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.

Radial Basis Function Networks Applied in Bacterial Classification Based on MALDI-TOF-MS

The radial basis function networks were applied to bacterial classification based on the matrix-assisted laser desorption/ionization time-of-flight mass spectrometric (MALDI-TOF-MS) data. The classification of bacteria cultured at different time was discussed and the effect of the network parameters on the classification was investigated. The cross-validation method was used to test the trained networks. The correctness of the classification of different bacteria investigated changes in a wide range from 61.5% to 92.8%. Owing to the complexity of biological effects in bacterial growth, the more rigid control of bacterial culture conditions seems to be a critical factor for improving the rate of correctness for bacterial classification.

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.

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.

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.

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.

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.

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.

Comparative study of honeycomb optimization using Kriging and radial basis function

Structural optimization for crashworthiness criteria is of particular significance especially at early stage of design. The comparative study of Kriging and radial basis function network （RBFN） was performed in order to improve the crashworthiness effects of honeycomb. Improving the crashworthiness characteristic of honeycomb was achieved using LS-OPT~ and domain reduction strategy. This optimization is performed on the basis of validated numerical simulation to establish the approximated model to illustrate the relationship between the responses and design variables. The results showed that Kriging meta-model is excelled in accuracy, robustness and efficiency compared to radial basis function （RBF） and crashworthiness characteristic of honeycomb is improved by 4%.

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.

Generalization Capabilities of Feedforward Neural Networks for Pattern Recognition

This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.

基于混合双层自组织径向基函数神经网络的优化学习算法

针对传统方法采用先训练后测试两阶段学习机制极易导致的过拟合或欠拟合问题,提出一种基于混合双层自组织径向基函数神经网络的优化学习(hybrid bilevel self-organizing radial basis function neural network optimization learning,Hb-SRBFNN-OL)算法。首先,将训练过程和测试过程集成到一个统一的框架中,规避过拟合或欠拟合问题。其次,基于进化学习机制,提出上下2层的交互式优化学习算法,上层基于网络复杂度和测试误差自组织调整网络结构,下层采用列文伯格-马夸尔特(Levenberg Marquardt,LM)算法作为优化器对自组织径向基函数神经网络(self-organizing radial basis function neural network,SO-RBFNN)的连接权值进行优化。最后,利用来自多个子网络的综合信息生成模型的最终输出,加速网络全局收敛。为验证所提方法的可行性,分别在多个分类和预测任务中进行了测试实验。结果表明,在与传统神经网络结构相似甚至更好的测试和分类精度下,该方法不仅能实现更快的训练收敛,而且能进化成更精简紧凑的径向基函数神经网络(radial basis function neural network,RBFNN)模型。尤其在污水处理过程中总磷的质量浓度预测实验中,测试集中均方根误差(root mean squared error,RMSE)最高可降低48.90%,实际场景实验结果验证了所提算法的精确性更佳且泛化能力更强。

Fractional Gradient Descent RBFNN for Active Fault-Tolerant Control of Plant Protection UAVs

With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.

Prediction of coal ash fusion temperature using constructive-pruning hybrid method for RBF networks

A constructive-pruning hybrid method （CPHM） for radial basis function （RBF） networks is proposed to improve the prediction accuracy of ash fusion temperatures （AFT）. The CPHM incorporates the advantages of the construction algorithm and the pruning algorithm of neural networks, and the training process of the CPHM is divided into two stages： rough tuning and fine tuning. In rough tuning, new hidden units are added to the current network until some performance index is satisfied. In fine tuning, the network structure and the model parameters are further adjusted. And, based on components of coal ash, a model using the CPHM is established to predict the AFT. The results show that the CPHM prediction model is characterized by its high precision, compact network structure, as well as strong generalization ability and robustness.