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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.

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.

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.

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.

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.

This study investigates the fitting techniques for notch fatigue curves, seeking a more reliable method to predict the lifespan of welded structures.

Building on the fatigue test results of butt and cruciform joints, this research delves into the selection of fitting methods for the notch fatigue curve of welded joints. Both empirical formula and finite element methods (FEMs) were employed to assess the notch stress concentration factor at the toe and root of the two types of welded joints. Considering the mean stress correction and weld misalignment coefficients, the notch fatigue life curves were established using both direct and indirect methods.

An engineering example was employed to discern the differences between the direct and indirect approaches. The findings highlight the enhanced reliability of the indirect method for fitting the fatigue life curve.

While the notch stress approach is extensively adopted due to its accurate prediction of component fatigue life, most scholars have overlooked the importance of its curve fitting methods. Existing literature scantily addresses the establishment of these curves. This paper offers a focused examination of fatigue curve fitting techniques, delivering valuable perspectives on method selection.

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.

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.

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.

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.