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建立了结构同时含有概率、模糊、凸集变量时的可靠性分析模型。首先对模糊变量取一截集水平α,得到与模糊变量向量相对应的区间向量,将问题化为仅含有随机变量和凸集变量的混合可靠性问题。其次根据随机和凸集两类变量的混合可靠性方法,得到截集水平α下,以凸集变量为自变量的可靠度的均值,即截集水平α下的结构混合可靠度值。然后,将结构混合可靠度在截集水平区间[0,1]内进行积分,得到三类变量混合的结构总体可靠度。对所定义可靠度指标的物理意义进行了解释,并以某典型功能函数为例,进行了公式推导。最后,给出了算例分析,方法的可行性及合理性得到了验证。算例还表明,当忽略模糊变量的模糊性质,或改变凸集变量的数学型式,都会引起可靠度结果的失真,因此在工程实际中,必须全面客观地处理各类不确定性变量,才能得到正确可信的可靠性分析结论。
The reliability analysis model is established when the structure contains both probability, fuzzy and convex variables. First, a fuzzy set of level α is taken as the fuzzy variable, and the interval vector corresponding to the fuzzy variable vector is obtained, which turns the problem into a mixed reliability problem with only random variables and convex set variables. Secondly, according to the mixed reliability method of random and convex sets of variables, we obtain the mean value of the reliability of the set with the convex set variables as the independent variable under the cutoff level α, that is, the mixed reliability of the structure under the cutoff level α. Then, the structural reliability of mixture is integrated in the interval [0,1], and the overall structural reliability of the three types of variables is obtained. The physical meaning of the defined reliability index is explained, and a typical function function is taken as an example to deduce the formula. Finally, a case study is given, and the feasibility and rationality of the method are verified. The example also shows that when ignoring the fuzzy nature of fuzzy variables or changing the mathematical types of convex variables, the distortion of reliability results will be caused. Therefore, in engineering practice, all kinds of uncertain variables must be dealt with objectively and objectively Correct and credible reliability analysis conclusion.