结构疲劳寿命分析的模糊凸集模型

A FUZZY CONVEX SET MODEL FOR ANALYSIS OF STRUCTURAL FATIGUE LIFE

针对刚性凸集模型在表达实际参数不确定性时的局限,提出了寿命参数的模糊集合模型及寿命估计方法.根据区间模型的内切和外接椭球确定了模糊集合边界的内、外缘及超椭球尺度参数的隶属函数,建立了疲劳寿命估计的模糊约束集.提出了基于Taylor二次展式和Lagrange条件极值法的寿命估计方法,构建了疲劳寿命的模糊极大集和模糊极小集.给出了模糊凸集约束下疲劳寿命极值求解的模拟算法.通过工程算例,对模糊凸集方法、凸集方法和概率方法进行了比较,结果表明,当统计数据缺乏时,模糊集合方法更贴切实际,计算结果更准确合理,是对凸模型方法和概率方法的发展和完善.

In order to overcome the limitations of the ordinary convex set in expressing the uncertainty of the actual parameters, a fuzzy set model for fatigue life parameters and corresponding method for fatigue life estimation were proposed. Based on the internal and external ellipsoid models of the interval model, the inside and outside edges of the fuzzy boundary and the membership function for the scale parameter were determined. Thus the fuzzy constraint set for fatigue life was built. Based on the Taylor series and Lagrange multiplier method, an approach for estimating the extreme values of fatigue life in the ordinary set was proposed. The fuzzy maximal set and fuzzy minimal set were constructed. Through the normaliza- tion of the hyper ellipsoid model and spherical coordinate conversion, the sample points within the fuzzy set can be extracted and the extreme values of the fatigue life under fuzzy constraints can be simulated. In the project example, the proposed method was compared with those based on the rigid convex set model and probabilistic model. The results illustrated that the proposed method is closer to practical engineering and can provide more reasonable conclusions, so it is the development and improvement of the convex model method and the probabilistic method.