基于单元重要度分析的失效路径确定方法

Determining the failure path based on the element importance of the structure

在大型复杂结构中枚举失效路径为NP-hard问题,工程可靠度分析及优化只能关注结构中具有代表性的部分失效路径。传统失效路径搜索方法多基于最弱链条理论,首失效单元取决于单元可靠度,而不是其失效影响,找到的可能是冗余单元,对应的失效路径在结构体系失效模式中不具代表性。本文依据单元失效导致的结构能量变化梯度和各单元传递荷载两种方法分别确定各单元在结构体系失效中的重要度,由单元重要度确定系统的首失效单元及其失效路径。分析表明:基于关键单元得到的失效路径更具代表性,因为其失效概率远大于传统失效路径的失效概率。通过单元近似传递荷载判定的最关键单元与单元对应的能量变化梯度得到的结果一致,是一种合理、便捷的简化近似分析方法。

It is an NP-hard problem to enumerate all of failure paths of a large complex structure. Most failure paths are neglected in structure reliability analysis and optimization except some typical failure paths which have bigger or biggest failure probabilities. Classical methods to determine the failure paths are based on the theory of the weakest chain. The first failure element is not determined by its serious harms but its own failure probability. The redundant elements may be selected as the first failure element, and its failure path is not typical, Two rules are applied to judge whether the element is important to lead structure failure. The degree of energy change caused by an element failure and the element transferring load. The most important element is selected as the first failure element to search the failure path. Case study shows that the failure path based on the element importance is more typical because its failure probability is bigger than the result using the classical method. The key elements selected by two rules are same. It mains the element transferring load is a reasonable and simple method to determine the key element.