模糊约束集合下结构疲劳寿命估计方法

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。将超椭球模型的尺度参数作为一个正模糊数，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，从而确定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。通过超椭球凸集的归一化和球坐标转换，实现了模糊集合域内样本点的抽取和模糊约束下的疲劳寿命估计。通过工程算例，对模糊集合方法、凸模型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。

Estimation of structural fatigue lifetime under fuzzy constraints set

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 method for fatigue life estimation were proposed. The scale parameter of the hyper ellipsoid model was considered to be a positive fuzzy number. The inner and outer ellipsoid model on the basis of the interval model were the inside and outside edge the fuzzy set, and the membership function of the scale parameter was 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 lifetime in the ordinary set was proposed. The fuzzy maximal set and fuzzy minimal set were constructed. Through the normalization of the hyper ellipsoid model and spherical coordinate conversion, the sample points inside the fuzzy set can be extracted and estimation of fatigue life under fuzzy constraints can be realized. In a project example, the proposed method was compared with the convex set method and the probabilistic method. The results illustrated that the fuzzy set method is closer to the engineering practice and can provide more reasonable solutions, so it is a development and improvement of previous methods.