Modified L-P小波最小二乘支持向量机及在动态系统辩识中的应用

Least Square Support Vector Machine with Modified L-P Wavelet Kernel and Its Application in Dynamic System Identification

为了提高动态系统的辩识品质,提出了一种新的可调带宽多维支持向量小波核函数—modified L-P小波核函数。理论上证明了这种核函数是满足平移不变核定理的支持向量核函数。由于该核函数具有平移伸缩正交性,而且适用于信号的局部分析、信噪分离和突变信号的检测,从而提升了支持向量机的泛化性能。应用Modified L-P小波核作为最小二乘支持向量机的核函数,可以简化计算复杂性,提高学习效率。回归实验和动态系统辩识的仿真结果表明,Modified L-P小波核函数最小二乘支持向量机的建模和逼近能力优于基于L-P小波核函数或高斯核函数最小二乘支持向量机,更适合工程应用。

To improve the qualities of dynamic system identification, a novel multi-dimensional support vector wavelet kernel function was proposed, i.e. modified L-P wavelet kernel function. It is proved that this kernel function satisfies translation-invariant kernel condition and can be used as a kernel function for SVM （Support Vector Machine）. This function is not only an orthogonal function, but also is especially suitable for local signal analysis, signal-noise separation and detection of jumping signals, thus enhances the generalization ability of the SVM. Using modified L-P wavelet function as the support vector kernel function, the Least Square Support Vector Machine with modified L-P Wavelet Kernel was proposed Simulation results show that the Least Square Support Vector Machine with proposed modified L-P wavelet Kernel fimction is better than that with L-P wavelet kernel or Gauss kernel in modeling and approximation abilities, and more adaptive to engineering application.