基于模糊凸集的结构非概率可靠性综合模型

A non-probabilistic model of structural reliability based on fuzzy convex set model

在小样本或极小样本问题中,由于参数波动的确切范围难以确定,普通刚性凸集模型含有难以估量和控制的误差,其适用性受到限制.鉴于此,研究建立了一种新的不确定性模型——模糊凸集模型,并通过在刚性凸集中引入一个新的参数——模糊扩展参数,建立了几种典型的模糊凸集模型.在模糊凸集模型的基础上,建立了一种非概率可靠性的综合模型,采用Gauss-Legendre求积方法解决了指标求解所涉及的积分问题.算例表明,采用基于模糊凸集的非概率可靠性综合模型度量小样本结构的可靠性更加合理,可靠性指标的求解方法正确可行.

In small sample size problems, it is difficult to judge and control the errors of the ordinary rigid convex model. In view of this, a new uncertainty model named fuzzy convex set model was built, whose properties were systematically researched. Some typical models were established by introducing a new parameter named fuzzy extending parameter into the ordinary convex models. A comprehensive and integral reliability model was presented on the basis of the new uncertainty model. The Gauss-Legendre integral formula was used for the reliability calculation. Two examples were given and showed the rationality and feasibility of the proposed uncertainty and reliability models.