A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.     

基于分数阶最大相关熵算法的混沌时间序列预测

为提高最大相关熵算法对混沌时间序列的预测速度和精度,提出了一种新的分数阶最大相关熵算法.在采用最大相关熵准则的基础上,利用分数阶微分设计了一种新的权重更新方法.在alpha噪声环境下,采用新的分数阶最大相关熵算法对Mackey-Glass和Lorenz两类具有代表性的混沌时间序列进行预测,并分析了分数阶的阶数对混沌时间序列预测性能的影响.仿真结果表明:与最小均方算法、最大相关熵算法以及分数阶最小均方算法三类自适应滤波算法相比,所提分数阶最大相关熵算法在混沌时间序列预测中能够有效地抑制非高斯脉冲噪声干扰的影响,具有较快收的敛速度和较低的稳态误差.     

基于迭代误差补偿的混沌时间序列最小二乘支持向量机预测算法

本文分析了传统支持向量机预测算法产生的误差特性,发现产生的预测误差不同于噪声,具有较强的规律性,单一的预测模型遗漏了许多混沌序列中的确定性分量.经过误差补偿后,残差的冗余信息减少,随机性增强.在此基础上,本文提出一种基于迭代误差补偿的最小二乘支持向量机预测算法,能够通过多模型联合预测更加有效地逼近混沌系统的映射函数,在预测精度上取得了大幅度的提升.此外,算法通过留一交叉验证法的方法能够在预测前自动优化模型参数组合,克服了现有算法无法仅利用先验信息优化预测模型参数的缺陷.对MackeyGlass和Lorenz混沌时间序列进行了仿真实验,实验结果优于相关文献记载方法的预测性能,在性能指标上好于现有算法一个数量级.     

Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine

Some problems in using v-support vector machine (v-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming v-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.     

Discussion of Some Problems About Nonlinear Time Series Prediction Using ν-Support Vector Machine

Some problems in using ν-support vector machine (ν-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming ν-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.     

语音信号序列的Volterra预测模型

对给定的英语音素、单词和语句进行了采集并完成预处理. 分别应用互信息法和Cao 氏法确定了实际采集的语音信号序列的延迟时间和嵌入维数, 以完成语音序列的相空间重构. 通过计算实际采集的语音信号序列的最大Lyapunov指数, 完成了语音信号的混沌特性识别, 判定其具有混沌特性. 引入Volterra级数, 提出了一种具有显式结构的语音信号非线性预测模型. 为克服最小均方误差算法在Volterra模型系数更新时固有的缺点, 在最小二乘法基础上, 应用基于后验误差假设的可变收敛因子技术, 构建了一种基于Davidon-Fletcher-Powell算法的二阶Volterra 模型(DFPSOVF), 并将其应用于具有混沌特性的语音信号序列预测. 仿真结果表明: DFPSOVF非线性预测模型对于单帧和多帧语音信号均具有更好的预测精度, 优于线性预测模型, 并且能够很好地反映语音序列变化的趋势和规律, 完全可以满足语音预测的要求; 可以根据语音信号序列的嵌入维数选取预测模型的记忆长度. 所提出模型可以为语音信号重构和压缩编码开辟一条新途径, 以改善语音信号处理方法的复杂度和处理效果.     

非高斯冲激干扰下基于Softplus函数的核自适应滤波算法

针对非高斯环境下一般自适应滤波算法性能严重下降问题,本文提出了一种基于Softplus函数的核分式低次幂自适应滤波算法(kernel fractional lower algorithm based on Softplus function,SP-KFLP),该算法将Softplus函数与核分式低次幂准则相结合,利用输出误差的非线性饱和特性通过随机梯度下降法更新权重.一方面利用Softplus函数的特点在保证了SP-KFLP算法具有良好的抗脉冲干扰性能的同时提高了其收敛速度;另一方面将低次幂误差的倒数作为权重向量更新公式的系数,利用误差突增使得权重向量不更新的方法来抵制冲激噪声,并对其均方收敛性进行了分析.在系统辨识环境下的仿真表明,该算法很好地兼顾了收敛速度和跟踪性能稳定误差的矛盾,在收敛速度和抗脉冲干扰鲁棒性方面优于核最小均方误差算法、核分式低次幂算法和S型核分式低次幂自适应滤波算法.     

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     

一种时间序列的弱非线性检验方法

时间序列的非线性是判定该时间序列具有混沌特性的必要条件.提出一种基于线性和非线性AR模型归一化多步预测误差比值的非线性检验量δ_NAR,采用替代数据法来检测时间序列中的弱非线性.以Lorenz时间序列为例,分析了估计非线性检验量δ_NAR时各相关参数对弱非线性检测性能的影响.通过混沌时间序列非线性检测试验,对4种混沌时间序列中的3种,非线性检验量δ_NAR都表现出比基于AIC模型选择准则的非线性检验量相似文献   

基于改进教学优化算法的Hermite正交基神经网络混沌时间序列预测

针对传统预测模型对混沌时间序列预测精度低、收敛速度慢及模型结构复杂的问题, 提出了基于改进教学优化算法的Hermite正交基神经网络预测模型. 首先, 将自相关法和Cao方法相结合对混沌时间序列进行相空间重构, 以获得重构延迟时间向量; 其次, 以Hermite正交基函数为激励函数构成Hermite正交基神经网络, 作为预测模型; 最后, 将模型参数优化问题转化为多维空间上的函数优化问题, 利用改进教学优化算法对预测模型进行参数优化, 以建立预测模型并进行预测分析. 分别以Lorenz 系统和Liu系统为模型, 通过四阶Runge-Kutta法产生混沌时间序列作为仿真对象, 并进行单步及多步预测对比实验. 仿真结果表明, 与径向基函数神经网络、回声状态网络、最小二乘支持向量机及基于教学优化算法的Hermite正交基神经网络预测模型相比, 所提预测模型具有更高的预测精度、更快的收敛速度和更简单的模型结构, 验证了该模型的高效性, 便于推广和应用.     

Nonlinear adaptive filters for high-speed LED based underwater visible light communication [Invited]

Underwater visible light communication(UVLC) is expected to act as an alternative candidate in nextgeneration underwater 5 G wireless optical communications. To realize high-speed UVLC, the challenge is the absorption, scattering, and turbulence of a water medium and the nonlinear response from imperfect optoelectronic devices that can bring large attenuations and a nonlinearity penalty. Nonlinear adaptive filters are commonly used in optical communication to compensate for nonlinearity. In this paper, we compare a recursive least square(RLS)-based Volterra filter, a least mean square(LMS)-based digital polynomial filter,and an LMS-based Volterra filter in terms of performance and computational complexity in underwater visible light communication. We experimentally demonstrate 2.325 Gb/s transmission through 1.2 m of water with a commercial blue light-emitting diode. Our goal is to assist the readers in refining the motivation, structure,performance, and cost of powerful nonlinear adaptive filters in the context of future underwater visible light communication in order to tap into hitherto unexplored applications and services.     

交通流量序列混沌特性分析及DFPSOVF预测模型

以实际采集的交通流量序列作为研究对象, 分别应用互信息法和虚假邻点法确定其延迟时间和最佳嵌入维数, 完成交通流量序列的相空间重构. 通过计算交通流量序列的饱和关联维数和最大Lyapunov指数判定其混沌特性. 以最小均方(LMS)算法为基础, 构建了一种基于Davidon-Fletcher-Powell方法的二阶Volterra模型(DFPSOVF), 其应用了一种可随输入信号变化而实时变化的基于后验误差假设的可变收敛因子技术. DFPSOVF模型避免了在Volterra模型中采用LMS自适应算法调整系数时参数选择不当引起的问题. 将DFPSOVF模型应用于具有混沌特性的短时交通流量预测, 结果表明: 当模型记忆长度与交通流量序列的嵌入维数选择一致时, 模型的预测精度较高, 可以满足交通诱导和交通控制的需要, 为智能交通控制提供了新方法、新思路及工程应用参考. 关键词： 交通流量 混沌 DFPSOVF模型 预测     

Least mean square error difference minimum criterion for adaptive chaotic noise canceller

The least mean square error difference (LMS-ED) minimum criterion for an adaptive chaotic noise canceller is proposed in this paper. Different from traditional least mean square error minimum criterion in which the error is uncorrelated with the input vector, the proposed LMS-ED minimum criterion tries to minimize the correlation between the error difference and input vector difference. The novel adaptive LMS-ED algorithm is then derived to update the weights of adaptive noise canceller. A comparison between cancelling performances of adaptive least mean square (LMS), normalized LMS (NLMS) and proposed LMS-ED algorithms is simulated by using three kinds of chaotic noises. The simulation results clearly show that the proposed algorithm outperforms the LMS and NLMS algorithms in achieving small values of steady-state excess mean square error. Moreover, the computational complexity of the proposed LMS-ED algorithm is the same as that of the standard LMS algorithms.     

基于P范数的核最小对数绝对差自适应滤波算法

为了进一步提高在a稳定分布噪声背景下非线性自适应滤波算法的收敛速度,本文提出了一种新的基于p范数的核最小对数绝对差自适应滤波算法(kernel least logarithm absolute difference algorithm based on p-norm, P-KLLAD).该算法结合核最小对数绝对差算法和p范数,一方面利用最小对数绝对差准则保证了算法在a稳定分布噪声环境下良好的鲁棒性,另一方面在误差的绝对值上添加p范数,通过p范数和一个正常数a来控制算法的陡峭程度,从而提高该算法的收敛速度.在非线性系统辨识和Mackey-Glass混沌时间序列预测的仿真结果表明,本文算法在保证鲁棒性能的同时提高了收敛速度,并且在收敛速度和鲁棒性方面优于核最小均方误差算法、核分式低次幂算法、核最小对数绝对差算法和核最小平均p范数算法.     

声光自适应信号处理技术在扩频通信中的应用

研究了声光滤波的工作原理,用布拉格器件作模拟抽头延迟线完成横向滤波。讨论了LMS自适应滤波的基本方法,给出了声光自适应LMS滤波的实现方法并用于扩频通信的窄带干扰抑制中。对扩频通信进行干扰抑制的滤波过程通常是一个自适应过程,采用声光自适应滤波技术,不仅能抑制窄带干扰,而且能提高系统的处理增益和分辨率。     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

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.     

Adaptive RAKE receiver in chaos based pilot-added DS-CDMA system

This paper presents the theoretical analysis of adaptive multiuser RAKE receiver scheme in frequency selective fading channel for direct-sequence code division multiple access (DS-CDMA) system. Least mean square (LMS) algorithm is used to estimate the channel coefficients. Chaotic sequences are used as spreading sequence and corresponding bit error rate (BER) in closed form is derived for imperfect channel estimation conditions. Performances of chaotic sequences are compared with pseudorandom noise (PN) sequences. Under perfect synchronization assumption, various simulation results are shown to investigate the performance of the proposed system.     

连续混沌信号的离散余弦变换域二次实时滤波预测

提出了少参数二阶Volterra滤波器的一种离散余弦变换(DCT)域二次滤波实现结构及其NLMS自适应算法，并用这种DCT域二次滤波预测器研究了三种连续混沌信号的非线性实时多步预测性能. 仿真研究结果表明：(1) 这种DCT域二次滤波预测器比少参数二阶Volterra滤波器的一步预测均方误差性能提高了100倍，表明这种实现结构简单、易实现，且具有更好的收敛性能；（2）采用这种滤波预测器对三种连续混沌时间序列的实时多步预测性能明显优于局域法的多步预测性能. 关键词： 混沌 实时预测 NLMS自适应算法     

Adaptive nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise systems

An adaptive nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise control systems is proposed to attenuate the nonlinear and non-Gaussian noises. Inspired by the structure of the Hammerstein or Wiener model, the proposed controller is realized by the static nonlinear memory function mapping on the basis of a single neuron. A generalized filtered-X gradient descent algorithm based on an integrated evaluation criterion is developed to adaptively adjust the weights of the controller, where the weighted sum of Renyi's quadratic error entropy and the mean square error is applied as the integrated performance index, which improves the performance of the adaptive algorithm by introducing the information entropy. In addition, the convergence of the proposed approach is analyzed, and the computational complexity among different methods is investigated. The proposed scheme can effectively attenuate the nonlinear and non-Gaussian noises and has a relative simple structure and less learning parameters. The simulation results demonstrate the validity of the proposed method for attenuating the nonlinear and non-Gaussian noises.