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结构体系的失效概率数学上可以表示为结构体系失效域上联合概率密度函数的积分,一般情况下很难直接积分求解。近几十年来,结构体系可靠度分析一直是可靠度领域的一个研究热点,人们提出许多方法,如:Monte-Carlo法、重要性抽样法与界限法和概率网络估算技术等,这些算法在求解精度、计算效率、收敛性和易使用性等方面是不同的。本文采用优化算法(改进的可行方向法、序列线性规划和序列二次规划法)进行串联体系可靠度分析,并且与其他算法(HL-RF法、Monte-Carlo法和重要性抽样法)的结果以及一些精确解进行了比较。结果表明,相对于其他算法,基于优化算法的可靠度分析适用性广,在收敛性和健实性等方面具有明显的优势。
The probability of failure of a structural system can be expressed mathematically as the integral of the joint probability density function on the failure domain of a structural system, which is difficult to solve by integral solution in general. In recent decades, reliability analysis of structural systems has been a hot area of research in the field of reliability. Many methods have been proposed, such as Monte-Carlo method, importance sampling method, boundary method and probability network estimation technique, Accuracy, computational efficiency, convergence and ease of use are different. In this paper, the reliability of the series system is analyzed by using the optimization algorithm (improved feasible direction method, sequence linear programming and sequence quadratic programming method), and the results of other series of algorithms (HL-RF method, Monte-Carlo method and importance sampling method) And some exact solutions are compared. The results show that, compared with other algorithms, reliability analysis based on optimization algorithm has wide applicability and has obvious advantages in terms of convergence and robustness.