Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method,this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors,which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens.The experimental results show that,the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system,and the nonlinear invariants such as correlation dimension,Lyapunov exponent and Kolmogorov entropy are still reserved.It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.

PARAMETERS DETERMINATION METHOD OF PHASE-SPACE RECONSTRUCTION BASED ON DIFFERENTIAL ENTROPY RATIO AND RBF NEURAL NETWORK

Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.

Gradient method for blind chaotic signal separation based on proliferation exponent

A new method to perform blind separation of chaotic signals is articulated in this paper, which takes advantage of the underlying features in the phase space for identifying various chaotic sources. Without incorporating any prior information about the source equations, the proposed algorithm can not only separate the mixed signals in just a few iterations, but also outperforms the fast independent component analysis(FastICA) method when noise contamination is considerable.

KLT-based local linear prediction of chaotic time series

In the reconstructed phase space,based on the Karhunen-Lo(?)ve transformation(KLT),the new local linear prediction method is proposed to predict chaotic time series.A noise-free chaotic time series and a noise added chaotic time series are analyzed.The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series,and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.

Nonlinear chaotic characteristic in leaching process and prediction of leaching cycle period

A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.

水轮机空化声发射信号降噪与混沌图像特征提取

针对水轮机空化声发射信号存在噪声影响信号特征有效提取的问题,本文建立了基于傅里叶分解与多分辨奇异值分解的降噪和混沌特征提取的水轮机空化声发射信号处理方法。采用傅里叶分解算法将水轮机空化声发射信号分解为若干个固有频带函数,计算其相关系数。利用多分辨奇异值分解算法对相关系数较小的固有频带函数进行降噪,再将降噪后的固有频带函数与相关系数较大的固有频带函数进行重构,完成信号降噪。结果表明:将相空间重构得到相轨迹图和Poincaré截面图作为信号特征,本文降噪方法可以更好实现水轮机空化声发射信号降噪;混沌特征图像可以反映空化状态变化规律。

基于相空间重构和卷积神经网络的混沌信号识别方法

针对卷积神经网络在处理一维信号时会由于网络模型参量过多导致算法收敛慢和过拟合问题,提出了一种基于相空间重构和卷积神经网络的混沌振动信号智能识别方法。首先,利用时间延迟法将一维混沌振动信号重构为二维吸引子图;然后,通过扫描转换法将其转换为标准像素图输入卷积神经网络模型;最后,借助卷积神经网络强大的图像分类能力,实现仿真和试验混沌振动信号的智能识别。结果表明:该方法能对含噪声的混沌振动信号进行有效识别,在信噪比超过10 dB时分类准确率仍可达100%,不仅具有良好的泛化性、稳定性和通用性,还消除了训练的过拟合现象,能较好地应用于工程实际中。

A New Chaotic Function and Its Cryptographic Usage

Wheeler pointed out that the period of Matthews' cha-otic function (MCF) is often too short to be suitable for crypto-graphic usage in the manner of computer statistics,but this state-ment was given only through digital computation. In this paper,we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic func-tions working together we presented a modified MCF (MMCF) that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.

植物茎干水分系统混沌动力学特性分析

植物水分系统由于与周围环境的非线性相互作用,通常表现出复杂的时空格局。为了探究植物水分系统中的混沌特性,该研究以相空间重构、相关维数(correlation dimension,CD)、最大李雅普诺夫指数(largest Lyapunov exponent,LLE)为基础,研究了植物茎干水分时间序列中可能存在的混沌行为,研究树种包括海棠、花楸、黄丁香、铅笔柏和杨树。结果表明,植物水分系统存在混沌现象,且植物水分动态特性由控制变量数量有限的确定性系统决定。不同种类植物的茎干水分混沌参数普遍存在差异,同种植物生长状态相近时茎干水分的混沌参数相近,当生长状态出现差异时混沌参数随之发生变化。对不同生长状态的植物茎干水分混沌参数分析发现,杨树在干旱胁迫下LLE不高于0.006,而对照组平均值为0.010,木质部破坏胁迫后LLE不高于0.007,而对照组平均值为0.019,表明混沌参数可有效表征植物茎干水分数据变化趋势,并与植物生长状态存在联系,可以尝试利用这一规律对植物生长状态进行预测与回溯。该研究尝试从混沌理论的角度分析植物水分系统的复杂性,可为理解植物水分动力学的混沌行为提供新的途径。

变压器绕组松动故障的混沌特征分析方法

为了更加有效地对变压器绕组松动故障进行监测与识别,提出了一种变压器绕组松动故障的混沌特征分析方法。首先,针对振动信号的混沌动力学特性,采用互信息量法和G-P算法分别确定延迟时间和嵌入维数,对变压器振动信号进行相空间重构;其次,通过判断最大Lyapunov指数是否为正,进而证明变压器振动信号的混沌特性,在此基础上分析不同程度的绕组松动故障对相空间轨迹变化的影响;最后,将关联维数、Kolmogorov熵和最大Lyapunov指数作为一组混沌特征用以量化变压器绕组发生松动故障前后振动信号的混沌特性。结果表明:变压器振动信号的最大Lyapunov指数均大于0,证实了其具有混沌特性,所得到的混沌特征能够有效反映变压器绕组松动故障。研究结果为变压器绕组松动状态监测提供了一种理论依据。

以时间序列分析为基准的航站楼安检客流预测

目前在民航旅客流量预测方面,仍存在诸如序列粒度考虑过粗、未涉及到未来一天某个短时段内流量预测等问题。在单一时段内利用安全检查技术开展客流预测工作是交通系统的重要部分。为此,首先针对安检客流时间序列进行相空间重构;其次,使用Wolf方法进行安检客流时间序列混沌性判别;再次,采用BP神经网络预测方法对混沌时间序列进行预测;最后,讨论一天的高峰时间,并将该时段划分为2 min,3 min,5 min,10 min等时间间隔,利用曲线拟合方法对每天的客流趋势进行相似性分析。文中数据来源于北京首都国际机场T3航站楼安检客流数据。实验结果表明,文中方案具有较好的预测性能,在高峰期情况下,以2 min为时间间隔,采用BP神经网络方法能够在短时间内完成人员与资源动态调度。

混沌系统吸引子的编选方法

为了将混沌系统不同状态的吸引子同时选择出来,以便对系统进行更深入的研究,该文引入了吸引子编选器概念,并在理论上进行了证明。吸引子编选器提供了一种在不同系统参数下选择典型吸引子,并在相位空间中灵活排序的有效技术。通过对类Chen系统进行动力学分析,确定了吸引子编选器的参数,并按照设定顺序将类Chen系统不同状态的吸引子在相位空间进行排列。吸引子编选器使混沌系统在安全通信等领域更具有应用潜力。

金属矿山岩层能量释放规律及相应的安全预警系统

基于对岩层变形进行长期观测的基础上,提出岩层能量释放的分析方法,通过对地层能量释放时间序列数据进行相空间重构,揭示了岩层能量释放点之间距离的演化规律,建立了岩层能量释放预测模型。结果表明,岩层能量释放具有混沌特征,充分显示其内在规律,建立岩层稳定预警系统为安全开采提供技术保障。

基坑变形混沌特征识别与非线性预测模型研究

混沌理论特征识别是进行混沌时间序列分析和预测的前提。普通的线性数学算法已经无解决基坑变形所遇到的问题,为了研究基坑变形监测数据的非线性复杂问题,采用混沌非线性理论方法,首先求取基坑变形时间序列的延迟时间和嵌入维数,其次对基坑监测数据进行相空间重构,最后对比分析加权一阶局域预测模型以及RBF神经网络混沌预测模型的预测结果,实验表明RBF神经网络混沌预测模型预测精度最高,同时也说明了混沌预测模型更适合短期预测。最终证明了RBF神经网络混沌预测模型应用在基坑变形监测中的可行性与有效性。

相空间小波网络模型及其在水文中长期预测中的应用

简述了相空间小波网络模型原理和算法，并通过实例讨论了其在水文中的应用。研究结果初步表明，小波分析及由其发展出的小波网络模型在水文分析中是可行的、合理的。数学分析工具更为先进，将混沌重建相空间理论和小波网络模型相结合，对揭示水文动力系统复杂的非线性结构是很有效的，在水文中长期预测中具有较大优越性。

边坡变形时序非线性判定及混沌预测研究

以探讨边坡变形性质及混沌预测可行性为目的,基于混沌理论利用相空间重构技术对其变形时间序列进行混沌特征判定,试验显示变形系统具有混沌特性,可用混沌相关理论进行研究;基于混沌相空间重构技术,笔者构建了多种混沌预测模型进行混沌预计研究,分析各类模型的工程实际应用效果;针对单次监测时序预测精度较低的问题,提出累加时序预测方案,训练结果显示,短期预测精度变形累计值基本控制在5%以内,高程值预测相对误差均低于1%,预测精度较高,可以用于工程实际。

成矿元素巨量聚集的混沌机制——斑岩型和构造蚀变岩型矿床例析

成矿元素含量的变化受控于成矿系统内部的动力学过程,具有较强的随机性与混沌特征,对其变化特征的定量刻画有助于深入理解成矿过程,并为找矿预测提供理论依据。本文以三江普朗斑岩型铜矿的Cu元素与胶东大尹格庄构造蚀变岩型金矿的Au元素品位序列为研究对象,运用混沌时间序列分析法中的相空间重构技术、吸引子的关联维及最大Lyapunov指数解析了Cu与Au元素品位序列的分布特征。结果显示:斑岩型铜矿强矿化和中矿化Cu元素品位的饱和关联维介于4.42与9.69之间,饱和嵌入维介于25与28之间,最大Lyapunov指数介于0.0021与0.0661之间,弱矿化勘探线Cu元素关联维没有出现饱和现象,最大Lyapunov指数随着嵌入维的增大,由正数变为负数;构造蚀变岩型金矿的强矿化勘探线Au元素的关联维为3.18,饱和嵌入维为23,最大Lyapunov指数为0.0082,而中矿化和弱矿化勘探线Au元素的关联维没有出现饱和现象,且随着嵌入维的增大,最大Lyapunov指数由正数变为负数,表明斑岩型中-强矿化地区的Cu元素和构造蚀变岩型强矿化区域的Au元素品位序列具有混沌动力学特征,而弱矿化地区的Cu元素及中弱矿化地区的Au元素品位序列则具有更强的随机性特征;同时,具有混沌特征的斑岩型铜矿的饱和嵌入维和关联维及最大Lyapunov指数的均值都大于蚀变岩型矿床,说明斑岩型铜矿比蚀变岩型矿床的元素具有更强混沌特性与更复杂的控制因素,如温度、硫化作用、流体不混溶、蚀变叠加等。

短期电力负荷的小波—混沌时序预测

提出了一种基于2层小波分解的混沌时序相空间重构预测模型。该模型利用小波分解原始负荷时间序列为周期项、趋势项和随机项,采用不同的混沌相空间重构高低频信号,再分别用相应的小波神经网络工具箱拟合混沌吸引子,将其输出进行信号重构得到最终预测结果。该方法兼有频率特征提取和相空间重构的优点,使短期电力负荷时序列的动力学系统得到更加细致的恢复。通过对欧洲电力负荷竞赛数据的实验证明了所提方法的有效性,仿真结果表明方法预测精度优于常规混沌时序预测方法。针对神经网络预测不稳定的问题给出了一种解决措施,并提出了一种小波神经网络工具箱,该方法比编程实现的小波网络可以大幅度提高训练速度,尤其适合于大批量数据的训练,对小波神经网络的推广应用和混沌时序预测具有重要意义。

参考作物腾发量的混沌性识别及预测

本文应用饱和关联维数法对海河流域张北站从1966～2005年50年的参考作物腾发量序列进行混沌性识别，结果表明该序列存在一定的混沌特性。同时，运用自相关函数法和饱和关联维数法确定了该序列重构相空间的嵌入维数和延迟时间，并在此基础上进行了相空间的重构。建立了混沌局域法预测模型对相空间的演化进行了计算，实现了参考作物腾发量的预测，并与时间序列自回归（AR）模型和基于气象资料的BP神经网络模型预测结果进行了比较。结果表明，预测效果比BP网络模型稍差，但明显优于AR模型。这为解决缺乏气象资料地区参考作物腾发量预测问题提供了新的思路。