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针对桥式起重机主梁可靠性计算中存在的多维小失效概率问题,引入了马尔科夫链蒙特卡罗子集模拟法。该方法通过选择合适的中间失效事件,进而可以将较小的失效概率用一系列较大的中间失效事件条件概率的乘积来表达,失效域内的样本采用Metropolis-Hastings(M-H)抽样方法生成。文中给出了子集模拟法求解多维小失效概率的基本步骤,并通过算例验证了所提方法的可行性和有效性。数值算例和工程算例的结果均表明,在计算结果近似相同的情况下,子集模拟法比直接蒙特卡罗法计算效率提高了近90%,其为多维小失效概率的起重机金属结构可靠性计算提供了一个有效方法。
Aimed at the multi-dimensional small failure probability in the reliability calculation of girder of overhead traveling crane, Markov chain Monte Carlo simulation method is introduced. By selecting appropriate intermediate failure events, the method can express the smaller failure probability as a series of products with larger probabilities of intermediate failure events. Samples in the failure domain are generated by the Metropolis-Hastings (M-H) sampling method. In this paper, we give the basic steps of sub-set simulation to solve the small multi-dimensional failure probability, and verify the feasibility and effectiveness of the proposed method through examples. Numerical results and engineering examples show that the sub-set simulation method can improve the computational efficiency by nearly 90% compared with the direct Monte-Carlo method when the calculated results are approximately the same, which is reliable for the crane with a small multi-dimensional probability of failure Sex calculation provides a valid method.