Multi-objective optimization method for high-speed train suspension parameters based on surrogate model

Abstract

This invention discloses a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, belonging to the field of rail transit vehicle dynamics optimization technology. The method includes the following steps: S1, constructing a high-speed train dynamics model and determining vehicle dynamic performance evaluation indicators; S2, screening key parameters of the suspension system and analyzing their impact on dynamic performance; S3, establishing a PSO-SVM model; S4, multi-objective optimization of high-speed train suspension parameters: constructing a multi-objective optimization model and combining it with AHP to comprehensively evaluate and select the optimal optimization scheme. This invention, employing the above-mentioned multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, can significantly reduce the computational burden of high-precision dynamic models, achieve rapid optimization of high-speed train suspension parameters and synergistic improvement of multiple dynamic performance characteristics, providing an efficient and feasible technical path for the design of high-speed train suspension system parameters.

Description

Technical Field

[0001] This invention relates to the field of rail transit vehicle dynamics optimization technology, and in particular to a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model. Background Technology

[0002] The parameters of the high-speed train suspension system have a significant impact on vehicle dynamics, and optimization methods can improve these performance characteristics. However, suspension system design involves multiple complex factors, including nonlinear coupling relationships between system parameters and mutual constraints between different dynamic performance indicators. Essentially, the optimization design of suspension systems falls under the category of problems with multiple optimization objectives and various constraints.

[0003] In traditional research, suspension parameter optimization typically relies on high-precision multibody dynamics models for simulation analysis. When the parameter dimension is high or large-scale optimization searches are required, the computational cost of the model is high, and the simulation time is long, making it difficult to meet the needs of efficient optimization in engineering. Furthermore, the optimization problem of locomotive and rolling stock systems not only requires in-depth research into various individual disciplines but also necessitates interdisciplinary comprehensive analysis and design, further complicating the optimization problem.

[0004] Therefore, it is necessary to introduce a surrogate model, which can reduce the computational burden brought by the high-precision dynamic model on the one hand, and improve the efficiency of multi-objective optimization on the other hand, so as to achieve rapid optimization of suspension system parameters and coordinated performance improvement.

[0005] Existing research has yielded significant results in surrogate model construction and its integration with intelligent optimization algorithms. However, differences still exist among different surrogate models in terms of prediction accuracy and generalization ability. Therefore, it is necessary to conduct a systematic comparison of surrogate models and optimize their parameters using optimization algorithms to further improve their predictive performance and engineering applicability. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, thereby solving the problems mentioned in the background art.

[0007] To achieve the above objectives, this invention provides a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, comprising the following steps: S1. High-speed train dynamics model: Based on the theory of multibody system dynamics, a high-speed train dynamics model is constructed, and key nonlinear components are modeled in detail to provide a basis for subsequent simulation and to determine the vehicle dynamics performance evaluation index. S2. Screening of key parameters of the suspension system: The optimal Latin hypercube experimental design method was used to construct sample data, and Spearman correlation analysis and Pareto contribution analysis were combined to screen out key parameters; S3. Agent Model Construction and Parameter Optimization: Construct an SVM agent model, introduce the Particle Swarm Optimization (PSO) algorithm to optimize the key parameters of SVM, and establish a PSO-SVM model. S4. Multi-objective optimization of high-speed train suspension parameters: Using key parameters as design variables and various dynamic performance indicators as optimization objectives, a multi-objective optimization model is constructed; rapid prediction is performed based on the PSO-SVM model, the NSGA-III algorithm is used to find the Pareto optimal solution set, and the optimization scheme is comprehensively evaluated and selected by combining AHP.

[0008] Therefore, the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model described above has the following beneficial effects: (1) This invention constructs a multibody dynamics model of a high-speed train and achieves an accurate description of the primary and secondary suspension systems and wheel-rail relationship through reasonable topology definition and force element equivalence method, which can more realistically reflect the dynamic response characteristics of the vehicle under complex operating conditions.

[0009] (2) The PSO-SVM model constructed in this invention can effectively capture the nonlinear relationship between suspension parameters and dynamic response, and has a greater advantage in overall prediction effect and adaptability to new data. It can replace the high-cost dynamic model while ensuring prediction accuracy.

[0010] (3) This invention proposes a multi-objective optimization method that integrates the NSGA-III algorithm and the PSO-SVM surrogate model. By introducing a reference point mechanism and a niche selection strategy, the PSO-SVM model is used to achieve rapid prediction of dynamic performance indicators, thereby significantly improving the optimization computation efficiency.

[0011] (4) This invention analyzes the distribution characteristics of the two-dimensional and three-dimensional Pareto fronts, reveals the inherent trade-off between safety, stability and stability indicators, and uses AHP to comprehensively evaluate the Pareto optimal solution. Through weight analysis, the suspension parameter scheme with the best overall performance is selected.

[0012] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a proxy model according to the present invention. Figure 2This is the vehicle system topology of an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a proxy model according to the present invention; Figure 3 The following are characteristic curves of an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention: (a) is the damping of the anti-snake-like shock absorber, and (b) is the lateral stop. Figure 4 This is a high-speed train model, which is an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a proxy model according to the present invention. Figure 5 This invention provides a dynamic performance correlation analysis of high-speed trains based on a proxy model-based multi-objective optimization method for high-speed train suspension parameters. Figure 6 The contribution distribution results of each dynamic performance index in the embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention are as follows: (a) wheel load reduction rate, (b) derailment coefficient, (c) lateral stability, (d) comfort, and (e) critical speed. Figure 7 This is a flowchart of the PSO-SVM method for multi-objective optimization of high-speed train suspension parameters based on a proxy model, as described in this invention. Figure 8 The following are the derailment coefficient prediction results of the embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention: (a) is a comparison of the prediction results of the training set, and (b) is a comparison of the prediction results of the test set. Figure 9 The following are the stationarity prediction results of the embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention: (a) is a comparison of the prediction results of the training set, and (b) is a comparison of the prediction results of the test set. Figure 10 The following are the critical speed prediction results of the embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention: (a) is a comparison of the prediction results of the training set, and (b) is a comparison of the prediction results of the test set. Figure 11 This is a hyperplane distribution map showing the reference points of an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a proxy model according to the present invention. Figure 12 This is a schematic diagram of the niche-based individual selection mechanism in an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention. Figure 13 This is the Pareto front between wheel load reduction rate and derailment coefficient in an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a surrogate model of the present invention. Figure 14This is a three-dimensional Pareto front distribution of the derailment coefficient, stability index, and comfort index of a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, as described in this invention. Figure 15 This is a hierarchical model of an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on a proxy model according to the present invention. Figure 16 This is a comparison of the optimization rates of embodiments of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention; Figure 17 The graphs show the trend of stability at different speeds in an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention. (a) represents lateral stability, and (b) represents vertical stability. Figure 18 This is a comparison of safety before and after optimization in an embodiment of the multi-objective optimization method for high-speed train suspension parameters based on the surrogate model of the present invention. (a) is the derailment coefficient, and (b) is the wheel load reduction rate. Figure 19 The graph shows the trend of the high-speed train suspension parameter multi-objective optimization method based on the surrogate model of the present invention. (a) is the wheel load reduction rate, and (b) is the derailment coefficient. Detailed Implementation

[0014] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0016] Example Please see Figures 1-19 This invention provides a multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, comprising the following steps: S1. Establishment of high-speed train dynamics model.

[0017] S11. Combining the Lagrange equation of the second kind and the Newton-Euler equation, establish the complete dynamic equations of the many-body system, whose general form can be expressed as: in, Let z be the generalized coordinate of the system. for, for, for, for, It is a generalized force vector.

[0018] S12. Analysis of the main structure of the high-speed train bogie.

[0019] Primary suspension system: Connecting the wheels and frame, including helical steel springs, vertical dampers, and other related components. In dynamic modeling, the helical steel springs and primary vertical dampers are typically simplified as linear spring-damped parallel force elements, while the swingarm rubber nodes are simulated using triaxial stiffness force elements.

[0020] The secondary suspension system, located between the vehicle body and the primary suspension, includes air springs, dampers, and lateral stops. Under high-speed operating conditions, it exhibits nonlinear characteristics and requires refined processing: the air springs are equivalent to parallel force elements containing three-dimensional stiffness and damping; the anti-hunting dampers and lateral stops are both constructed using nonlinear spline curve force elements to accurately reproduce their mechanical properties.

[0021] S13. Based on multibody dynamics theory and the main structure of the bogie, a dynamic model of high-speed train is constructed.

[0022] S131, Degrees of freedom of the vehicle system.

[0023] The high-speed train dynamics model constructed in this embodiment consists of a car body, two frames, four wheelsets, and eight axle boxes, containing a total of 15 rigid bodies. The degree of freedom allocation of each rigid body is shown in Table 1 below.

[0024] Table 1 Degrees of freedom of the high-speed train dynamics simulation model

[0025] like Figure 2 As shown, in the vehicle system topology modeling, force element #5 is used to accurately reflect its linear mechanical characteristics, ensuring computational efficiency. A special force element #6 is used to realistically reflect the actual behavior of the suspension system. The complete six-degree-of-freedom motion of the reference coordinate system with the vehicle body, frame, and wheelsets in three-dimensional space is represented by hinge #7.

[0026] S132, Simplification of nonlinear force elements.

[0027] To improve the simulation accuracy of the model under complex working conditions, this invention sets both the anti-hunting damper and the lateral stop as nonlinear elements, and their characteristic curves are shown in [the diagram / image / etc.]. Figure 3 In (a) and (b) of the text.

[0028] S133, Vehicle dynamics model establishment.

[0029] Build a model in SIMPACK, such as Figure 4 As shown in Table 2, the basic parameters of the high-speed train dynamics model are as follows.

[0030] Table 2 Basic parameters of vehicle dynamics

[0031] S14. Vehicle dynamics performance evaluation indicators.

[0032] S141. Vehicle running stability.

[0033] Stability index: Sperling index, used to evaluate the impact of lateral and vertical vibrations on ride comfort during vehicle operation.

[0034] Comfort index: A key indicator for evaluating the average comfort of passengers and crew, calculated by weighting vibration acceleration and combining it with statistical methods.

[0035] Operational quality: Divided into two categories: vertical and lateral acceleration, with the measurement point layout consistent with the stability index.

[0036] S142, Vehicle operation safety.

[0037] Derailment coefficient: Train derailment is a complex safety issue, usually caused by the combined effect of multiple factors.

[0038] Wheel load reduction rate: This reflects the change in vertical load on the wheels during dynamic operation. The higher the value, the higher the risk of the vehicle losing load or even derailing.

[0039] Lateral force of wheel and axle: used to assess the magnitude of lateral forces during vehicle operation and their impact on the track structure.

[0040] S143, vehicle swerving stability.

[0041] Critical speed is a key indicator for measuring the stability of serpentine motion, and it is generally divided into the following two types of critical speeds: Linear critical speed: The operating speed at which a system transitions from stability to instability is defined as the linear critical speed.

[0042] Nonlinear critical speed: The speed at which the lateral displacement amplitude of the wheelset first stabilizes and converges (less than 0.1 mm) is the nonlinear critical speed.

[0043] S2. Screening of key parameters of the suspension system and analysis of their impact on dynamic performance.

[0044] S21, Design Methodology.

[0045] This embodiment selects the optimal Latin hypercube experimental design method to construct sample points, which can provide a uniform and representative sample distribution with fewer trials. It is suitable for exploring high-dimensional design spaces and can effectively avoid estimation bias caused by local clustering of samples.

[0046] S22. Identification and screening of key parameters of the suspension system.

[0047] S221. Correlation analysis based on Spearman correlation coefficient, the calculation formula is as follows: ; in, n For the sample size, di This indicates the difference in rank. Positive values ​​indicate positive correlation, and negative values ​​indicate negative correlation.

[0048] One hundred sample points were extracted using the optimal Latin hypercube experimental design for analysis, with the suspension parameters set to range from ±50% of their initial values. Dynamic performance indicators were selected as response indicators, and the Spearman correlation coefficients between each design parameter and the dynamic performance indicators were calculated. The results are as follows: Figure 5 As shown, the wheel load reduction rate is negatively controlled by the air spring stiffness and the primary vertical stiffness. The derailment coefficient is negatively affected by various suspension parameters, with the primary vertical stiffness having the strongest effect. Lateral stability is highly sensitive to the two types of damping parameters and is positively correlated. The critical speed is mainly affected by the secondary lateral damping damping, which has a very strong negative correlation with the secondary system. The anti-snake stiffness plays only a secondary role.

[0049] S222. Parameter importance analysis based on Pareto contribution.

[0050] The Pareto contribution analysis method is introduced to quantitatively assess the importance of each parameter from the perspective of response change amplitude, in order to identify key parameters with significant nonlinear characteristics. The contribution distribution results of each dynamic performance index are as follows: Figure 6 As shown, the effects of suspension system parameters on vehicle dynamics have a clear hierarchical structure: primary suspension parameters mainly concern operational safety, secondary suspension parameters dominate stability and comfort, and secondary lateral damper damping plays a decisive role in high-speed stability.

[0051] S222, Key Parameter Screening Results.

[0052] Based on indicators such as safety, stability, comfort, and high-speed stability, parameters ranking high in sensitivity or contribution were selected as key optimization variables. Safety-related parameters were the primary consideration, while stability and stability indicators were also taken into account. Specific information on the selected key parameters is shown in Table 3 below.

[0053] Table 3 Key Suspension Parameters

[0054] By screening key parameters, we not only reduced the dimensionality of design variables, but also laid the foundation for subsequent proxy model construction and multi-objective optimization analysis.

[0055] S3, Agent Model Construction and Parameter Optimization.

[0056] S31. Data preprocessing and model evaluation methods.

[0057] S311. Data preprocessing: This embodiment uses the min-max normalization method to normalize the data before model training.

[0058] S312. Model Validation: Performance validation is performed using cross-validation. Cross-validation involves repeatedly dividing the training and validation sets, allowing the model to be trained and tested on different subsets of data, thus more objectively reflecting the model's generalization ability.

[0059] In the k-fold cross-validation method, the original training sample set is divided into k subsets on average. Each time, one subset is selected as the validation set, while the remaining k-1 subsets are combined as the training set. This process is repeated k times. This method ensures that each data subset is used as both the training and validation set once, effectively reducing the randomness of the evaluation results caused by a single random data partition, and making the model performance evaluation more objective and reliable.

[0060] S313. Model Evaluation Index: Select the coefficient of determination (… R 2 The coefficient of determination (COD) and root mean square error (RMSE) are used as evaluation metrics. The COD measures the model's ability to fit the changing trends of the sample data. R 2 The closer the value is to 1, the smaller the RMSE, indicating better performance.

[0061] S32. Construction and performance analysis of the benchmark proxy model.

[0062] S321, SVM kernel function selection analysis.

[0063] To analyze the impact of different kernel functions on the predictive performance of the SVM surrogate model, the derailment coefficient, lateral stationarity, and critical velocity were selected as representative indicators of safety, stationarity, and serpentine motion stability, respectively. A k-fold cross-validation method was used to evaluate the model performance to reduce the impact of sample partitioning randomness on the evaluation results. Three kernel functions were selected for comparative experiments, and... R 2 The model performance was evaluated using RMSE, and the results are shown in Table 4 below.

[0064] Table 4. Impact of kernel function on model accuracy

[0065] Overall, the RBF kernel function has significant advantages in both accuracy and stability, and can fit the dynamic response of the suspension system well. Therefore, RBF is selected as the kernel function for the SVM model.

[0066] S322, SVM parameter selection analysis.

[0067] Training is performed using randomly selected parameters. The parameters are... C The value range is [0.1, 100], parameter g The value range is [0.001, 10], and the results are shown in Table 5 below.

[0068] Table 5. Influence of Randomly Selected Parameters on Model Accuracy

[0069] It can be seen that the predictive performance of the SVM model is affected by the parameters. C and g It has a strong dependency, so it is necessary to introduce an optimization algorithm to perform global optimization in order to obtain a better combination of parameters.

[0070] S33. A method for optimizing surrogate model parameters based on intelligent optimization algorithms.

[0071] S331. Selection of parameter optimization method.

[0072] Particle Swarm Optimization (PSO) uses cooperative iteration of particles in the search space, enabling it to quickly approach the optimal solution with fewer computations. This high search efficiency makes it particularly suitable for Optimization Vector Machines (SVMs). With the help of PSO, SVMs can efficiently tune their parameters, maximizing the model's predictive performance.

[0073] S332, PSO-SVM parameter optimization process.

[0074] Introducing the PSO algorithm into the SVM parameter optimization process maps particle positions to ( C ,g By combining parameters and using the model prediction error as the fitness function to conduct a global search, the prediction accuracy and generalization performance of the model can be effectively improved. Figure 7 As shown.

[0075] Performance analysis of S333 and PSO-SVM models.

[0076] The predictive performance of the optimized model was analyzed and validated. During model construction, 80 sets were used as the training set and 20 sets as the test set. The model input consisted of the stiffness and damping parameters of the suspension system, and the output consisted of dynamic indicators such as safety, stability, and critical speed.

[0077] The optimal parameter combinations for each dynamic index were obtained using PSO-SVM. The optimal parameter for the derailment coefficient was: C =67.230、 g =0.101, the optimal parameter for stationarity is C =86.332、 g =0.908, the optimal parameter for critical velocity is C =69.492、 g =0.075.

[0078] The PSO-SVM prediction model was constructed, and the prediction results for each dynamic index are as follows: Figures 8-10 As shown. Overall, using the PSO algorithm to optimize the parameters of the SVM model can effectively improve prediction accuracy and the model's adaptability to unknown data, thereby obtaining more reliable prediction results.

[0079] S4. Multi-objective optimization of high-speed train suspension parameters.

[0080] S41. Construction of a multi-objective optimization model for high-speed train suspension parameters.

[0081] S411, Selection of design variables.

[0082] Based on the suspension system structure and its impact on vehicle dynamics, the following key parameters are selected as optimization variables: primary spring vertical stiffness. K 2 Longitudinal stiffness of axle box swing arm node K 4 air spring lateral and longitudinal stiffness K 6 Air spring vertical damping C 2 Secondary transverse damper damping C 3 .

[0083] S412. Optimize the objective function.

[0084] Optimization targets include the derailment coefficient. D Wheel load reduction rate L lateral stability index of vehicle body Wy Comfort index NMV and operational stability indicators V As an optimization evaluation indicator.

[0085] S413, Constraints.

[0086] To ensure that the optimized results meet the requirements of high-speed train operation safety and passenger comfort, the derailment coefficient response value... D ( x )≤0.8, wheel load reduction rate L ≤0.8, comfort N MV ≤1.5, lateral stability W y ( x )≤2.5, in addition, let and Upper and lower limits are defined separately. To ensure the engineering feasibility of the optimization results, the range of design variables is set to ±50% of the initial design parameters. The formula for the constructed multi-objective optimization model is as follows: ; ; ; In summary, a multi-objective optimization model for the suspension system parameters of high-speed trains is established. Solving this model yields the optimal suspension parameters that meet the requirements, thus providing a basis for subsequent multi-objective optimization calculations using the NSGA-III algorithm.

[0087] S42. Multi-objective optimization based on NSGA-III.

[0088] S421, Reference point mechanism and niche selection method.

[0089] NSGA-III uses the number of niches at a reference point to assess its crowding level, and combines this with a niche selection strategy to select superior individuals, guiding the population to be evenly distributed on the Pareto front, and finally obtaining a well-distributed optimal solution set.

[0090] First, generate a reference point, assuming the target space has a dimension of . m Each target is divided into equal parts h Segment, number of reference points Pnum for: ; Taking a three-objective optimization problem as an example, after the objective value is normalized, the reference points are restricted to a triangular plane with vertices (1,0,0), (0,1,0), and (0,0,1). Dividing each objective function into four equal parts, the number of reference points is 15. The hyperplane distribution of the reference points is shown in the figure below. Figure 11 As shown.

[0091] Determine the minimum population size Zimin This allows us to construct ideal points and determine the intercepts of the hyperplane formed by the extreme points on each coordinate axis using linear equations. ai .

[0092] Based on the above steps, a normalization operation is further performed, and its mathematical expression is as follows: ; Through the normalization process, objective functions with different dimensions can be mapped to a unified scale space, thereby ensuring the rationality of subsequent distance calculations.

[0093] Based on this, a niche preservation mechanism is employed to prioritize the selection of individuals from niches with lower individual density (i.e., lower crowding) around the reference point, thereby ensuring that the resulting solution set has good uniform distribution characteristics. The core steps of the NSGA-III algorithm and the individual selection process are illustrated below. Figure 12 As shown.

[0094] S422, Parameter setting and optimization process.

[0095] This paper combines the PSO-SVM surrogate model with the NSGA-III multi-objective genetic algorithm to optimize the parameters of the high-speed train suspension system. The PSO-SVM model is used to quickly predict the dynamic performance under different parameter sets, while the NSGA-III algorithm searches for the optimal parameter combination through population evolution, thereby achieving multi-objective optimization. During the operation of the NSGA-III algorithm, it is necessary to reasonably set the population size, number of iterations, and genetic operation parameters. The main parameters of the algorithm are selected as follows: Population size P op =300; Maximum number of iterations maxGen =500; Crossover probability cP =0.9; Mutation probability vP =0.1.

[0096] Furthermore, the decision variables in the model are set to have a dimension of 5, and the number of objective functions is also 5. According to the requirements of the NSGA-III algorithm, a corresponding set of reference points is generated based on the dimension of the objective functions to ensure a uniform distribution of the Pareto solution set in the objective space.

[0097] S43, Pareto front distribution and characteristic analysis.

[0098] S431, Two-dimensional Pareto front characteristic analysis.

[0099] After calculation, the Pareto optimal solution set for optimizing the suspension system parameters is obtained. For example... Figure 13 As shown, the Pareto front distribution between wheel load reduction rate and derailment coefficient is presented. This coupling relationship reflects the mutual influence between vertical and lateral responses in the vehicle dynamics system, and the optimal trade-off between the two safety indicators.

[0100] S432, 3D Pareto Front Characteristic Analysis.

[0101] The three-dimensional Pareto front distributions of derailment coefficient, stability index, and comfort index are as follows: Figure 14 As shown, there is a strong coupling relationship between the derailment coefficient R2, the stability index R3, and the comfort index R5. Moreover, the multi-objective optimization results do not have a unique optimal solution, but rather form a series of engineering-significant compromise solutions among safety, stability, comfort, and critical speed.

[0102] S44. Optimization Scheme Decision and Analysis Based on AHP.

[0103] A multi-attribute decision-making method is introduced to further filter the Pareto solution set. In this embodiment, the Analytic Hierarchy Process (AHP) is used to comprehensively evaluate the optimal Pareto solution, thereby determining the suspension parameter scheme with the best comprehensive performance.

[0104] S441. Optimization scheme decision-making method based on AHP.

[0105] S4411, Hierarchical structure model construction.

[0106] The Analytic Hierarchy Process (AHP) typically divides evaluation elements into three layers: the objective layer, the criterion layer, and the alternative layer. The objective layer represents the overall optimal dynamic performance of the high-speed train; the criterion layer includes various dynamic performance parameters; and the alternative layer comprises the optimized solutions selected from the Pareto optimal solution set. Its structure is as follows: Figure 15 As shown.

[0107] S4412. Establish the judgment matrix.

[0108] In constructing the judgment matrix, it is necessary to perform pairwise relative importance comparisons on the evaluation indicators belonging to the same upper-level objective. The importance judgment of the evaluation indicators is as follows: aijThe judgment matrix can be represented as: ; The judgment matrix satisfies: ; To quantitatively characterize the importance of each pair of factors, this embodiment introduces the 1–9 scale method, the meaning of which is shown in Table 6 below.

[0109] Table 6. Methods for determining the scaling of a matrix

[0110] Following the principle of prioritizing the safety of high-speed train operation, the derailment coefficient and wheel load reduction rate have a direct impact on vehicle operation safety and are therefore of the highest importance. Lateral stability index and comfort index together reflect the quality of train operation and are of secondary importance. Nonlinear critical speed is of relatively lowest importance under the working conditions studied in this paper.

[0111] The judgment matrix is ​​constructed as follows: ; S4413. Perform a consistency check on the judgment matrix.

[0112] The formula for calculating the judgment matrix is ​​shown in the following equation: ; The matrix order in the formula is 5, and the calculation yields... =5.506, =0.014.

[0113] To quantify the degree of consistency of the judgment matrix, the consistency ratio is used. CR The calculation formula is: ; When the consistency ratio is satisfied: CR <0.1; Calculations show that =1.12, CR =0.013, which is less than 0.1, indicating that the consistency of the judgment matrix is ​​good, and the weight result obtained is reasonable and reliable.

[0114] S4414, Weight Calculation Method.

[0115] The weights of each indicator are calculated based on the eigenvalues ​​of the judgment matrix and their corresponding eigenvectors. The calculation formula is as follows: Aw=λ max w; After normalization, the weight vector can be obtained: ; in, wi Indicates the first i The weighting coefficients of each dynamic performance index in the comprehensive evaluation, and satisfying the normalization constraint conditions: ; The weights of the five dynamic performance indicators—wheel load reduction rate, derailment coefficient, stability, comfort, and critical speed—in the comprehensive evaluation are calculated as follows: W=(0.344,0.344,0.129,0.129,0.055) T ; The weighting results show that safety indicators account for the highest proportion, followed by stability and smoothness, which is in line with the engineering design principle of prioritizing safety in high-speed train operation.

[0116] S442. Determination of Optimization Scheme and Analysis of Results.

[0117] Based on the AHP weighting results, the Pareto optimal solution is comprehensively evaluated, and the scheme with the best overall performance is selected. The corresponding suspension parameters are shown in Table 7 below.

[0118] Table 7 Comparison of suspension system parameters before and after optimization

[0119] To evaluate the prediction accuracy and reliability of the surrogate model's optimization results, the optimized suspension parameters were input into the SIMPACK software for simulation calculations. The dynamic response under simulation conditions was compared with the prediction results of the surrogate model, and the error rate and optimization rate were calculated. The overall optimization rate was defined as the arithmetic mean of the optimization rates of each individual indicator. The performance comparison results of the schemes before and after optimization are summarized in Table 8.

[0120] Table 8 Comparison of Performance Indicators and Verification Results of Optimization Schemes

[0121] It can be seen that the errors between the predicted and simulated values ​​of each performance index are small, with the maximum error being less than 5%, indicating that the PSO-SVM surrogate model has excellent prediction accuracy and the optimization results also show high reliability.

[0122] In summary, this optimization scheme achieves a good balance between safety, comfort, and stability, with significant overall optimization effects and high engineering application value. (Optimization rate comparison follows.) Figure 16 As shown.

[0123] S45. Verification of the dynamic performance of the optimized scheme.

[0124] The optimized scheme is input into SIMPACK for simulation calculation. By comparing the changes in dynamic performance under various operating conditions before and after optimization, the impact of the optimized scheme on vehicle operating performance is analyzed.

[0125] S451. Operational stability analysis.

[0126] The train was set to run on a straight track with a length of 2000m. The measured track irregularity excitation of the Beijing-Tianjin Railway was applied within the range of 30m to 2000m. The simulation results are shown in Table 9.

[0127] Table 9. Simulation data on stability before and after optimization

[0128] The trend of stability at different speeds is shown in the figure. Figure 17 As shown in the figure, the optimized suspension parameters can effectively reduce vehicle vibration levels, improve train running stability, and thus improve ride comfort.

[0129] S452, Operational safety analysis.

[0130] A typical track condition with a curve radius of 7000m and a superelevation of 175mm was selected, with a speed of 300km / h and actual track irregularities on the Beijing-Tianjin line applied. The safety comparison before and after optimization is shown in the figure below. Figure 18 As shown.

[0131] It can be seen that after optimization, the overall trend of the derailment coefficient and wheel load reduction rate is basically the same as before optimization, but the fluctuation amplitude and extreme values ​​have decreased.

[0132] The derailment coefficient and wheel load reduction rate at different speeds were calculated and analyzed, and the results are shown in Table 10.

[0133] Table 10 Safety simulation data before and after optimization

[0134] The corresponding trend chart is as follows Figure 19 As shown in the curve, when the train speed gradually approaches the equilibrium speed, the wheel-rail forces are more coordinated, the lateral dynamic response is weakened, and thus the safety performance is improved.

[0135] Comparing the results before and after optimization, it can be seen that the optimized scheme can effectively reduce the wheel load reduction rate and derailment coefficient at all speed levels.

[0136] In summary, the optimized suspension parameters can effectively improve the wheel-rail interaction state of the vehicle, and enhance the lateral stability and operational safety of the train during curve passage.

[0137] Therefore, the present invention adopts the above-mentioned multi-objective optimization method for high-speed train suspension parameters based on the surrogate model. The multi-objective optimization method constructed by combining the PSO-SVM surrogate model with the NSGA-III algorithm can significantly reduce the computational burden of high-precision dynamic models, realize the rapid optimization of high-speed train suspension parameters and the synergistic improvement of multiple dynamic performances, and provide an efficient and feasible technical path for the design of high-speed train suspension system parameters.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-objective optimization method for high-speed train suspension parameters based on a surrogate model, characterized in that, Includes the following steps: S1. High-speed train dynamics model: Based on the theory of multibody system dynamics, a high-speed train dynamics model is constructed, and key nonlinear components are modeled in detail to provide a basis for subsequent simulation and to determine the vehicle dynamics performance evaluation index. S2. Screening of key parameters of the suspension system: The optimal Latin hypercube experimental design method was used to construct sample data, and Spearman correlation analysis and Pareto contribution analysis were combined to screen out key parameters; S3. Agent Model Construction and Parameter Optimization: Construct an SVM agent model, introduce the Particle Swarm Optimization (PSO) algorithm to optimize the key parameters of SVM, and establish a PSO-SVM model. S4. Multi-objective optimization of high-speed train suspension parameters: Using key parameters as design variables and various dynamic performance indicators as optimization objectives, a multi-objective optimization model is constructed; rapid prediction is performed based on the PSO-SVM model, the NSGA-III algorithm is used to find the Pareto optimal solution set, and the optimization scheme is comprehensively evaluated and selected by combining AHP.

2. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. Combining the second type of Lagrange equations and the Newton-Euler equations, we establish the theoretical foundation for multibody dynamics. S12. Analyze the main structure of the high-speed train bogie, including the primary suspension system that connects the wheels and the frame and the secondary suspension system that connects the bogie to the car body; S13. Based on multibody dynamics theory and the main structure of the bogie, a dynamic model of a high-speed train is constructed. S14. Determine the vehicle dynamics performance evaluation indicators, including vehicle running smoothness, vehicle running safety, and serpentine motion stability.

3. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 2, characterized in that, The specific steps of S13 are as follows: S131. Divide the vehicle into rigid body components and define the degrees of freedom of the car body, frame, wheelsets and axle box; S132. Set the anti-hunting damper and the lateral stop as nonlinear elements to complete the simplification of nonlinear force elements; S133. Based on S131 and S132, a high-speed train dynamics model is constructed in SIMPACK.

4. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 3, characterized in that: The key parameters selected by S2 include the vertical stiffness of the primary spring, the longitudinal stiffness of the axle box swing arm node, the lateral and longitudinal stiffness of the air spring, the vertical damping of the air spring, and the damping of the secondary lateral damper.

5. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 4, characterized in that, The specific steps of S3 are as follows: S31. Data Preprocessing and Model Evaluation Methods: Mini-maximum normalization is used to preprocess the sample data; k-fold cross-validation is used for performance verification; and the coefficient of determination and root mean square error are selected as evaluation indicators. S32. Benchmark Proxy Model Construction and Performance Analysis: Build an SVM proxy model, select kernel function and parameters for SVM, and analyze the performance of SVM in predicting the dynamic indicators of suspension systems. S33. Parameter optimization method for surrogate models based on intelligent optimization algorithms: An optimization algorithm is introduced to optimize the parameters of the SVM surrogate model, thereby improving the prediction accuracy and generalization performance of the SVM model.

6. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 5, characterized in that, The specific steps of S3 are as follows: S321, SVM kernel function selection analysis: Derailment coefficient, lateral stability and critical velocity are selected as safety, stability and serpentine motion stability indicators, respectively. The k-fold cross-validation method is used to evaluate the model performance and RBF is selected as the SVM kernel function. S322, SVM Parameter Selection Analysis: Different parameters were randomly selected for training to examine the effect of SVM-related parameters on model performance.

7. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 6, characterized in that, The specific steps of S33 are as follows: S331. Selection of parameter optimization method: Particle swarm optimization algorithm (PSO) is selected to optimize SVM parameters and construct PSO-SVM optimization model. S332, PSO-SVM Parameter Optimization Process: The PSO algorithm is introduced into the SVM parameter optimization process, mapping the particle position to ( C , g The parameters are combined, and the model prediction error is used as the fitness function to carry out a global search; S333 and PSO-SVM Model Performance Analysis: The predictive performance of the optimized model is analyzed and verified.

8. The multi-objective optimization method for high-speed train suspension parameters based on a surrogate model according to claim 7, characterized in that, The specific steps of S4 are as follows: S41. Combining vehicle dynamics theory and relevant specifications, key parameters in the suspension system are selected as design variables, and vehicle dynamics performance indicators are used as optimization objectives to establish a multi-objective optimization model for high-speed train suspension parameters. S42. Multi-objective optimization based on NSGA-III: The NSGA-III algorithm judges the population crowding by the number of reference point niches, and selects high-quality individuals by combining niche selection strategy to guide the population to converge uniformly to the Pareto front; configure the population size, number of iterations and genetic operation parameters, execute the iterative optimization process, and obtain the Pareto optimal solution set of the suspension system parameter optimization. S43. Pareto Front Distribution and Characteristic Analysis: Trade-off analysis was conducted on the two-dimensional and three-dimensional Pareto front solution sets to provide a basis for subsequent optimization scheme selection; S44. Optimization Scheme Decision and Analysis Based on AHP: Construct an AHP hierarchical model, including the objective layer, criterion layer and scheme layer, establish a judgment matrix, calculate weights, and select the scheme with the best comprehensive performance. S45. Optimization Scheme Dynamic Performance Verification: Input the optimized scheme into SIMPACK for simulation calculation. By comparing the changes in dynamic performance under various operating conditions before and after optimization, analyze the impact of the optimized scheme on vehicle operating performance.

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