Time-variant reliability analysis using polynomial chaos expansion

Abstract

An accurate structural reliability analysis throughout time needs to consider the random character of the material properties, geometry and loadings as well as their time variability. Such assessment can be done using time-variant reliability methods. However, progress in this field has been stagnant mainly because of the extremely high computational cost in stochastic analysis with timedependent limit states and the error that would rise in nonlinear cases. A method based on the polynomial chaos (PC) expansion is proposed to address these issues. First, the time-variant reliability analysis is transformed into a time-invariant one by discretizing the time-dependent limit state over the structure lifetime into instantaneous limit states. Then, a principle component analysis (PCA) is performed followed by PC expansions of the retained components. The complex time-dependent limit state function is therefore substituted by a polynomial surrogate model on which Monte-Carlo simulation (MCS) can be performed at a lower computational cost. Three examples are dealt with to demonstrate the efficacy of the proposed method.