改进的并行子空间优化算法及其在飞机概念设计中的应用

Improving GSECSSO Algorithm and Applying It to Aircraft Conceptual Design

分析了基于全局敏度方程的并行子空间优化算法容易发生收敛过程振荡和优化早熟的原因,在保持原算法减少约束个数和降低设计变量维度优点的条件下,进行了以下方面的改进:①去除了可能导致收敛过程振荡的折衷系数;②将可能导致优化早熟的固定累积约束参数设置为自适应可变参数。算例表明改进后算法收敛性能有很大提高。将该算法用于某通用航空飞机的概念设计,考虑气动、重量和性能3个学科,很好地解决了各学科间复杂耦合带来的计算困难,证实了该算法的有效性。

Aim. Existing GSECSSO （ Global Sensitivity Equation based Concurrent Subspace Optimization） algorithm suffers, in our opinion, from two shortcomings： （1） sometimes its convergence is oscillatory; （2） sometimes its convergence is premature. We now offer an improved GSECSSO algorithm that we believe can much suppress these two shortcomings. In the full paper, we explain our improved GSECSSO algorithm and its application in some detail; in this abstract we just add some pertinent remarks to listing the two topics of explanation. The first topic is： improved GSECSSO algorithm. Its two subtopics are mathematical model （subtopic 1.1 ）, and key .improvements of convergence （subtopic 1.2）. In subtopic 1.1, we perform optimization at discipline level while carrying out the system analysis and solution of Global Sensitivity Equation （GSE） at system level. In sub-subtopic 1.2. 1, we point out that trade-off coefficients may allow the violation of the constraints in some suboptimization to reduce the objective function and therefore the use of trade-off coefficients is purposefully avoided in our improved GSECSSO algorithm. In sub-subtopic 1.2.2, we modify the parameter p of KS （Kresselmeier-Steinhauser） function to start from its small value and increase it with a user-defined step length, thus making the design point gradually approach the optimal point on the active constraint and preventing premature convergence. The second topic is： numerical examples and the analysis of their results. In this topic, the results of the gear box example, given in Figs. 1 and 2 in the full paper, show preliminarily that oscillatory convergence is much suppressed by using our improved GSECSSO algorithm. More importantly, in this topic we apply the improved GSECSSO algorithm to the conceptual design of a general purpose aircraft. The conceptual design case is divided into the three disciplines of Aerodynamics, Weight and Performance. The application indicates that the improved GSECSSO algorithm has fast convergence and is practical.