CAJ | 학술논문

在许多工程优化设计问题中,由于需要采用费时的数值模拟方法获得目标函数和约束函数值,出现了优化时间过长、优化难度大的问题. 为了提高设计效率,缩短优化设计周期,代理模型方法受到人们的欢迎. 近些年来,为了进一步提高设计效率,人们在传统代理模型基础上又发展了一些更高效、预测精度更高的新型代理模型,如变可信度模型、梯度增强的代理模型等. 为了研究新型代理模型在优化设计中的优化效率和优化效果,首先结合代理模型、多点加点准则及多种传统优化算法,发展了一套适用于代理模型、梯度增强的代理模型的通用优化算法框架,基于该框架,采用典型的数值算例对当前应用较为广泛的Kriging模型和近些年来发展的梯度增强的Kriging模型进行了对比研究. 结果显示,在假定目标函数的梯度与目标函数计算量相同的情况下,采用梯度增强的Kriging模型得到的优化结果在绝大多数情况下都优于采用Kriging模型得到的结果. 最后,应用翼型设计算例对两种代理模型进行了对比,其中目标函数的梯度采用与目标函数本身计算量基本一致的Adjoint方法获得;结果显示,梯度增强的Kriging模型表现优于Kriging模型.
재허다공정우화설계문제중,유우수요채용비시적수치모의방법획득목표함수화약속함수치,출현료우화시간과장、우화난도대적문제. 위료제고설계효솔,축단우화설계주기,대리모형방법수도인문적환영. 근사년래,위료진일보제고설계효솔,인문재전통대리모형기출상우발전료일사경고효、예측정도경고적신형대리모형,여변가신도모형、제도증강적대리모형등. 위료연구신형대리모형재우화설계중적우화효솔화우화효과,수선결합대리모형、다점가점준칙급다충전통우화산법,발전료일투괄용우대리모형、제도증강적대리모형적통용우화산법광가,기우해광가,채용전형적수치산례대당전응용교위엄범적Kriging모형화근사년래발전적제도증강적Kriging모형진행료대비연구. 결과현시,재가정목표함수적제도여목표함수계산량상동적정황하,채용제도증강적Kriging모형득도적우화결과재절대다수정황하도우우채용Kriging모형득도적결과. 최후,응용익형설계산례대량충대리모형진행료대비,기중목표함수적제도채용여목표함수본신계산량기본일치적Adjoint방법획득;결과현시,제도증강적Kriging모형표현우우Kriging모형.
In many engineering optimization design problems, the objective function ( s) as well as the constraint function ( s ) are really computationally expensive. To reduce the computational time and shorten the design process, surrogate models are often used. In recent years, to further improve the design efficiency, a variety of new surrogate models are developed as extensions from the traditional models and verified to have higher efficiency for prediction, such as the variable?fidelity models and gradient?enhanced models. To investigate the design optimization efficiency when these new surrogate models are used, a universal surrogate?based optimization frame?work, which combines the surrogate models, multi sample point infill criteria, and multi?type traditional optimiza?tion algorithms, is developed first. Then, several typical analytical optimization problems are employed to compare the optimization efficiency when the widely used Kriging and a newly developed GEK are used respectively. The re?sults and their analysis show preliminarily that, for most cases, GEK get better optimal solution with the same com?putational expense. Finally, an engineering problem, the airfoil inverse design is introduced for comparison; the gradients of the objective functions used to construct the GEK are obtained by the efficient adjoint method. The re?sults and their analysis also show preliminarily that, when using the GEK, not only the efficiency, but also the opti?mal solution can be improved as compared with the Kriging model.