A complex valued radial basis function network for equalization offast time varying channels

This paper presents a complex valued radial basis function (RBF) network for equalization of fast time varying channels. A new method for calculating the centers of the RBF network is given. The method allows fixing the number of RBF centers even as the equalizer order is increased so that a good performance is obtained by a high-order RBF equalizer with small number of centers. Simulations are performed on time varying channels using a Rayleigh fading channel model to compare the performance of our RBF with an adaptive maximum-likelihood sequence estimator (MLSE) consisting of a channel estimator and a MLSE implemented by the Viterbi algorithm. The results show that the RBF equalizer produces superior performance with less computational complexity.     

Robust nonlinear channel equalization using WNN trained by symbiotic organism search algorithm

In the present world of ‘Big Data,’ the communication channels are always remaining busy and overloaded to transfer quintillion bytes of information. To design an effective equalizer to prevent the inter-symbol interference in such scenario is a challenging task. In this paper, we develop equalizers based on a nonlinear neural structure (wavelet neural network (WNN)) and train it's weighted by a recently developed meta-heuristic (symbiotic organisms search algorithm). The performance of the proposed equalizer is compared with WNN trained by cat swarm optimization (CSO) and clonal selection algorithm (CLONAL), particle swarm optimization (PSO) and least mean square algorithm (LMS). The performance is also compared with other equalizers with structure based on functional link artificial neural network (trigonometric FLANN), radial basis function network (RBF) and finite impulse response filter (FIR). The superior performance is demonstrated on equalization of two non-linear three taps channels and a linear twenty-three taps telephonic channel. It is observed that the performance of the gradient algorithm based equalizers fails in the presence of burst error. The robustness in the performance of the proposed equalizers to handle the burst error conditions is also demonstrated.     

Communication channel equalization using wavelet network

Wavelet network (WN) based on wavelet decomposition principle is applied to channel equalization for both linear and non-linear channels. The WN is trained by extended Kalman filter (EKF) based recursive algorithm and is compared with EKF based multi-layered perceptron (MLP) and radial basis function neural network (RBFNN). Exhaustive simulation study reveals the superiority of the WN based equalizer in terms of bit error rate performance, compared to the above equalizer scheme.     

Nonlinear magnetic storage channel equalization using minimalresource allocation network (MRAN)

This letter presents the application of the recently developed minimal radial basis function neural network called minimal resource allocation network (MRAN) for equalization in highly nonlinear magnetic data storage channels. Using a realistic magnetic channel model, MRAN equalizer's performance is compared with the nonlinear neural equalizer of Nair and Moon (1997), referred to as maximum signal-to-distortion ratio (MSDR) equalizer. MSDR equalizer uses a specially designed neural architecture where all the parameters are determined theoretically. Simulation results indicate that MRAN equalizer has better performance than that of MSDR equalizer in terms of higher signal-to-distortion ratios.     

基于径向基函数神经网络的混沌背景谐波提取

为提高强混沌背景下谐波信号的提取能力,给出混沌系统的单步预测模型,提出了一种新的径向基函数神经网络模型.由混沌吸引子的维数来确定网络的输入,并给出了基于卡尔曼滤波器的动态学习算法,利用学习算法可以在网络训练时同时确定径向基神经网络隐层中心和输出层权值,提高了网络的收敛速度和预测性能.通过对Bossler混沌背景下低信噪比谐波信号的提取进行计算机认真实验,并且实验表明信噪比最低达一27dB时,仍能有效提取出谐波信号,验证了算法的有效性和可行性.     

An adaptive decision feedback equalizer based on the combination of the FIR and FLNN

To compensate the linear and nonlinear distortions and to track the characteristic of the time-varying channel in digital communication systems, a novel adaptive decision feedback equalizer (DFE) with the combination of finite impulse response (FIR) filter and functional link neural network (CFFLNNDFE) is introduced in this paper. This convex nonlinear combination results in improving the convergence speed while retaining the lower steady-state error at the cost of a small increasing computational burden. To further improve the performance of the nonlinear equalizer, we derive here a novel simplified modified normalized least mean square (SMNLMS) algorithm. Moreover, the convergence properties of the proposed algorithm are analyzed. Finally, computer simulation results which support analysis are provided to evaluate the performance of the proposed equalizer over the functional link neural network (FLNN), radial basis function (RBF) neural network and linear equalizer with decision feedback (LMSDFE) for time-invariant and time-variant nonlinear channel models in digital communication systems.     

Implementation of the RBF neural chip with the back-propagation algorithm for on-line learning

This article presents the hardware implementation of the floating-point processor (FPP) to develop the radial basis function (RBF) neural network for the general purpose of pattern recognition and nonlinear control. The floating-point processor is designed on a field programmable gate array (FPGA) chip to execute nonlinear functions required in the parallel calculation of the back-propagation algorithm. Internal weights of the RBF network are updated by the online learning back-propagation algorithm. The on-line learning process of the RBF chip is compared numerically with the results of the RBF neural network learning process written in the MATLAB program. The performance of the designed RBF neural chip is tested for the real-time pattern classification of the XOR logic. Performances are evaluated by comparing results from the MATLAB through extensive experimental studies.     

A clustering technique for digital communications channelequalization using radial basis function networks

The application of a radial basis function network to digital communications channel equalization is examined. It is shown that the radial basis function network has an identical structure to the optimal Bayesian symbol-decision equalizer solution and, therefore, can be employed to implement the Bayesian equalizer. The training of a radial basis function network to realize the Bayesian equalization solution can be achieved efficiently using a simple and robust supervised clustering algorithm. During data transmission a decision-directed version of the clustering algorithm enables the radial basis function network to track a slowly time-varying environment. Moreover, the clustering scheme provides an automatic compensation for nonlinear channel and equipment distortion. Computer simulations are included to illustrate the analytical results.     

径向基函数神经网络的一种构造算法

提出了径向基函数(RBF)神经网络参数的一种新的学习算法——分类优化迭代算法。在此基础上,设计了RBF网络的一种构造算法。仿真结果表明了本文方法的有效性。     

Prediction of reservoir sensitivity using RBF neural network with trainable radial basis function

Reservoir sensitivity prediction is an important basis for designing reservoir protection program scientifically and exploiting oil and gas resources efficiently. Researchers have long endeavored to establish a method to predict reservoir sensitivity, but all of the methods have some limitations. Radial basis function (RBF) neural network, which provided a powerful technique to model non-linear mapping and the learning algorithm for RBF neural networks, corresponds to the solution of a linear problem, therefore it is unnecessary to establish an accurate model or organize rules in large number, and it enjoys the advantages such as simple network structure, fast convergence rate, and strong approximation ability, etc. However, different radial basis function has different non-linear mapping ability, and different data require different radial basis functions. Nowadays, the choice of radial basis function in the network is based on experience or test result only, which exerts a great adverse impact on the network performance. In this study, a new RBF neural network with trainable radial basis function was proposed by the linear combination of common radial basis functions. The input parameters of the network were the influence factors of reservoir sensitivity such as porosity and permeability, etc. The output parameter was the corresponding sensitivity index. The network was trained and tested with the data collected from our own experiments. The results showed that the new RBF neural network is effective and improved, of which the accuracy is obviously higher than the network with single radial basis function for the prediction of reservoir sensitivity.     

基于径向基函数神经网络的非线性模型辨识

从径向基函数（RBF）神经网络原理分析出发，提出了一种基于RBF神经网络学习算法，用于对非线性对象模型的拟合与辩识，并将此方法用于实际非线性模型的学习与辩识。结果表明，基于RBF的神经网络可快速完成对样本的学习与拟合，对具有连续特性的线性与非线性模型，具有快速实时的学习速度和优良的学习性能。     

基于AQPSO的RBF神经网络自组织学习

针对径向基函数(RBF)神经网络的结构设计及参数优化问题,提出一种自适应量子粒子群优化(AQPSO)算法.将RBF神经网络的网络规模及参数映射到粒子的空间位置,定义权值平均最优位置,从而对量子粒子群优化(QPSO)中$L_{i,j     

用RBF神经网络预测材料力学性能的研究

由于径向基函数(RBF)神经网络有易学,动态仿真性强,较强的输入输出映射功能和全局最优逼近的结构特点,因此将之用于预测麦杆增强复合板材力学性能。高斯函数表示形式简单,径向对称,光滑性好和解析性好,所以模型采用高斯函数作为隐含层基函数,k均值聚类法确定径向基函数的参数,运用最小二乘法确定权值。结合影响复合板材力学性能因素的特点和变化规律,以成型温度、成型压力、纤维含量、保温时间、拉伸强度、冲击韧性等为对象建立预测复合板材力学性能的模型,用它来优化模压成型的工艺参数,找出最佳工艺参数的范围。结果表明,径向基函数神经网络具有较好的学习和泛化能力,在预测力学性能中效果较好。     

Combined projection and kernel basis functions for classification in evolutionary neural networks

This paper proposes a hybrid neural network model using a possible combination of different transfer projection functions (sigmoidal unit, SU, product unit, PU) and kernel functions (radial basis function, RBF) in the hidden layer of a feed-forward neural network. An evolutionary algorithm is adapted to this model and applied for learning the architecture, weights and node typology. Three different combined basis function models are proposed with all the different pairs that can be obtained with SU, PU and RBF nodes: product–sigmoidal unit (PSU) neural networks, product–radial basis function (PRBF) neural networks, and sigmoidal–radial basis function (SRBF) neural networks; and these are compared to the corresponding pure models: product unit neural network (PUNN), multilayer perceptron (MLP) and the RBF neural network. The proposals are tested using ten benchmark classification problems from well known machine learning problems. Combined functions using projection and kernel functions are found to be better than pure basis functions for the task of classification in several datasets.     

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

一种优化的RBF神经网络模型用于网络流量预测

采用径向基RBF神经网络对网络流量数据的时间序列进行建模与预测。采用传统的学习算法对RBF网络训练时,对网络流量数据容易出现过拟合现象,提出了自适应量子粒子群优化AQPSO算法,用于训练RBF神经网络的基函数中心和宽度,并结合最小二乘法计算网络权值,改善了RBF神经网络的泛化能力。实验结果表明,采用AQPSO算法获得的RBF神经网络模型具有泛化能力强、稳定性良好的特点,在网络流量预测中有一定的实用价值。     

基于ART 的RBF 网络结构设计

针对径向基函数(RBF)网络隐层结构难以确定的问题,基于自适应共振理论(ART)网络良好的在线分类特性,提出一种RBF网络结构设计算法。该算法将ART网络的聚类特性用于RBF网络结构设计中,通过对输入向量与已存模式的相似度比较将输入向量进行分类,确定隐含层节点个数和初始参数,使网络具有精简的结构。对典型非线性函数逼近的仿真结果表明,所提出的结构具有快速的学习能力和良好的逼近能力。     

一种改进PSO优化RBF神经网络的新方法

为了克服神经网络模型结构和参数难以设置的缺点,提出了一种改进粒子群优化的径向基函数(RBF)神经网络的新方法.首先将最近邻聚类用于RBF神经网络隐层中心向量的确定,同时对引入适应度值择优选取的原则对基本粒子群算法进行改进,采用改进粒子群(IMPSO)算法对最近邻聚类的聚类半径进行优化,合理的确定了RBF神经网络的隐层结构.将改进PSO优化的RBF神经网络应用于非线性函数逼近和混沌时间序列预测,经实验仿真验证.与基本粒子群(PSO)算法,收缩因子粒子群(CFA PSO)算法优化的RBF神经网络相比较,其在识别精度和收敛速度上都有了显著的提高.     

Online identification of nonlinear multivariable processes using self‐generating RBF neural networks

This paper addresses the problem of online model identification for multivariable processes with nonlinear and time‐varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self‐organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP‐RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input‐output data pairs in real‐time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF‐based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP‐RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)‐based approaches for the case of non‐Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self‐generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time‐varying multivariable non‐isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP‐RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society