基于改进遗传算法的结构静力响应区间分析

Interval Analysis of Structural Static Response Using Improved Genetic Algorithm

不确定性是影响结构响应的重要因素。结构中许多不确定性参数分布特征不明确,不能使用随机模型或模糊模型进行描述,只能使用区间模型。以区间模型考虑结构不确定性时,结构响应区间的计算量和精度之间的矛盾始终没有得到较好的解决。遗传算法是一个很好的区间求解算法,但传统遗传算法单次运行只能求解一个响应最值。因此,本文在传统遗传算法中加入多个适应度函数,对遗传操作进行了改进,构建了并行优化遗传算法(GAPO),并使用GAPO同时求解结构多个响应的区间。使用一个桁架杆轴应力区间算例验证了GAPO,结果表明GAPO能同时求解多个结构静力响应的最值,并能在保证计算精度的条件下显著降低结构静力响应区间的计算量。

Uncertainty is an important factor affecting structural responses.The distribution characteristics of many uncertain parameters in the structure are ambiguous,so the parameter cannot be described by stochastic model or fuzzy model,but only by interval model.When structural uncertainty is described by interval model,the contradiction between the computational cost and the accuracy of structural response bounds has not been resolved well.Genetic algorithm is a good bound-solving algorithm,but only one response boundcan be obtained in a single run of the traditional genetic algorithm.Therefore,in this paper,multiple fitness functions are added to the traditional genetic algorithm,the genetic operation is improved,and a Genetic Algorithm for Parallel Optimization(GAPO)is constructed and used to solve the bounds on multiple structural response simultaneously.An example of finding the bounds on the axial stress of multiple truss members is used to verify the proposed algorithm.The research results show that GAPO can solve the bounds of multiple structural responses simultaneously and significantly reduce the computational cost when solving the bounds on structural static responses while ensuring the accuracy.