Conditional reliability analysis in high dimensions based on controlled mixture importance sampling and information reuse

In many contexts, it is of interest to assess the impact of selected parameters on the failure probability of a physical system. To this end, one can perform conditional reliability analysis, in which the probability of failure becomes a function of these parameters. Computing conditional reliability requires recomputing failure probabilities for a sample sequence of the parameters, which strongly increases the already high computational cost of conventional reliability analysis. We alleviate these costs by reusing information from previous reliability computations in each subsequent reliability analysis of the sequence. The method is designed using two variants of importance sampling and performs information transfer by reusing importance densities from previous reliability analyses in the current one. We put forward a criterion for selecting the most informative importance densities, which is robust with respect to the input space dimension, and use a recently proposed density mixture model for constructing effective importance densities in high dimensions. The method controls the estimator coefficient of variation to achieve a prescribed accuracy. We demonstrate its performance by means of two engineering examples featuring a number of pitfall features such as strong non-linearity, high dimensionality and small failure probabilities (10⁻⁵to10⁻⁹).