Time-dependent mechanism reliability analysis based on envelope function and vine-copula function

Abstract

Time-dependent reliability analysis is an important and challenging issue due to the time-dependent motion and loadings of a mechanism. In this paper, a general framework and corresponding methods are proposed to deal with the time-dependent reliability analysis of a mechanism effectively. The envelope function is used to estimate the finite expansion points, which converts the time-dependent reliability problem to the time-independent reliability problem under the general probability distribution. The covariance matrix is then derived with the vine-copula function to describe the correlation of the performance at the obtained expansion points. With the covariance matrix, the joint probability density function (PDF) is acquired based on the kernel density estimation (KDE) method. The time-dependent reliability is finally estimated by the integral. The case study with different conditions is provided to validate the efficiency and accuracy of the proposed approach.