Crack Fault Diagnosis and Location Method for a Dual-Disk Hollow Shaft Rotor System Based on the Radial Basis Function Network and Pattern Recognition Neural Network

The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics caused by the crack rather than estimating the crack depth and position based on the obtained vibration signals.In this paper,a novel crack fault diagnosis and location method for a dual-disk hollow shaft rotor system based on the Radial basis function(RBF)network and Pattern recognition neural network(PRNN)is presented.Firstly,a rotor system model with a breathing crack suitable for a short-thick hollow shaft rotor is established based on the finite element method,where the crack's periodic opening and closing pattern and different degrees of crack depth are considered.Then,the dynamic response is obtained by the harmonic balance method.By adjusting the crack parameters,the dynamic characteristics related to the crack depth and position are analyzed through the amplitude-frequency responses and waterfall plots.The analysis results show that the first critical speed,first subcritical speed,first critical speed amplitude,and super-harmonic resonance peak at the first subcritical speed can be utilized for the crack fault diagnosis.Based on this,the RBF network and PRNN are adopted to determine the depth and approximate location of the crack respectively by taking the above dynamic characteristics as input.Test results show that the proposed method has high fault diagnosis accuracy.This research proposes a crack detection method adequate for the hollow shaft rotor system,where the crack depth and position are both unknown.

A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification

ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.

Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms

Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.

Comparison Between Radial Basis Function Neural Network and Regression Model for Estimation of Rice Biophysical Parameters Using Remote Sensing

The radial basis function （RBF） emerged as a variant of artificial neural network. Generalized regression neural network （GRNN） is one type of RBF, and its principal advantages are that it can quickly learn and rapidly converge to the optimal regression surface with large number of data sets. Hyperspectral reflectance （350 to 2500 nm） data were recorded at two different rice sites in two experiment fields with two cultivars, three nitrogen treatments and one plant density （45 plants m^-2）. Stepwise multivariable regression model （SMR） and RBF were used to compare their predictability for the leaf area index （LAI） and green leaf chlorophyll density （GLCD） of rice based on reflectance （R） and its three different transformations, the first derivative reflectance （D1）, the second derivative reflectance （D2） and the log-transformed reflectance （LOG）. GRNN based on D1 was the best model for the prediction of rice LAI and CLCD. The relationships between different transformations of reflectance and rice parameters could be further improved when RBF was employed. Owing to its strong capacity for nonlinear mapping and good robustness, GRNN could maximize the sensitivity to chlorophyll content using D1. It is concluded that RBF may provide a useful exploratory and predictive tool for the estimation of rice biophysical parameters.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

Application of Radial Basis Function Network in Sensor Failure Detection

Aim To detect sensor failure in control system using a single sensor signal. Methods A neural predictor was designed based on a radial basis function network(RBFN), and the neural predictor learned the sensor signal on line with a hybrid algorithm composed of n means clustering and Kalman filter and then gave the estimation of the sensor signal at the next step. If the difference between the estimation and the actural values of the sensor signal exceeded a threshold, the sensor could be declared to have a failure. The choice of the failure detection threshold depends on the noise variance and the possible prediction error of neural predictor. Results and Conclusion\ The computer simulation results show the proposed method can detect sensor failure correctly for a gyro in an automotive engine.

Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization

Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collaborative Optimization （CO） is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.

Application of Near Infrared Diffuse Reflectance Spectroscopy with Radial Basis Function Neural Network to Determination of Rifampincin Isoniazid and Pyrazinamide Tablets

Partial least squares（PLS）,back-propagation neural network（BPNN）and radial basis function neural network（RBFNN）were respectively used for estalishing quantative analysis models with near infrared（NIR）diffuse reflectance spectra for determining the contents of rifampincin（RMP）,isoniazid（INH）and pyrazinamide（PZA）in rifampicin isoniazid and pyrazinamide tablets.Savitzky-Golay smoothing,first derivative,second derivative,fast Fourier transform（FFT）and standard normal variate（SNV）transformation methods were applied to pretreating raw NIR diffuse reflectance spectra.The raw and pretreated spectra were divided into several regions,depending on the average spectrum and RSD spectrum.Principal component analysis（PCA）method was used for analyzing the raw and pretreated spectra in different regions in order to reduce the dimensions of input data.The optimum spectral regions and the models＇ parameters were chosen by comparing the root mean square error of cross-validation（RMSECV）values which were obtained by leave-one-out cross-validation method.The RMSECV values of the RBFNN models for determining the contents of RMP,INH and PZA were 0.00288,0.00226 and 0.00341,respectively.Using these models for predicting the contents of INH,RMP and PZA in prediction set,the RMSEP values were 0.00266,0.00227 and 0.00411,respectively.These results are better than those obtained from PLS models and BPNN models.With additional advantages of fast calculation speed and less dependence on the initial conditions,RBFNN is a suitable tool to model complex systems.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

An Adaptive Identification and Control SchemeUsing Radial Basis Function Networks

In this paper, adaptive identification and control of nonlinear dynamical systems are investigated using radial basis function networks (RBF). Firstly, a novel approach to train the RBF is introduced, which employs an adaptive fuzzy generalized learning vector quantization (AFGLVQ) technique and recursive least squares algorithm with variable forgetting factor (VRLS). The AFGLVQ adjusts the centers of the RBF while the VRLS updates the connection weights of the network. The identification algorithm has the properties of rapid convergence and persistent adaptability that make it suitable for real-time control. Secondly, on the basis of the one-step ahead RBF predictor, the control law is optimized iteratively through a numerical stable Davidon's least squares-based (SDLS) minimization approach. Four nonlinear examples are simulated to demonstrate the effectiveness of the identification and control algorithms.

Estimation of vegetation biophysical parameters by remote sensing using radial basis function neural network

Hyperspectral reflectance (350~2500 nm) data were recorded at two different sites of rice in two experiment fields including two cultivars, and three levels of nitrogen (N) application. Twenty-five Vegetation Indices (VIs) were used to predict the rice agronomic parameters including Leaf Area Index (LAI, m2 green leaf/m2 soil) and Green Leaf Chlorophyll Density (GLCD, mg chlorophyll/m2 soil) by the traditional regression models and Radial Basis Function Neural Network (RBF). RBF emerged as a variant of Artificial Neural Networks (ANNs) in the late 1980’s. A large variety of training algorithms has been tested for training RBF networks. In this study, Original RBF (ORBF), Gradient Descent RBF (GDRBF), and Generalized Regression Neural Network (GRNN) were employed. Results showed that green waveband Normalized Difference Vegetation Index (NDVIgreen) and TCARI/OSAVI have the best prediction power for LAI by exponent model and ORBF respectively, and that TCARI/OSAVI has the best prediction power for GLCD by exponent model and GDRBF. The best performances of RBF are compared with the traditional models, showing that the relationship between VIs and agronomic variables are further improved when RBF is used. Compared with the best traditional models, ORBF using TCARI/OSAVI improves the prediction power for LAI by lowering the Root Mean Square Error (RMSE) for 0.1119, and GDRBF using TCARI/OSAVI improves the prediction power for GLCD by lowering the RMSE for 26.7853. It is concluded that RBF provides a useful exploratory and predictive tool when applied to the sensitive VIs.

Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network

Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps： first, decomposing cutting torque components from the original signals by wavelet packet decomposition （WPD）; second, extracting wavelet coefficients of different wear states （i.e., slight, normal, or severe wear） with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network （RBFNN）. The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective.

Adaptive integral dynamic surface control based on fully tuned radial basis function neural network

An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.

DETERMINING THE STRUCTURES AND PARAMETERS OF RADIAL BASIS FUNCTION NEURAL NETWORKS USING IMPROVED GENETIC ALGORITHMS

The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error term is used as the best criterion of optimizing the structures and parameters of networks. It is shown from the simulation results that the method not only improves the approximation and generalization capability of RBFNNs ,but also obtain the optimal or suboptimal structures of networks.

STUDY OF RECOGNITION TECHNIQUE OF RADAR TARGET'S ONE-DIMENSIONAL IMAGES BASED ON RADIAL BASIS FUNCTION NETWORK

This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence between the RBFN and the estimate of Parzen window probabilistic density is proved. It is pointed out that the I/O functions in RBFN hidden units can be generalized to general Parzen window probabilistic kernel function or potential function, too. This paper discusses the effects of the shape parameter a in the RBFN and the forgotten factor A in RLSA on the results of the recognition of three kinds of kernel function such as Gaussian, triangle, double-exponential, at the same time, also discusses the relationship between A and the training time in the RBFN.

State of charge estimation of Li-ion batteries in an electric vehicle based on a radial-basis-function neural network

The on-line estimation of the state of charge （SOC） of the batteries is important for the reliable running of the pure electric vehicle in practice. Because a nonlinear feature exists in the batteries and the radial-basis-function neural network （RBF NN） has good characteristics to solve the nonlinear problem, a practical method for the SOC estimation of batteries based on the RBF NN with a small number of input variables and a simplified structure is proposed. Firstly, in this paper, the model of on-line SOC estimation with the RBF NN is set. Secondly, four important factors for estimating the SOC are confirmed based on the contribution analysis method, which simplifies the input variables of the RBF NN and enhttnces the real-time performance of estimation. FiItally, the pure electric buses with LiFePO4 Li-ion batteries running during the period of the 2010 Shanghai World Expo are considered as the experimental object. The performance of the SOC estimation is validated and evaluated by the battery data from the electric vehicle.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.

Comparison of Radial Basis Function Neural Network and Response Surface Methodology for Predicting Performance of Biofilter Treating Toluene

Biofiltration is emerging as a promising cost effective technique for the Volatile Organic Compounds (VOCs) removal from industrial waste gases. In the present investigation a comparative modeling study has been carried out using Radial Basis Function Neural Network (RBFN) and Response Surface Methodology (RSM) to predict and optimize the performance of a biofilter system treating toluene (a model VOC). Experimental biofilter system performance data collected over a time period by daily measurement of inlet VOC concentration, retention time, pH, temperature and packing moisture content was used to develop the mathematical model. These independent variables acted as the inputs to the mathematical model developed using RSM and RBFN, while the VOC removal efficiency was the biofilter system performance parameter to be predicted. The data set was divided into two parts: 60% of data was used for training phase and remaining 40% of data was used for the testing phase. The average % error for RSM and RBFN were 7.76% and 3.03%, and R2 value obtained were 0.8826 and 0.9755 respectively. The results indicated the superiority of RBFN in the prediction capability due to its ability to approximate higher degree of nonlinearity between the input and output variables. The optimization of biofilter parameters was also done using RSM to optimize the biofilter performance. RSM being structured in nature enabled the study of interaction effect between the independent variables on biofilter performance.

Prediction of Parkinson’s Disease Using Improved Radial Basis Function Neural Network

Parkinson’s disease is a neurogenerative disorder and it is difficult to diagnose as no therapies may slow down its progression.This paper contributes a novel analytic system for Parkinson’s Disease Prediction mechanism using Improved Radial Basis Function Neural Network(IRBFNN).Particle swarm optimization(PSO)with K-means is used to find the hidden neuron’s centers to improve the accuracy of IRBFNN.The performance of RBFNN is seriously affected by the centers of hidden neurons.Conventionally K-means was used to find the centers of hidden neurons.The problem of sensitiveness to the random initial centroid in K-means degrades the performance of RBFNN.Thus,a metaheuristic algorithm called PSO integrated with K-means alleviates initial random centroid and computes optimal centers for hidden neurons in IRBFNN.The IRBFNN uses Particle swarm optimization K-means to find the centers of hidden neurons and the PSO K-means was designed to evaluate the fitness measures such as Intracluster distance and Intercluster distance.Experimentation have been performed on three Parkinson’s datasets obtained from the UCI repository.The proposed IRBFNN is compared with other variations of RBFNN,conventional machine learning algorithms and other Parkinson’s Disease prediction algorithms.The proposed IRBFNN achieves an accuracy of 98.73%,98.47%and 99.03%for three Parkinson’s datasets taken for experimentation.The experimental results show that IRBFNN maximizes the accuracy in predicting Parkinson’s disease with minimum root mean square error.

Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.