Adaptive Approximation of the First-crossing PDF for Time-variant Reliability Analysis

An adaptive probability distribution model of first-crossing time point is proposed for the time-varying reliability of mechanical products over their whole life cycle, which can obtain the evolution of reliability during the life cycle and provide a tool for reliability analysis and design of mechanical products over their whole life cycle. To address the difficulty of estimating the first crossing rate model in the traditional first-crossing time-variant reliability method. Firstly, an adaptive surrogate model is proposed for the first-crossing time point based on support vector regression. Secondly, Latinized partially stratified sampling (LPSS) is employed to estimate the fourth origin moments of first-crossing time point surrogate model. The adaptive learning function is constructed by combining the uniform design with the nearest point to the first-order moment of the surrogate model as the center. Then, the maximum error of each order moment of two adjacent iterations is used as the convergence condition to build the optimal surrogate model for the first-crossing time point. Finally, based on the optimal surrogate model, the probability distribution function of the first-crossing time point is solved using the kernel density function to obtain the time-variant reliability trend during the product life cycle. The effectiveness of the proposed method is verified by three examples. © 2024 Chinese Mechanical Engineering Society. All rights reserved.