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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 variables is a necessary work in engineering design and safety assessment.According to the reliability model of multi-failure modes often appearing in engineering practice, this paper proposes the global joint probability distribution of multi-dimensional response function of basic variables to multi-failure modes Importance measure index-Importance measure 1.At the same time, according to the characteristics of reliability design, this paper establishes two important measure indexes of the local probability distribution function of multi-dimensional response function in multi-failure mode, that is, Importance of response probability distribution measure - importance measure 2 and the importance of system failure probability measure - importance measure 3, the nature of the deduction, the similarities and differences between the three measures of importance and the scope of application, and given A standard method for solving three kinds of importance measures is shown. From the solving process of this standard method, it can be seen that importance measures 2 and 3 can be obtained simultaneously while solving the basic measure 1, which measures the importance of multidimensional response function functions That is to say, this standard method can provide more reference information for the designer without increasing the computation amount.Finally, with the numerical and engineering The example verifies the correctness and feasibility of the proposed index and method.