the formula, b is the coefficient matrix, Y is the output matrix, g is the response value, x is the input vector, and s is the vector dimension; According to the least quadratic regression method, the chaotic polynomial coefficients are obtained: b=(ψ T (ψ) -1 ψ T Y (5) In the formula, b is the coefficient matrix, Y is the output matrix, and ψ is the polynomial matrix; Step S226: Use the leave-one-out method to perform a posteriori cross error estimation: In the formula, k is the number of original models established by the leave-one-out method, g(x i ) is x i The original model response output at point is the proxy model output, g PCE (x i )The output value of the chaotic polynomial agent constructed at xi, is the mean of the response values ​​of k chaotic polynomial proxy models; in the construction of the chaotic polynomial model cycle, according to the smallest ε Loocv Obtain the best chaotic polynomial expansion order; Based on the obtained chaotic polynomial coefficients, the statistical information of random output is obtained; the response mean is equal to the coefficient of the chaotic polynomial constant term, and the variance σ c Equal to the sum of squares of the remaining coefficients of the chaotic polynomial constant term: In the formula, μ c and E[Y] is the response mean, σ c 2 and Var[Y] is the response variance, α i is the expansion coefficient; Φ i (X) is the standardized orthogonal polynomial basis; P is the highest order of the orthogonal polynomial.

7. A high-speed train bogie dynamics performance game optimization method as claimed in claim 6, characterized in that: Step S3 includes: Step S31: constructing a game pattern; Step S32: dividing the strategy set; Step S33: Utility function construction.

8. A high-speed train bogie dynamics performance game optimization method as claimed in claim 7, characterized in that: In step S31, the stability and security indicators are used as leaders, and the stability indicators are used as followers to construct a game pattern; Step S32 includes steps S321 to S3210: Step S321: clarifying the system output to be analyzed and the parameters that may affect the output; Step S322: Select a local or global sensitivity analysis method; Step S323: Generate a sample combination of parameters by a sampling method, for evaluating the response of the output to the parameter change; Step S324: Calculate the sensitivity coefficient of each parameter to the output; Step S325: clustering the sensitivity analysis results using fuzzy C-means clustering; Step S326: Initialize parameters, Including, selecting the number of clusters, setting the fuzzy coefficient, initializing the membership matrix and setting the error threshold; Step S327: Calculate cluster centers; Step S328: Update the membership matrix; Step S329: Check convergence conditions; Step S3210: output the result; In step S33, the lateral acceleration of the bottom end of the bogie frame (y1) is used as the evaluation index of the snaking motion stability, the derailment coefficient (y2), the wheel weight reduction rate (y3), the wheel axle lateral force (y4), and the wheel-rail vertical force (y5) are used as the evaluation indexes of the curve passing performance, and the vertical stability (y6) and the lateral stability (y7) are used as the evaluation indexes of the stability. The construction of the utility function refers to converting the dynamic evaluation index into the goal of each game player. First, the dynamic evaluation index is converted into the satisfaction s by formula (8): i ; Among them, the stability only uses the lateral acceleration (y1) at the bottom of the frame as the evaluation index, and its comprehensive index is formula (9); In the formula, y i is the kinetic index, y min and max are the minimum and maximum values ​​of the corresponding kinetic indicators of the samples; s i is the satisfaction value of the corresponding dynamics index; μ1=s1 (9) In the formula, μ1 is the satisfaction value of the stability index, s1 is the satisfaction value of the lateral acceleration at the bottom of the frame; The curve passes through the comprehensive safety performance index composed of four satisfaction levels, and its comprehensive satisfaction value is constructed using the AHP method: μ2=0.57s2+0.21s3+0.11s4+0.11s5 (10) Wherein, μ2 is the satisfaction value of safety index, s2 is the satisfaction value of derailment coefficient, s3 is the satisfaction value of wheel load reduction rate, s4 is the satisfaction value of wheel axle lateral force, and s5 is the satisfaction value of wheel-rail vertical force; The stability adopts Sperling as the evaluation index, among which the lateral and longitudinal stability have the same importance, so the comprehensive performance index of stability is as follows: μ3=0.5s6+0.5s7 (11) In the formula, μ3 is the satisfaction value of the stability index, s6 is the satisfaction value of the vertical stability, and s7 is the satisfaction value of the lateral stability; The mean value of the comprehensive dynamic evaluation index (M μi ) and standard deviation (S μi ) weighted sum to calculate the comprehensive evaluation index robustness metric (R i ); R i =0.5M μi +0.5S μi (12) In the formula, R i is the robustness metric of the comprehensive evaluation index, M μi is the mean value of the comprehensive evaluation index of dynamics, S μi is the standard deviation of the comprehensive evaluation index of dynamics.

9. A high-speed train bogie dynamics performance game optimization method as claimed in claim 8, characterized in that: Step S4 includes: Step S41: constructing a game model; Step S42: Obtaining a master-slave balance.

10. A high-speed train bogie dynamics performance game optimization method according to claim 9, characterized in that: Step S41: construct a game model; assume that there are N leaders and M followers in the game; the master-slave game is expressed as the following multi-objective optimization problem: In the formula, x v represents the strategy of the vth leader, y s Denotes the sth follower strategy; X v is the vth leader’s strategy sentence, Y s is the strategy set of the sth follower; F v is the utility function of the vth participant in the upper layer, f s is the utility function of the sth participant in the lower layer; Step S42: Find the master-slave equilibrium; the specific steps are S421-S425, where (1≤n≤N, 1≤m≤M) represents all the game participants in the solution process: S421: Setting the convergence index ε; S422: Initialize the number of cycles i = 0, and randomly generate an initial strategy μ in the strategy set i ={x n i ,y m i }; S423: Leader Optimization, μ i ={x n i ,y m i } is the initial design variable, keeping y m i is a constant, by adjusting x n i To optimize F, a sub-Nash game is played among multiple participants of the leader to obtain the optimized strategy combination {x n i+1 ,y m i }; S424: Optimization of followers, with {x n i+1 ,y m i } is the design variable, keeping x n i+1 is a constant, by adjusting y m i To optimize f, that is, to play a sub-Nash game among multiple participants of the followers under the result of the leader, and obtain the optimized strategy combination {x n i+1 ,y m i+1 }; S425: Convergence judgment, such as ||μ i -μ i+1 ||≤ε, the loop terminates, μ i+1 ={x n i+1 ,y m i+1 } is the desired master-slave game equilibrium; otherwise, set i=i+1 and return to S423.

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