Structural reliability analysis by univariate decomposition and numerical integration

This paper presents a new and alternative univariate method for predicting component reliability of mechanical systems subject to random loads, material properties, and geometry. The method involves novel function decomposition at a most probable point that facilitates the univariate approximation of a general multivariate function in the rotated Gaussian space and one-dimensional integrations for calculating the failure probability. Based on linear and quadratic approximations of the univariate component function in the direction of the most probable point, two mathematical expressions of the failure probability have been derived. In both expressions, the proposed effort in evaluating the failure probability involves calculating conditional responses at a selected input determined by sample points and Gauss–Hermite integration points. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure.