Two multifidelity kriging-based strategies to control discretization error in reliability analysis exploiting a priori and a posteriori error estimators. (1st January 2023) - Mell, Ludovic; Rey, Valentine; Schoefs, Franck
Highlights: We propose two methods to control the discretization error introduced by the finite element method during the construction of kriging-based metamodels that will be used for the estimation of probability of failure by Monte Carlo samplig. AGSK-MCS (Adaptive Guaranteed State Kriging - Monte Carlo Sampling) relies discretization error bounds on the performance function that can be obtained from a posteriorierror estimators. This algorithm only uses learning points for which error bounds enable to guarantee the state (safe of failure) to build the kriging-based metamodel. This meta-model is built from computations done on 2 different mesh sizes and is therefore a multi fidelity meta model. AMSK-MCS (Adaptive Mesh Size Kriging - Monte Carlo Sampling) is a method that takes advantage of the mesh convergence rate of the finite element problem to compute a mesh size parameterized Kriging metamodel (AMSK). It enables to compute the probability of failure at any mesh size thus allowing a reliability-based mesh convergence study. By tending the mesh size to 0, it offers the possibility to compute an estimation of the probability of failure no polluted by the discretization error. Abstract: This paper presents two approaches to tackle the issue of discretization error in the reliability assessment of structures. The first method (AGSK-MCS for Adaptive Guaranteed State Kriging Monte Carlo Sampling) uses discretization error bounds to guarantee the state safe or failed of the points used to build the Kriging metamodel of the limit state function. Two kriging metamodels interpolating lower and upper bounds can be constructed. These metamodels allow to compute discretization error bounds on the probability of failure through Monte Carlo sampling, which can then be used to validate the choice of the mesh. However, discretization error bounds are not available for any solver and any mechanical problem. In that case, a Mesh Size parameterized Kriging (MSK) metamodel can be used to check mesh convergence of the probability of failure. First, finite element simulations are spread on different mesh sizes. Second, the metamodel is used to compute the probability of failure for a given set of mesh sizes using Monte Carlo estimation. The mesh convergence of the probability of failure can be checked and may guide the user toward remeshing. These two strategies are illustrated on two 2-D mechanical problems.