Optimizing radial basis function neural network based on rough sets and affinity propagation clustering algorithm

A novel method based on rough sets (RS) and the affinity propagation (AP) clustering algorithm is developed to optimize a radial basis function neural network (RBFNN). First, attribute reduction (AR) based on RS theory, as a preprocessor of RBFNN, is presented to eliminate noise and redundant attributes of datasets while determining the number of neurons in the input layer of RBFNN. Second, an AP clustering algorithm is proposed to search for the centers and their widths without a priori knowledge about the number of clusters. These parameters are transferred to the RBF units of RBFNN as the centers and widths of the RBF function. Then the weights connecting the hidden layer and output layer are evaluated and adjusted using the least square method (LSM) according to the output of the RBF units and desired output. Experimental results show that the proposed method has a more powerful generalization capability than conventional methods for an RBFNN.     

基于径向基函数网络的浮游植物活体三维荧光光谱分类

将小波变换与神经网络相结合,对浮游植物活体的三维荧光光谱进行分类．首先利用小波变换对数据进行压缩,然后利用径向基函数（Radial Basis Function,RBF）神经网络对光谱曲线进行逼近,从而进行物种的识别,平均识别率高达95．8％．结果表明,该方法较传统的统计方法更方便、准确率更高．     

基于径向基函数网络的FBG传感光谱的重构

针对光纤Bragg光栅(FBG)解调系统中由于传感器部分脱粘、数据采集的量化误差引起的系统性能的非理想性,FBG反射回的光谱会发生失真。如果直接利用峰值检测法进行波长检测,存在较大的检测误差。于是便提出了用径向基函数网络(RBFN)拟合光纤光栅反射后的失真光谱的方法,此法与峰值检测法、高斯曲线拟合法相比,能够更大程度地减小波长检测的误差,提高解调的精度,并且,能够对多个光栅光谱进行重构。     

基于增强径向函数神经网络的错误定位方法

结合径向基函数神经网络与正交实验设计理论,提出了一种增强径向基函数神经网络错误定位算法.根据选择的测试用例执行得到源程序的语句覆盖信息和执行结果;通过神经网络计算出每条语句的可疑度值,并通过正交实验设计方法自适应调整神经网络中的参数值;最后按照可疑度值由高到低的顺序逐条检查程序的可疑语句进行错误定位.通过实验对所提出方法与径向基函数神经网络算法以及反向传播神经网络算法进行比较分析,结果表明,基于增强径向基函数神经网络算法具有更精确的错误定位效果和更显著的定位效率.     

Consideration effect of uncertainty in power system reliability indices using radial basis function network and fuzzy logic theory

Reliability assessment of composite power systems is a critical and important part of power investigations especially in the market-driven environments. Therefore, the reliability indices as criteria for the comparison of the reliability of the power systems should be evaluated precisely and carefully. Because of the nonlinear behavior of the systems as the effect of different parameters like weather conditions, load pattern changes and some others, reliability indices always contain much uncertainty. In this paper a neuro-fuzzy based method is proposed to reduce the degree of the uncertainty in the reliability indices and therefore to evaluate the reliability of the composite power systems precisely. Fuzzy logic theory makes it possible to make use of the human experts knowledge in the reliability evaluations. Also by the use of RBFNN and its powerful characteristic to learn any nonlinear mapping between two states it would be possible to evaluate the reliability indices for every short time interval needed so that reliability evaluation in real time would be achievable and feasible.In this paper the RBFNN is trained by the training patterns that are achieved by the use of fuzzy logic theory, then the results are examined on a standard Reliability Test System (RTS-96).     

Fuzzy radial basis function network: a parallel design

The fuzzy radial basis function (FRBF) network comprises an integration of the principles of a radial basis function (RBF) network and the fuzzy c-means (FCM) algorithm. A programmable parallel architecture design is proposed for the FRBF, both for FCM clustering at the hidden layer and the weight training at the output layer of the network. The behavior of the system is described in terms of processor utilization. The performance of the parallel design is quantitatively evaluated.     

基于径向基函数神经网络的网络流量识别模型

提出了一种基于径向基函数神经网络的网络流量识别方法。根据实际网络中的流量数据,建立了一个基于RBF神经网络的流量识别模型。先介绍了RBF神经网络的结构设计及学习算法,针对RBF神经网络在隐节点过多的情况下算法过于复杂的缺点,采用了优化的算法计算隐含层节点。仿真实验证明,该模型具有较好的准确率、低复杂度、高识别效果和良好的自适应性。     

Control of chaotic dynamical systems using radial basis function network approximators

This paper presents a general control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. For many chaotic systems that can be decomposed into a sum of a linear and a nonlinear part, under some mild conditions the RBFN can be used to well approximate the nonlinear part of the system dynamics. The resulting system is then dominated by the linear part, with some small or weak residual nonlinearities due to the RBFN approximation errors. Thus, a simple linear state-feedback controller can be devised, to drive the system response to a desirable set-point. In addition to some theoretical analysis, computer simulations on two representative continuous-time chaotic systems (the Duffing and the Lorenz systems) are presented to demonstrate the effectiveness of the proposed method.     

The improved radial basis function neural network and its application

Compared with other feed-forward neural networks, radial basis function neural networks (RBFNN) have many advantages which make them more suitable for nonlinear system modeling, and they have recently received considerable attention. In this paper, a RBFNN is employed to model strongly nonlinear systems. First, the problems of nonlinear system modeling are analyzed, and then the structure of the RBFNN as well as the training algorithm are improved to solve these problems. Finally, an industrial high-purity distillation column, which is a strongly nonlinear system, is successfully modeled with the improved RBFNN. Owing to the complexities of a nonlinear system, it is necessary to use a real-time model correction method to modify the parameters of the RBFNN model in real time. One efficient method is proposed in this paper. The idea is to employ the Givens transformation to modify the parameters of the RBFNN-based model. This work was presented, in part, at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996     

Application of a radial basis function artificial neural network to seismic data inversion

We investigate here the performance and the application of a radial basis function artificial neural network (RBF-ANN) type, in the inversion of seismic data. The proposed structure has the advantage of being easily trained by means of a back-propagation algorithm without getting stuck in local minima. The effects of network architectures, i.e. the number of neurons in the hidden layer, the rate of convergence and prediction accuracy of ANN models are examined. The optimum network parameters and performance were decided as a function of testing error convergence with respect to the network training error. An adequate cross-validation test is run to ensure the performance of the network on new data sets. The application of such a network to synthetic and real data shows that the inverted acoustic impedance section was efficient.     

Application of radial basis function neural network for differential relaying of a power transformer

Function approximation has been found in many applications. The radial basis function network is one of the approaches which has shown a great promise in this sort of problems because of its faster learning capacity. The application of RBF neural network for differential relaying of power transformer is presented in this paper. Performance of this model is compared with feed-forward neural network (FFNN). The proposed method of power transformer protection is evaluated using simulation performed with EMTP package. The proposed model requires less training time and is more accurate in prediction as compared to FFNN.     

A forecasting system for car fuel consumption using a radial basis function neural network

A predictive system for car fuel consumption using a radial basis function (RBF) neural network is proposed in this paper. The proposed work consists of three parts: information acquisition, fuel consumption forecasting algorithm and performance evaluation. Although there are many factors affecting the fuel consumption of a car in a practical drive procedure, in the present system the relevant factors for fuel consumption are simply decided as make of car, engine style, weight of car, vehicle type and transmission system type which are used as input information for the neural network training and fuel consumption forecasting procedure. In fuel consumption forecasting, to verify the effect of the proposed RBF neural network predictive system, an artificial neural network with a back-propagation (BP) neural network is compared with an RBF neural network for car fuel consumption prediction. The prediction results demonstrated the proposed system using the neural network is effective and the performance is satisfactory in terms of fuel consumption prediction.     

Effect of different basis functions on a radial basis function network in prediction of drill flank wear from motor current signals

The Gaussian kernel has almost exclusively been used as the basis function of the cluster centers (hidden layer nodes) of a radial basis function network (RBFN) in most of its applications, especially in tool condition monitoring (TCM) problems. This study explores the possible usage of a set of five other basis functions in addition to the standard Gaussian function, in one such important TCM problem, i.e., prediction of drill flank wear. The analysis focuses on a comparative study of the wear prediction capabilities of the RBFN employing these six different basis functions for a wide range of the basis width parameter (wherever applicable) and changing the number of cluster centers in the hidden layer. This analysis is carried out following a series of experiments employing high speed steel (HSS) drills for drilling holes on mild steel workpieces, under different sets of cutting conditions (spindle speed, feed-rate and drill diameter) and noting the root mean square (RMS) value of spindle motor current as well as the average flank wear in each case. The results show that other basis functions can also match the performance of the Gaussian kernel, and depending upon the nature of application at hand and the requirements of time and space, the use of basis functions other than the Gaussian kernel may just prove advantageous.     

Speech recognition using pulse-coupled neural networks with a radial basis function

We have developed a novel pulse-coupled neural network (PCNN) for speech recognition. One of the advantages of the PCNN is in its biologically based neural dynamic structure using feedback connections. To recall the memorized pattern, a radial basis function (RBF) is incorporated into the proposed PCNN. Simulation results show that the PCNN with a RBF can be useful for phoneme recognition. This work was presented in part at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002     

基于RBF神经网络曲线重构的算法研究

提出一种基于径向基(RBF)函数神经网络的曲线重构学习方法,即由描述物体轮廓特征的样本点作为RBF神经网络的学习样本,利用RBF神经网络强大的函教逼近能力对样本点进行学习和训练,从而仿真出包含这些样本点的原始曲线,同时对于曲线一些样本点缺少的情况下,仍然能构通过调整参数训练得到这些样本点的原始拟和曲线.实验表明,基于径向基(RBF)函数的神经网络具有很强的物体边界描述能力和缺损修复能力.     

Design of a radial basis function neural network with a radius-modification algorithm using response surface methodology

A radial basis function (RBF) neural network was designed for time series forecasting using both an adaptive learning algorithm and response surface methodology (RSM). To improve the traditional RBF networks forecasting capability, the generalized delta rule learning method was employed to modify the radius of the kernel function. Then RSM was utilized to explore the mean square error response surface so that the appropriate combination of network parameters, such as the number of hidden nodes and the initial learning rates, could be found. Extensive studies were performed on the effect of the initial values of connection weights on the accuracy of the backpropagation learning method that was employed in the training of the RBF artificial neural network. The effectiveness of the neural network with the proposed radius-modification technique and the RSM method was demonstrated with an example of forecasting intensity pulsations of a laser. It was found that, by utilizing the proposed techniques, the neural network provided a more accurate prediction of the response.     

Probabilistic self-organizing map and radial basis function networks

We propose in this paper a new learning algorithm probabilistic self-organizing map (PRSOM) using a probabilistic formalism for topological maps. This algorithm approximates the density distribution of the input set with a mixture of normal distributions. The unsupervised learning is based on the dynamic clusters principle and optimizes the likelihood function. A supervised version of this algorithm based on radial basis functions (RBF) is proposed. In order to validate the theoretical approach, we achieve regression tasks on simulated and real data using the PRSOM algorithm. Moreover, our results are compared with normalized Gaussian basis functions (NGBF) algorithm.     

基于EMD-RBF网络的车辆动态称重信号处理方法

针对动态称重数据处理的复杂性,以常见的两轴车辆为研究对象,对汽车轴完全驶上称重台的信号进行经验模分解(EMD)求得剩余分量的平均值,并以前轴、后轴的剩余分量的平均值、平均速度、上台信号上升斜率、下台信号下降斜率为径向基函数(RBF)网络的输入,利用RBF网络对系统进行非线性建模。以静态测量结果为相对真值进行仿真,其出现的最大相对误差为1.4%,而简单平均值的测试误差达到2.1%,结果表明:该方法比直接输入台上信号的平均值具有更高的测试精度。     

基于多技术融合加权平滑的径向基函数神经网络熔融指数预报

针对在对聚丙烯熔融指数进行预测时优势数据和优势变量不突出影响预测精度、数据平滑度不够影响泛化性能的问题,提出了基于多技术融合加权平滑的径向基函数神经网络预报模型。综合运用了在时间尺度基于空间欧氏距离加权、在变量维度上基于灰色关联和线性回归误差加权两种数据加权方案,基于过程变量差分序列欧氏距离的平滑和局部线性平滑两种数据平滑方案,解决了模型精度和泛化性低的问题。为进一步改进模型性能,采用带误差补偿的非线性自回归滑动平均模型框架和径向基函数神经网络,利用自校正预测控制算法和分段线性变学习率算法,对模型进行优化。结合某厂真实数据对模型进行验证,预报结果在泛化集上为：平均相对误差( MRE )1.32%、均方根误差(RMSE)0.0459。与其他方法进行了详细的比较分析,结果表明该模型具有良好的预报精度和泛化性能,在大时滞工业过程领域具有一定的应用价值。