基于单元重要度分析的失效路径确定方法
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摘要
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.
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.
引文
[1]宋笔锋,张永苍.结构体系失效概率计算方法及应用[M].北京:国防工业出版社,2011.
[2]杨瑞刚.失效路径长度对结构系统安全可靠性的影响[J].安全与环境学报,2009,9(2):115-120.
[3]王攀,吕震宙,李贵杰.参数不确定情况下结构系统重要性分析[J].中国科学:技术科学,2011,41(11):1512-1518.
[4]SI S B,DUI H Y,CAI Z Q,et al.Integrated importance measure of component states based on the loss of the performance[J].IEEE Transactions on Reliability,2012,61(1):192-202.
[5]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用[J].建筑结构学报,2002,23(4):2-9.
[6]陈宇旋.基于可靠度的结构优化设计研究[D].广州:华南理工大学,2010.
[7]张雷明,刘西拉.框架结构能量流网络及其初步应用[J].土木工程学报,2007,40(3):45-49.
[8]张朝阳.桁架结构系统可靠度计算[D].北京:国防科技大学,2002.
[2]杨瑞刚.失效路径长度对结构系统安全可靠性的影响[J].安全与环境学报,2009,9(2):115-120.
[3]王攀,吕震宙,李贵杰.参数不确定情况下结构系统重要性分析[J].中国科学:技术科学,2011,41(11):1512-1518.
[4]SI S B,DUI H Y,CAI Z Q,et al.Integrated importance measure of component states based on the loss of the performance[J].IEEE Transactions on Reliability,2012,61(1):192-202.
[5]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用[J].建筑结构学报,2002,23(4):2-9.
[6]陈宇旋.基于可靠度的结构优化设计研究[D].广州:华南理工大学,2010.
[7]张雷明,刘西拉.框架结构能量流网络及其初步应用[J].土木工程学报,2007,40(3):45-49.
[8]张朝阳.桁架结构系统可靠度计算[D].北京:国防科技大学,2002.