An advanced mixed-degree cubature formula for reliability analysis

Abstract

Efficient assessment of mechanical system reliability subject to arbitrary probability distributions and dependent input parameters signifies an important yet challenging task. To tackle this problem, this study proposes a new moment-based method for reliability analysis of complex mechanical systems which incorporates the advanced mixed-degree cubature formula and vine copula function. To start with, a method integrating the vine copula function and Rosenblatt transformation is developed for transferring the uncertainty with dependent random variables, in which the vine copula is applied for depicting the correlation between random variables. An advanced mixed-degree cubature formula is then established for calculating statistical moments of performance function, which enables to capture sufficient uncertainty information of variables after rotating integral node. The Hermite polynomial model is adopted here to reconstruct the probability distribution of performance function with the statistical moments. To demonstrate the effectiveness of the proposed method, four illustrative examples are implemented in this study, in which Monte Carlo Simulation (MCS) and dimension-reduction techniques, are performed for comparisons. The results show that the proposed method can handle multi-dimensional correlation effectively and well balance computational accuracy and efficiency for both statistical moments and probability distribution evaluations.