模糊分布参数条件下结构系统的近似效应分析

针对结构系统中随机变量的分布参数具有不确定性的问题, 采用模糊数来描述分布参数的主观不确定性, 并且利用隶属度来衡量主观不确定性的大小. 在不同隶属度水平下, 分别建立了输出响应和失效概率的主效应和总效应模型, 研究了两种模型和隶属度水平之间的关系, 并且给出分布参数不确定性的平均效应指标. 针对所提指标计算量大的问题, 通过对输出响应的各阶矩进行一阶泰勒展开, 建立了两种指标的计算方法. 算例结果验证了所提指标的合理性和所提方法的高效性.

AN APPROXIMATE EFFECT ANALYSIS OF STRUCTURAL SYSTEM WITH FUZZY DISTRIBUTION PARAMETERS

In order to analyze the effect of the epistemic uncertainty of the random input variables’ distribution parameters on the structure system,the fuzzy variables are introduced to describe the epistemic uncertainty and the membership levels are employed to measure the degree of the epistemic uncertainty.Two effect indicators, main effect and total effect,for the output response and failure probability are proposed at each possibility level,respectively,and then their relationships with the membership levels are investigated in detail.Finally the expected effect indicators are presented to define the effect of each parameter on the system.In order to reduce the computational cost of the proposed indicators,a new method is proposed by the Taylor expansion for the moments of the output response.Three examples are utilized to demonstrate the reasonabihty of the proposed indices and the efficiency of the proposed method.