基于球面线抽样与数值积分的结构失效概率分析方法

STRUCTURAL RELIABILITY ANALYSIS ALGORITHM BASED ON SPHERICAL LINE SAMPLING AND NUMERICAL INTEGRATION

  • 摘要: 应用Monte Carlo方法(MCS)估计结构失效概率是基于可靠度理论评估结构安全性能的核心内容之一。但传统MCS方法在处理高维、稀有事件模拟等问题时,不同程度地会面临抽样数量急剧增大、性能退化等固有困难。为改善上述问题,首先基于多维球空间视角下结构失效概率的积分形式,结合数值积分技术,对其抽样+积分策略进行了说明。在此基础上,联合应用球面线抽样方法以及高斯积分策略,发展了估计结构失效概率的球面线抽样积分方法。该方法通过对随机空间径向每一高斯积分点所对应的球面相对失效概率(失效域面积占整个球面比值)进行球面线抽样以估计其数值,进而结合灵活的高斯积分形式将抽样结果沿径向积分,从而实现结构失效概率的高效求解。以三个典型算例为研究对象,对方法正确性和性能特点进行了验证探讨。结果表明:各算例失效概率Pf估计值相对标准MCS解的误差均低于1%,且方法能够适应2000维高维可靠度问题的计算求解;与当前多种流行算法相比,其具有良好的高维适应性和灵活拓展性。方法展现出优良的精度效率以及适用性,为实际结构可靠度的高效评估提供了方法参考。

     

    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.

     

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