混沌时间序列全局预测新方法——连分式法

拓展了多项式逼近理论，利用连分式法建立了混沌时间序列非线性全局预测模型，此模型替代混沌序列的动力学方程，实现对其动力学特性分析，达到预测目的. 理论分析和仿真实验表明，连分式法能够有效预测一些混沌序列，该方法预测精度高，并且能得到显式的预测表达式. 关键词： 混沌时间序列 全局预测 连分式     

基于混沌算子网络的时间序列多步预测研究

结合相空间重构理论和时间序列分析理论,提出一种用于时间序列多步预测的网络模型.网络采用多个混沌算子加权求和的形式构成.网络各层单元采用固定权值连接,混沌算子的控制参数利用混沌优化算法进行训练调节,从而控制预测网络的动力学行为.利用已知时间序列数据构造出训练样本,训练样本在网络训练过程中仅使用一次,促使网络的动力学特性随时间的推移而变化,并逐渐逼近被预测系统的动力学特性,最终完成对未来时刻数据的预测.在对理论数据进行预测分析时,通过计算预测序列的Lyapunov指数验证了预测网络的有效性.在对实际时间序列的预测过程中,该网络表现出了良好的预测性能.仿真结果表明,该预测网络可对多种时间序列在一定的预测步长范围内实现有效的预测.     

道路交通流状态的多参数融合预测方法

针对道路交通流普遍存在的混沌特性以及单交通参数不足 以全面反映交通流状态的实际情况,考虑交通动力学系统中多个 交通参数之间的关联关系,提出一种新的多参数混沌时间序列预 测算法.该算法在相空间重构理论的基础上,借助Bayes估计将多个参数在 同一高维相空间中进行相点最优融合,从而增加重构相空间的系统信息量, 使得相空间的相点轨迹更加逼近原交通系统的动力学行为.同时借鉴单 参数混沌时间序列预测方法,从不同角度对动力学系统的运动状态进行描 述,以实现多参数时间序列的混沌预测.实验结果表明,通过融合多交通参数时 间序列,获得了更加完整的交通流状态变化特征.与单交通参数时间序列的预测 结果相比,其预测误差显著降低,均衡系数相应增大,提高了交通流状态预测的准确率.     

多元混沌时间序列的多核极端学习机建模预测

多元混沌时间序列广泛存在于自然、经济、社会、工业等领域. 对多元混沌时间序列进行建模预测有助于人类更好地管理, 控制与决策. 针对多元混沌时间序列的建模预测问题, 本文提出一种基于多核极端学习机的预测方法. 首先对多元混沌时间序列进行相空间重构, 将多元混沌时间序列序列的时间相关性转化为空间相关性. 提出一种结合多核学习算法与核极端学习机模型的多核极端学习机建立相空间中输入输出数据的非线性映射. 多核极端学习机模型结合了多核学习算法的数据融合能力以及核极端学习机的训练简便优势. 基于Lorenz混沌时间序列预测和San Francisco河流月径流量预测的仿真实验表明, 与其他常见混沌时间序列预测方法相比, 本文提出的基于多核极端学习机的多元混沌时间序列预测方法具有更小的预测误差.     

基于平稳小波和相空间重构的激光混沌预测

提出了一种激光混沌时间序列预测算法.该算法通过平稳小波分解，将原始数据序列分解为与原序列等长的尺度系数和小波系数，利用坐标延迟理论，重建各级尺度系数和各级小波系数的相空间,再根据混沌吸引子的稳定性和分形性,在相空间中对尺度系数和小波系数进行预测,进而通过平稳小波重构算法,实现了时间序列的非线性预测.该算法对数据可以进行更平滑的处理，比无小波算法预测的时间范围更长.通过仿真试验说明，原始时间数据序列被成功的重建，说明算法能够有效的对非线性动态系统的时间序列进行建模和预测.     

基于多元局部多项式方法的混沌时间序列预测

根据Takens定理，把混沌时间序列构造为一组序列对，然后用多元局部多项式方法来预测其序列.这种核估计方法可以结合局域法与全局法的优点，使得预测的精度更高.仿真结果表明，该方法非常有效.     

基于最大Lyapunov指数的多变量混沌时间序列预测

参考基于最大Lyapunov指数的单变量混沌时间序列预测方法,提出一种通过选取多个邻近重构向量,预测多变量混沌时间序列的局域法.采用新方法对两个完全不同的Rssler方程的耦合系统,Rssler方程和Hyper Rssler方程的耦合系统的多变量混沌时序进行一步和多步预测,结果表明了该方法的有效性,且算法具有较强的抗噪能力.讨论了参考邻近点数和预测结果的关系. 关键词： Lyapunov指数 混沌时间序列预测 多变量时间序列 最小二乘法     

基于在线小波支持向量回归的混沌时间序列预测

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 关键词： 混沌时间序列 支持向量回归 在线学习 小波核     

基于Cholesky分解的增量式RELM及其在时间序列预测中的应用

针对应用于混沌时间序列预测的正则极端学习机(RELM)网络结构设计问题,提出一种基于Cholesky分解的增量式RELM训练算法.该算法通过逐次增加隐层神经元的方式自动确定最佳的RELM网络结构,并以Cholesky分解方式计算其输出权值,有效减小了隐层神经元递增过程的计算代价.混沌时间序列预测实例表明,该算法可有效实现最佳RELM网络结构的自动确定,且计算效率高.利用该算法训练后的RELM预测模型具有预测精度高的优点,适用于混沌时间序列预测. 关键词： 神经网络 极端学习机 混沌时间序列 时间序列预测     

采用优化极限学习机的多变量混沌时间序列预测

基于优化极限学习机理论, 提出一种多变量混沌时间序列预测方法. 该方法利用复合混沌和混沌变尺度算法对极限学习机的模型参数进行搜索和优化, 以提高极限学习机的泛化性能; 然后利用优化后的极限学习机对Rossler耦合系统的多变量混沌时序进行一步和多步预测, 并且与同类算法进行了比较, 结果表明了该方法的有效性, 且算法具有较强的抗噪能力; 最后讨论了预测结果和隐层神经元数目的关系.     

Chaotic signal detection and estimation based on attractor sets: applications to secure communications

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.     

动力学变换法探测连续系统不稳定周期轨道

本文利用动力学变换方法和庞加莱截面方法对两种连续混沌动力学系统进行不稳定周期轨道探测研究, 并对Lorenz系统进行了替代数据法检验.结果表明:基于庞加莱截面的动力学变换改进算法 可有效探测连续混沌动力学系统中的不稳定周期轨道.     

Model-based detector and extraction of weak signal frequencies from chaotic data

Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Henon map, chaotic circuit, and NH(3) laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series.     

MULTISTAGE ADAPTIVE HIGHER-ORDER NONLINEAR FINITE IMPULSE RESPONSE FILTERS FOR CHAOTIC TIME SERIES PREDICTIONS

A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.     

一种新型广义RBF神经网络在混沌时间序列预测中的研究

提出了一种新颖的广义径向基函数神经网络模型,其径向基函数(RBF)的形式由生成函数确定.然后,给出了易实现的梯度学习算法,同时为了进一步提高网络的收敛速度和网络性能,又给出了基于卡尔曼滤波的动态学习算法.为了验证网络的学习性能，采用基于卡尔曼滤波算法的新型广义RBF网络预测模型对Mackey-Glass混沌时间序列和Henon映射进行了仿真.结果表明,所提出的新型广义RBF神经网络模型能快速、精确地预测混沌时间序列,是研究复杂非线性动力系统辨识和控制的一种有效方法. 关键词： 广义径向基函数神经网络 卡尔曼滤波 梯度下降学习算法 混沌时间序列 预测     

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.     

Modelling of chaotic systems based on modified weighted recurrent least squares support vector machines

Positive Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially. In this paper, we propose the modified version of the support vector machines (SVM) to deal with this problem. Based on recurrent least squares support vector machines (RLS-SVM), we introduce a weighted term to the cost function tocompensate the prediction errors resulting from the positive global Lyapunov exponents. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to the Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.     

Improving the prediction of chaotic time series

One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.     

用于混沌时间序列自适应预测的一种少参数二阶Volterra滤波器

研究了二阶Volterra滤波器的一种乘积耦合近似实现结构及其非线性NLMS自适应算法,并用这种少参数二阶Volterra滤波器(RPSOVF)研究了一些混沌信号的非线性自适应预测性能.仿真研究结果表明:所给出的非线性NLMS自适应算法能够保证这种RPSOVF的稳定性和收敛性,且RPSOVF用这种非线性NLMS自适应算法能够自适应预测一些混沌时间序列. 关键词： 混沌 非线性自适应预测 Volterra滤波器 非线性NLMS自适应算法     

Application of permutation entropy method in the analysis of chaotic,noisy, and chaotic noisy series

We have considered a permutation entropy method for analyzing chaotic, noisy, and chaotic noisy series. We have introduced the concept of permutation entropy from a survey of some features of information entropy (Shannon entropy), described the algorithm for its calculation, and indicated the advantages of this approach in the analysis of time series; the application of this method in the analysis of various model systems and experimental data has also been demonstrated.