Efficient variance-based reliability sensitivity analysis for Monte Carlo methods

Abstract

In the application of state-of-the-art reliability methods, often the quantification of the influence of the stochastic parameter properties with respect to the estimated failure probability is requested. In an iterative improvement of the investigated structure or system, this is usually done within the reliability-based design approach. In the framework of an uncertainty quantification, often classical variance-based sensitivity measures are used to quantify the global influence of the input variation to the variation of the interesting output quantities. This global variance-based approach gives as well a good estimate of the input variable influence on the computed failure probability, as long as the investigated limit state function is almost linear and the input variables are almost normally distributed. For strongly nonlinear analysis for example investigating stability problems of engineering structures, the classical global variance-based approach might lead to a wrong quantification of the input variable importance with respect to the failure probability, especially in case of multiple failure regions.

In this paper, a Monte Carlo based approach for the quantification of the importance of the scattering input parameters with respect to the failure probability is presented. Using the basic idea of the alpha-factors of the First Order Reliability Method, this approach was developed to analyze correlated input variables as well as arbitrary marginal parameter distributions.

Based on an efficient transformation scheme using the importance sampling principle, only a single analysis run by a plain or variance-reduced Monte Carlo method is required to give a sufficient estimate of the introduced parameter sensitivities. Several application examples are presented and discussed in the paper.