混合变量情况下基本变量对可靠度取值特征的影响分析  

Exploring Importance Analysis of Fuzzy Memberhship Functions for Structural System with Mixed Uncertain Variables

作　　者：李维[1] 吕震宙[1] 李璐祎[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《西北工业大学学报》2011年第3期335-340,共6页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(NSFC10572117;50875213);新世纪优秀人才支持计划(NCET-05-0868);航空基金(2007ZA53012);民口863计划(2007AA04Z401)资助

摘　　要：对于同时包含模糊不确定性和随机不确定性的结构系统模型,依据基本变量不确定性到模型输出的传递理论以及无条件可靠度和条件可靠度隶属函数之间的差异,分别给出了衡量基本随机变量和模糊变量对可靠度取值特征影响的重要性指标,并在这基础上定义了衡量基本随机变量对其影响的稳定性指标。文中采用迭代法或Monte Carlo法完成条件和无条件可靠度的计算,而后采用数值积分就算所定义的重要性和稳定性指标。文中所定义的重要性指标容易理解,计算简单省时,对具体的基本随机变量分布和模糊变量隶属函数的具体形式没有限制,适用于各种功能函数的形式,它直接基于随机变量分布函数和模糊变量的隶属函数进行求解,是一种全局的灵敏度指标。文中首先采用Monte Carlo和迭代法法对一线性算例展开分析,结果一致,证明了文中定义的指标符合稳定性的要求,随后采用迭代法对后续算例进行了重要性分析,证明了上述优点。Aim. The introduction of the full paper reviews a poses what we believe to be our new exploration, which is number of papers in the open literature and then proexplained in section 1. The core of section 1 is： ＂For structural system models with both fuzzy uncertainties and random uncertainties, according to the idea of uncertainties from basic variables to the model output, and the difference between unconditional and conditional membership functions of the fuzzy reliability, new importance measures are defined to the reliability membership character diver- sification due to random variables and fuzzy variables respectively, and a stability index of the importance measure of random variables is defined subsequently. The defined importance measure is easy to apprehend, can save much computation time and has no restriction either to the distribution of random variables or the membership function of fuzzy variables, since all evaluation is based on the probability density function of basic random variables and the membership function of basic fuzzy variables, and the presented importance measures are global sensitivity indicators. ＂ Section 2 applies the findings of our exploration to examples 1 and 2. The Monte Carlo simulation results for example 1 are presented in Table 1 and Fig. 3. For examples 2, we use the UUA （unified un method, which is based on the first order reliability method, to abtain the results： Table 3 and certainty analysis） Fig. 4. The results of all examples and their analysis show preliminarly that our new exploration is promising but needs to be improved.

关 键 词：不确定性 随机变量 模糊变量 重要性指标 可靠度取值特征 

分 类 号：TB114.3[理学—概率论与数理统计]