Structural reliability assessment through surrogate based importance sampling with dimension reduction

Highlights: • Rare event Probability estimation for reliability analysis. • High dimension input variables. • Dimension reduction techniques for high dimensional inputs of a performance function involved in a failure probability. • Metamodel based importance sampling coupled with a sufficient dimension reduction technique. We present a method for reliability assessment in extreme conditions from a numerical simulator through surrogate based importance sampling. As proposed in recent works in the literature, a Kriging surrogate is used to build an approximation of the limit state function and the optimal importance density. Our contribution is then the use of a sufficient dimension reduction method which enables the construction of the limit state function metamodel in lower dimension. The so called augmented failure probability and correction factor are recast in this dimension reduction framework. Simple strategies for metamodel refinement in the dimension reduction subspace are described and, in the case of Gaussian inputs, a computationally efficient MCMC scheme aimed at sampling the quasi-optimal importance density is presented. The case of non-Gaussian inputs is also laid out and it is argued and demonstrated through simulations that this approach can reduce the number of calls to the computer model, which is a crucial factor in reliability analysis. Advantages of this method are also supported by numerical simulations carried on an industrial case study concerned with the extreme response prediction of a wind turbine under wind loading.