Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Large Scattered Data Fitting Based on Radial Basis Functions

Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.

Comparative Study of Radial Basis Functions for PDEs with Variable Coefficients

The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential equations.Since the radial basis functions are meshless algorithms,its approximation is easy to implement and mathematically simple.In this paper,the commonly⁃used multiquadric RBF,conical RBF,and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable coefficients.Numerical results were provided to show the good performance of the three RBFs as numerical tools for a wide range of problems.It is shown that the conical RBF numerical results were more stable than the other two radial basis functions.From the comparison of three commonly⁃used RBFs,one may obtain the best numerical solutions for boundary value problems.

Regional Logistics Demand Forecast Based on Least Square and Radial Basis Function

Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies.It has the characteristics of a small amount of data and being nonlinear,so the traditional prediction method can not guarantee the accuracy of prediction.Taking Xiamen City as an example,this paper selects the primary industry,the secondary industry,the tertiary industry,the total amount of investment in fixed assets,total import and export volume,per capita consumption expenditure,and the total retail sales of social consumer goods as the influencing factors,and uses a combining model least square and radial basis function(LS-RBF)neural network to analyze the related data from years 2000 to 2019,so as to predict the logistics demand from years 2020 to 2024.The model can well fit the training data,and the experimental results obtained from the comparison between the predicted value and the actual value in 2019 show that the error rate is very small.Therefore,the prediction results are reasonable and reliable.This method has high prediction accuracy,and it is suitable for irregular regional logistics demand forecast.

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.

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.

STUDY OF RECOGNITION TECHNIQUE OF RADAR TARGET'S ONE-DIMENSIONAL IMAGES BASED ON RADIAL BASIS FUNCTION NETWORK

This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence between the RBFN and the estimate of Parzen window probabilistic density is proved. It is pointed out that the I/O functions in RBFN hidden units can be generalized to general Parzen window probabilistic kernel function or potential function, too. This paper discusses the effects of the shape parameter a in the RBFN and the forgotten factor A in RLSA on the results of the recognition of three kinds of kernel function such as Gaussian, triangle, double-exponential, at the same time, also discusses the relationship between A and the training time in the RBFN.

Application of least squares vector machines in modelling water vapor and carbon dioxide fluxes over a cropland

Least squares support vector machines (LS-SVMs), a nonlinear kemel based machine was introduced to investigate the prospects of application of this approach in modelling water vapor and carbon dioxide fluxes above a summer maize field using the dataset obtained in the North China Plain with eddy covariance technique. The performances of the LS-SVMs were compared to the corresponding models obtained with radial basis function (RBF) neural networks. The results indicated the trained LS-SVMs with a radial basis function kernel had satisfactory performance in modelling surface fluxes; its excellent approximation and generalization property shed new light on the study on complex processes in ecosystem.

Sensitivity Analysis of Radial Basis Function Networks for River Stage Forecasting

Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addressing the criticisms of their black-box behaviour. Such analysis of RBFNs for hydrological modelling has previously been limited to exploring perturbations to both inputs and connecting weights. In this paper, the backward chaining rule that has been used for sensitivity analysis of MLPs, is applied to RBFNs and it is shown how such analysis can provide insight into physical relationships. A trigonometric example is first presented to show the effectiveness and accuracy of this approach for first order derivatives alongside a comparison of the results with an equivalent MLP. The paper presents a real-world application in the modelling of river stage shows the importance of such approaches helping to justify and select such models.

不同容量下并网模式交流微电网短路故障早期检测与区域定位

随着分布式电源(distributed generation,DG)的容量变化,微电网原有的供电结构发生改变,使得潮流大小、方向和功率结构发生变化,对快速检测和定位微电网中的短路故障区域提出了挑战。在MATLAB/Simulink中搭建低压交流微电网模型;通过高尺度小波能量谱算法对微电网与大电网公共连接点(point of common coupling,PCC)处检测到的电流进行分解,提取适应不同容量情况的短路故障特征值,实现了不同容量下微电网短路故障的早期检测;利用小波能量谱特征结合基于正交最小二乘法(orthogonal least square,OLS)的径向基函数(radial basis function,RBF)神经网络算法提出一种适用于不同容量微电网的短路故障区域定位方法,并进行仿真验证;在此基础上设计并网模式微电网短路故障保护硬件系统,并进行实验验证。结果表明,所设计的保护系统能够快速、准确地同时实现并网模式下交流微电网短路故障的早期检测与区域定位。

微带天线设计及在局部放电检测中的应用

电气设备的局部放电既是绝缘劣化的主要因素,又是有效表征绝缘缺陷的重要参量。对局部放电进行准确检测,可以及时发现危及设备安全的潜在故障。特高频检测具有实时性好、抗干扰强的优势,在放电检测中应用广泛,但现有微带天线传感器受结构尺寸限制,工作带宽难以提高。本文采用部分接地板技术结合斜切式曲流技术改善结构,综合考虑天线尺寸与工作带宽的非线性关系优化尺寸,在保持天线面积不变的前提下扩展工作带宽,并以聚酰亚胺为基底研制了新型微带天线传感器。针对尺寸优化过程中存在的单尺寸参数调整导致天线性能不稳定的问题,提出利用径向基(RBF)神经网络建立多尺寸与工作带宽之间的关系模型,运用改进白鲸优化(IBWO)算法优化天线尺寸。仿真结果表明新型柔性微带天线尺寸缩小了59.59%;工作带宽由0.598~0.6 GHz增加到0.3~3 GHz,完全满足局部放电检测的应用需求。通过模拟局部放电检测试验,并与阿基米德螺旋天线、立体螺旋天线进行比较测试,结果显示新型柔性微带天线具有更高效的检测性能。

基于APID-RBF神经网络的光伏MPPT方法

针对光照强度急速变化和局部阴影时光伏发电系统最大功率点追踪响应速度慢、多峰值等问题,提出一种基于RBF神经网络与自适应PID控制相结合的控制方法。首先,采用RBF神经网络对环境的实时变化直接跟踪光伏最大功率点。然后,利用自适应PID的辅助修正,抑制光伏电池输出功率的波动。神经网络能提升在复杂环境下的跟踪速度,自适应PID能增强对神经网络误差的消除能力,提升跟踪精度。仿真结果表明,APIDRBF双控策略具有稳态性能高和控制精度高等优点,能有效提高光伏发电效率和稳定性。

RBF-CSR方法及其应用于裂解装置建模的研究

RBF-CSR是在分析RBF-PLS的基础上提出的新方法。它保留了RBF-PLS的优点:采用神经网络的结构, 又用数学方法直接求解,免去了ANN冗长的训练过程和其它诸多欠缺。RBF-CSR方法可以在更宽广的空间内寻找最优的网络参数,它所建立的模型具有很高的预报精度和良好的稳定性,又有简洁的解析形式,便于优化等进一步的计算和处理。该方法已成功地应用于裂解装置的建模。

基于新型神经网络的电网故障诊断方法

故障诊断对于事故后系统快速恢复正常运行具有重要的意义。该文提出应用新型径向基函数 (RadialBasisFunc tion ,RBF)神经网络解决故障诊断问题 ,文中将正交最小二乘 (Orthogonalleastsquare)算法扩展用于优化RBF神经网络参数。并应用传统的BP神经网络解决同样的问题以进行比较。在 4母线测试系统中的计算机仿真结果证明 ,在解决故障诊断这一类问题时 ,RBF神经网络优于BP神经网络模型 。

基于正交最小二乘法的径向基神经网络模型

为提高神经网络模型的预测精度以及提高模型的计算效率,减少获得高精度模型的计算量,构建了基于正交最小二乘法的高斯径向基神经网络模型结构,给出了最小二乘法高斯径向基神经网络的递归模型.依据样本点序列信息,给出了高斯径向基函数中心参数的确定方法,并采用正交最小二乘法回归迭代,从而获得隐层同输出层间的连接权参数值.采用混沌Lorenz时间序列预测问题对该设计的网络模型进行验证,并同其他文献对该序列预测的精度以及迭代所需的时间作对比.结果表明,采用该设计方法获得的网络模型具有时间预测精度高及计算效率高等优点.

基于频域特征提取与信息融合的磨机负荷软测量

提出了基于频域特征提取与多传感器信息融合的磨机负荷(ML)软测量新方法。针对磨矿过程主要依靠人工经验定性判断ML状态,难以定量检测ML参数的现状,通过融合磨机筒体振动、振声及驱动电机电流信号,建立了以料球比、矿浆浓度、充填率为输出的ML软测量模型。该方法首先采用快速傅里叶变换(FFT)将时域振动及振声信号转换为频谱变量,再对频谱变量通过主元分析(PCA)进行谱特征提取,然后采用径向基函数(RBF)变换生成的激活矩阵实现谱特征的非线性映射,最后采用偏最小二乘(PLS)算法建立以谱特征、激活矩阵、电流信号为输入的回归模型,从而有效克服了多传感器信息之间及RBF变换引起的多重共线性等问题。实验表明,该方法能够较准确地检测ML参数,融合多传感器的软测量方法具有更好的预测效果。

基于神经网络的开关磁阻电机无位置传感器控制

论文提出了基于自适应径向基函数(radialbasisfunction,RBF)神经网络的开关磁阻电机(SRM)无位置传感器控制新方法。该方法构造了一个隐层节点初始个数为零的RBF网络,通过在训练过程中不断按照自适应算法添加和删除隐层单元,形成一个结构简单、紧凑的网络来实现电机电压、磁链与转子位置之间的非线性映射,实现SRM的无位置传感器控制。网络训练分为离线训练和在线训练两个部分。利用训练样本按给出的自适应算法对网络进行离线训练,确定RBF网络隐层节点的个数及位置;按递推最小二乘法(RLS)在线修正隐层与输出层之间的连接权。仿真及实验结果表明,该方法能够实现电机的准确换相,从而实现了位置传感器的消去。

基于投影寻踪的非线性鲁棒偏最小二乘法及应用

来自工业现场的数据往往具有非线性特性且包含离群点,利用非线性偏最小二乘法(partia lleast squares,PLS)建模易受离群点的影响.针对这一问题,结合径向基函数(radial basis function,RBF)网络,本文提出了一种基于投影寻踪的非线性鲁棒PLS方法.该方法首先利用RBF变换将自变量与因变间的非线性关系转化为线性关系;然后利用投影寻踪算法提取变换后自变量的鲁棒偏最小二乘法成分;最后建立鲁棒PLS成分与因变量之间的鲁棒线性回归模型.将该方法应用于湿法冶金萃余液pH值软测量建模问题,结果验证了其有效性.