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.

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.

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.

A Simple Hybrid Recursive Learning Algorithm with High Generalization Performance for Radial Basis Function Neural Network

In this paper, we propose a simple learning algorithm for non\|linear function approximation and system modeling using minimal radial basis function neural network with high generalization performance. A hybrid algorithm is constructed, which combines recursive n \|means clustering algorithm with a simple recursive regularized least squares algorithm (SRRLS). The n \|means clustering algorithm adjusts the centers of the network, while the SRRLS constructs a parsimonious network which makes the generalization performance of the network well. The SRRLS algorithm needs no matrix computing, so it has a lower computational cost and no ill\|conditional problem. Because of the recursive manner, this algorithm is suitable for on\|line applications. The effectiveness of this algorithm is demonstrated by two benchmark examples.

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function （RBF） neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.

A Self-Organizing RBF Neural Network Based on Distance Concentration Immune Algorithm

Radial basis function neural network(RBFNN) is an effective algorithm in nonlinear system identification. How to properly adjust the structure and parameters of RBFNN is quite challenging. To solve this problem, a distance concentration immune algorithm(DCIA) is proposed to self-organize the structure and parameters of the RBFNN in this paper. First, the distance concentration algorithm, which increases the diversity of antibodies, is used to find the global optimal solution. Secondly,the information processing strength(IPS) algorithm is used to avoid the instability that is caused by the hidden layer with neurons split or deleted randomly. However, to improve the forecasting accuracy and reduce the computation time, a sample with the most frequent occurrence of maximum error is proposed to regulate the parameters of the new neuron. In addition, the convergence proof of a self-organizing RBF neural network based on distance concentration immune algorithm(DCIA-SORBFNN) is applied to guarantee the feasibility of algorithm. Finally, several nonlinear functions are used to validate the effectiveness of the algorithm. Experimental results show that the proposed DCIASORBFNN has achieved better nonlinear approximation ability than that of the art relevant competitors.

Groundwater level prediction based on hybrid hierarchy genetic algorithm and RBF neural network

As the traditional non-linear systems generally based on gradient descent optimization method have some shortage in the field of groundwater level prediction, the paper, according to structure, algorithm and shortcoming of the conventional radial basis function neural network （RBF NN）, presented a new improved genetic algorithm （GA）： hybrid hierarchy genetic algorithm （HHGA）. In training RBF NN, the algorithm can automatically determine the structure and parameters of RBF based on the given sample data. Compared with the traditional groundwater level prediction model based on back propagation （BP） or RBF NN, the new prediction model based on HHGA and RBF NN can greatly increase the convergence speed and precision.

A Novel Method for Solving Ordinary Differential Equations with Artificial Neural Networks

This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial conditions. In particular, we employ a feed-forward Multilayer Perceptron Neural Network (MLPNN), but bypass the standard back-propagation algorithm for updating the intrinsic weights. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial or boundary conditions and contains no adjustable parameters. The second part involves a feed-forward neural network to be trained to satisfy the differential equation. Numerous works have appeared in recent times regarding the solution of differential equations using ANN, however majority of these employed a single hidden layer perceptron model, incorporating a back-propagation algorithm for weight updation. For the homogeneous case, we assume a solution in exponential form and compute a polynomial approximation using statistical regression. From here we pick the unknown coefficients as the weights from input layer to hidden layer of the associated neural network trial solution. To get the weights from hidden layer to the output layer, we form algebraic equations incorporating the default sign of the differential equations. We then apply the Gaussian Radial Basis function (GRBF) approximation model to achieve our objective. The weights obtained in this manner need not be adjusted. We proceed to develop a Neural Network algorithm using MathCAD software, which enables us to slightly adjust the intrinsic biases. We compare the convergence and the accuracy of our results with analytic solutions, as well as well-known numerical methods and obtain satisfactory results for our example ODE problems.

Nonlinear modelling of a SOFC stack by improved neural networks identification

The solid oxide fuel cell (SOFC) is a nonlinear system that is hard to model by conventional methods. So far,most existing models are based on conversion laws,which are too complicated to be applied to design a control system. To facilitate a valid control strategy design,this paper tries to avoid the internal complexities and presents a modelling study of SOFC per-formance by using a radial basis function (RBF) neural network based on a genetic algorithm (GA). During the process of mod-elling,the GA aims to optimize the parameters of RBF neural networks and the optimum values are regarded as the initial values of the RBF neural network parameters. The validity and accuracy of modelling are tested by simulations,whose results reveal that it is feasible to establish the model of SOFC stack by using RBF neural networks identification based on the GA. Furthermore,it is possible to design an online controller of a SOFC stack based on this GA-RBF neural network identification model.

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.

A new sequential learning algorithm for RBF neural networks

Due to their inherent imperfections, it is hard to use the static neural networks for nonlinear time-varying process modeling and prediction, and the minimal resource allocation network (MRAN) is difficult to be realized for its too many regulation parameters. A new sequential learning algorithm for radial basis function (RBF) neural networks based on local projection named Local Projection Network (LPN) is proposed in this paper. The results of validation for several benchmark problems with the new algorithm show that the presented LPN not only has the same level as M-RAN in network size and precision of the outputs, but also has fewer regulation parameters and is more predictable.

Estimation of water saturation by using radial based function artificial neural network in carbonate reservoir:A case study in Sarvak formation

Water saturation determination in core laboratory is known as a cost and time consuming labor.Hitherto,many scientists attempted to estimate accurately water saturation from well-logging data which has a continuous record without losing information.Therefore,various model were introduced to relate reservoir properties and water saturation.Since carbonate reservoir is very heterogeneous in shape and size of pore throat,the relation between water saturation and other carbonates reservoir properties is very complex,and causes considerable overall errors in water saturation calculation.By increasing the usage and improvement of soft computing methods in engineering problems,petroleum engineers have been attended them to measure the petrophysical properties of the reservoir.In this study,a radial basis function neural network(RBFNN)improved by genetic algorithm has been employed to estimate formation water saturation by using conventional well-logging data.The used logging and core data have been gathered from a carbonated formation from one of oilfield located in south-west Iran,and finally their results of the proposed model were compared with the core analysis results.By checking the testing data from another well,it showed this method had a 0.027 for mean square errors and its correlation coefficient is equal to 0.870.These results implied on high accuracy of this model for oil saturation degree estimation.While the common methods like Archie,had a 0.041 mean square error and 0.720 of the correlation coefficient,which indicate a high ability of RBF model than the other usual empirical methods.

Prediction of Salinity Variations in a Tidal Estuary Using Artificial Neural Network and Three-Dimensional Hydrodynamic Models

The simulation of salinity at different locations of a tidal river using physically-based hydrodynamic models is quite cumbersome because it requires many types of data, such as hydrological and hydraulic time series at boundaries, river geometry, and adjusted coefficients. Therefore, an artificial neural network (ANN) technique using a back-propagation neural network (BPNN) and a radial basis function neural network (RBFNN) is adopted as an effective alternative in salinity simulation studies. The present study focuses on comparing the performance of BPNN, RBFNN, and three-dimensional hydrodynamic models as applied to a tidal estuarine system. The observed salinity data sets collected from 18 to 22 May, 16 to 22 October, and 26 to 30 October 2002 (totaling 4320 data points) were used for BPNN and RBFNN model training and for hydrodynamic model calibration. The data sets collected from 30 May to 2 June and 11 to 15 November 2002 (totaling 2592 data points) were adopted for BPNN and RBFNN model verification and for hydrodynamic model verification. The results revealed that the ANN (BPNN and RBFNN) models were capable of predicting the nonlinear time series behavior of salinity to the multiple forcing signals of water stages at different stations and freshwater input at upstream boundaries. The salinity predicted by the ANN models was better than that predicted by the physically based hydrodynamic model. This study suggests that BPNN and RBFNN models are easy-to-use modeling tools for simulating the salinity variation in a tidal estuarine system.

Two-layer networked learning control using self-learning fuzzy control algorithms

Since the existing single-layer networked control systems have some inherent limitations and cannot effectively handle the problems associated with unreliable networks, a novel two-layer networked learning control system (NLCS) is proposed in this paper. Its lower layer has a number of local controllers that are operated independently, and its upper layer has a learning agent that communicates with the independent local controllers in the lower layer. To implement such a system, a packet-discard strategy is firstly developed to deal with network-induced delay and data packet loss. A cubic spline interpolator is then employed to compensate the lost data. Finally, the output of the learning agent based on a novel radial basis function neural network (RBFNN) is used to update the parameters of fuzzy controllers. A nonlinear heating, ventilation and air-conditioning (HVAC) system is used to demonstrate the feasibility and effectiveness of the proposed system.

Satellite Image Classification Using a Hybrid Manta Ray Foraging Optimization Neural Network

A semi supervised image classification method for satellite images is proposed in this paper.The satellite images contain enormous data that can be used in various applications.The analysis of the data is a tedious task due to the amount of data and the heterogeneity of the data.Thus,in this paper,a Radial Basis Function Neural Network(RBFNN)trained using Manta Ray Foraging Optimization algorithm(MRFO)is proposed.RBFNN is a three-layer network comprising of input,output,and hidden layers that can process large amounts.The trained network can discover hidden data patterns in unseen data.The learning algorithm and seed selection play a vital role in the performance of the network.The seed selection is done using the spectral indices to further improve the performance of the network.The manta ray foraging optimization algorithm is inspired by the intelligent behaviour of manta rays.It emulates three unique foraging behaviours namelys chain,cyclone,and somersault foraging.The satellite images contain enormous amount of data and thus require exploration in large search space.The spiral movement of the MRFO algorithm enables it to explore large search spaces effectively.The proposed method is applied on pre and post flooding Landsat 8 Operational Land Imager(OLI)images of New Brunswick area.The method was applied to identify and classify the land cover changes in the area induced by flooding.The images are classified using the proposed method and a change map is developed using post classification comparison.The change map shows that a large amount of agricultural area was washed away due to flooding.The measurement of the affected area in square kilometres is also performed for mitigation activities.The results show that post flooding the area covered by water is increased whereas the vegetated area is decreased.The performance of the proposed method is done with existing state-of-the-art methods.

An adaptive machine learning-based optimization method in the aerodynamic analysis of a finite wing under various cruise conditions

Conventional wing aerodynamic optimization processes can be time-consuming and imprecise due to the complexity of versatile flight missions.Plenty of existing literature has considered two-dimensional infinite airfoil optimization,while three-dimensional finite wing optimizations are subject to limited study because of high computational costs.Here we create an adaptive optimization methodology built upon digitized wing shape deformation and deep learning algorithms,which enable the rapid formulation of finite wing designs for specific aerodynamic performance demands under different cruise conditions.This methodology unfolds in three stages:radial basis function interpolated wing generation,collection of inputs from computational fluid dynamics simulations,and deep neural network that constructs the surrogate model for the optimal wing configuration.It has been demonstrated that the proposed methodology can significantly reduce the computational cost of numerical simulations.It also has the potential to optimize various aerial vehicles undergoing different mission environments,loading conditions,and safety requirements.

A fuzzy immune algorithm and its application in solvent tower soft sensor modeling

An improved immune algorithm is proposed in this paper. The problems, such as convergence speed and optimization precision, existing in the basic immune algorithm are well addressed. Besides, a fuzzy adaptive method is presented by using the fuzzy system to realize the adaptive selection of two key parameters （possibility of crossover and mutation）. By comparing and analyzing the results of several benchmark functions, the performance of fuzzy immune algorithm （FIA） is approved. Not only the difficulty of parameters selection is relieved, but also the precision and stability are improved. At last, the FIA is ap- plied to optimization of the structure and parameters in radial basis function neural network （RBFNN） based on an orthogonal sequential method. And the availability of algorithm is proved by applying RBFNN in modeling in soft sensor of solvent tower.

Ensemble hybrid machine learning methods for gully erosion susceptibility mapping: K-fold cross validation approach

Gully erosion is one of the important problems creating barrier to agricultural development.The present research used the radial basis function neural network(RBFnn)and its ensemble with random sub-space(RSS)and rotation forest(RTF)ensemble Meta classifiers for the spatial mapping of gully erosion susceptibility(GES)in Hinglo river basin.120 gullies were marked and grouped into four-fold.A total of 23 factors including topographical,hydrological,lithological,and soil physio-chemical properties were effectively used.GES maps were built by RBFnn,RSS-RBFnn,and RTF-RBFnn models.The very high susceptibility zone of RBFnn,RTF-RBFnn and RSS-RBFnn models covered 6.75%,6.72%and 6.57%in Fold-1,6.21%,6.10%and 6.09%in Fold-2,6.26%,6.13%and 6.05%in Fold-3 and 7%,6.975%and 6.42%in Fold-4 of the basin.Receiver operating characteristics(ROC)curve and statistical techniques such as mean-absolute-error(MAE),root-mean-absolute-error(RMSE)and relative gully density area(R-index)methods were used for evaluating the GES maps.The results of the ROC,MAE,RMSE and R-index methods showed that the models of susceptibility to gully erosion have excellent predictive efficiency.The simulation results based on machine learning are satisfactory and outstanding and could be used to forecast the areas vulnerable to gully erosion.

利用Gaussian型RBF网络进行函数逼近的构造性估计

前馈人工神经网络有着极其广泛的应用 ,如何估计隐层神经元数及相应的逼近误差 ,一直是确定前馈网络结构的难点和关键。 RBF网络是一种最重要的前馈神经网络 ,本文给出了利用 Gaussian型 RBF网络逼近连续函数或 Lebesgue-可积函数时的构造性的隐层单元数显式估算式及相应的显式逼近误差估算式。文中的结论也易于推广到离散样本的情形。这些结论对于提高 Guassian型 RBF在实际应用时的计算精度和减少计算量具有一定的指导意义。