基于空间分解的参数优化径向基函数近似模型构造方法

doi:10.11772/j.issn.1001-9081.2015.01.0179

计算机应用 ›› 2015, Vol. 35 ›› Issue (1): 179-182.DOI: 10.11772/j.issn.1001-9081.2015.01.0179

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

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

收稿日期:2014-08-12 修回日期:2014-09-23 出版日期:2015-01-01 发布日期:2015-01-26
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.

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

WU Zongyu, LUO Wencai

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

摘要/Abstract

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

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

中图分类号:

TP391.9

吴宗谕, 罗文彩. 基于空间分解的参数优化径向基函数近似模型构造方法[J]. 计算机应用, 2015, 35(1): 179-182.

WU Zongyu, LUO Wencai. Construction method of radial basis function approximation model based on parameter optimization of space decomposition[J]. Journal of Computer Applications, 2015, 35(1): 179-182.

参考文献

[1] YAO W, CHEN X, LUO W, et al. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles [J]. Progress in Aerospace Sciences, 2011, 47(6): 450-479.
[2] BALESDENT M, BÉREND N, DÉPINCÉ P, et al. A survey of multidisciplinary design optimization methods in launch vehicle design [J]. Structural and Multidisciplinary Optimization, 2012, 45(5): 619-642.
[3] MARTINS J R R A, LAMBE A B. Multidisciplinary design optimization: a survey of architectures [J]. AIAA Journal, 2013, 51(9): 2049-2075.
[4] DEB A, CHOU C C, DUTTA U, et al. Practical versus RSM-based MDO in vehicle body design [J]. SAE International Journal of Passenger Cars-Mechanical Systems, 2012, 5(1): 110-119.
[5] QUEIPO N V, HAFTKA R T, SHYY W, et al. Surrogate based analysis and optimization [J]. Progress in Aerospace Sciences, 2005, 41(1): 1-28.
[6] ALIPANAH A, ESMAEILI S. Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function [J]. Journal of Computational and Applied Mathematics, 2011, 235(18): 5342-5347.
[7] DAVYDOV O, OANH D T. On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation [J]. Computer and Mathematics with Applications, 2011, 62(5): 2143-2161.
[8] WANG L, WANG X, ZHAN H, et al. The error analysis of element-free method based on radial basis function used in mechanical problems [J]. Mechanics in Engineering, 2013, 35(2): 67-72. (王立鹏,王欣彦,战洪仁,等.基于径向基函数的无单元法求解力学问题误差分析[J].力学与实践,2013,35(2):67-72.)
[9] BAYONA V, MOSCOSO M, KINDELAN M. Optimal variable shape parameter for multiquadric based RBF-FD method [J]. Journal of Computational Physics, 2012, 231(6): 2466-2481.
[10] MAO W, MU X, ZHENG Y, et al. Leave-one-out cross-validation-based model selection for multi-output support vector machine [J]. Neural Computing and Applications, 2014, 24(2): 441-451.
[11] BAYONA V, MOSCOSO M, KINDELAN M. Optimal constant shape parameter for multiquadric based RBF-FD method [J]. Journal of Computational Physics, 2011, 230(19): 7384-7399.
[12] XIANG S, WANG K, AI Y, et al. Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation [J]. Applied Mathematical Modelling, 2012, 36(5): 1931-1938.
[13] ZHOU F, ZHANG J, SHENG X, et al. Shape variable radial basis function and its application in dual reciprocity boundary face method [J]. Engineering Analysis with Boundary Elements, 2011, 35(2): 244-252.

[1]	严海升, 马新强. 基于径向基函数的多目标回归特征构建算法[J]. 计算机应用, 2021, 41(8): 2219-2224.
[2]	金滔, 董秀成, 李亦宁, 任磊, 范佩佩. 改进的粒子群优化算法优化分数阶PID控制器参数[J]. 计算机应用, 2019, 39(3): 796-801.
[3]	李方伟, 李骐, 朱江. 改进的基于隐马尔可夫模型的态势评估方法[J]. 计算机应用, 2017, 37(5): 1331-1334.
[4]	张广胜, 刘伟. 考虑服务时效的物流服务供应链应急任务分配[J]. 计算机应用, 2016, 36(8): 2335-2339.
[5]	李明旭, 邓欣, 王进, 王潇, 张笑谋. 基于人工神经网络的秀丽隐杆线虫趋温性行为的建模与仿真[J]. 计算机应用, 2016, 36(7): 1909-1913.
[6]	张进, 丁胜, 李波. 改进的基于粒子群优化的支持向量机特征选择和参数联合优化算法[J]. 计算机应用, 2016, 36(5): 1330-1335.
[7]	姚晟, 徐风, 汪杰. 多粒度粗糙集模型中属性子集序列的构造方法[J]. 计算机应用, 2016, 36(11): 2950-2953.
[8]	宋竹, 秦志光, 邓伟伟, 赵玉平. 微观交通仿真系统的近邻查询算法[J]. 计算机应用, 2015, 35(2): 572-577.
[9]	张华伟魏萌. 基于云免疫算法的认知无线网络参数优化[J]. 计算机应用, 2014, 34(3): 628-631.
[10]	杨学峰王高程耀瑜. 基于径向基函数的多帧图像超分辨重建算法[J]. 计算机应用, 2014, 34(1): 142-144.
[11]	李书玲刘蓉张鎏钦刘红. 基于改进型SVM算法的语音情感识别[J]. 计算机应用, 2013, 33(07): 1938-1941.
[12]	罗庚合. 基于可拓聚类的极限学习机神经网络[J]. 计算机应用, 2013, 33(07): 1942-1945.
[13]	韩亮姜孜锜蒲秀娟. 光学4f系统灰度误差补偿的实现[J]. 计算机应用, 2013, 33(07): 1973-1975.
[14]	杨秋娟周世生罗如柏. 基于径向基函数神经网络的柔印专色配色系统[J]. 计算机应用, 2013, 33(06): 1787-1789.
[15]	夏国清廖粤峰王璐. 四旋翼无人飞行器混合控制系统研究[J]. 计算机应用, 2013, 33(03): 858-861.

基于空间分解的参数优化径向基函数近似模型构造方法

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics