Abstract:
In reliability theory, the failure probability evaluation is one of the core contents of structural safety performance assessments, and this is often achieved by Monte Carlo simulation (MCS). However, the traditional MCS may face inherent difficulties of huge sampling workload and precision degeneration (also known as the curse of dimension) to some extent when evaluating the high-dimensional and low-level failure probability events. To tackle this issue, the idea of sampling method hybridized with numerical integration is illustrated firstly upon the hyper-spherical integral form of failure probability and upon numerical integration techniques. Thereafter the spherical line sampling method is employed and combined together with the Gaussian integration technique, which forms the hybrid method for structural failure probability estimation. To execute the calculation, the method initially estimates the relative failure probability on the hyper-spherical surface with the designated radii via spherical line sampling. And the designated radii are all determined by the Gaussian quadrature points. Then with the flexible Gaussian integration form, the failure probability evaluation is finally achieved by the integration of sampling results along the radius direction. In order to validate the method, three cases are used to check the applicability for the reliability analysis. The results reveal that the case estimation errors are all within 1%, and that the calculation operates well for 2000-dimensional reliability problems. Moreover, in comparison with some popular MCS methods, the evaluation by the method presented has good precision, high-dimensional applicability and flexible solving mechanism. On account of the performance exhibited, the method provides a feasible solution for the efficient assessment of structural reliability.