Track structure parameter multi-objective optimization method considering train and foundation effects

Abstract

The invention provides a rail structure parameter multi-objective optimization method considering a train and a basic effect, and multi-objective parameter optimization in the whole process from dynamic modeling to BP neural network model proxy to genetic algorithm-TOPSIS evaluation is realized. In the aspect of model construction, a nonlinear dynamic analysis model of a train-rail-base structure coupling system is established, the geometric dimensions and mechanical parameters of each structure and the coupling effect between a rail and a train and between the rail and a lower base structure are fully considered, and the reliability of the dynamic model is verified through comparison with field test data; in the aspect of proxy model establishment, a reasonable interval of track structure parameters is considered, an initial sample point set of the track structure parameters is obtained by adopting an optimal Latin hypercube test design method, a system optimization target is determined, a dynamic response index corresponding to the parameter sample point set is calculated, and a target function proxy model is constructed by utilizing a BP neural network; and rapid and efficient calculation of a large number of working conditions is realized.

Description

Technical Field

[0001] This invention belongs to the field of track technology, specifically relating to a multi-objective optimization method for track structure parameters that takes into account the roles of trains and foundations. Background Technology

[0002] As a core infrastructure of railway transportation systems, the quality of track structure design directly affects the safety, smoothness, and comfort of train operation, as well as the construction and long-term maintenance costs of the entire line. With the rapid development of high-speed railways and the increasing density and complexity of urban rail transit networks, the demand for track structure optimization is rising. High-speed trains operate at high speeds, resulting in intense wheel-rail dynamic interaction, placing stringent requirements on track smoothness and stability. Inappropriate track structure parameter design can easily lead to accelerated deterioration of track geometry, increased component damage, and even induce train derailment risks, seriously threatening operational safety. In the field of urban rail construction, since lines are mostly located in urban built-up areas with high environmental sensitivity and limited space, the optimization requirements for track structures mainly focus on vibration and noise reduction, necessitating optimization of track stiffness and damping configuration to minimize the impact of vibration and noise on surrounding buildings and residents. Furthermore, with the future development of railways at even higher speeds, track structures face even more severe dynamic challenges. This requires track structure design to seek optimal matching parameters for dynamic performance at higher speeds to ensure sufficient stability and safety during operation.

[0003] Existing research on track structure parameter optimization design largely relies on finite element software to establish finite element models of ballastless track structures, studying the influence of different geometric and material parameters on the mechanical properties of the track structure and optimizing them, and determining their reasonable range of variation. Existing research rarely considers the coupling effect between the train and the substructure, and existing track structure design methods are mostly based on engineering experience or analysis of the influence of single performance indicators (such as strength and deformation), making it difficult to systematically handle multi-variable, multi-objective comprehensive optimization problems. Optimization methods are often limited to local parameter adjustments or empirical trial and error, lacking global optimality guarantees, and have insufficient ability to predict and optimize the complex dynamic behavior of the train-track-foundation coupled system. To address these shortcomings, this invention proposes a multi-objective optimization method for track structure parameters that considers the effects of the train and the foundation. By constructing a dynamic analysis model and a surrogate model, a large number of working conditions are calculated quickly and efficiently to provide a basis for optimization. Continuous iteration using a multi-objective algorithm and a comprehensive evaluation method are employed to assess and rank the results, obtaining the optimal solution and corresponding track structure parameters for different design requirements. This effectively coordinates the contradictions among various performance indicators, achieving optimal comprehensive performance of the track structure throughout its entire life cycle. Summary of the Invention

[0004] The purpose of this invention is to propose a multi-objective optimization method for track structure parameters based on BP neural networks and NSGA-II, employing dynamic theory and artificial intelligence optimization algorithms. This method ensures optimal dynamic performance of the track structure during railway operation, achieving an optimal balance between train safety, comfort, and structural vibration. In terms of model construction, a nonlinear dynamic analysis model of the train-track-foundation coupled system is established, fully considering the geometric dimensions and mechanical parameters of each structure, as well as the coupling effects between the track, train, and substructure. The reliability of the dynamic model is verified by comparing it with field test data. Regarding the establishment of the surrogate model, considering the reasonable range of track structure parameters, the optimal Latin hypercube experimental design method is used to obtain the initial sample point set of track structure parameters. The system optimization objective is determined, and the dynamic response index corresponding to the parameter sample point set is calculated. A surrogate model of the objective function is constructed using a BP neural network, enabling rapid and efficient calculation for a large number of operating conditions. In terms of multi-objective optimization, through continuous optimization iteration using the NSGA-II genetic algorithm, a Pareto optimal solution set for multiple optimization objectives is obtained. After sorting using the TOPSIS comprehensive evaluation method, the optimal solutions and corresponding track parameters for different design requirements are determined.

[0005] A multi-objective optimization method for track structure parameters considering the effects of trains and foundations includes:

[0006] S1. Establish a nonlinear dynamic analysis model for the train-track-foundation coupled system: This dynamic analysis model includes, from top to bottom, the vehicle dynamics model, the track structure finite element model, and the substructure (roadbed, bridge, and tunnel, etc.) model.

[0007] S2. Construct a surrogate model of the objective function to fit the implicit complex functional relationship between system parameters and response indicators;

[0008] First, determine the reasonable range of track structure parameters and obtain the initial sample point set of track structure parameters;

[0009] Next, the system optimization objective is determined, and the dynamic response index corresponding to the parameter sample point set is calculated using the dynamic analysis model obtained in step S1, and a surrogate model of the objective function is constructed.

[0010] Then examine whether its error meets the requirements to verify the accuracy of the surrogate model method;

[0011] The constructed proxy model is used for multi-objective optimization in step S3;

[0012] S3 Multi-Objective Optimization of Track Structure Parameters

[0013] The optimal solution set for the optimization objective is obtained by using a multi-objective algorithm, and the optimal solution and corresponding track structure parameters for different design requirements are determined by a comprehensive evaluation method.

[0014] Preferably, in step S1, the dynamic model is based on the principle of constant total elastic potential energy and wheel-rail coupled nonlinear elements. The vehicle is simulated as a multi-rigid-body system with secondary suspension, wherein: the car body, frame, and wheelsets are all simulated as 6-DOF rigid bodies with rotation; the primary and secondary suspensions are simulated using spring-damped elements; the rails and track slabs are simulated using Bernoulli-Euler beam elements and medium-thick plate elements, respectively; the lower support structure is simulated using beam, plate, and spatial isoparametric elements with damping; and the interaction between any substructure or subcomponent is simulated using spring-damped elements based on a multi-scale coupling method.

[0015] Preferably, in step S2, the optimal Latin hypercube sampling method, namely OLHS, is used to obtain the initial sample point set, and the sample points are distributed with a high degree of uniformity in the probability space.

[0016] Preferably, in step S2, a BP neural network is used as a surrogate model to fit the implicit complex relationship between structural parameters and response optimization indicators.

[0017] Preferably, in step S3, the NSGA-II genetic algorithm is used to perform continuous multi-objective optimization iterations to obtain the Pareto optimal solution set of the optimization objective.

[0018] Preferably, in step S3, the ranking is evaluated using the TOPSIS comprehensive evaluation method to determine the optimal solution and corresponding orbital parameters for different design requirements.

[0019] Compared with the prior art, the beneficial effects of the present invention are:

[0020] 1. The simulation of track structure dynamics considering the coupling effect between the train and the substructure was realized, and a BP neural network surrogate model for dynamic analysis was constructed, which can quickly and efficiently calculate a large number of working conditions to provide a basis for optimization.

[0021] 2. A multi-objective optimization method for the design of key parameters of track structure was constructed. After determining the optimization parameters and optimization objectives, the method uses the NSGA-II genetic algorithm to perform multi-parameter multi-objective optimization, finds a balance point among multiple objectives, and can achieve the comprehensive optimal solution of all objectives. Compared with the traditional single-parameter single-objective analysis and optimization, it is more comprehensive and has real physical significance. Attached Figure Description

[0022] Figure 1 This is a dynamic model diagram of the train-track-foundation coupled system of the present invention.

[0023] Figure 2 This is a diagram of the metro train-embedded track-tunnel dynamic analysis model of the present invention, wherein (a) is a cross section of the vehicle-track-tunnel coupling model; and (b) is a side section of the vehicle-track-tunnel coupling model.

[0024] Figure 3 The diagram shows a comparison of the fixed-point vibration acceleration results at the tunnel wall vibration pickup point of the present invention, where (a) is the vibration acceleration time history; (b) is the frequency domain result based on Fourier transform; (c) is the frequency-division vibration acceleration level; and (d) is the frequency-division vibration level.

[0025] Figure 4 The following is a distribution diagram of the design variables for 200 sets of sample points in this invention, where (a) is the three-dimensional projection of the sample points (µ1-µ2-µ5); and (b) is the three-dimensional projection of the sample points (µ3-µ4-µ6).

[0026] Figure 5 This is a schematic diagram of the BP neural network model of the present invention;

[0027] Figure 6 The proxy model R of this invention 2 Value and E map Value comparison chart, where (a) is the coefficient of determination R. 2 Value; (b) is the mean absolute percentage error E map value;

[0028] Figure 7 The Pareto optimal solution set diagram of the present invention is shown, where (a) is y1-y2-y3-y4; and (b) is y5-y6-y7-y8.

[0029] Figure 8 The diagram shows a comparison before and after optimization of the present invention, where (a) represents the vertical force of the wheel and rail; (b) represents the vertical vibration acceleration of the rail; (c) represents the lateral vibration acceleration of the track slab; and (d) represents the frequency division of the vertical vibration level of the tunnel wall.

[0030] Figure 9 This is a flowchart of the optimization method of the present invention; Detailed Implementation

[0031] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] A multi-objective optimization method and system for track structure parameters, the method comprising the following steps:

[0033] (1) Establish a nonlinear dynamic analysis model for the train-track-foundation coupled system: This dynamic analysis model includes, from top to bottom, a vehicle dynamic model, a refined track structure model, and the substructure (roadbed, bridges, and tunnels, etc.), such as Figure 1 As shown;

[0034] In terms of specific dynamic modeling techniques, the subway train-embedded track-tunnel coupled system (such as...) Figure 2 Taking the example shown, the embedded track consists of rails, filling material surrounding the rails, and track slabs. Based on the vehicle-track coupled dynamics theory, the subway train, embedded track structure, and tunnel are considered as a whole system. Introducing the energy variational principle, a dynamic analysis model of the subway train-embedded track-tunnel is established, expressed by the following equation:

[0035] (1)

[0036] This dynamic model is based on the finite element method and the variational principle of energy. The vehicle is simulated as a multi-rigid-body system with secondary suspension. The car body, frame, and wheelsets are all simulated as 6-DOF point masses with rotation. The primary and secondary suspensions are simulated using spring-damped elements. The rails and track slabs are simulated using Bernoulli-Euler beam elements and medium-thick plate elements, respectively. The continuous filling material within the rail grooves is simulated as linear spring-damped elements. The interaction matrix coupling between the rails and track slabs is achieved through linear integration, and the coupling stiffness matrix formula is as follows:

[0037] (2)

[0038] in: , , , , , ;

[0039] , ,

[0040] ;

[0041] , ,

[0042] , , ,

[0043] In the formula, is the set of numbers for the interaction elements between the rail and the track slab, where n is the total number of elements; x0 is the longitudinal relative position parameter between the rail beam element and the track slab element; y0 is the local abscissa of the contact element on the track slab element; x1 and x2 are the corresponding local coordinates of the viscoelastic spring-damping element in the rail element; Natural coordinates; The node coordinates are (±1); , , These are the shape functions of the rail beam element in the longitudinal, transverse, and vertical directions, respectively. , , These are the shape functions of the track slab element in the longitudinal, transverse, and vertical directions, respectively. and These are the longitudinal dimensions of the rail beam unit and the track slab unit; The width of the plate unit; Equivalent longitudinal stiffness of the filling material (N / m) 2 ); Equivalent lateral stiffness of the filling material (N / m) 2 ); Equivalent vertical stiffness of the filling material (N / m) 2 The symbol "T" indicates vector transpose.

[0044] The formation method of the rail-track slab coupled damping matrix is ​​the same as the above formula, only the stiffness coefficient " "、 " "and" "Use damping coefficient" "、 " "、 " "A replacement is sufficient;"

[0045] Figure 3 This paper presents a comparison of the time-domain / frequency-domain / vibration acceleration level / vibration magnitude of the fixed-point vibration acceleration at the vibration pickup point of the tunnel wall, based on on-site monitoring data of a subway line and the calculation results of this model. Figure 3 (a) It can be seen that the calculation results of the numerical model constructed by this method are basically consistent with the time history curve characteristics of the measured results; from Figure 3 (b) The Fourier transform results show that the measured results and the numerical results are quite similar in the frequency domain components; Figure 3 The vibration acceleration level and vibration level analysis results of (cd) show that the calculation model also has high reliability in vibration level analysis. However, due to the uncertainties in structural parameters and track surface irregularities, there are inevitably some differences between the measured and simulated results in terms of vibration frequency and amplitude.

[0046] (2) Construct a surrogate model of the objective function to fit the implicit functional relationship between system parameters and response indicators;

[0047] (2.1) Determine the reasonable range of track structure parameters and use optimal Latin hypercube sampling to obtain the initial sample point set of track structure parameters.

[0048] Six parameters that are most sensitive to the embedded track structure, namely the vertical stiffness (µ1), vertical damping (µ2), lateral stiffness (µ3), lateral damping (µ4), vertical stiffness (µ5), and vertical damping (µ6) of the filler material in the track groove, are selected as optimization targets.

[0049] Optimal Latin hypercube sampling method The sample point set obtained by Optimal Latin Hypercube Sampling (OLHS) has a high degree of uniformity in the probability space, and it is chosen as the sampling method. Considering the requirements for the rationality of the track structure design, the range of experimental parameters is set as shown in Table 1. Based on the optimal Latin hypercube sampling method, 200 sets of experimental samples were obtained, and the distribution of the experimental sample points is as follows: Figure 3 As shown.

[0050] Table 1. Range of test parameters

[0051]

[0052] (2.2) Determine the system optimization objective, use the dynamic analysis model obtained in step (1) to calculate the dynamic response index corresponding to the parameter sample point set, and construct the objective function proxy model.

[0053] Backpropagation (BP) neural networks are multilayer feedforward neural network models trained using the backpropagation algorithm, exhibiting good performance in handling nonlinear problems. Embedded track structures are complex, and dynamic responses such as acceleration need to be calculated numerically. Parameter optimization is a continuous iterative improvement process, requiring multiple numerical simulations using the subway train-embedded track-tunnel dynamic analysis model, which is time-consuming and computationally intensive. Therefore, a surrogate model strategy is adopted, using a BP neural network to fit the implicit functional relationship between system parameters and response indicators.

[0054] Using the vertical Sperling index (y1), wheel-rail vertical force (y2), wheel-rail lateral force (y3), rail vertical vibration acceleration (y4), rail lateral vibration acceleration (y5), track slab vertical vibration acceleration (y6), track slab lateral vibration acceleration (y7), and tunnel wall vertical frequency-division vibration level (y8) as the optimization objective function, the optimization objective function index corresponding to the parameter sample point set is calculated using the dynamic analysis model obtained in step (1).

[0055] Will Figure 4 The sample parameters were used as the input layer of the neural network, and the calculation results were used as the output layer. A single-hidden-layer BP neural network was constructed using the MATLAB Neural Network Toolbox. The established dataset was divided into training and testing datasets in an 8:2 ratio. After data normalization, the network performance was evaluated by extracting and comparing training errors, testing errors, and correlation coefficients. The optimal model performance was obtained after multiple training iterations. The constructed BP neural network model had a learning rate of 0.01 and an objective error of 1 × 10⁻⁶. -6 The maximum number of iterations is 1000, and the number of neurons in the hidden layer is 9. (See diagram below.) Figure 5 As shown.

[0056] (2.3) Examine whether its error meets the requirements and verify the accuracy of the surrogate model method.

[0057] The effectiveness of proxy models is typically measured using the coefficient of determination R. 2 and mean absolute percentage error E map The Mean Absolute Percentage Error (MAPE) is used to evaluate model performance, and the calculation formula is as follows:

[0058] (3)

[0059] (4)

[0060] In the formula, n is the number of test points. Values ​​calculated for the dynamic model. These are the predicted values ​​from the response surface model. The mean value is calculated for the dynamic model.

[0061] Based on 200 sets of sample parameters and calculation results from the experiment, the R-value of the BP neural network was calculated. 2 Value and E map To demonstrate the reliability of the BP neural network model, the LSSVM method was introduced for accuracy comparison and verification. The comparison and verification results are as follows: Figure 6As shown, the R² values ​​of the BP neural network model for fitting and predicting the vertical Sperling index (y1), wheel-rail vertical force (y2), wheel-rail lateral force (y3), rail vertical vibration acceleration (y4), rail lateral vibration acceleration (y5), track slab vertical vibration acceleration (y6), track slab lateral vibration acceleration (y7), and tunnel wall vertical frequency-division vibration level (y8) are shown. 2 The values ​​were 0.9866, 0.9553, 0.9763, 0.9583, 0.9525, 0.9721, 0.9550, and 0.9541, all above 0.95, indicating that the overall prediction accuracy of the model is high, and the R-value of the LSSVM surrogate model is also high. 2 The values ​​are all smaller than those of the BP neural network model. The average absolute percentage error of the BP neural network model in fitting y1, y2, y3, y4, y5, y6, y7, and y8 is 0.0020%, 0.6831%, 0.2723%, 0.3868%, 3.7038%, 2.2506%, 2.2161%, and 0.2694%, respectively, showing good performance. In contrast, the E value of the LSSVM surrogate model is significantly lower. map The values ​​are all greater than those of the BP neural network model, indicating a larger prediction error and inferior model performance compared to the BP neural network model. (The last sentence appears to be incomplete and possibly refers to a different model, R.) 2 Value and E map Compared with the previous model, the BP neural network model has higher accuracy. Therefore, the BP neural network model was selected as the surrogate model to replace the dynamic simulation for multi-objective optimization.

[0062] (3) Multi-objective optimization of orbital structure parameters

[0063] The optimal solution set for the optimization objective is obtained by using a multi-objective algorithm, and the optimal solution and corresponding track structure parameters for different design requirements are determined by a comprehensive evaluation method.

[0064] The NSGA-II genetic algorithm has the advantages of fast running speed and good solution set convergence. When performing multi-objective optimization, it is necessary to first establish a multi-objective optimization mathematical model. From the perspective of global optimization of multiple indicators such as vertical Sperling index y1, wheel-rail vertical force y2, wheel-rail lateral force y3, rail vertical vibration acceleration y4, rail lateral vibration acceleration y5, track slab vertical vibration acceleration y6, track slab lateral vibration acceleration y7, and tunnel wall vertical frequency-division vibration level y8, an embedded multi-objective optimization mathematical model for key parameters of the track structure is established.

[0065] (5)

[0066] In the formula, These are the design variables: vertical stiffness, vertical damping, lateral stiffness, lateral damping of the filling material in the rail groove, and vertical stiffness and damping of the track slab. To design the upper limit value of the variable, This is the lower limit value for the design variable.

[0067] TOPSIS uses Euclidean distance to determine the distance between the evaluation object and the ideal solution, enabling it to fully extract data information based on existing data and achieve comprehensive evaluation and ranking. The specific formula is as follows:

[0068] (6)

[0069] In the formula, It is the proximity index between the m-th solution in the optimal solution set and the optimal level. The larger the value, the closer it is to the optimal level; n is the number of objective functions; k mn The values ​​of the objective functions for each solution set after forward processing and weighting are given. The minimum value in each objective function, i.e., the optimal solution; The maximum value in each objective function is the worst solution.

[0070] The embedded orbital structure parameters were optimized using the NSGA-II genetic algorithm with a multi-objective target. The population size was set to 50, the crossover probability to 0.8, the mutation probability to 0.05, and the number of iterations to 400. After fast non-dominated sorting and crowding calculation, individuals with high fitness were selected from the population. Selection, crossover, and mutation operations were then used to continuously optimize the population iteratively until the maximum number of iterations (400) was reached, yielding the Pareto optimal solution set. Figure 7 As shown.

[0071] Considering the varying importance of each optimization objective in different practical application scenarios, different weight matrices are assigned to the vertical Sperling index (y1), wheel-rail vertical force (y2), wheel-rail lateral force (y3), rail vertical vibration acceleration (y4), rail lateral vibration acceleration (y5), track slab vertical vibration acceleration (y6), track slab lateral vibration acceleration (y7), and tunnel wall vertical frequency division vibration level (y8). The method then uses the TOPSIS method to comprehensively evaluate and rank the solutions in the obtained Pareto optimal solution set, obtaining the optimal solutions under different design requirements, as shown in Table 2.

[0072] Table 2. Pareto Optimal Solutions under Different Design Requirements

[0073]

[0074] Table 3 Comparison of parameters before and after optimization

[0075]

[0076] Table 4 Comparison of Response Before and After Optimization

[0077]

[0078] Tables 3 and 4 show the comparison of various track structure parameters and corresponding dynamic characteristics before and after optimization in the optimized scheme. As can be seen from the tables, eight indicators, including the vertical Sperling index, have decreased compared to before optimization. The optimization effect is more significant in the rail and track slab sections. Specifically, the wheel-rail vertical force, wheel-rail lateral force, rail vertical vibration acceleration, rail lateral vibration acceleration, track slab vertical vibration acceleration, track slab lateral vibration acceleration, and tunnel wall vertical frequency-division vibration level have decreased by 7.24%, 5.39%, 18.47%, 26.54%, 13.22%, 28.88%, and 6.51%, respectively. This verifies the feasibility and effectiveness of the proposed multi-objective optimization method based on the BP neural network model. The research results can provide technical support and engineering guidance for subsequent embedded track parameter design and improvement research. The comparison diagrams of wheel-rail vertical force, rail vertical vibration acceleration, track slab lateral vibration acceleration, and tunnel wall vertical frequency-division vibration level are shown below. Figure 8 As shown.

[0079] like Figure 9 The diagram illustrates the process of optimizing embedded track structure parameters in this example. A dynamic analysis model of a subway train-embedded track-tunnel is established, and its reliability is verified by comparing it with field test data. The reasonable range of embedded track structure parameters is determined, and the initial sample point set of track structure parameters is obtained using the optimal Latin hypercube experimental design method. The system optimization objective is determined, and the dynamic response index corresponding to the parameter sample point set is calculated. A surrogate model of the objective function is constructed using a higher-order response surface. Based on the sample parameter set and the calculation results of the dynamic model, the error is examined to verify whether it meets the requirements, thus validating the accuracy of the surrogate model method. The Pareto solution set of the optimization objective is obtained using the NSGA-II genetic algorithm, and the optimal solution and corresponding track parameters for different design requirements are determined using the TOPSIS evaluation method.

[0080] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0081] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A track structure parameter multi-objective optimization method considering trains and foundation actions, characterized in that, The method comprises the following steps: S1, establishing a nonlinear dynamics analysis model of a train-track-foundation structure coupling system: the dynamics analysis model comprises a vehicle dynamics model, a track structure finite element model, and a lower foundation structure, i.e., an embankment, a bridge and a tunnel model, from top to bottom, and the reliability of the dynamics model is verified by comparison with field test data; S2, constructing a target function surrogate model to fit the implicit complex function relationship between system parameters and response indicators; First, the reasonable interval of the track structure parameters is determined, and an initial sample point set of the track structure parameters is obtained; Then, the system optimization target is determined, the dynamics response indicators corresponding to the parameter sample point set are calculated by using the dynamics analysis model obtained in step S1, and a target function surrogate model is constructed; Then, it is examined whether the error meets the requirements, and the accuracy of the surrogate model method is verified; The constructed surrogate model is used for multi-objective optimization in step S3; S3, multi-objective optimization of track structure parameters The optimal solution set of the optimization target is obtained by using a multi-objective algorithm, and the optimal solution and the corresponding track structure parameters for different design requirements are determined by a comprehensive evaluation method.

2. The track structure parameter optimization multi-objective method of claim 1, wherein, In step S1, the dynamics model is based on the principle of constant total potential energy and the nonlinear wheel-rail coupling element, the vehicle simulation is a multi-rigid-body system with secondary suspension, wherein: the car body, the frame and the wheel set are simulated as 6-DOF rigid bodies with rotation, the primary and secondary suspensions are simulated by spring-damping elements; the steel rail and the track slab are simulated by Bernoulli-Euler beam elements and plate elements, respectively; the lower supporting structure is simulated by beam, plate and space element damping; the interaction between any substructure or subcomponent is simulated by spring-damping elements according to the multi-scale coupling method.

3. The track structure parameter optimization multi-objective method of claim 1, wherein, In step S2, the optimal Latin hypercube sampling method, i.e., OLHS, is used to obtain the initial sample point set, and the sample points are uniformly distributed in the probability space.

4. The track structure parameter optimization multi-objective method of claim 1, wherein, In step S2, a BP neural network is used as a surrogate model to fit the implicit complex relationship between the structure parameters and the response optimization indicators.

5. The track structure parameter optimization multi-objective method of claim 1, wherein, In step S3, the NSGA-II genetic algorithm is used for continuous multi-objective optimization iteration to obtain the Pareto optimal solution set of the optimization target.

6. The track structure parameter optimization multi-objective method of claim 1, wherein, In step S3, the TOPSIS comprehensive evaluation method is used for evaluation and ranking to determine the optimal solution and the corresponding track parameters for different design requirements.

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