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How to get a lighter and stronger anti-rolling torsion bar has become a barrier for the development of high-speed railway vehicles. The purpose of this paper is to realize the multi-objective optimization of an anti-rolling torsion bar with a Modified Non-dominated Sorting Genetic Algorithm III (MNSGA-III), which aims to obtain a better design scheme of an anti-rolling torsion bar device.

First, the Non-dominated Sorting Genetic Algorithm III (NSGA-III) uses a simulated binary crossover (SBX) operator and a polynomial mutation operator, while the MNSGA-III algorithm proposed in this paper introduces an arithmetic crossover and an adaptive mutation operator to change the crossover and mutate operator in NSGA-III. Second, two algorithms are tested by ZDT3, ZDT4 functions. Both algorithms set the same population size and evolutionary generation, and then compare the results of NSGA-III and MNSGA-III. Finally, MNSGA-III is applied to the multi-objective model of an anti-rolling torsion bar which is established by taking the mass and stiffness of the torsion bar as the optimization object. After that, it obtains the Pareto solution set by solving the multi-objective model with MNSGA-III. The only optimal solution selected from the Pareto solution set is compared with the traditional design scheme of an anti-rolling torsion bar.

The MNSGA-III converges faster than NSGA-III. Besides, MNSGA-III has better diversity of Pareto solutions than NSGA-III and is closer to the ideal Pareto frontier. Comparing with the results before the optimization, it shows that the volume of the anti-rolling torsion bar reduces by 1.6 percent and the stiffness increases by 3.3 percent. The optimized data verifies the effectiveness of this method proposed in this paper.

The simulated binary crossover operator and polynomial mutation operator of NSGA-III are changed into an arithmetic crossover operator and an adaptive mutation operator, respectively, which improves the optimization performance of the algorithm.

This paper proposes an improved fatigue life analysis method for optimal design of electric multiple units (EMU) gear, which aims at defects of traditional Miner fatigue cumulative damage theory.

A fatigue life analysis method by modifying S–N curve and considering material difference is presented, which improves the fatigue life of EMU gear based on shape modification optimization. A corrected method for stress amplitude, average stress and S–N curve is proposed, which considers low stress cycle, material difference and other factors. The fatigue life prediction of EMU gear is carried out by corrected S–N curve and transient dynamic analysis. Moreover, the gear modification technology combined with intelligent optimization method is adopted to investigate the approach of fatigue life analysis and improvement.

The results show that it is more corresponded to engineering practice by using the improved fatigue life analysis method than the traditional method. The function of stress and modification amount established by response surface method meets the requirement of precision. The fatigue life of EMU gear based on the intelligent algorithm for seeking the optimal modification amount is significantly improved compared with that before the modification.

The traditional fatigue life analysis method does not consider the influence of working condition and material. The life prediction results by using the method proposed in this paper are more accurate and ensure the safety of the people in the EMU. At the same time, the combination of intelligent algorithm and gear modification can improve the fatigue life of gear on the basis of accurate prediction, which is of great significance to the portability of EMU maintenance.

This paper aims to establish the relationship between crosswind speed and pantograph-catenary lateral deviation, as well as quantify the influence of crosswind speed and rod size uncertainty on pantograph-catenary contact reliability.

The closed vector method is used to establish the pantograph-catenary kinematics formula. A new prediction model is proposed by using the bird swarm algorithm to optimize the grey model. The lateral deviation of the pantograph and catenary is predicted via the new model. Then the relationship between the effective length of the rod and operating mileage is inferred by combining the effective length theory with the Gamma process, as well as the pantograph-catenary contact reliability model is established according to reliability theory.

The results obtained show the impacts of uncertainty design parameters of pantograph rods on pantograph-catenary contact reliability index, and the results at crosswind speed of 0 ms⁻¹ and 5 ms⁻¹ are 5.0630 and 4.1442, respectively. The reliability decreases with the increasing crosswind speed, and can be greater than the reliability calculated for rod size degradation due to long-term use.

Most preceding works on pantograph-catenary contact reliability were based on principles of dynamics, without considering the pantograph-catenary relative motion. This research reveals the law of pantograph-catenary relative motion for uncertainty design parameters and crosswind, and quantifies the reliability from the angle of kinematics.

This paper proposes an intelligent fault diagnosis method, which aims to obtain the outstanding fault diagnosis results of the gearbox.

An intelligent fault diagnosis method based on energy entropy-weighted complementary ensemble empirical mode decomposition (EWCEEMD) and support vector machine (SVM) optimized by whale optimization algorithm (WOA) is proposed. The raw signal is first denoised by the wavelet noise reduction method. Then, complementary ensemble empirical mode decomposition (CEEMD) is used to generate several intrinsic mode functions (IMFs). Next, energy entropy is used as an indicator to measure the sensibility of the IMF and converted into a weight coefficient by function. After that, IMFs are linearly weighted to form the reconstruction signal, and several features are extracted from the new signal. Finally, the support vector machine optimized by the whale optimization algorithm (WOA-SVM) model is used for gearbox fault classification using feature vectors.

The fault features extracted by this method have a better clustering effect and clear boundaries under each fault mode than the unimproved method. At the same time, the accuracy of fault diagnosis is greatly improved.

In most studies of fault diagnosis, the sensitivity of IMF has not been appreciated. In this paper, energy entropy is chosen to quantify sensitivity. In addition, high classification accuracy can be achieved by applying WOA-SVM as the final classification model, improving the efficiency of fault diagnosis as well.

To address the shortcomings of the traditional back propagation (BP) neural network agent model, such as insufficient fitting accuracy and low computational efficiency, an improved method is proposed.

In this study, an improved sparrow search algorithm (ISSA) is developed to optimize the reliability calculation of the BP neural network (ISSA-BP) using an enhanced BP neural network model. The traditional sparrow search algorithm is enhanced by incorporating a golden sine strategy to improve its position-updating mechanism, thereby overcoming its tendency to converge prematurely to local optima. Additionally, an opposition-based learning strategy is integrated to explore the reverse solution around the optimal solution of the sparrow search algorithm, mitigating the risk of local optima.

The results of the test function demonstrate that the proposed method significantly enhances fitting accuracy while maintaining computational efficiency. Finally, by applying this approach to the metro bogie frame as a case study, the structural reliability of the bogie frame is evaluated using the Monte Carlo method, providing valuable insights for subsequent analysis and structural optimization.

The use of the surrogate model approach for structural reliability analysis significantly improves solution efficiency. Furthermore, the integration of ISSA with the BP neural network enhances both fitting accuracy and computational efficiency, demonstrating the superiority and practicality of the proposed method.

Aiming at the inefficiency of solving the Sobol index using the traditional mathematical analytical method, a Sobol global sensitivity analysis method is proposed.

In this paper, a support vector regression (SVR) surrogate model is constructed to solve the Sobol index. The optimal combination of SVR hyperparameters is obtained by using the improved beluga whale optimization (IBWO). Meanwhile, in order to solve the problem that Sobol sequences will form correlation regions in high-dimensional space leading to the uneven distribution of sampling points, a scrambled strategy is introduced in the Sobol sensitivity analysis using IBWO-SVR. Thus, the IBWO-SVR-SS sensitivity analysis model is established.

The results of two test functions show that the method further improves the accuracy of the sensitivity analysis. Finally, the first-order Sobol index and second-order Sobol index are solved by the IBWO-SVR-SS method using the metro bogie frame as an engineering example. Through the analysis results, the key design parameters of the frame and the design parameter combinations with more obvious coupling relationships are identified, providing a strong reference for the subsequent analysis and structural optimization.

Sobol sensitivity analysis using the surrogate model method can effectively improve the efficiency of the solution. In addition, IBWO is used for the optimization of the SVR hyperparameters to improve the accuracy and efficiency of the optimization, and finally, the correction of the Sobol sequence through the introduction of the disruption strategy also further improves the accuracy of the sensitivity analysis of Sobol.