Failure Probability Assessment using co-Kriging Surrogate Models

Abstract

Industries, among them the aeronautics industry, have to justify the reliability of the structures they design. Static and modal analyzes are the classical methods to validate designs. Nowadays, these are not sufficient anymore, and the damage tolerance approaches, characterizing the severity of a flaw occurring in the designed assembly, are thenceforth commonly used. Various methods such as boundary element models or finite elements models (classical or extended formulation) can be applied. These methods may introduce conservatism into the model that may be an issue with respect to some of the design constraints (light-weighting, final cost...). Moreover, they are often computationally expensive.This paper proposes a methodology for the computation of sudden failure probability applied to industrial assemblies at a reasonable computational cost while keeping a similar level of accuracy considering the computed probabilities. To that purpose, two strategies are coupled. First, a sub-modeling strategy is set up. It allows to reduce the restitution time by considering separately all the critical zones. The critical areas are identified through a dedicated methodology based on the assessment of maximal principal stresses. For each of them, a surrogate model is built based on a limited number of numerical simulations. Even though this solution allows non negligible gain on the restitution time, a co- Kriging multi-fidelity approach is also applied. The surrogate model is built thanks to the combination of two sampling databases that are computed using XFEM simulations with different levels of refinement. Thanks to this methodology, a response with an equivalent level of accuracy is built-up. The failure probability is finally determined by running a large Monte-Carlo analysis based on the previously built surrogate models. The gains, limitations and perspectives to improve the current methodology are discussed.