A Stochastic Collocation Method for Uncertainty Analysis of Fatigue Damage Prognosis

Abstract

This article proposes a stochastic collocation method to investigate the uncertainty quantification in fatigue damage prognosis where experimental data are limited and only interval bounds on uncertain parameters are given. The method derived from tensor-products or sparse grids consists in a Galerkin approximation in random space, requires the use of structured collocation point sets and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. The distribution of remaining useful life can be acquired by dividing each interval into several small parts and assuming the corresponding random variable obeys uniform distribution in the small range. Compared with Monte Carlo method and interval arithmetic, this approach is much more efficient, time-saving and gets more accurate predictions. An experimental investigation of fatigue life prediction of a metallic plate with a central crack is presented to demonstrate the efficiency and effectiveness of the proposed method.