多失效模式下的模式重要性测度及解法

针对工程中普遍存在的多失效模式系统可靠性问题,为提高或改进设计,需要研究失效模式对系统不确定性的影响因素。基于前人提出的基本变量重要性测度,提出了三种模式重要性测度:模式对系统失效概率的重要性测度、模式对系统响应量概率分布的重要性测度和模式功能函数与系统功能函数的相关系数。这三种模式重要性测度从不同的角度反映了失效模式对多模式系统不确定性的贡献。初步讨论了三种模式重要性测度的性质以及其所服务的工程目的,同时给出了模式重要性测度的标准数字模拟求解方法。根据本文提出的模式重要性测度,可以得到模式对系统不确定性的贡献的排序,从而为可靠性设计提供指导。给出了数值算例和工程算例,以说明所提出的模式重要性测度的合理性和可行性。

Mode importance measures under multiple failure modes and their solutions

For structural system with multiple failure modes extensively present in engineering practice,effects of failure modes on the system uncertainties need to be considered,upon which the design work can be improved.Enlightened by the concept of importance measures for basic variables,three mode importance measures are established to reflect the effects of failure modes on the system uncertainties,i.e.importance measures of failure modes on the system failure probability,importance measures of failure modes on the probabilistic distribution of the system response,and the correlation coefficient between the single failure mode and the system.Properties of these three mode importance measures are discussed,as well as the numerical simulation method employed to solve them.Based on the theories proposed here,the ranking of the contributions of failure modes can be obtained,thus providing design guidelines for engineers.Numerical and engineering examples are probed into later,to demonstrate the feasibility and rationality of the proposed mode importance measures.