最小二乘小波支持向量机在非线性系统辨识中的应用

Least Squares Wavelet Support Vector Machines and Its Application to Nonlinear System Identification

基于小波分解和支持向量核函数的条件,提出了一种多维允许支持向量小波核函数.该核函数不仅是近似正交的,而且适用于信号的局部分析、信噪分离和突变信号的检测,从而提高了支持向量机的泛化能力.基于小波核函数和正则化理论提出了最小二乘小波支持向量机(LS WSVM)并将LS WSVM用于非线性系统的辨识,提高了辨识效果,减少了计算量.仿真结果表明:LS WSVM在同等条件下比传统支持向量机的辨识精度提高约13 1%,因而更适合于工程应用.

Based on the wavelet decomposition and conditions of the support vector kernel function, a novel multi-dimension admissible support vector wavelet kernel function was presented, which is not only approximately orthonormal, but also is especially suitable for local signal analysis, signal-noise separation and detection of jumping signals, thus enhances the generalization ability of the support vector machine (SVM). According to the wavelet kernel function and the regularization theory, a least square wavelet support vector machine (LS-WSVM) was proposed to greatly simplify the solving process of WSVM. The LS-WSVM was then applied to the nonlinear system identification to test the validity of the wavelet kernel function, and it is demonstrated that the modeling ability is improved and computation burden is alleviated. Computer simulations show that the identification accuracy of the LS-WSVM is higher than the traditional SVM about 13.1% under the same conditions, and it is more adaptive to engineering applications.