A multi-fidelity boundary element method for structural reliability analysis with higher-order sensitivities

Abstract

A novel multi-fidelity modelling methodology for structural reliability analysis using the Boundary Element Method (BEM) with an Implicit Differentiation Method (IDM) is presented. The higher-order sensitivities of the elastostatic BEM equations with respect to changes in several geometric variables have been derived for the first time for use with the IDM for conducting reliability analyses with the Second-Order Reliability Method (SORM), a more accurate alternative to FORM for problems with non-linear limit state functions. Multi-fidelity formulations involving the IDM have also been derived for the first time, making use of the metamodeling technique Kriging. The use of multi-fidelity modelling enables the creation of a model that has similar accuracy to a high-fidelity model, but with a computational cost similar to that of a low-fidelity model. The IDM is validated through a numerical example for which the analytical solution is known. A further two examples featuring an I-beam section and a triangular support bracket with a large number of variables are also investigated. Overall, it has been shown that the proposed IDM/multi-fidelity modelling methodology significantly improved the efficiency and accuracy of the reliability analyses when applied to complex problems involving a large number of random variables under high levels of uncertainty.