Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network

A computationally efficient pipelined functional link artificial recurrent neural network (PFLARNN) is proposed for nonlinear dynamic system identification using a modification real-time recurrent learning (RTRL) algorithm in this paper. In contrast to a feedforward artificial neural network (such as a functional link artificial neural network (FLANN)), the proposed PFLARNN consists of a number of simple small-scale functional link artificial recurrent neural network (FLARNN) modules. Since those modules of PFLARNN can be performed simultaneously in a pipelined parallelism fashion, this would result in a significant improvement in its total computational efficiency. Moreover, nonlinearity of each module is introduced by enhancing the input pattern with nonlinear functional expansion. Therefore, the performance of the proposed filter can be further improved. Computer simulations demonstrate that with proper choice of functional expansion in the PFLARNN, this filter performs better than the FLANN and multilayer perceptron (MLP) for nonlinear dynamic system identification.     

Pipelined functional link artificial recurrent neural network with the decision feedback structure for nonlinear channel equalization

This paper presents a computationally efficient nonlinear adaptive filter by a pipelined functional link artificial decision feedback recurrent neural network (PFLADFRNN) for the design of a nonlinear channel equalizer. It aims to reduce computational burden and improve nonlinear processing capabilities of the functional link artificial recurrent neural network (FLANN). The proposed equalizer consists of several simple small-scale functional link artificial decision feedback recurrent neural network (FLADFRNN) modules with less computational complexity. Since it is a module nesting architecture comprising a number of modules that are interconnected in a chained form, its performance can be further improved. Moreover, the equalizer with a decision feedback recurrent structure overcomes the unstableness thanks to its nature of infinite impulse response structure. Finally, the performance of the PFLADFRNN modules is evaluated by a modified real-time recurrent learning algorithm via extensive simulations for different linear and nonlinear channel models in digital communication systems. The comparisons of multilayer perceptron, FLANN and reduced decision feedback FLANN equalizers have clearly indicated the convergence rate, bit error rate, steady-state error and computational complexity, respectively, for nonlinear channel equalization.     

A hierarchical alternative updated adaptive Volterra filter with pipelined architecture

The pipelined adaptive Volterra filters (PAVFs) with a two-layer structure constitute a class of good low-complexity filters. They can efficiently reduce the computational complexity of the conventional adaptive Volterra filter. Their major drawbacks are low convergence rate and high steady-state error caused by the coupling effect between the two layers. In order to remove the coupling effect and improve the performance of PAVFs, we present a novel hierarchical pipelined adaptive Volterra filter (HPAVF)-based alternative update mechanism. The HPAVFs with hierarchical decoupled normalized least mean square (HDNLMS) algorithms are derived to adaptively update weights of its nonlinear and linear subsections. The computational complexity of HPAVF is also analyzed. Simulations of nonlinear system adaptive identification, nonlinear channel equalization, and speech prediction show that the proposed HPAVF with different independent weight vectors in nonlinear subsection has superior performance to conventional Volterra filters, diagonally truncated Volterra filters, and PAVFs in terms of initial convergence, steady-state error, and computational complexity.     

Pipelined robust M-estimate adaptive second-order Volterra filter against impulsive noise

The main limits on adaptive Volterra filters are their computational complexity in practical implementation and significant performance degradation under the impulsive noise environment. In this paper, a low-complexity pipelined robust M-estimate second-order Volterra (PRMSOV) filter is proposed to reduce the computational burdens of the Volterra filter and enhance the robustness against impulsive noise. The PRMSOV filter consists of a number of extended second-order Volterra (SOV) modules without feedback input cascaded in a chained form. To apply to the modular architecture, the modified normalized least mean M-estimate (NLMM) algorithms are derived to suppress the effect of impulsive noise on the nonlinear and linear combiner subsections, respectively. Since the SOV-NLMM modules in the PRMSOV can operate simultaneously in a pipelined parallelism fashion, they can give a significant improvement of computational efficiency and robustness against impulsive noise. The stability and convergence on nonlinear and linear combiner subsections are also analyzed with the contaminated Gaussian (CG) noise model. Simulations on nonlinear system identification and speech prediction show the proposed PRMSOV filter has better performance than the conventional SOV filter and joint process pipelined SOV (JPPSOV) filter under impulsive noise environment. The initial convergence, steady-state error, robustness and computational complexity are also better than the SOV and JPPSOV filters.     

Pipelined Chebyshev Functional Link Artificial Recurrent Neural Network for Nonlinear Adaptive Filter

A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously be performed in a pipelined parallelism fashion, and this would lead to a significant improvement in its total computational efficiency. Furthermore, contrasted with the architecture of a pipelined RNN (PRNN), each module of PCFLARNN is a CFLARNN whose nonlinearity is introduced by enhancing the input pattern with Chebyshev functional expansion, whereas the RNN of each module in PRNN utilizing linear input and first-order recurrent term only fails to utilize the high-order terms of inputs. Therefore, the performance of PCFLARNN can further be improved at the cost of a slightly increased computational complexity. In addition, due to the introduced nonlinear functional expansion of each module in PRNN, the number of input signals can be reduced. Computer simulations have demonstrated that the proposed filter performs better than PRNN and RNN for nonlinear colored signal prediction, nonstationary speech signal prediction, and chaotic time series prediction.      

Generalized spline nonlinear adaptive filters

A new nonlinear filter, which employs an adaptive spline function as the basis function is designed in this paper. The input signal to this filter is used to generate suitable parameters to update the control points in a spline function. The update rule for updating the control points have been derived and a mean square analysis has been carried out. The output of the spline functions are suitably combined together to obtain the filter response. This filter is called the generalized spline nonlinear adaptive filter (GSNAF). The proposed GSNAF is similar to a functional link artificial neural network (FLANN), considering a functional expansion using spline basis functions. GSNAF has been shown to offer improved accuracy in benchmark classification scenarios and provide enhanced modeling accuracy in single input single output as well as in multiple input multiple output dynamic system identification cases.     

Improved functional link artificial neural network via convex combination for nonlinear active noise control

A method relying on the convex combination of two normalized filtered-s least mean square algorithms (CNFSLMS) is presented for nonlinear active noise control (ANC) systems with a linear secondary path (LSP) and nonlinear secondary path (NSP) in this paper. The proposed CNFSLMS algorithm-based functional link artificial neural network (FLANN) filter, aiming to overcome the compromise between convergence speed and steady state mean square error of the NFSLMS algorithm, offers both fast convergence rate and low steady state error. Furthermore, by replacing the sigmoid function with the modified Versorial function, the modified CNFSLMS (MCNFSLMS) algorithm with low computational complexity is also presented. Experimental results illustrate that the combination scheme can behave as well as the best component and even better. Moreover, the MCNFSLMS algorithm requires less computational complexity than the CNFSLMS while keeping the same filtering performance.     

Nonlinear channel equalization for QAM signal constellation usingartificial neural networks

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.     

Functional link artificial neural network applied to active noise control of a mixture of tonal and chaotic noise

Many practical noises emanating from rotating machines with blades generate a mixture of tonal and the chaotic noise. The tonal component is related to the rotational speed of the machine and the chaotic component is related to the interaction of the blades with air. An active noise controller (ANC) with either linear algorithm like filtered-X least mean square (FXLMS) or nonlinear control algorithm like functional link artificial neural network (FLANN) or Volterra filtered-X LMS (VFXLMS) algorithm shows sub-optimal performance when the complete noise is used as reference signal to a single controller. However, if the tonal and the chaotic noise components are separated and separately sent to individual controller with tonal to a linear controller and chaotic to a nonlinear controller, the noise canceling performance is improved. This type of controller is termed as hybrid controller. In this paper, the separation of tonal and the chaotic signal is done by an adaptive waveform synthesis method and the antinoise of tonal component is produced by another waveform synthesizer. The adaptively separated chaotic signal is fed to a nonlinear controller using FLANN or Volterra filter to generate the antinoise of the chaotic part of the noise. Since chaotic noise is a nonlinear deterministic noise, the proposed hybrid algorithm with FLANN based controller shows better performance compared to the recently proposed linear hybrid controller. A number of computer simulation results with single and multitone frequencies and different types of chaotic noise such as logistic and Henon map are presented in the paper. The proposed FLANN based hybrid algorithm was shown to be performing the best among many previously proposed algorithms for all these noise cases including recorded noise signal.     

Pipelined recurrent fuzzy neural networks for nonlinear adaptive speech prediction.

A class of pipelined recurrent fuzzy neural networks (PRFNNs) is proposed in this paper for nonlinear adaptive speech prediction. The PRFNNs are modular structures comprising a number of modules that are interconnected in a chained form. Each module is implemented by a small-scale recurrent fuzzy neural network (RFNN) with internal dynamics. Due to module nesting, the PRFNNs offer a number of desirable attributes, including decomposition of the modeling task, enhanced temporal processing capabilities, and multistage dynamic fuzzy inference. Tuning of the PRFNN adaptable parameters is accomplished by a series of gradient descent methods with different weighting of the modules and the decoupled extended Kalman filter (DEKF) algorithm, based on weight grouping. Extensive experimentation is carried out to evaluate the performance of the PRFNNs on the speech prediction platform. Comparative analysis shows that the PRFNNs outperform the single-RFNN models in terms of the prediction gains that are obtained and computational efficiency. Furthermore, PRFNNs provide considerably better performance compared to pipelined recurrent neural networks, for models with similar model complexity.     

基于高斯混合飞蛾优化算法的Wiener模型辨识

针对Wiener模型辨识问题,结合函数连接型神经网络(FLANN)和飞蛾优化算法(MFO)的优势,提出了一种新型的辨识方案。利用FLANN来拟合静态非线性模块,通过将辨识问题转化为优化问题来对线性部分和非线性部分的参数同时进行更新。为了提升飞蛾优化算法的辨识性能,将高斯混合分布思想引入飞蛾种群初始化以及位置更新中,提出了一种新型的高斯混合飞蛾优化算法(GMFO),并通过测试函数验证了其寻优性能。最后通过仿真实验结果证明了所提出辨识方案的有效性和鲁棒性。     

An FPGA-based parallel architecture for on-line parameter estimation using the RLS identification algorithm

A parallel architecture for an on-line implementation of the recursive least squares (RLS) identification algorithm on a field programmable gate array (FPGA) is presented. The main shortcoming of this algorithm for on-line applications is its computational complexity. The matrix computation to update error covariance consumes most of the time. To improve the processing speed of the RLS architecture, a multi-stage matrix multiplication (MMM) algorithm was developed. In addition, a trace technique was used to reduce the computational burden on the proposed architecture. High throughput was achieved by employing a pipelined design. The scope of the architecture was explored by estimating the parameters of a servo position control system. No vendor dependent modules were used in this design. The RLS algorithm was mapped to a Xilinx FPGA Virtex-5 device. The entire architecture operates at a maximum frequency of 339.156 MHz. Compared to earlier work, the hardware utilization was substantially reduced. An application-specific integrated circuit (ASIC) design was implemented in 180 nm technology with the Cadence RTL compiler.     

双层无迹卡尔曼滤波

针对无迹卡尔曼滤波（Unscented Kalman fllter,UKF）在强非线性系统中估计效果差的问题,提出了双层无迹卡尔曼滤波（Double layer unscented Kalman filter,DLUKF）算法,该算法用带权值的采样点表征先验分布,而后用内层UKF算法对每个采样点进行更新,最后引入外层UKF算法的更新机制得到估计值和估计协方差.仿真结果表明,相比于传统算法,所提的DLUKF算法可以在较低计算负载下获得较高滤波估计精度.     

系统辨识算法的复杂性、收敛性及计算效率研究

实践中经常会遇到大型计算问题和优化问题, 使得求解问题算法的复杂性、计算量和计算精度等成为突出问题, 特别是大规模非线性多变量系统的辨识. 对此, 提出几个有趣的研究课题: 1) 利用信息滤波技术和多新息辨识理论研究能提高辨识精度的大规模系统辨识理论与方法; 2) 利用递阶辨识原理研究维数高、变量数目多、计算量小的多变量系统递阶辨识方法; 3) 利用鞅收敛理论建立非线性多变量系统辨识方法的收敛理论; 4) 利用并行计算与递阶计算技术提高辨识算法的计算效率, 以解决一类大规模非线性多变量系统的模型化问题.

     

基于脉冲推力的半被动双足机器人无模型神经网络控制

研究了半被动双足机器人的平面稳定行走控制问题。以最简行走模型为动力学模型,采用沿支撑腿方向的脚后跟脉冲推力作为行走动力源。考虑到系统模型的非线性特征,将基于三角函数扩展的函数链接型人工神经网络控制算法引入到机器人系统中,以产生系统所需的脉冲推力。并采用基于数据驱动的无模型同步扰动随机逼近算法对神经网络的权值进行更新。利用庞加莱映射方法分析了半被动双足机器人行走的稳定条件。在理论分析的基础上,对该算法进行了仿真研究。仿真结果表明：文中所提算法在收敛快速性上要优于迭代学习控制算法,可以实现双足机器人平面上的稳定周期行走。且雅可比矩阵的特征值均位于单位圆内,满足系统的稳定条件。     

MEMS陀螺仪漂移和噪声的分析和补偿

对陀螺仪数据分析的传统方法是使用kalman滤波器做尾数据处理来降低随机误差,由于陀螺仪传感器随着外界环境的变化的影响会有非线性误差,传统的kalman滤波算法处理的是线性误差,因此引进了适用于非线性系统的EKF滤波.为了快速滤除系统在实际环境中产生的噪声,对传统的中值滤波算法进行了改进,降低其计算复杂度,提出差分-均值中值滤波法.本文首先使用阿伦(ALLAN)方差分析了陀螺仪的误差特性,对于这些误差源分别提出了偏移校正的方法,之后建立自动回归-滑动平均模型(ARMA模型)对陀螺仪数据进行误差建模分析,最后使用EKF算法降低随机误差.实验结果表明该方法比传统的方法滤波效果好、计算复杂度低、实时性好.     

Nonlinear dynamic system identification using Chebyshev functionallink artificial neural networks

A computationally efficient artificial neural network (ANN) for the purpose of dynamic nonlinear system identification is proposed. The major drawback of feedforward neural networks, such as multilayer perceptrons (MLPs) trained with the backpropagation (BP) algorithm, is that they require a large amount of computation for learning. We propose a single-layer functional-link ANN (FLANN) in which the need for a hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. The novelty of this network is that it requires much less computation than that of a MLP. We have shown its effectiveness in the problem of nonlinear dynamic system identification. In the presence of additive Gaussian noise, the performance of the proposed network is found to be similar or superior to that of a MLP. A performance comparison in terms of computational complexity has also been carried out.     

基于混合滤波最大期望算法的高速列车建模

针对高速列车非线性单质点模型的特殊结构及含有隐含变量问题, 提出一种基于混合滤波的最大期望辨识方法. 借助递阶辨识理论, 将高铁列车状态空间模型分解为线性子系统模型和非线性子系统模型. 进而, 分别利用卡尔曼滤波和粒子滤波对速度和位移状态进行联合估计. 最后, 使用最大期望方法辨识高铁列车子系统模型参数, 解决了隐含变量辨识问题. 和传统方法相比, 本文所提出方法计算量小, 且具有较高的辨识精度. 仿真对比实验结果验证了该方法的有效性.     

基于集员滤波的二阶Volterra自适应归一化最小平均P范数算法

针对Volterra非线性滤波算法计算复杂度呈幂级数增加的问题,提出了一种α稳定分布噪声下的基于集员滤波的二阶Volterra自适应滤波新算法。由于集员滤波的目标函数考虑了所有输入和期望输出的信号对,通过误差幅值的p次方的门限判决,更新Volterra滤波器的权向量,不仅有效降低了算法复杂度,而且提高了自适应算法对输入信号相关性的鲁棒性;并推导给出了权向量的更新公式。仿真结果表明,该算法计算复杂度低、收敛速度快,对噪声及输入信号相关性有较强的鲁棒性。     

Efficient prediction of exchange rates with low complexity artificial neural network models

In recent years forecasting of financial data such as interest rate, exchange rate, stock market and bankruptcy has been observed to be a potential field of research due to its importance in financial and managerial decision making. Survey of existing literature reveals that there is a need to develop efficient forecasting models involving less computational load and fast forecasting capability. The present paper aims to fulfill this objective by developing two novel ANN models involving nonlinear inputs and simple ANN structure with one or two neurons. These are: functional link artificial neural network (FLANN) and cascaded functional link artificial neural network (CFLANN). These have been employed to predict currency exchange rate between US$ to British Pound, Indian Rupees and Japanese Yen. The performance of the proposed models have been evaluated through simulation and have been compared with those obtained from standard LMS based forecasting model. It is observed that the CFLANN model performs the best followed by the FLANN and the LMS models.