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

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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.

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.

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.

Artificial neural network modeling of water quality of the Yangtze River system:a case study in reaches crossing the city of Chongqing

An effective approach for describing complicated water quality processes is very important for river water quality management. We built two artificial neural network(ANN) models,a feed-forward back-propagation(BP) model and a radial basis function(RBF) model,to simulate the water quality of the Yangtze and Jialing Rivers in reaches crossing the city of Chongqing,P. R. China. Our models used the historical monitoring data of biological oxygen demand,dissolved oxygen,ammonia,oil and volatile phenolic compounds. Comparison with the one-dimensional traditional water quality model suggest that both BP and RBF models are superior; their higher accuracy and better goodness-of-fit indicate that the ANN calculation of water quality agrees better with measurement. It is demonstrated that ANN modeling can be a tool for estimating the water quality of the Yangtze River. Of the two ANN models,the RBF model calculates with a smaller mean error,but a larger root mean square error. More effort to identify out the causes of these differences would help optimize the structures of neural network water-quality models.

Modeling and optimum operating conditions for FCCU using artificial neural network

A self-organizing radial basis function(RBF) neural network(SODM-RBFNN) was presented for predicting the production yields and operating optimization. Gradient descent algorithm was used to optimize the widths of RBF neural network with the initial parameters obtained by k-means learning method. During the iteration procedure of the algorithm, the centers of the neural network were optimized by using the gradient method with these optimized width values. The computational efficiency was maintained by using the multi-threading technique. SODM-RBFNN consists of two RBF neural network models: one is a running model used to predict the product yields of fluid catalytic cracking unit(FCCU) and optimize its operating parameters; the other is a learning model applied to construct or correct a RBF neural network. The running model can be updated by the learning model according to an accuracy criterion. The simulation results of a five-lump kinetic model exhibit its accuracy and generalization capabilities, and practical application in FCCU illustrates its effectiveness.

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.

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.

Neural-networks-based Modelling and a Fuzzy Neural Networks Controller of MCFC

Molten Carbonate Fuel Cells (MCFC) are produced with a highly efficient and clean power generation technology which will soon be widely utilized. The temperature characters of MCFC stack are briefly analyzed. A radial basis function (RBF) neural networks identification technology is applied to set up the temperature nonlinear model of MCFC stack, and the identification structure, algorithm and modeling training process are given in detail. A fuzzy controller of MCFC stack is designed. In order to improve its online control ability, a neural network trained by the I/O data of a fuzzy controller is designed. The neural networks can memorize and expand the inference rules of the fuzzy controller and substitute for the fuzzy controller to control MCFC stack online. A detailed design of the controller is given. The validity of MCFC stack modelling based on neural networks and the superior performance of the fuzzy neural networks controller are proved by Simulations.

Application of Nonlinear Predictive Control Based on RBF Network Predictive Model in MCFC Plant

This paper described a nonlinear model predictive controller for regulating a molten carbonate fuel cell (MCFC). A detailed mechanism model of output voltage of a MCFC was presented at first. However, this model was too complicated to be used in a control system. Consequently, an off line radial basis function (RBF) network was introduced to build a nonlinear predictive model. And then, the optimal control sequences were obtained by applying golden mean method. The models and controller have been realized in the MATLAB environment. Simulation results indicate the proposed algorithm exhibits satisfying control effect even when the current densities vary largely.

基于Bezier曲线的气膜冷却孔出口孔形优化

提出一种基于Bezier曲线的气膜冷却孔出口参数化构型方法,通过调整Bezier曲线的控制点,改变气膜冷却孔的出口形状。采用拉丁超立方抽样(LHS)和数值模拟的方法,获得大量不同气膜冷却孔出口形状下的气膜冷却效果,结合径向基函数神经网络(RBF-NN)所构建的预测模型和遗传算法(GA)进行气膜冷却孔出口形状优化。结果表明:优化后的气膜冷却孔可以有效抑制肾形涡对(CVP)的强度与大小,减小冷却气流与热主流的掺混损失;优化后的气膜冷却孔具有扩张的冷却通道,降低了冷却气流出口法向上的动量,有效抑制了冷却气流对于热主流的穿透,提升了气膜冷却效率;在吹风比M=0.91的情况下,最优孔形的气膜冷却效率较圆孔和扇形孔分别提升了40.48%和17.82%。

智能汽车轨迹跟踪MPC-RBF-SMC协同控制策略研究

针对自动驾驶车辆行驶过程中模型失配以及外部环境干扰导致车辆轨迹跟踪环节精确性不高的问题,提出了一种结合车辆运动学模型预测控制(MPC)、径向基(RBF)神经网络和滑模控制(SMC)的轨迹跟踪控制策略。通过建立车辆运动学MPC模型计算当前状态车辆期望横摆角速度,并将其与实际横摆角速度的偏差输入RBF-SMC控制器,利用RBF快速逼近非线性模型的特点,结合滑模控制输出前轮转角,实现车辆的横向轨迹跟踪控制。仿真结果表明,与传统的控制器相比,该方法轨迹跟踪精度显著提高,并在不同行驶工况下表现出较好的鲁棒性。

无模型自适应滑模控制的微波加热过程温度控制

微波加热模型具有无限维、非线性和时变等特点,导致控制器难于设计和实现。针对此问题,提出了一种适用于微波加热过程的无模型自适应滑模控制方法。首先,对微波加热过程传热数学模型进行分析,建立了微波加热过程输入功率与温度之间的全格式动态线性化数据模型。然后,根据该数据模型设计了无模型自适应滑模控制器,并给出了数据模型中相关未知时变参数和未知干扰的估计算法。最后,利用COMSOL和MATLAB进行仿真,仿真结果验证了所提控制方法的有效性。

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.

A prediction method for the wax deposition rate based on a radial basis function neural network

The radial basis function neural network is a popular supervised learning tool based on machinery learning technology.Its high precision having been proven,the radial basis function neural network has been applied in many areas.The accumulation of deposited materials in the pipeline may lead to the need for increased pumping power,a decreased flow rate or even to the total blockage of the line,with losses of production and capital investment,so research on predicting the wax deposition rate is significant for the safe and economical operation of an oil pipeline.This paper adopts the radial basis function neural network to predict the wax deposition rate by considering four main influencing factors,the pipe wall temperature gradient,pipe wall wax crystal solubility coefficient,pipe wall shear stress and crude oil viscosity,by the gray correlational analysis method.MATLAB software is employed to establish the RBF neural network.Compared with the previous literature,favorable consistency exists between the predicted outcomes and the experimental results,with a relative error of 1.5%.It can be concluded that the prediction method of wax deposition rate based on the RBF neural network is feasible.

Detection of Cholangiocarcinoma with Fourier Transform Infrared Spectroscopy and Radial Basis Function Neural Network Classification

The aim of this study was to explore the possibility of applying Fourier transform infrared（FTIR） spec- troscopy as a medical diagnostic toot based on a neural network classifier for detecting and classifying cholangiocar- cinoma. A total of 51 cases of bile duct tissues were obtained and later characterized by FTIR spectroscopy prior to pathological diagnosis. The criteria for classification included 30 parameters for each FTIR spectra, including peak position（P）, intensity（/） and full width at half-maximum（FWHM）, were measured, calculated and subsequently com- pared against the normal and cancer groups. The FTIR spectra were classified by the radial basis function（RBF） net- work model. For establishing the RBF, 23 cases were used to train the RBF classifier, and 28 cases were applied to validate the model. Using the RFB model, nine parameters were observed to be pronouncedly different between can- cerous and normal tissue, including I1640, I1550, 11460,/1400, I1250, I1120,/10g0, Ii040 and P1040. In the RBF training classi- fication, the accuracy, sensitivity, and specificity of diagnosis were 82.6%, 80.0%, and 84.6%, respectively. While validating the classification, the accuracy, sensitivity, and specificity of diagnosis were 78.6%, 75.0%, and 81.2%, respectively. The results suggest that FTIR spectroscopy combined with neural network classifier could be applied as a medical diagnostic tool in cholangiocarcinoma diagnosis.

基于分数阶自适应神经网络的电动舵机伺服系统摩擦干扰补偿控制

摩擦干扰力矩影响电动舵机伺服系统的跟踪性能,造成位置和速度跟踪偏差,甚至可能导致伺服系统不稳定。针对摩擦力矩干扰下的电动舵机伺服系统跟踪性能差的问题,本文提出了一种分数阶自适应神经网络摩擦补偿算法(FOANN),估计并补偿摩擦干扰力矩。首先,建立基于LuGre模型的电动舵机伺服系统模型,利用径向基神经网络估计模型中的不可测状态变量。其次,设计FOANN摩擦补偿控制器,利用李雅普诺夫稳定性理论证明电动舵机闭环系统的稳定性。最后,利用仿真和实验平台,对比分析了FOANN、传统PD控制和模型自适应控制的性能。结果表明,基于本文所提出的FOANN摩擦力矩补偿控制算法,电动舵机伺服系统的位置跟踪误差和速度跟踪误差均大幅减小,FOANN算法能够有效估计并补偿摩擦力矩,降低摩擦干扰对电机舵机伺服系统的影响,提高伺服系统的动态性能。

计及尾流的风电场智能等效建模及偏航优化控制

大型风电场中存在的尾流干扰会降低风电场整体输出功率,因此需要对风电场建立等效模型,并通过优化尾流分布来提升风电场整体功率输出能力。在所提出的新型风电场偏航优化框架中,提出了一种利用参数监督学习和正则化技术改进的径向基函数神经网络算法,并建立了面向多自由度偏航控制的风电场功率转换智能等效模型。在该模型的基础上,定义了以风电机组偏航角为决策变量的场级最大输出功率优化问题,提出了一种改进的精英多种群遗传算法并进行优化求解,得到各机组偏航角优化值以减少机组间尾流干扰。利用实际风电场布局和风况数据进行了仿真测试。结果表明:所建立的风电场功率转换智能等效模型与其实际特性吻合良好,在特定风况下,偏航优化控制使得风电场总功率提升718.79 kW;连续风况下,所提优化控制方法在不同风况下均有明显的优化效果,风电场总功率平均提升1208 kW,验证了所提出的新型风电场偏航优化框架在提升风电场整体输出功率上的优越性。