多失效模式下基本变量的重要性测度及其解法  

Importance measures of basic variable under multiple failure modes and their solutions

作　　者：崔利杰[1] 吕震宙[1] 赵新攀[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《中国科学：物理学、力学、天文学》2010年第12期1532-1541,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:10572117;50875213);新世纪优秀人才支持计划(编号:NCET-05-0868);航空基金(编号:2007ZA53012);国家高技术研究发展计划(编号:2007AA04Z401);科技重大专项基金(编号:2009ZX04014-015-03)资助项目

摘　　要：基本变量的重要性分析是工程设计及安全评估的一项必要工作.针对工程实际中经常出现的多失效模式可靠性模型,提出了基本变量对多失效模式下多维响应功能函数全局联合概率分布的重要性测度指标——重要性测度1.同时针对可靠性设计的特点,建立了多失效模式下基本变量对多维响应功能函数局部概率分布的两种重要性测度指标,即基本变量对失效域内多维响应概率分布的重要性测度——重要性测度2和对系统失效概率的重要性测度——重要性测度3,推导了其性质,比较了3种重要性测度的异同和适用范围,并给出了一种求解3种重要性测度的标准方法,从该标准方法的求解过程可以看出,在求解基本变量对多维响应功能函数重要性测度1的同时可求得重要性测度2和3,也即在不增加计算量的同时,该标准方法可为设计人员提供更多的参考信息.最后,以数值和工程算例验证了所提指标和方法的正确性和可行性.Importance analysis of basic variable is necessary for engineering design and probability safety assessment. For reliability model with multiple failure modes commonly used in engineering practice, an importance measure of the basic variable on the global joint probability distribution of multiple response performance functions is proposed and it is named as the importance measure 1. By taking the specialties of the reliability model into consideration, two importance measures are established to measure the effects of the basic variable on the local joint probability distribution, i.e. the importance measure of the basic variable on the local joint probability distribution in failure domain and that on system failure probability, which are named as the importance measure 2 and the importance measure 3 respectively. The properties of three importance measures are analyzed and verified, and their similarities, dissimilarities and applicability are discussed, too. A standard computational method is given to solve three importance measures, from which it is shown that the importance measures 2 and 3 are by products of the importance measure 1. Then more reference information can be provided to designer without adding computational cost by the given standard solutions. Finally, a numerical example and an engineering example are used to demonstrate the accuracy and feasibility of the proposed importance measures and their solutions.

关 键 词：重要性测度 多维响应功能函数模型 全局概率分布 局部概率分布 

分 类 号：TB114[理学—概率论与数理统计]