A new efficient method for estimating failure probability function

一种新的失效概率函数高效求解方法

¹ School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
² National Key Laboratory of Shock Wave and Detonation Physics, Mianyang 621900, China
³ National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, China
⁴ School of Aerospace Engineering, Xiamen University, Xiamen 361005, China

Received: 25 September 2024

Abstract

Estimation of the failure probability function plays a crucial role in reliability-based optimization design. However, efficiently and accurately estimating the failure probability function remains a challenge. Compared to the traditional double-loop Monte Carlo simulation(DMCS) method, the single-loop probabilistic reanalysis (PRA) method can alleviate the computational dependence of the failure probability function on the distribution parameters of input variables. Nevertheless, for problems involving small failure probabilities, the computational cost of PRA is still impractical for engineering applications. Therefore, to further improve the computational efficiency of the failure probability function, this paper combines importance sampling-based subset simulation(SS-IS) with the PRA method, and proposes a novel SS-IS-based PRA(SS-IS-PRA) method. The proposed method transforms the final small failure probability function into a product of a series of larger conditional failure probability functions and then estimates all conditional failure probability functions simultaneously with a set of input-output samples by virtue of the advantages of the PAR method. Furthermore, considering that the design points under different distribution parameters are normally different, a new strategy for constructing the importance sampling density function in the SS-IS-PAR method is proposed based on the idea of mixed importance sampling. Finally, two examples verify the effectiveness and efficiency of the proposed SS-IS-PRA method.

摘要

失效概率函数的求解在基于可靠性的优化设计中具有重要意义。然而, 如何高效且准确地求解失效概率函数依旧面临巨大的挑战。相对于传统的双层蒙特卡洛模拟(DMCS)方法, 单层概率重分析(PRA)方法虽然能够解除求解失效概率函数的计算量对输入变量分布参数的依赖性, 但对于小失效概率问题, 计算代价依然难以被工程实际所接受。因此, 为了进一步提高失效概率函数的求解效率, 从抽样方法入手, 将子集模拟重要抽样(SS-IS)与PRA方法相结合, 提出了一种基于SS-IS的PRA(SS-IS-PRA)方法。该方法能够将最终的小失效概率函数求解转化为一系列较大条件失效概率函数的乘积, 并借助于PRA的优越性采用一组输入-输出样本同时估计所有的条件失效概率函数。另外, 考虑到不同分布参数下的设计点不同, 还提出了一种新的基于混合重要抽样的重要抽样密度函数构造策略。通过2个算例验证了SS-IS-PRA方法的有效性和高效性。