Efficient Evaluation of Reliability-Oriented Sensitivity Indices

Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures

“…Advanced samplingbased estimation schemes for these first-order Sobol indices have been investigated in [36] but still require a lot of simulations to achieve convergence. Another efficient estimation procedure using SMC has been proposed recently by [31] as the first-order S 1 Y >s i can be rewritten as follows:…”

“…Estimationδ for all the inputs even if they give the same ranking asη i . It is due to the fact that the failure probability is too low as underlined in [31] and thus limits the use of ROSA Sobol indices in a sensitivity analysis context. As in the previous example, variability of obtained estimates is non negligible.…”

“…Various ROSA methods have been proposed. First, several global sensitivity methods have been developed: for instance, a failure probability-based method [14], variance decomposition-based methods [31,36,40,41], a method based on density perturbation [26] or, more recently, a quantile-oriented sensitivity approach [8]. Local sensitivity method (often based on partial derivatives of the failure probability with respect to distribution parameters) are also available, see for instance [12] for a comprehensive review of these methods.…”

“…In this paper we propose two new target and conditional ROSA moment-independent indicesη i and δ f i in order to alleviate some of the limitations of classical variance-based indices [31]. These proposed indices and variance-based indices require exactly the same simulation budget: for both methods, the entire simulation budget is devoted to sampling from the input distribution conditional on failure for which a variety of standard methods can be used, for instance adaptive importance sampling, subset simulations or, if the code is too expensive, surrogate models.…”

“…Y >s i to tend to zero when the failure probability is too low. Perrin and Defaux[31] underlined this limit for the use of Sobol indices in a sensitivity analysis context. The proposed indices δ f i andη i do not suffer from ROSA Sobol limitations as the input random variables could be dependent even if the interpretation of the indices may remain complicated.…”