FORM sensitivities to distribution parameters with the nataf transformation

Abstract

The Nataf transformation has been proven very useful in reliability assess- ment when marginal distributions are statistically known and linear correlation is sufficient for modeling the dependence between random inputs. Under the assump- tion that the use of FORM is appropriate for the problem of interest, it is often of importance to quantify how the FORM solution is sensitive to the distribution para- meters of the random inputs. Such information can be exploited in different contexts including optimal design under uncertainty. This chapter describes how sensitivities to marginal distribution parameters and linear correlation can be assessed numeri- cally in the context of FORM based on the Nataf transformation. The emphasis is on the accuracy of such sensitivities with no other approximations than the one due to numerical integration. In the presented examples, the accuracy of these sensitivi- ties is assessed w.r.t. reference solutions. The sensitivity to correlation brings useful information which are complementary to those w.r.t. marginal distribution parame- ters. High sensitivities may be detected such as illustrated in the context of stochastic crack growth based on the Virkler data set.