Augmented weighted low-discrepancy simulation with hyper-spherical ring for general reliability analysis

Abstract

Due to the increasing complexity of modern engineering systems, conventional reliability methods encounter significant challenges in dealing with high-dimensional stochastic problems. This study presents a hyper-spherical ring-augmented weighted low-discrepancy simulation (HSR-WLDS) method, which expands the applicability of original WLDS to high-dimensional reliability problems. Inspired from the geometric insights observed in the independent standard normal space, the proposed method innovatively integrates the well-established WLDS with a hyper-spherical transformation. This strategy leverages the rotational symmetry inherent in the joint probability density function (PDF), ensuring that the sample weights are solely dependent on the radius, thereby effectively mitigating the impact of extreme weights in high-dimensional spaces. Furthermore, by utilizing the important ring to concentrate computational efforts on critical areas, this method effectively mitigates computational complexity and enhances efficiency for estimating failure probabilities. The performance of the proposed method is verified through four numerical examples, encompassing highly nonlinear limit state function (LSF), multiple failure modes, and both component and system high-dimensional problems, as well as an engineering slope stability example. The results demonstrate the robustness and effectiveness of the proposed method, highlighting its superiority in high-dimensional reliability problems with improved computational efficiency.