基于权重比的车架多工况拓扑优化方法研究

Research on the method of multi-case topology optimization of frame structure based on the weight ratio

在赛车实际行驶过程中车架会受到各种工况的考验,因此在进行车架结构拓扑优化设计时必须同时考虑多个工况下车架的拓扑优化结果.然而,在进行多工况下拓扑结构设计时往往会遇到如何分配各个工况权重比的问题,各工况权重比的分配直接影响车架最终的拓扑结构.针对此问题进行研究,通过构造代理模型并利用遗传算法寻找最佳权重比.首先,采用折衷规划法建立同时考虑多个工况下车架刚度的拓扑优化综合目标函数模型;接着,采用最优拉丁超立方试验设计方法采样,构造径向基函数代理模型,并在代理模型的基础上利用NSGA-II进行求解,得到各个工况最佳权重比;最后,将获得的各个工况最佳权重比代入综合目标模型中进行拓扑计算,获得同时考虑各工况下车架刚度的拓扑结构.将该方法与获得权重比常用的层次分析法(AHP)和正交试验法(OED)进行比较,该方法较其他两种方法得到的综合目标值是最优的,车架所有工况的加权柔度是最低的.结果表明,所提出的方法很好地解决了多工况下拓扑优化权重比分配的问题,并且较其他方法具有明显的优越性.

The frame will be subject to the test of various conditions in the actual moving conditions.So a plurality of topology results under every condition must be considered when conducting topology optimization of the frame structure.While there is a common issue during the process of multi-case topology optimization about how to determine the weight ratio of respective condition and the final topology results of the frame depend directly on this distribution.This issue was showed a further study and a feasible solution to this problem with a combination of surrogate model and genetic algorithm was gaved.At first,a comprehensive object function maximizing the static stiffness under multi-case was defined by using compromise programming approach.And then,a Radial Basis Function surrogate model was constructed by using optimal Latin Hypercube Sampling,meanwhile,optimal weight ratios of every load condition had been obtained with the method of combining surrogate model with NSGA-II.At last,the optimal weight ratios obtained in the previous process were applied into the object function and a feasible topology result of the frame structure was got which had considered multi-case loads.Moreover,the contrastive study was carried out to compare the comprehensive objective optimization approach proposed in this study with those that determined the weight ratio by analytic hierarchyprocess（AHP）or orthogonal experimental design（OED）.Compared with the other two methods,this method had the lowest value of comprehensive objective function and the weighted compliance of all conditions was also the lowest.Results show that the method proposed in this paper is a good solution to obtain weight ratio of every condition in the process of topology optimization of a frame and is superior to reference methods.