基于在线小波支持向量回归的混沌时间序列预测

Prediction of chaotic time-series based on online wavelet support vector regression

混沌时间序列预测是非线性动力学研究中一个十分重要的问题,支持向量回归方法为其提供了一种有效的解决思路.通过分析新样本加入训练集后支持向量集的变化情况,建立了一种混沌时间序列预测的支持向量回归算法,具备了在线学习的特点.同时,针对混沌信号提出了一种满足小波框架的小波核函数,它不但能以较高的精度逼近任意函数,而且适合于混沌信号的局部分析,提高了支持向量回归的泛化能力.最后就Mackey-Glass混沌时间序列在线预测问题进行了大量仿真.结果表明,本文算法与现有的算法相比具有训练时间短、预测精度高等特点,有一定的理论及实用价值.

Support vector regression （SVR） is an effective method for the predication of chaotic time-series, which is a fundamental topic of nonlinear dynamics. Through analyzing the possible variation of support vector sets after new samples are inserted to the training set, a novel SVR algorithm is proposed; thus an online learning algorithm is set up. In connection with the specific characteristics of chaotic signals, a wavelet kernel satisfying wavelet frames is also presented. The wavelet kernel can approximate arbitrary functions, and is especially suitable for local processing; hence the generalization ability of SVR is improved. To illustrate the good performance of the online wavelet SVR, a benchmark problem, i.e. the online prediction of chaotic Mackey-Glass time-series, is considered. The simulation results indicate that the outperforms the existing algorithms in higher efficiency of learning as well as better accuracy of online wavelet SVR algorithm prediction.