Evaluation of the performance of backpropagation and radial basis function neural networks in predicting the drill flank wear

This study compares the performance of backpropagation neural network (BPNN) and radial basis function network (RBFN) in predicting the flank wear of high speed steel drill bits for drilling holes on mild steel and copper work pieces. The validation of the methodology is carried out following a series of experiments performed over a wide range of cutting conditions in which the effect of various process parameters, such as drill diameter, feed-rate, spindle speed, etc. on drill wear has been considered. Subsequently, the data, divided suitably into training and testing samples, have been used to effectively train both the backpropagation and radial basis function neural networks, and the individual performance of the two networks is then analyzed. It is observed that the performance of the RBFN fails to match that of the BPNN when the network complexity and the amount of data available are the constraining factors. However, when a simpler training procedure and reduced computational times are required, then RBFN is the preferred choice.     

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     

A review of genetic algorithms applied to training radial basis function networks

The problems associated with training feedforward artificial neural networks (ANNs) such as the multilayer perceptron (MLP) network and radial basis function (RBF) network have been well documented. The solutions to these problems have inspired a considerable amount of research, one particular area being the application of evolutionary search algorithms such as the genetic algorithm (GA). To date, the vast majority of GA solutions have been aimed at the MLP network. This paper begins with a brief overview of feedforward ANNs and GAs followed by a review of the current state of research in applying evolutionary techniques to training RBF networks.     

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.     

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.     

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.     

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     

Bi-modal derivative adaptive activation function sigmoidal feedforward artificial neural networks

In this work an adaptive mechanism for choosing the activation function is proposed and described. Four bi-modal derivative sigmoidal adaptive activation function is used as the activation function at the hidden layer of a single hidden layer sigmoidal feedforward artificial neural networks. These four bi-modal derivative activation functions are grouped as asymmetric and anti-symmetric activation functions (in groups of two each). For the purpose of comparison, the logistic function (an asymmetric function) and the function obtained by subtracting 0.5 from it (an anti-symmetric) function is also used as activation function for the hidden layer nodes’. The resilient backpropagation algorithm with improved weight-tracking (iRprop⁺) is used to adapt the parameter of the activation functions and also the weights and/or biases of the sigmoidal feedforward artificial neural networks. The learning tasks used to demonstrate the efficacy and efficiency of the proposed mechanism are 10 function approximation tasks and four real benchmark problems taken from the UCI machine learning repository. The obtained results demonstrate that both for asymmetric as well as anti-symmetric activation usage, the proposed/used adaptive activation functions are demonstratively as good as if not better than the sigmoidal function without any adaptive parameter when used as activation function of the hidden layer nodes.     

基于组合核函数的径向基过程神经网络及其在示功图诊断中的应用

针对复杂时间信号动态模式分类问题,提出了一种基于局部核函数与全局核函数组合的径向基过程神经网络(RBFPNN)模型。考虑时间信号过程特征的多样性和复杂性,以及核函数对信号分布形态特征的局部与全局表征能力,通过将具有全局性质的多项式核函数与具有局部性质的高斯核函数进行线性叠加,构成组合核函数,以此建立一种新的径向基过程神经网络,从信息模型上改善RBFPNN对动态样本复杂过程特征的抽取和记忆性质,提高网络对时间信号特征的辨识能力。分析了基于RBFPNN的性质,建立了基于混沌遗传算法CGA的模型参数优化算法。以基于示功图的往复运动机械工作状态诊断为例,实际资料处理结果验证了模型和算法的有效性。     

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.     

基于可拓理论的RBF神经网络研究及其应用

针对径向基函数（RBF）神经网络构造时其结构和参数难以确定的问题,结合可拓理论对输入样本和基函数的中心向量建立物元模型,并借鉴第2类型可拓神经网络（ENN2）的聚类思想,根据样本分布,采用可拓分析及可拓变换动态调整隐节点数目和基函数中心,从而提出基于可拓理论的RBF（ERBF）神经网络.同时,通过UCI标准数据集进行了测试,并通过应用实例进行了验证,结果表明,ERBF结构和参数的确定方法简单、收敛速度快,且泛化精度、鲁棒性和稳定性均显著提高.     

Optimal design of radial basis function neural networks for fuzzy-rule extraction in high dimensional data

The design of an optimal radial basis function neural network (RBFNF) is not a straightforward procedure. In this paper we take advantage of the functional equivalence between RBFN and fuzzy inference systems to propose a novel efficient approach to RBFN design for fuzzy rule extraction. The method is based on advanced fuzzy clustering techniques. Solutions to practical problems are proposed. By combining these different solutions, a general methodology is derived. The efficiency of our method is demonstrated on challenging synthetic and real world data sets.     

Modelling of a magneto-rheological damper by evolving radial basis function networks

This paper presents an approach to approximate the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper using evolving radial basis function (RBF) networks. Due to the highly nonlinear characteristics of MR dampers, modelling of MR dampers becomes a very important problem to their applications. In this paper, an alternative representation of the MR damper in terms of evolving RBF networks, which have a structure of four input neurons and one output neuron to emulate the forward and inverse dynamic behaviours of an MR damper, respectively, is developed by combining the genetic algorithms (GAs) to search for the network centres with other standard learning algorithms. Training and validating of the evolving RBF network models are achieved by using the data generated from the numerical simulation of the nonlinear differential equations proposed for the MR damper. It is shown by the validation tests that the evolving RBF networks can represent both forward and inverse dynamic behaviours of the MR damper satisfactorily.     

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.     

新型广义径向基函数神经网络结构研究

提出了一种新型的广义径向基函数(RBF)神经网络,并研究了该网络的学习方法.不同于传统三层结构的RBF网络,广义RBF网络增加了基函数输出加权层,并在输出层采用超曲面去逼近任意的非线性曲面.实例仿真结果表明,与传统的RBF网络相比,该网络具有良好的逼近性能,收敛速度快,可逼近任意多变量非线性函数.     

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.     

混合前馈型神经网络在入侵检测中的应用研究

提出一种基于混沌神经元的混合前馈型神经网络,用于检测复杂的网络入侵模式．这种神经网络具有混沌神经元的延时、收集、思维和分类的功能,避免了MLP神经网络仅能识别网络中当前的滥用入侵行为的弱点．对混合网络进行训练后,将该网络用于滥用入侵检测．使用DARPA数据集对该方法进行评估,结果表明该方法可有效地提高对具备延时特性的Probe和DOS入侵的检测性能．     

基于基函数展开的双隐层过程神经元网络及其应用

提出一类基于基函数展开的双隐层过程神经元网络模型．过程神经元隐层完成对输入信息过程模式特征的提取和对时间的聚合运算，非时变一般神经元隐层用于提高网络对系统输入输出之间复杂关系的映射能力．在输入空问中引入一组函数正交基，将输入函数和网络权函数表示为该组正交基的展开形式，利用基函数的正交性简化过程神经元聚合运算．以旋转机械故障诊断和油藏开发过程采收率的模拟为例，验证了模型和算法的有效性。     

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．