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| Nonlinear principal axis mapping method applied in design optimization |
| OU Hai-ying, LI Xiao-yu, FU Zhan-ping |
| (Qingdao Branch, Naval Aeronautical Engineering Institute, Qingdao 266041, China) |
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Abstract The dimension reduction theory for design optimization and a nonlinear principle axis mapping (NPAM) method were developed to express high-dimensional design space in two- or three-dimensional space, and to discover the intrinsic dimension and the latent variable of the optimization model. In NPAM, the experimental design method was used to obtain the design sample set. Then the nonlinear functions of principal axis were used to approximate the objective function and constraints. Thus the reduced-dimensional objective function and constraints were achieved. Case studies showed that NPAM has the ability to discover the intrinsic variable of data manifold and can express the panoramic picture of the multidimensional design space in two- or three-dimensional space. The panoramic picture can be used to analyze the character of optimization objective function and to choose optimization algorithm, to show tracks of optimization process, and to study optimization algorithms' character．
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Published: 26 February 2010
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设计优化中的非线性主轴降维映射法
为了在二维或三维空间中表达高维设计空间,分析多变量优化数学模型的本征维数及其所独立依赖的、有意义的和尽可能少的潜变量,发展了设计优化降维理论和非线性主轴降维映射法.非线性主轴降维映射法首先通过试验设计理论采样获得设计样本集,通过主轴的各种非线性函数逼近目标函数和约束,实现对高维目标函数和约束的降维处理.工程实例研究表明,非线性主轴降维映射法具有发现数据流形本征变量的能力,能够在二维或三维空间中展示多维设计空间全景图,从而用于分析目标函数性质和选择优化算法,展示优化迭代轨迹,研究优化算法的性质.
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