Reliability Sensitivity Analysis by the Axis Orthogonal Importance Sampling Method Based on the Box-Muller Transformation

Abstract

The axis orthogonal importance sampling method proves to be one version of efficient importance sampling methods since the quasi-Monte Carlo simulation is its basic ingredient, in which it is now a common practice to transform low-discrepancy sequences from the uniform distribution to the normal distribution by the well-known inverse transformation. As a valid transformation method for low-discrepancy sequences, the Box-Muller transformation is introduced into the axis orthogonal importance sampling method and compared with the inverse transformation in this paper for structural reliability sensitivity analysis. Three representative quasi-random sequences with low discrepancy are presented to generate samples following the target distribution and explore the interaction with the transformation method, which is used as a sample plan along the tangent plane at the most probable failure point in the axial orthogonal importance sampling for structural reliability analysis and reliability sensitivity analysis. The numerical experiments show that the reliability sensitivity analysis method by means of the Box-Muller transformation is a good alternative to the inverse transformation to generate samples from low-discrepancy sequences to the normal distribution. In particular, the scheme of the Box-Muller transformation combined with the Sobol sequence needs fewer samples with more accuracy and is more applicable for solving reliability sensitivity analysis in various nonlinear problems.