Probabilistic analysis based on combination of polynomial chaos and smart truncation schemes: application to fatigue crack growth.

Abstract

This work present an original uncertainty propagation method, called sprase-PCE, developed to assess the reliability of a cracked plate with spatially varying uncertain mechanical properties. It combines regression techniques to compute the unknown coefficients of the PCE-based metamodel and an efficient truncation scheme which uses prior available second order statistical moment information to identify the most important components of the polynomial chaos basis on the model responses of interest. In this way, the PCE coefficients corresponding to the components with weak effects are discarded, and the computational efforts devoted to solving the regression problem is significantly reduced. An economy index is introduced in the form of a ratio between the respective cardinalities of the sparse and the full chaos polynomial basis, which allows us to objectively assess the computational cost saving obtained by the proposed truncation scheme based on second moment information.