Metamodel-based importance sampling for structural reliability analysis

► The use of metamodels reduces the computational cost of reliability analyses.
► Surrogate-based reliability methods do not enable error quantification.
► Metamodel-based importance sampling enables error quantification.
► The failure probability is estimated onto the actual limit-state function.
► The accuracy of the estimate is measured in terms of a variance of estimation.

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate computational model (e.g.   a finite element model). In this respect simulation methods which may require 103−6103−6 runs cannot be used directly. Surrogate models such as quadratic response surfaces, polynomial chaos expansions or Kriging (which are built from a limited number of runs of the original model) are then introduced as a substitute for the original model to cope with the computational cost. In practice it is almost impossible to quantify the error made by this substitution though. In this paper we propose to use a Kriging surrogate for the performance function as a means to build a quasi-optimal importance sampling density. The probability of failure is eventually obtained as the product of an augmented probability computed by substituting the metamodel for the original performance function and a correction term which ensures that there is no bias in the estimation even if the metamodel is not fully accurate. The approach is applied to analytical and finite element reliability problems and proves efficient up to 100 basic random variables.