Modeling Research For Chaotic Time Series Based On Wavelet Analysis And Neural Networks

It is difficult to build models for the real-world chaotic systems because there are various characteristics, such as initial sensitivity and uncertainty, in the chaotic systems, which block the researches on chaotic systems. Meanwhile, data sets generated by the chaotic systems are usually polluted by noise came from measure or transmission process, and the influence degree of noise is usually differ as different research backgrounds and data sequences. The existence of noise will hide the inherent laws of chaotic signals and destroy the geometric structure of chaotic attractor, which lead to traditional modeling methods based on chaotic property are no longer applicable or with poor results. Thus, how to establish model utilizing chaotic time series is a problem needed to be solved urgently.Studying on the observed chaotic time series such as annually Sunspot time series and Mackey-Glass time series, this paper explores modeling methods based on the time frequency localization character of wavelet analysis and the modeling capability of neural network. The wavelet network will be employed to model the chaotic time series. In the construction process of the network, QROLS algorithm obtained by combining QR decomposition and orthogonal least squares (OLS) algorithm is proposed to realize the choice of hidden layer neurons in the wavelet network. In order to avoid the comparison between non-optimal nodes, block disposal strategy is applied which can greatly save the computing of wavelet Network. Then, for the so called "curse of the dimensional" of the wavelet networks, a new kind of linear 1-norm support vector machines (L1-SVM) will be applied to pre-select the hidden neurons, and it is hoped that, by leading structural risk minimization method of statistical learning theory into wavelet network, we can further enhance the generalization ability of the network. In optimization process of the 1-Norm support vector machine, Newton-Armijo algorithm based on gradient descent lead the computational complexity only depend on the smaller part between the numbers of training samples and characteristics, and the Ll-SVM with 1-norm of the regular forms spends less computation to get sparser solution, which is desired to be more applicable for the feature selection. To build more precise models from the noisy data sets, the multiresolution analysis learning algorithm (MRAL) for neural networks will be explored, which based on Multiresolution Analysis (MRA) of the wavelet transformation and nondominated sorting genetic algorithm-II (NSGA-II). Several different scaled signals of the error function will be used as the objectives, and NSGA-II algorithm is applied to optimize this multi-objective problem. And it is hoped that the MRAL algorithm can improve the learning ability of the feed-forward neural networks.