Reliability Analysis Based on Bregman Distances
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摘要: 针对概率结构可靠性问题,引入Bregman距离函数,建立了基于同伦算法(HM)的可靠性分析模型.利用极限状态方程,将可靠性指标求解转化为一个非线性约束优化问题.结合同伦思想的基本理论和Bregman距离函数,构造同伦方程组,采用路径跟踪算法对该方程组进行求解.通过相应的数值算例探讨了不同函数形式以及不同程度非线性问题的可靠性计算,并与其他方法计算结果进行了对比,分析结果表明该模型能够有效求解概率结构可靠性问题.Abstract: A reliability analysis model based on the homotopy algorithm was established to address probabilistic reliability problems of uncertain structures through introduction of Bregman distances. By means of the limit state equations, solution of the reliability index was transformed to a nonlinear constrained optimization problem. According to the homotopy theory and the Bregman distances, the system of homotopy equations was constructed and solved with the path-tracking algorithm. The reliability calculations for different types of functions and different degrees of nonlinear problems were discussed via numerical examples, and the results were compared with those out of previous methods. The results show that the proposed analysis model solves the probabilistic reliability problems of uncertain structures with high efficiency and good accuracy.
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Key words:
- homotopy algorithm /
- Bregman distance /
- reliability /
- path-tracking algorithm
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