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传统的优化方法在处理高维多目标问题上面临多重困难,针对高维多目标优化问题,进行合理的目标降维是一种实用高效的方法。本文首先讨论、研究了PCA目标降维算法在高维多目标应用中的思路,通过典型高维度目标测试函数中的应用,验证了降维方法的有效性,进一步将该方法推广应用于翼型气动隐身多学科综合设计中,对综合设计高维度目标空间进行主成分分析。利用主成分分析提取主成分并辨识“冗余”或者不重要的目标,将冗余目标去除或者作为约束加入到重要目标的优化过程中。结果显示,目标空间降维以后的优化设计结果满足力矩、阻力发散、巡航升阻比、低速升力特性以及隐身特性等综合设计的要求。进一步探讨、展望了该方法在飞行器多目标、多学科优化设计中的应用前景。
Traditional optimization methods face multiple difficulties when dealing with high-dimensional multi-objective problems. For the high-dimensional multi-objective optimization problems, it is a practical and efficient method to reduce the dimensions of the target. This paper first discusses and discusses the idea of PCA target dimension reduction algorithm in high-dimensional multi-target applications. Through the application of the typical high-dimensional target test function, the effectiveness of the dimensionality reduction method is verified. The method is further applied to airfoils Pneumatic stealth multidisciplinary integrated design, the principal component analysis of the integrated design of high-dimensional target space. Using principal component analysis to extract the principal components and identify “Redundant ” or unimportant targets, the redundant targets are removed or added as constraints to the optimization of important targets. The results show that the optimized design results after the dimension reduction of the target space meet the requirements of comprehensive design such as torque, resistance divergence, cruise lift-drag ratio, low-speed lift characteristics and stealth characteristics. Further exploration and prospect of the application of this method in multi-objective and multi-disciplinary optimization design of aircraft are prospected.