【作者】 韩旭； 陶友瑞； 姜潮；

【Author】 X.Han1,Y.R.Tao1,2,C.Jiang1 (1 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body of Hunan University Hunan 410082 China) (2 Department of Mechanical Engineering,Hunan Institute of Engineering,Hunan 411101 China)

【机构】 湖南大学汽车车身先进设计制造国家重点实验室； 湖南工程学院机械工程系；

【摘要】 多学科设计优化中面临的困难是结构复杂和计算量巨大,多学科设计优化中往往还包含多个相互矛盾的优化目标,因此多目标多学科设计优化是一个更为复杂的问题。本文将线性物理规划应用于多目标多学科设计优化之中,提出了一种高效、直观的方法来解决该问题。首先,设计者确定线性物理规划中各目标的偏好类型及偏好值,即设定各目标5个满意程度区间的边界值,然后利用ε约束法将多目标问题转换成单目标问题,即将多个目标中的一个作为优化目标,其余的目标转换为约束,且该约束的上界设定为某一个满意程度区间的边界值,再采用两级集成系统分析法进行多学科设计优化,从而得到一个设计优化方案(即一个非劣解)。当改变目标约束上界并且重新进行多学科设计优化时,就可得到多个设计方案(即多个非劣解)。各设计方案的优劣采用线性物理规划评价模型来实现,在该模型中先计算线性物理规划数学模型中的递增权值,再计算各设计方案的综合目标函数值,综合目标函数值最小的方案为最接近设计者意愿的方案,即最优方案。在该方法中,由于只求设计者确定的5个满意程度区间中的非劣解,这样既满足了设计者的要求又避免了求其它非劣解带来的计算成本增加,另外,线性物理规划可以从本质上把握设计者的偏好,也可以减轻多目标设计问题的计算负担,加之两级集成系统分析法是一种综合性能好的多学科设计优化方法,因此本文所提方法能够高效处理多目标多学科问题。本文给出了一个详细的多目标多学科设计优化模型,该模型为一个工程实例即减速器优化,它涉及三个学科(子系统)和两个目标(即体积和应力)。采用本文提出的方法对该模型进行了优化,从5个设计方案中求得了最优设计方案,最优解中的体积和应力值都在可容忍区间,从而也验证了该方法的有效性。通过该算例也说明该方法具有很好的工程应用价值。更多还原

【Abstract】 The challenge in multidisciplinary design optimization is the complexity of the system and the computational cost.Moreover,most multidisciplinary design optimization problems include multiple,conflicting objectives.Therefore,multi-objective multidisciplinary design optimization is more complex than single-objective multidisciplinary design optimization.In this paper,we present a novel method to deal with multi-objective multidisciplinary design optimization by integrating linear physical programming in bi-level integrated system synthesis.At first,designers decide to which criterion class the objectives belong,and choose the range targets for every objective.Designers describe their preference in terms of physical meaning parameters.Then the multi-objective problem is converted to single-objective problem with ε-constraint method.In anther words,one objective is selected as objective to be optimized and the other objectives are converted as additional constraints.One of the range targets is used as the upper bound of the additional constraints.A Pareto point is obtained by bi-level integrated system synthesis.Multiple design schemes can be obtained when the upper bound of the additional constraints is changed.All design schemes are evaluated by linear physical programming and the optimum design scheme can be found out.In the method,just the Pareto points in the ranges of differing degrees of desirability are solved.Comparison with conventional multi-objective multidisciplinary optimization,the method could achieve computational saving resulting from the reduction of the number of Pareto points.Moreover,linear physical programming can substantially reduce the computational intensity of large problems,and the performance of bi-level integrated system synthesis is good.Therefore,multi-objective multidisciplinary optimization can be dealt with by the presented method efficiently.A detailed multi-objective multidisciplinary optimization model is given in this paper.The model is a speed reduction machine model with two objectives (volume and stress) and three subsystems.The model is investigated to demonstrate the performance of the presented method.The optimal design scheme can be obtained from the five design schemes.The volume and stress of the optimal design scheme are in the tolerable range.The presented method can be applied in the engineering problems.更多还原