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.

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.

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.

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.

The Rate of Approximation of Gaussian Radial Basis Neural Networks in Continuous Function Space

There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks, and some approximation problems by Gaussian radial basis feedforward neural networks （GRBFNs） in some special function space have also been investigated. This paper considers the approximation by the GRBFNs in continuous function space. It is proved that the rate of approximation by GRNFNs with nd neurons to any continuous function f defined on a compact subset K R^d can be controlled by w（f, n^-1/2）, where w（f, t） is the modulus of continuity of the function f.

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.

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.

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.

Spatial prediction of soil organic carbon in coal mining subsidence areas based on RBF neural network

A quantitative research on the effect of coal mining on the soil organic carbon(SOC)pool at regional scale is beneficial to the scientific management of SOC pools in coal mining areas and the realization of coal low-carbon mining.Moreover,the spatial prediction model of SOC content suitable for coal mining subsidence area is a scientific problem that must be solved.Tak-ing the Changhe River Basin of Jincheng City,Shanxi Province,China,as the study area,this paper proposed a radial basis function neural network model combined with the ordinary kriging method.The model includes topography and vegetation factors,which have large influence on soil properties in mining areas,as input parameters to predict the spatial distribution of SOC in the 0-20 and 2040 cm soil layers of the study area.And comparing the prediction effect with the direct kriging method,the results show that the mean error,the mean absolute error and the root mean square error between the predicted and measured values of SOC content predicted by the radial basis function neural network are lower than those obtained by the direct kriging method.Based on the fitting effect of the predicted and measured values,the R^(2) obtained by the radial basis artificial neural network are 0.81,0.70,respectively,higher than the value of 0.44 and 0.36 obtained by the direct kriging method.Therefore,the model combining the artificial neural network and kriging,and considering environmental factors can improve the prediction accuracy of the SOC content in mining areas.

Hybridized Intelligent Neural Network Optimization Model for Forecasting Prices of Rubber in Malaysia

Rubber producers,consumers,traders,and those who are involved in the rubber industry face major risks of rubber price fluctuations.As a result,decision-makers are required to make an accurate estimation of the price of rubber.This paper aims to propose hybrid intelligent models,which can be utilized to forecast the price of rubber in Malaysia by employing monthly Malaysia’s rubber pricing data,spanning from January 2016 to March 2021.The projected hybrid model consists of different algorithms with the symbolic Radial Basis Functions Neural Network k-Satisfiability Logic Mining(RBFNN-kSAT).These algorithms,including Grey Wolf Optimization Algorithm,Artificial Bee Colony Algorithm,and Particle Swarm Optimization Algorithm were utilized in the forecasting data analysis.Several factors,which affect the monthly price of rubber,such as rubber production,total exports of rubber,total imports of rubber,stocks of rubber,currency exchange rate,and crude oil prices were also considered in the analysis.To evaluate the results of the introduced model,a comparison has been conducted for each model to identify the most optimum model for forecasting the price of rubber.The findings showed that GWO with RBFNN-kSAT represents the most accurate and efficient model compared with ABC with RBFNNkSAT and PSO with RBFNN-kSAT in forecasting the price of rubber.The GWO with RBFNN-kSAT obtained the greatest average accuracy(92%),with a better correlation coefficient R=0.983871 than ABC with RBFNN-kSAT and PSO with RBFNN-kSAT.Furthermore,the empirical results of this study provided several directions for policymakers to make the right decision in terms of devising proper measures in the industry to address frequent price changes so that the Malaysian rubber industry maintains dominance in the international markets.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.

RBF neural network regression model based on fuzzy observations

A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.

Improving Land Resource Evaluation Using Fuzzy Neural Network Ensembles

Land evaluation factors often contain continuous-, discrete- and nominal-valued attributes. In traditional land evaluation, these different attributes are usually graded into categorical indexes by land resource experts, and the evaluation results rely heavily on experts＇ experiences. In order to overcome the shortcoming, we presented a fuzzy neural network ensemble method that did not require grading the evaluation factors into categorical indexes and could evaluate land resources by using the three kinds of attribute values directly. A fuzzy back propagation neural network （BPNN）, a fuzzy radial basis function neural network （RBFNN）, a fuzzy BPNN ensemble, and a fuzzy RBFNN ensemble were used to evaluate the land resources in Guangdong Province. The evaluation results by using the fuzzy BPNN ensemble and the fuzzy RBFNN ensemble were much better than those by using the single fuzzy BPNN and the single fuzzy RBFNN, and the error rate of the single fuzzy RBFNN or fuzzy RBFNN ensemble was lower than that of the single fuzzy BPNN or fuzzy BPNN ensemble, respectively. By using the fuzzy neural network ensembles, the validity of land resource evaluation was improved and reliance on land evaluators＇ experiences was considerably reduced.

Trajectory linearization control of an aerospace vehicle based on RBF neural network

An enhanced trajectory linearization control （TLC） structure based on radial basis function neural network （RBFNN） and its application on an aerospace vehicle （ASV） flight control system are presensted. The influence of unknown disturbances and uncertainties is reduced by RBFNN thanks to its approaching ability, and a robustifying itera is used to overcome the approximate error of RBFNN. The parameters adaptive adjusting laws are designed on the Lyapunov theory. The uniform ultimate boundedness of all signals of the composite closed-loop system is proved based on Lyapunov theory. Finally, the flight control system of an ASV is designed based on the proposed method. Simulation results demonstrate the effectiveness and robustness of the designed approach.

Neural-Network-Based Terminal Sliding Mode Control for Frequency Stabilization of Renewable Power Systems

This paper addresses a terminal sliding mode control(T-SMC) method for load frequency control(LFC) in renewable power systems with generation rate constraints(GRC).A two-area interconnected power system with wind turbines is taken into account for simulation studies. The terminal sliding mode controllers are assigned in each area to achieve the LFC goal. The increasing complexity of the nonlinear power system aggravates the effects of system uncertainties. Radial basis function neural networks(RBF NNs) are designed to approximate the entire uncertainties. The terminal sliding mode controllers and the RBF NNs work in parallel to solve the LFC problem for the renewable power system. Some simulation results illustrate the feasibility and validity of the presented scheme.

Calculation method of ship collision force on bridge using artificial neural network

Ship collision on bridge is a dynamic process featured by high nonlinearity and instantaneity. Calculating ship-bridge collision force typically involves either the use of design-specification-stipulated equivalent static load, or the use of finite element method (FEM) which is more time-consuming and requires supercomputing resources. In this paper, we proposed an alternative approach that combines FEM with artificial neural network (ANN). The radial basis function neural network (RBFNN) employed for calculating the impact force in consideration of ship-bridge collision mechanics. With ship velocity and mass as the input vectors and ship collision force as the output vector, the neural networks for different network parameters are trained by the learning samples obtained from finite element simulation results. The error analyses of the learning and testing samples show that the proposed RBFNN is accurate enough to calculate ship-bridge collision force. The input-output relationship obtained by the RBFNN is essentially consistent with the typical empirical formulae. Finally, a special toolbox is developed for calculation efficiency in application using MATLAB software.

Global approximation based adaptive RBF neural network control for supercavitating vehicles

A global approximation based adaptive radial basis function（RBF） neural network control strategy is proposed for the trajectory tracking control of supercavitating vehicles（SV）.A nominal model is built firstly with the unknown disturbance.Next, the control scheme is established consisting of a computed torque controller（CTC） for the practical vehicle and an RBF neural network controller to estimate model error between the practical vehicle and the nominal model. The network weights are adapted by employing a Lyapunov-based design. Then it is shown by the Lyapunov theory that the trajectory tracking errors asymptotically converge to a small neighborhood of zero. The control performance of the proposed controller is illustrated by simulation.