Journal of Computer Applications ›› 2015, Vol. 35 ›› Issue (1): 179-182.DOI: 10.11772/j.issn.1001-9081.2015.01.0179

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Construction method of radial basis function approximation model based on parameter optimization of space decomposition

WU Zongyu, LUO Wencai   

  1. Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha Hunan 410073, China
  • Received:2014-08-12 Revised:2014-09-23 Online:2015-01-01 Published:2015-01-26

基于空间分解的参数优化径向基函数近似模型构造方法

吴宗谕, 罗文彩   

  1. 国防科学技术大学 高超声速冲压发动机技术重点实验室, 长沙410073
  • 通讯作者: 吴宗谕
  • 作者简介:吴宗谕(1991-),男,河南周口人,硕士研究生,主要研究方向:飞行器多学科优化设计;罗文彩(1975-),男,湖南邵东人,副教授,博士,主要研究方向:飞行器总体设计、多学科优化设计.

Abstract:

To improve the accuracy of Radial Basis Function (RBF) approximation model, the influencing factors on approximation accuracy were deeply studied. The truth that matrix condition number and shape parameter were two important factors of approximation accuracy was pointed out by analyzing the influence of rounding error over approximation accuracy thoroughly. The matrix condition number was decreased and the design freedom was increased by separating design space based on sensitivity analysis. Learning from the traditional RBF based on optimal shape parameter, the construction method of RBF approximation model based on parameter optimization of space decomposition was proposed. The numerical test results show that, in the two cases, the Root Mean Square Error (RMSE) of the proposed method is reduced by 51.3% and 58.0% respectively while comparing with the traditional method based on optimal shape parameter for construction of RBF approximation model. The proposed method has high approximate accuracy.

Key words: Radial Basis Function (RBF), approximation accuracy, condition number, parameter optimization, sensitivity analysis

摘要:

为了进一步提高径向基函数(RBF)近似模型的精度,对其近似精度影响因素进行了深入研究.深入分析了计算机舍入误差对RBF近似精度的影响,指出矩阵条件数和形状参数同为影响RBF模型近似精度的两个重要因素.结合灵敏度分析对设计空间进行了分解,改善了矩阵条件数,增加了设计自由度,在传统基于形状参数优化的RBF近似模型的基础上,提出了基于空间分解的参数优化RBF近似模型构造方法.数值实验结果表明,在两个测试算例中,所提方法较传统基于形状参数优化的RBF近似模型构造方法的均方根误差(RMSE)分别减小了51.3%、58.0%,具有更高的近似精度.

关键词: 径向基函数, 近似精度, 条件数, 参数优化, 灵敏度分析

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