同时考虑状态和变量模糊性的可靠性灵敏度分析方法

A Different Sensitivity Analysis for Fuzzy Random Reliability with both Fuzzy Failure State and Fuzzy Safety State Considered

文章同时考虑状态和变量的模糊性,提出了模糊随机可靠性灵敏度分析的通用数字方法,推导了模糊随机可靠性灵敏度数字模拟解的方差和变异系数。当模糊变量隶属函数为正态型时,可将模糊随机可靠性灵敏度转化为随机可靠性灵敏度。针对工程中常见的对称三角型隶属函数,基于尾部拟合误差平方和最小的原则,提出一种模糊变量隶属函数近似等价正态化的最小二乘方法。计算结果表明:最小二乘法近似精度较高,是一种工程可选方法。同时发现,状态模糊性对失效概率及可靠性灵敏度结果都有较大影响,忽略客观存在的状态模糊性,有可能得到偏危险的评估结果。

For structure with fuzzy state and fuzzy variables, a general numerical simulation method is presented for fuzzy-random reliability sensitivity （F-RRS） estimation. In the case that fuzzy variables possess Gaussian membership functions, the F-RRS can directly be transformed into RRS, which can be easily solved by the available methods. For symmetric triangular membership functions, an equivalent transformation from the symmetric triangular membership functions to the Gaussian ones is established by the use of Minimum Least Squares （MLS）. Details of what we have just written can be found in sections 1,2 and 3 of the full paper. Section 4 gives three numerical examples, whose calculated results are presented respectively in Table 1 （ example 1 ）, Table 2（ example 2） and Table 4（example 3） ; in these tables, we compare our method with two existing ones and find that, in our opinion, our method qualifies to be applied to engineering problems, as an alternative to the two existing ones. For example 1, we present additional reliability sensitivity results in Figs. 1 through 7 ; the analysis of these results shows preliminarily that： （ 1 ） the effect of the fuzziness of state on failure probability is significant; （2） actually existing fuzziness cannot be neglected; otherwise dangerous evaluations may be obtained.