SVM-HDMR高维非线性近似模型构造法  

SVM-HDMR approximation model construction method for high dimensional nonlinear problems

作　　者：李亮[1] 孙秦[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《计算机工程与应用》2013年第15期6-9,共4页Computer Engineering and Applications

基　　金：中航工业产学研创新项目(No.Cxy2010xG18)

摘　　要：为了构造高维下的近似模型,将最小二乘支持向量机(LS-SVM)引入切割高维模型表示(Cut-HDMR),提出了SVM-HDMR高维非线性近似模型构造法,给出了相应的自适应采样和模型构造算法。该方法利用Cut-HDMR将高维问题转化为一系列低维问题,用LS-SVM求解这些低维问题。数值算例的测试结果表明该方法具有较好的近似精度,且与传统近似方法相比极大地降低了计算成本,从而更适用于高维工程问题的求解。In order to construct approximation model for high dimensional problems, Least Squares Support Vector Machine （LS-SVM） is introduced into High Dimensional Model Representation （HDMR）, and a modified approximation model con-struction method called SVM-HDMR for high dimensional nonlinear problems and corresponding adaptive sampling and model construction algorithm are proposed. This method transforms high dimensional problem into a series of low dimensional problems using Cut-HDMR, and then these low dimensional problems are solved using LS-SVM. The results of numerical examples show that the new method has good approximation quality and reduces computational expense dramatically, so it is more suitable for high dimensional problems.

关 键 词：近似模型 最小二乘支持向量机(LS-SVM) 切割高维模型表示(Cut-HDMR) 自适应采样 

分 类 号：O241.3[理学—计算数学]