A high-speed train bogie dynamics performance game optimization method

Abstract

The application relates to a high-speed train bogie dynamics performance game optimization method, which comprises steps S1-S4: step S1: constructing a high-speed train dynamics simulation agent model, comprising dynamics simulation model construction and agent model training; step S2: constructing an uncertainty quantification model, comprising uncertainty representation and uncertainty propagation; step S3: constructing a game model, comprising game pattern construction, strategy set division and utility function construction; and step S4: solving the game model. The method can consider random changes in the high-speed train running process and ensure the overall optimization of the dynamics performance.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of dynamics performance optimization method, specifically, to a kind of high-speed train bogie dynamics performance game optimization method. BACKGROUND

[0002] Bogie is the running device that supports, traction and brake car body and can rotate relative to car body, is the core component that determines train operation safety and quality and restricts speed promotion.Dynamics performance design is the core of bogie design, and different suspension parameter matching settings directly affect the running performance of vehicle, and the matching of suspension parameters is more difficult due to the severe requirements.At the same time, suspension parameters have random uncertainty in the process of train operation, such as random fluctuation of parameters caused by manufacturing error, rubber aging, temperature change, etc., and the influence of random change of suspension parameters on dynamics performance is more severe with the increase of speed, so that the parameter matching result lacks adaptability, and the dynamics performance is poor, and even endangers the safety of train operation.In the past, it is difficult to meet the dynamics performance robustness requirement under the influence of random factors for deterministic optimization design.The optimization of high-speed train bogie dynamics performance considering the influence of random factors can reduce the influence of random change of suspension parameters on dynamics performance, and has important significance for bogie design and development.

[0003] At present, the research on high-speed train bogie dynamics performance pays more and more attention to the influence of random factors on bogie, and the distribution characteristics of dynamics indexes are obtained by using Monte Carlo method, which more truly and comprehensively reflects the dynamics performance of vehicle.Obviously, the high calculation cost of using the above method for numerical simulation model of nonlinear track vehicle in suspension parameter design is unacceptable.During the optimization process of bogie dynamics performance indexes, most of the current researches only consider the optimization of single performance index, ignoring the overall optimization of performance indexes under the mutual influence. SUMMARY

[0004] The present application aims to: in combination with the above technical development and existing deficiencies, a bogie suspension parameter design method is needed, which can consider the random change in the process of high-speed train operation while ensuring the overall optimization of dynamics performance.

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

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

[0007] Step S2: constructing 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: determining design variables, constraint intervals, and optimization objectives;

[0013] Step S13: sampling simulation;

[0014] Step S14: dividing proxy model samples;

[0015] Step S15: training a proxy model;

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

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

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

[0019] S121: determining design variables, selecting suspension parameters to be optimized;

[0020] S122: determining constraint intervals, specifying the range of suspension parameters that can be selected;

[0021] S123: determining optimization objectives, determining the dynamics indicators 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 dynamics performance indicators;

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

[0026] Step S14: dividing proxy model samples

[0027] The data set is randomly divided into a training set and a test set using a random sample division rule;

[0028] Step S15: Train the agent model;

[0029] Based on the above division of the sample training set and test set, the proxy model is trained using the training set;

[0030] Step S16: Proxy model accuracy verification.

[0031] Step S2 includes:

[0032] Step S21: Uncertainty characterization analysis;

[0033] Step S22: Uncertainty propagation analysis, constructing a chaotic multinomial model.

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

[0035] Step S22 includes steps S221-S226:

[0036] Step S221: Initialize the sample set;

[0037] Step S222: Set 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] In the formula, A(M,p,q) is the set of candidate chaotic polynomial bases for a specific input and order, M is the dimension of the input, N is the design variable space, α is the input vector, p is the order of the chaotic polynomial, and ||·|| q It is the q-norm; when q is 1, it is the standard truncation; when q < 1, higher-order interaction terms will be removed, and the smaller q is, the more will be removed;

[0041] Step S224: Minimum angular regression, based on which a sparser set of chaotic polynomial bases is obtained;

[0042] Step S225: Calculate the coefficients of the chaotic polynomial using the least squares method. Substitute the sample and the corresponding function response value into the right and left sides of the chaotic polynomial model, respectively, to 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 the standard random variable;

[0045]

[0046] 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;

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

[0048] b = (ψ T ψ) -1 ψ T Y (5)

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

[0050] Step S226: Posterior cross error estimation is performed by using the leave-one-out method:

[0051]

[0052] where k is the number of original models established by the leave-one-out method, g(x i ) is the response output of the original model at the x i point, i.e., the output of the surrogate model, g PCE (x i ) is the output value of the chaotic polynomial surrogate constructed at x i , and is the average of the response values of the k chaotic polynomial surrogate models; in the chaotic polynomial model construction loop, the best chaotic polynomial expansion order is obtained according to the smallest ε Loocv ;

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

[0054]

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

[0056] Step S3 includes:

[0057] Step S31: A game pattern is constructed;

[0058] Step S32: policy set division;

[0059] Step S33: utility function construction.

[0060] In step S31, the stability and safety indexes are taken as leaders, and the smoothness index is taken as a follower to construct a game pattern;

[0061] Step S32 includes steps S321-S3210:

[0062] Step S321: explicitly define 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 change in the parameters;

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

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

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

[0068] Step S327: calculate the cluster center;

[0069] Step S328: update the membership matrix;

[0070] Step S329: check the convergence condition;

[0071] Step S3210: output the results;

[0072] In step S33, the bogie frame bottom transverse acceleration (y1) is taken as the stability evaluation index of the hunting motion, the derailment coefficient (y2), the wheel load reduction rate (y3), the wheel axle lateral force (y4), and the wheel rail vertical force (y5) are taken as the evaluation indexes of the curve negotiation performance, and the vertical smoothness (y6) and the lateral smoothness (y7) are taken as the evaluation indexes of the smoothness. The utility function construction refers to converting the dynamic evaluation indexes into the objectives of respective game parties. First, the dynamic evaluation indexes are converted into the satisfaction degree s i by formula (8); wherein the stability only takes the frame bottom transverse acceleration (y1) as the evaluation index, and the comprehensive index is formula (9);

[0073]

[0074] In the formula, y iAs a dynamic index, y min and y max These are the minimum and maximum values ​​of the corresponding kinetic index for the sample, respectively; s i This corresponds to the satisfaction value of the dynamic index;

[0075] μ1=s1 (9)

[0076] In the formula, μ1 is the satisfaction value of the stability index, and s1 is the satisfaction value of the lateral acceleration at the bottom of the frame.

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

[0078] μ2=0.57s2+0.21s3+0.11s4+0.11s5 (10)

[0079] In the formula, μ2 is the satisfaction value of the safety index, s2 is the satisfaction value of the derailment coefficient, s3 is the satisfaction value of the wheel load reduction rate, s4 is the satisfaction value of the wheel axle lateral force, and s5 is the satisfaction value of the wheel-rail vertical force.

[0080] Stationarity is evaluated using Sperling as the evaluation metric, with horizontal and vertical stationarity having equal importance. Therefore, the comprehensive stationarity performance index is as follows:

[0081] μ3=0.5s6+0.5s7 (11)

[0082] In the formula, μ3 is the satisfaction value of the stationarity index, s6 is the satisfaction value of the vertical stationarity, and s7 is the satisfaction value of the horizontal stationarity.

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

[0084] R i =0.5M μi +0.5S μi (12)

[0085] In the formula, R i To comprehensively evaluate the robustness of the indicators, M μi S represents the mean of the comprehensive evaluation index of dynamics. μi The standard deviation is the comprehensive evaluation index for dynamics.

[0086] Step S4 includes:

[0087] Step S41: Construct a game theory model;

[0088] Step S42: Determine master-slave balance.

[0089] Step S41: Construct a game model; let there be N leaders and M followers in the game; the master-follower game is represented as the following multi-objective optimization problem:

[0090]

[0091] In the formula, x v Let y represent the strategy of the v-th leader. s Let X be the strategy of the s-th follower; v For the v-th leader strategy statement, Y s Let F be the set of follower strategies for the s-th follower; v Let f be the utility function of the v-th participant in the upper layer. s Let be the utility function of the s-th 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 game participants in the solution process:

[0093] S421: Set the convergence metric ε;

[0094] S422: Initialize the loop count i = 0, and randomly generate an initial policy μ from the policy set. i ={x n i ,y m i};

[0095] S423: Leader optimization, with μ i ={x n i ,y m i} represents the initial design variable, keeping y constant. m i It is a constant, and by adjusting x n i To optimize F, a sub-Nash game is played among multiple participants with a leader, yielding the optimized strategy combination {x}. n i +1 ,y m i};

[0096] S424: Follower optimization, with {x n i+1 ,y m i} is the design variable, keeping x constant. n i+1 It is a constant, and by adjusting y mi To optimize f, we conduct a sub-Nash game among multiple followers under the leader's outcome to obtain the optimized strategy combination {x}. n i+1 ,y m i+1};

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

[0098] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0099] (1) In practice, the inventors found that considering the random variation of suspension parameters in the design can more comprehensively reflect the changes in dynamic performance and obtain more robust dynamic performance. Based on this, they proposed to use the uncertainty quantification method to obtain the random variation characteristics of high-speed train dynamics by analyzing the random variation of bogie suspension parameters.

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

[0101] (3) In practice, the inventors found that existing uncertainty quantification methods are designed for uncertainty analysis, i.e., dynamic performance index analysis is performed with clearly defined suspension parameter settings. These methods cannot meet the high time costs associated with the extensive simulation requirements during the optimization process. Therefore, this invention proposes an uncertainty quantification method suitable for suspension parameter optimization design, improving both computation time and accuracy.

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

[0103] (5) In practice, the inventors discovered that existing game-solving methods require the construction of three elements of a game model: participants, strategy space, and strategy set. They found that these elements correspond one-to-one with the design variables, design space, and constraints in multi-objective optimization. To address this, the inventors proposed a game optimization modeling method for uncertainty in high-speed train suspension parameters, constructing a robust game model for high-speed train dynamics.

[0104] (6) In practice, the inventors found that in solving traditional game theory models, population updates and iterations are still required, and tens of thousands of simulation calculations are needed. Therefore, the inventors adopted proxy model technology to replace the expensive simulation calculations. The calculation results can be used to build uncertainty quantification models, increase the number of iterations and improve optimization efficiency. Attached Figure Description

[0105] Figure 1 A flowchart for quantifying the uncertainty of adaptive sparse chaotic polynomials.

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

[0107] Figure 3 The graph shows the change in the game utility function.

[0108] Figure 4 To compare the distribution of dynamic indicators before and after optimization. Detailed Implementation

[0109] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0110] Therefore, the following detailed description of embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0111] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the embodiments of the present invention can be combined with each other.

[0112] A game-theoretic optimization method for the dynamic performance of high-speed train bogies includes steps S1-S4:

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

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

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

[0116] Step S4: Solve the game theory model.

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

[0118] Step S11: Construct a dynamic 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: Train the agent model.

[0123] Step S16: Proxy model accuracy verification.

[0124] Step S11: Construct the dynamic simulation model. This includes S111-S112:

[0125] S111: Based on the actual operation of high-speed trains, set basic parameters and construct a dynamic model of the high-speed train. The basic parameters include at least: track gauge, weight, and moment of inertia.

[0126] S112: Set typical line operating parameters, which should include at least: operating speed, track irregularities, curve radius, and superelevation.

[0127] Step S12: Determine the design variables, constraint intervals, and optimization objective. This includes S121-S123:

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

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

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

[0131] Step S13: Sampling Simulation. Includes 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 range of values ​​of each variable into n equal intervals.

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

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

[0136] (4) Random arrangement: 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: Combine design variables and corresponding dynamic performance indices to form sample values ​​for constructing a dynamic surrogate model.

[0139] Step S14: Divide the proxy model samples

[0140] The dataset is randomly divided into training and test sets using a randomized sample partitioning rule. Preferably, the partitioning is proportional, with 80% for training and 20% for testing.

[0141] Step S15: Train the agent model.

[0142] Based on the above division of the sample training and test sets, the training set is used to train several surrogate models. Preferably, the surrogate model is one of radial basis function, kriging, or artificial neural network.

[0143] Step S16: Proxy model accuracy verification. Includes S161-S162:

[0144] Step S161: Verify the accuracy of the aforementioned surrogate models using the test set in the sample, and evaluate the accuracy of the surrogate models using error analysis, including at least the following methods:

[0145] Root mean square error (RMSE): Measures the difference between the predicted value and the actual value.

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

[0147] Residual analysis: Check the deviation between the model's predicted values ​​and the actual values, and analyze whether there are systematic errors. Step S162: Select the surrogate model with the highest accuracy to replace the simulation model for subsequent optimization.

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

[0149] Step S21: Uncertainty characterization analysis;

[0150] Step S22: Uncertainty propagation analysis, i.e., constructing a chaotic multinomial model.

[0151] Step S21: Uncertainty characterization analysis.

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

[0153] Step S22: Uncertainty propagation analysis, i.e., constructing a chaotic multinomial model.

[0154] Uncertainty propagation studies how to estimate output uncertainty given uncertainty in a given input. Compared to traditional Monte Carlo simulations, chaotic polynomial methods can achieve similar accuracy to MCS with a small number of samples, and can more easily obtain the mean and variance of the response in the optimization loop. Non-embedded chaotic polynomial methods treat uncertainty propagation as a black box, representing random variables as a weighted sum of orthogonal polynomials, focusing only on the mapping relationship between input and output. A chaotic polynomial surrogate model of the output response is constructed to realize uncertainty propagation, thus serving uncertainty optimization.

[0155] Preferably, the chaotic polynomial is constructed as follows: response function y = g(x) (x = [x1, ..., x2)). i ,…,x d The output response under chaotic polynomial theory is represented as a p-order truncated chaotic polynomial model.

[0156]

[0157] In the formula, b i Φ represents the coefficients of the chaotic polynomial. i It is an orthogonal polynomial; p is the order of the polynomial model (usually greater than 3); ξ is the standard random variable ξ = [ξ1,…,ξ] i ,…,ξ d ], ξ i With the original variable x i Based on the probability distribution type of the original variable, and through probability distribution transformation, topological conjugate relations, or the selection of orthogonal polynomials, the original variable x is transformed. i Mapped to a standard random variable distribution suitable for chaotic multinomial expansion.

[0158] The construction of the aforementioned traditional chaotic polynomial model mainly involves two aspects: polynomial selection and order determination.

[0159] Polynomial selection: This means selecting a suitable polynomial basis based on the type of input distribution.

[0160] Order determination: The order is determined manually based on experience or by conducting incremental experiments (increasing the order step by step for model building and accuracy analysis).

[0161] To address the curse of dimensionality problem caused by excessively high input dimensions and polynomial orders, the inventors propose an adaptive sparse chaotic polynomial modeling method. This method optimizes the polynomial selection and order determination steps, avoiding the curse of dimensionality problem in dimensional model construction and accelerating the efficiency of model construction.

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

[0163] Step S221: Initialize the sample set;

[0164] Step S222: Set 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] In the formula, A(M,p,q) is the set of candidate chaotic polynomial bases for a specific input and order, M is the dimension of the input, N is the design variable space, α is the input vector, p is the order of the chaotic polynomial, and ||·|| q Let q be the q-norm. When q is 1, it represents the standard truncation; when q < 1, higher-order interaction terms will be removed, and the smaller q is, the more terms will be removed.

[0168] Step S224: Least angular regression. Based on least angular regression, a sparser set of chaotic polynomial bases is obtained. Least angular regression can select the corresponding orthogonal polynomial bases according to the probability distribution of random parameters. The algorithm selects the polynomial basis functions that are most correlated with the response variables and constructs a sparse polynomial chaotic expansion.

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

[0170]

[0171] 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 the standard random variable.

[0172]

[0173] 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.

[0174] The coefficients of the chaotic polynomial can be obtained using the least quadratic regression method:

[0175] b = (ψ) T ψ) -1 ψ T Y (5)

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

[0177] Step S226: Estimate the posterior cross-error using the leave-one-out method:

[0178]

[0179] In the formula, k is the number of original models established by the leave-one-out method, and g(x) i ) is x i The original model response output at the point is the surrogate model output, g PCE (x i The chaotic polynomial proxy constructed in x i The output value at that location, Let ε be the mean of the response values ​​of k chaotic polynomial surrogate models. In the loop of constructing the chaotic polynomial model, this can be determined based on the minimum ε. Loocv To obtain the optimal order of the chaotic polynomial expansion.

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

[0181]

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

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

[0184] Step S31: Constructing the game structure. The game structure includes at least three elements: game actors, strategy set, and utility function. It has the following mapping relationship with dynamic optimization design: the three game actors correspond to three bogie dynamic performance indicators (stability, safety, and smoothness); each game actor's strategy corresponds to the mean distribution of bogie suspension parameters under random fluctuations; the robustness measure under the game strategy set is the utility function of the corresponding game actor. High-speed trains mostly operate on straight lines. While ensuring the stability of high-speed trains during straight-line travel and the performance during curved travel, efforts are also made to improve the train's smoothness. Therefore, this invention uses stability and safety indicators as leaders and smoothness indicators as followers to construct the game structure.

[0185] Step S32: Strategy set partitioning. In the game's main strategies, the strategy set in this invention does not correspond to the number of game participants. The solution method is to set each objective as a player, convert the design variable set into the strategy set of each player, and use a strategy set partitioning method combining sensitivity analysis and fuzzy clustering. The strategy set partitioning method combining sensitivity analysis and fuzzy clustering is as follows: Steps S321-S3210:

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

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

[0188] Step S323: Generate a sample combination of parameters using a sampling method (such as Latin hypercube sampling) to evaluate the output response to parameter changes;

[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: Cluster the sensitivity analysis results using fuzzy C-means clustering;

[0191] Step S326: Initialize parameters, including selecting the number of clusters, setting fuzzy coefficients, 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 the convergence conditions;

[0195] Step S3210: Output the result.

[0196] Step S33: Utility function construction. The lateral acceleration (y1) at the bottom of the bogie frame is used as the stability evaluation index for the serpentine motion. The derailment coefficient (y2), wheel load reduction rate (y3), wheel-axle lateral force (y4), and wheel-rail vertical force (y5) are used as evaluation indices for curve-passing performance. Vertical stability (y6) and lateral stability (y7) are used as stability evaluation indices. Utility function construction refers to converting the dynamic evaluation indices into the objectives of each player. First, equation (8) converts the dynamic evaluation indices into satisfaction s. i The stability is evaluated using only the lateral acceleration (y1) at the bottom of the frame, and its comprehensive index is given by equation (9).

[0197]

[0198] In the formula, y i As a dynamic index, y min and y max These represent the minimum and maximum values ​​of the corresponding kinetic index for the sample, respectively. i This corresponds to the satisfaction value of the dynamic index.

[0199] μ1=s1 (9)

[0200] In the formula, μ1 is the satisfaction value of the stability index, and s1 is the satisfaction value of the lateral acceleration at the bottom of the frame.

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

[0202] μ2=0.57s2+0.21s3+0.11s4+0.11s5 (10)

[0203] In the formula, μ2 is the satisfaction value of the safety index, s2 is the satisfaction value of the derailment coefficient, s3 is the satisfaction value of the wheel load reduction rate, s4 is the satisfaction value of the wheel axle lateral force, and s5 is the satisfaction value of the wheel-rail vertical force.

[0204] Stationarity is evaluated using Sperling as the evaluation metric, with horizontal and vertical stationarity having equal importance. Therefore, the comprehensive stationarity performance index is as follows:

[0205] μ3=0.5s6+0.5s7 (11)

[0206] In the formula, μ3 is the satisfaction value of the stationarity index, s6 is the satisfaction value of the vertical stationarity, and s7 is the satisfaction value of the horizontal stationarity.

[0207] Random variations in suspension parameters cause the dynamic evaluation indices to exhibit randomness. The mean represents the overall dynamic performance, while the standard deviation represents the dynamic performance's resistance to interference. Game-theoretic optimization design needs to consider both objectives simultaneously; therefore, the mean (M) of the comprehensive dynamic evaluation index is adopted. μi ) and standard deviation (S μi The robustness measure of the weighted and calculated comprehensive evaluation index (R) i ).

[0208] R i =0.5M μi +0.5S μi (12)

[0209] In the formula, R i To comprehensively evaluate the robustness of the indicators, M μi S represents the mean of the comprehensive evaluation index of dynamics. μi The standard deviation is the comprehensive evaluation index for dynamics.

[0210] Step S4: Solve the game theory model.

[0211] Step S41: Construct the game model. This invention constructs a two-leader-one-follower game model. The leaders make the first decision, engaging in a non-cooperative Nash game and reaching a Nash equilibrium. The followers then observe the leaders' Nash equilibrium and make their own decisions. Finally, when the leaders' payoffs can no longer be increased, a master-follower game equilibrium is reached. The definition and solution steps are given below: Assume there are N leaders and M followers in the game; the master-follower game can be represented as the following multi-objective optimization problem:

[0212]

[0213] In the formula, x v Let y represent the strategy of the v-th leader. s Let X be the strategy of the s-th follower; v For the v-th leader strategy statement, Y s Let F be the set of follower strategies for the s-th follower; v Let f be the utility function of the v-th participant in the upper layer. s Let be the utility function of the s-th participant in the lower layer.

[0214] Step S42: Determine the leader-follower equilibrium. Specific steps are shown in S421-S425, where (1≤n≤N, 1≤m≤M) (N is the number of leaders, M is the number of followers) represents all game participants in the solution process.

[0215] S421: Set the convergence metric ε;

[0216] S422: Initialize the loop count i = 0, and randomly generate an initial policy μ from the policy set. i ={x n i ,y m i};

[0217] S423: Leader optimization, with μ i ={x n i ,y m i} represents the initial design variable, keeping y constant. m i It is a constant, and by adjusting x n i To optimize F, we need to conduct a sub-Nash game among multiple participants with a leader to obtain the optimized strategy combination {x}. n i+1 ,y m i};

[0218] S424: Follower optimization, with {x n i+1 ,y m i} is the design variable, keeping x constant. n i+1 It is a constant, and by adjusting y m i To optimize f, we conduct a sub-Nash game among multiple followers under the leader's outcome to obtain the optimized strategy combination {x}. n i+1 ,y m i+1};

[0219] S425: Convergence criterion, such as ||μ i -μ i+1 If ||≤ε, the loop terminates, μ i+1 ={x n i+1 ,y m i+1 This represents the desired master-slave game equilibrium. 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 herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.

Claims

1. A game-theoretic optimization method for the dynamic performance of high-speed train bogies, characterized in that: Including steps S1-S4: Step S1: Construct a proxy model for high-speed train dynamics simulation, including dynamics simulation model construction and proxy model training; Step S2: Construct an uncertainty quantification model, including uncertainty characterization and uncertainty propagation; Step S3: Construct the game model, including game pattern construction, strategy set partitioning, and utility function construction; Step S4: Solve the game theory model; Step S1 in detail Includes the following steps S11-S16; Step S11: Construct a dynamic simulation model; Step S12: Determine the design variables, constraint intervals, and optimization objectives; including S121-S123: S121: Determine the design variables and select the suspension parameters that need to be optimized; S122: Determine the constraint interval and clarify the selectable range of suspension parameters; S123: Determine the optimization objective and the dynamic 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: Input the extracted sample values ​​into the simulation model to calculate the dynamic performance index; S133: Combine design variables and corresponding dynamic performance indicators to form sample values ​​for constructing a dynamic surrogate model; Step S14: Divide the proxy model samples The dataset is randomly divided into training and test sets using a random sample partitioning rule. Step S15: Train the agent model; Based on the above division of the sample training set and test set, the proxy model is trained using the training set; Step S16: Proxy model accuracy verification; Step S2 includes steps S21-S22; In step S21, a probabilistic method is used to characterize its random uncertainty and to clarify the range of random variation of the suspension parameters; Step S22 includes steps S221-S226: Step S221: Initialize the sample set; Step S222: Set 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) In the formula, A(M,p,q) is the set of candidate chaotic polynomial bases for a specific input and order, M is the dimension of the input, N is the design variable space, α is the input vector, p is the order of the chaotic polynomial, and ||·|| q It is the q-norm; when q is 1, it is the standard truncation; when q < 1, higher-order interaction terms will be removed, and the smaller q is, the more will be removed; Step S224: Minimum angular regression, based on which a sparser set of chaotic polynomial bases is obtained; Step S225: Calculate the coefficients of the chaotic polynomial using the least squares method. Substitute the sample and the corresponding function response value into the right and left sides of the chaotic polynomial model, respectively, to 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 the 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; The coefficients of the chaotic polynomial are obtained using the least quadratic regression method: 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: Estimate the posterior cross-error using the leave-one-out method: In the formula, k is the number of original models established by the leave-one-out method, and g(x) i ) is x i The original model response output at point g is the surrogate model output. PCE (x i The chaotic polynomial proxy constructed in x i The output value at that location, Let ε be the mean of the response values ​​of k chaotic polynomial surrogate models; in the loop of constructing the chaotic polynomial model, based on the minimum ε Loocv To obtain the optimal order of the chaotic polynomial expansion; Based on the obtained chaotic polynomial coefficients, statistical information of the random output is obtained; the mean of the response is equal to the coefficient of the constant term of the chaotic polynomial, and the variance σ c Equal to the sum of the squares of the remaining coefficients of the constant term in the chaotic polynomial: In the formula, μ c And E[Y] is the mean of the response, σ c 2 And Var[Y] is the response variance, α i Φ is the expansion coefficient; i (X) is the standardized orthogonal polynomial basis; P is the highest order of the orthogonal polynomial.

2. The game-theoretic optimization method for the dynamic performance of a high-speed train bogie as described in claim 1, characterized in that: Step S3 includes: Step S31: Construct the game theory framework; Step S32: Strategy set partitioning; Step S33: Utility function construction.

3. The game-theoretic optimization method for the dynamic performance of a high-speed train bogie as described in claim 2, characterized in that: In step S31, stability and security indicators are used as leaders, and stability indicators are used as followers to construct the game pattern. Step S32 includes steps S321-S3210: Step S321: Identify 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 using a sampling method to evaluate the output response to parameter changes; Step S324: Calculate the sensitivity coefficient of each parameter to the output; Step S325: Cluster the sensitivity analysis results using fuzzy C-means clustering; Step S326: Initialize parameters, This includes selecting the number of clusters, setting fuzzy coefficients, initializing the membership matrix, and setting the error threshold; Step S327: Calculate cluster centers; Step S328: Update the membership matrix; Step S329: Check the convergence conditions; Step S3210: Output the result; In step S33, the lateral acceleration (y1) at the bottom of the bogie frame is used as the evaluation index for the stability of the serpentine motion, the derailment coefficient (y2), the wheel load reduction rate (y3), the lateral force of the wheel axle (y4), and the vertical force of the wheel and rail (y5) are used as the evaluation index for the curve passing performance, and the vertical stability (y6) and lateral stability (y7) are used as the evaluation index for stability. The utility function construction refers to converting the dynamic evaluation index into the goal of each player. First, the dynamic evaluation index is converted into the satisfaction s by equation (8). i The stability is evaluated using only the lateral acceleration (y1) at the bottom of the frame, and its comprehensive index is given by equation (9). In the formula, y i As a dynamic index, y m in and y m ax represents the minimum and maximum values ​​of the corresponding dynamic index for the sample, respectively; s i This corresponds to the satisfaction value of the dynamic index; μ1=s1 (9) In the formula, μ1 is the satisfaction value of the stability index, and s1 is the satisfaction value of the lateral acceleration at the bottom of the frame. The curve is composed of four satisfaction levels based on the overall safety performance index, and its overall satisfaction value is constructed using the AHP method: μ2=0.57s2+0.21s3+0.11s4+0.11s5 (10) In the formula, μ2 is the satisfaction value of the safety index, s2 is the satisfaction value of the derailment coefficient, s3 is the satisfaction value of the wheel load reduction rate, s4 is the satisfaction value of the wheel axle lateral force, and s5 is the satisfaction value of the wheel-rail vertical force. Stationarity is evaluated using Sperling as the evaluation metric, with horizontal and vertical stationarity having equal importance. Therefore, the comprehensive stationarity performance index is as follows: μ3=0.5s6+0.5s7 (11) In the formula, μ3 is the satisfaction value of the stationarity index, s6 is the satisfaction value of the vertical stationarity, and s7 is the satisfaction value of the horizontal stationarity. The mean value of the comprehensive dynamic evaluation index (Mμ) i ) and standard deviation (Sμ) i The robustness measure of the weighted and calculated comprehensive evaluation index (R) i ); R i =0.5M μi +0.5S μi (12) In the formula, R i To comprehensively evaluate the robustness of the indicators, M μi S represents the mean of the comprehensive evaluation index of dynamics. μi The standard deviation is the comprehensive evaluation index for dynamics.

4. The game-theoretic optimization method for the dynamic performance of a high-speed train bogie as described in claim 3, characterized in that: Step S4 includes: Step S41: Construct a game theory model; Step S42: Determine master-slave balance.

5. The game-theoretic optimization method for the dynamic performance of a high-speed train bogie as described in claim 4, characterized in that: Step S41: Construct a game model; let there be N leaders and M followers in the game; the master-follower game is represented as the following multi-objective optimization problem: In the formula, x v Let y represent the strategy of the v-th leader. s Let X be the strategy of the s-th follower; v For the v-th leader strategy statement, Y s Let F be the set of follower strategies for the s-th follower; v Let f be the utility function of the v-th participant in the upper layer. s Let be the utility function of the s-th 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 game participants in the solution process: S421: Set the convergence metric ε; S422: Initialize the loop count i = 0, and randomly generate an initial policy μ from the policy set. i ={x n i ,y m i }; S423: Leader optimization, with μ i ={x n i ,y m i } represents the initial design variable, keeping y constant. m i It is a constant, and by adjusting x n i To optimize F, a sub-Nash game is played among multiple participants with a leader, yielding the optimized strategy combination {x}. n i+1 ,y m i }; S424: Follower optimization, with {x n i+1 ,y m i } is the design variable, keeping x constant. n i+1 It is a constant, and can be adjusted by ym i To optimize f, we conduct a sub-Nash game among multiple followers under the leader's outcome to obtain the optimized strategy combination {x}. n i+1 ,y m i+1 }; S425: Convergence criterion, such as ||μ i -μ i+1 If ||≤ε, the loop terminates, μ i+1 ={x n i+1 ,y m i+1 If the result is the desired master-slave game equilibrium, then set i = i + 1 and return to S423.

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