摘要
随着混沌理论和混沌应用技术的不断发展,混沌时间序列的分析与预测已经成为混沌信号研究领域的热点。混沌应用技术的发展涉及诸多领域,包括：声学、光学、化学、水文学、地震混沌特性、天气预报的“蝴蝶效应”、以及股票市场的混沌特性等。
目前,混沌时间序列预测的方法主要有：全域法、局域法、基于最大Lyapunov指数法、非线性自适应滤波法和基于核机器学习方法等。在基于核机器学习算法中,支持向量机(Support Vector Machine, SVM)和相关向量机(Relevance Vector Machine, RVM)由于鲁棒性好,泛化性能强,收敛速度快,预测精度高,受到了国内外学者广泛关注。
在SVM和RVM中,单核函数由于自身存在的一些性质,导致其不可能同时具有良好的泛化能力和学习能力,从而影响预测精度。本文利用全局核函数和局部核函数线性组合的方法构造组合核函数,使其结合二者的优点,同时获得较好的泛化能力和学习能力。将该组合核函数运用于SVM和RVM对典型混沌时间序列的预测算法中。通过仿真证明,组合核函数的预测性能优于单核函数。
将该组合核函数运用于对实际的混沌序列预测中。实现了太阳黑子序列预测和电力负荷预测的有效预测。通过仿真得出：该组合核函数能够准确预测实际工程中的混沌序列,更好的服务于工程实践。
With the chaos theory and the application of chaos technology increasing, the chaotic time series analysis and prediction has become a hotspot in the research field of chaos signal. The application of chaos technology development involves many fields, including:acoustic, optical, chemical, hydrology, chaotic characteristics of earthquake, the" Butterfly Effect" of weather forecast, and the stock market chaos characteristic.
At present, the prediction of the chaotic time series methods include:global prediction method, local prediction method, based on the maximum Lyapunov exponent prediction method, a nonlinear adaptive filter prediction method and based on kernel machine learning prediction method. In the kernel machine learning algorithm, The support vector machine (Support Vector Machine, SVM) and the relevance vector machine (Relevance Vector Machine, RVM) have paid close attention to by domestic and foreign scholars,because of the good robustness, strong generalization ability, fast convergence speed, high accuracy.
In SVM and RVM, the single kernel function because of its some properties, resulting in they may have good generalization ability and learning ability,affecting the forecasting accuracy. This paper uses global and local kernels linear combination to construct combined kernel function, which combines the advantages of the two, and has good generalization ability and learning ability. The combined kernel function is used in SVM and RVM on the typical chaotic time series prediction algorithm. The simulation results show that the predicted ability of combined kernel function is better than the single kernel function.
The combined kernel is applied to the prediction of actual chaotic sequences. Achieving the effective prediction of the sunspot series and power load. The predicted results show: The combination of kernel functions can accurately predict the chaotic sequence in the actual project, to better serve the engineering practice.
引文
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