Spherical Layer Sampling Method for Probability Evaluation on Structural Failure

When the traditional Monte Carlo sampling method is applied to complex reliability problems such as small failure probability, there are some shortcomings such as low efficiency and limited accuracy. To solve this problem, a spherical layer sampling analysis method is developed. Firstly, by dividing the distance and direction parameters, the standard normal random vector is reconstructed, and its standard normality and mutual independence are verified. Thereafter, based on a layered sampling strategy, the standard normal space with the radius beyond first order reliability index is divided into multiple spherical layers, which are then sampled by the reconstructed vector layer by layer. Combined with the full probability formula, a spherical layer sampling algorithm is developed to estimate the structural failure probability. Finally, three typical examples are taken as objects of interest, and the performance of the algorithm is verified through comparative analysis. The results show that, the proposed algorithm has high sampling efficiency and convergence performance, and the error of calculation results is within 3%. Compared with other algorithms, its estimation variance is smaller, and it can effectively solve complex reliability problems such as multiple design check points. The algorithm has advantages in sampling efficiency, scope of application, and stability, and is more suitable for solving and analyzing the reliability of actual complex structures.