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.

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.

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.

Adaptive proportional integral differential control based on radial basis function neural network identification of a two-degree-of-freedom closed-chain robot

A closed-chain robot has several advantages over an open-chain robot, such as high mechanical rigidity, high payload, high precision. Accurate trajectory control of a robot is essential in practical-use. This paper presents an adaptive proportional integral differential （PID） control algorithm based on radial basis function （RBF） neural network for trajectory tracking of a two-degree-of-freedom （2-DOF） closed-chain robot. In this scheme, an RBF neural network is used to approximate the unknown nonlinear dynamics of the robot, at the same time, the PID parameters can be adjusted online and the high precision can be obtained. Simulation results show that the control algorithm accurately tracks a 2-DOF closed-chain robot trajectories. The results also indicate that the system robustness and tracking performance are superior to the classic PID method.

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.

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.

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.

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.

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.

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.

Development of Trees Management System Using Radial Basis Function Neural Network for Rain Forecast

Agriculture and farming are mainly dependent on weather especially in Malaysia as it received heavy rainfall throughout the years. An efficient crop or tree management system with a weather forecast needed for suitable planning of farming operation. Radial Basis Function Neural Network (RBFNN) algorithm was used in this study to predict rainfall and the main focus of this study is to analyze the factor that affects the performance of neural model. This study found that the model works better the more hidden nodes and the optimum learning rate is 0.01 with the RMSE 49% and the percentage accuracy is 57%. Besides that, it is found that the meteorology data also affect the model performance. Future research can be conducted to improve the rainfall forecast of this study and improve the tree management system.

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.

Rough set and radial basis function neural network based insulation data mining fault diagnosis for power transformer

Rough set (RS) and radial basis function neural network (RBFNN) based insulation data mining fault diagnosis for power transformer is proposed. On the one hand rough set is used as front of RBFNN to simplify the input of RBFNN and mine the rules. The mined rules whose “confidence” and “support” is higher than requirement are used to offer fault diagnosis service for power transformer directly. On the other hand the mining samples corresponding to the mined rule, whose “confidence and support” is lower than requirement, are used to be training samples set of RBFNN and these samples are clustered by rough set. The center of each clustering set is used to be center of radial basis function, i.e., as the hidden layer neuron. The RBFNN is structured with above base, which is used to diagnose the case that can not be diagnosed by mined simplified valuable rules based on rough set. The advantages and effectiveness of this method are verified by testing.

Face Recognition Based on Wavelet Packet Coefficients and Radial Basis Function Neural Networks

An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function (RBF) neural network is presented. The face images are decomposed by 2-level two-dimensional (2-D) wavelet packet transformation. The wavelet packet coefficients obtained from the wavelet packet transformation are averaged using two different proposed methods. In the first method, wavelet packet coefficients of individual samples of a class are averaged then decomposed. The wavelet packet coefficients of all the samples of a class are averaged in the second method. The averaged wavelet packet coefficients are recognized by a RBF network. The proposed work tested on three face databases such as Olivetti-Oracle Research Lab (ORL), Japanese Female Facial Expression (JAFFE) and Essexface database. The proposed methods result in dimensionality reduction, low computational complexity and provide better recognition rates. The computational complexity is low as the dimensionality of the input pattern is reduced.

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.

Situation Awareness and Sensitivity Analysis for Absorption of Grid-connected Renewable Energy Power Generation Integrating Robust Optimization and Radial Basis Function Neural Network

The significance of situation awareness(SA) in power systems has increased to enhance the utilization of gridconnected renewable energy power generation(REPG). This paper proposes a real-time calculation architecture based on the integration of robust optimization(RO) and artificial intelligence. First, the time-series simulation of the REPG consumption capacity is carried out under the current grid operating conditions. RO is employed in this simulation, given the randomness of the REPG output and the grid load. Then, the radial basis function neural network(RBFNN) is trained with the results under different parameters using the artificial fish swarm algorithm(AFSA), enabling the neural network(NN) to be the replacement for the time-series simulation model. The trained NN can quickly perceive the REPG absorption situation within the predefined grid structure and period. Moreover, the Sobol' method is adopted to conduct the global sensitivity analysis for different parameters based on the input-output samples obtained by the trained NN. Finally, the simulation experiments based on the modified IEEE 14-bus system prove the real-time performance and accuracy of the proposed SA architecture.

Accurate prediction of different forecast horizons wind speed using a recursive radial basis function neural network

Environmental considerations have prompted the use of renewable energy resources worldwide for reduction of greenhouse gas emissions.An accurate prediction of wind speed plays a major role in environmental planning,energy system balancing,wind farm operation and control,power system planning,scheduling,storage capacity optimization,and enhancing system reliability.This paper proposes an accurate prediction of wind speed based ona Recursive Radial Basis Function Neural Network(RRBFNN)possessing the three inputs of wind direction,temperature and wind speed to improve modern power system protection,control and management.Simulation results confirm that the proposed model improves the wind speed prediction accuracy with least error when compared with other existing prediction models.

Analytic design of information granulation-based fuzzy radial basis function neural networks with the aid of multiobjective particle swarm optimization

Purpose–The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation(IG-FRBFNN)and their optimization realized by means of the Multiobjective Particle Swarm Optimization(MOPSO).Design/methodology/approach–In fuzzy modeling,complexity,interpretability(or simplicity)as well as accuracy of the obtained model are essential design criteria.Since the performance of the IG-RBFNN model is directly affected by some parameters,such as the fuzzification coefficient used in the FCM,the number of rules and the orders of the polynomials in the consequent parts of the rules,the authors carry out both structural as well as parametric optimization of the network.A multi-objective Particle Swarm Optimization using Crowding Distance(MOPSO-CD)as well as O/WLS learning-based optimization are exploited to carry out the structural and parametric optimization of the model,respectively,while the optimization is of multiobjective character as it is aimed at the simultaneous minimization of complexity and maximization of accuracy.Findings–The performance of the proposed model is illustrated with the aid of three examples.The proposed optimization method leads to an accurate and highly interpretable fuzzy model.Originality/value–A MOPSO-CD as well as O/WLS learning-based optimization are exploited,respectively,to carry out the structural and parametric optimization of the model.As a result,the proposed methodology is interesting for designing an accurate and highly interpretable fuzzy model.

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.

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.