Purpose Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components. Design/methodology/approach First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory. Findings Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods. Practical implications In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements. Originality/value The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Purpose In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem. Design/methodology/approach The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination. Findings The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively. Originality/value Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit (EMU) car body, it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties. To address this issue, a multi-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar. A hybrid optimization strategy combining the design of experiment (DoE) sampling and non-linear programming by quadratic lagrangian (NLPQL) is presented to deal with the design optimization model. To characterize the effect of time on the structural performance of the torsion bar, the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints. Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar. A physical programming approach is used to improve the designer's preference and to make the optimization results more consistent with engineering practices. Moreover, the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

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