基于小波核偏最小二乘回归方法的混沌系统建模研究

Modelling of chaotic systems using wavelet kernel partial least squares regression method

基于核学习的强大非线性映射能力,结合用于回归建模的线性偏最小二乘(PLS)算法,提出一种小波核偏最小二乘(WKPLS)回归方法.该方法基于支持向量机使用的经典核函数技巧,将输入映射到高维非线性的特征空间,在特征空间中,构造线性的PLS回归模型.PLS方法利用输入与输出变量之间的协方差信息提取潜在特征,而可允许的小波核函数具有近似正交以及适用于信号局部分析的特性.因此,结合它们优点的WKPLS方法显示了更好的非线性建模性能.将WKPLS方法应用在非线性混沌动力系统建模上,并与基于高斯核的核偏最小二乘方法进行了比较.仿真结果表明,所提出的WKPLS方法能精确地逼近未知非线性混沌动力系统,且在同等条件下的逼近精度较高.

Based on the powerful nonlinear mapping ability of kernel learning,and in combination with the partial least square（PLS） algorithm for linear regression,a wavelet kernel partial least square（WKPLS） regression method is proposed.By the method,the input-output data are firstly mapped to a nonlinear higher dimensional feature space,a linear PLS regression model is then constructed by the classic kernel transformation trick used in support vector machines.The PLS approach utilizes the covariance between input and output variables to extract latent features,and the wavelet kernel which is an admissible support vector kernel function is characterized by its local analysis and approximate orthogonality.Hence,the proposed WKPLS method combining PLS approach with wavelet kernel function shows excellent learning performance for modeling nonlinear dynamic systems.The WKPLS is then applied to modelling of several chaotic dynamical systems and compared with the kernel partial least squares（KPLS） method using Gaussian kernel function.Simulation results confirm that the WKPLS identifier is fast and can accurately approximate unknown chaotic dynamical system,and its approximation accuracy is higher than the KPLS under the same conditions.