An eccentric radial-based importance sampling method for reliability analysis

Abstract

By introducing a Beta-hypersphere centered at the origin of a standard normal space coordinate system and with reliability index Beta as the radius in the safety domain, traditional Radial-Based Importance Sampling (RBIS) method can improve the efficiency of the reliability analysis by avoiding the evaluation of the Limit State Function (LSF) of the safety sample located in the Beta-hypersphere. However, the evaluation of LSF in most safety samples outside the Beta-hypersphere cannot be avoided in the RBIS. In order to further improve the efficiency of the RBIS, an Eccentric RBIS (ERBIS) method is proposed by introducing an eccentric hypersphere. Compared to the Beta-hypersphere, the eccentric hypersphere is centered along the straight line connecting the origin of the coordinate system and the most probable failure point, and its radius is made larger than that of the Beta-hypersphere, so that it can envelope more safety samples than the Beta-hypersphere and avoid the excess evaluation of LSF. Meanwhile, an optimization model is established for obtaining the eccentric hypersphere locating the safety region and with the largest radius, and two strategies, including the sampling method and sequential decoupling method, are proposed for searching the optimal eccentric hypersphere. Fourteen numerical examples, a ten-bar truss structure example and an aero-engine turbine disk example are presented to demonstrate the advantages of the proposed ERBIS method. The presented examples show that almost 80%-100% LSF evaluations required in the RBIS method could be avoided in the proposed ERBIS method.