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The Analysis of Gauss Radial Basis Functions and Its Application in Locating Olivine on the Moon 认领 引用
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作者 SONG Shicang SONG Xiaoyuan SONG Shuhan 《应用数学》 北大核心 2026年第1期173-181,共9页
Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the m... Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme. 展开更多
关键词 Gauss function Radial basis function Machine learning Lunar olivine locating Data fitting
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Applying the Radial Basis Function Method to Estimate the Distribution of Total Suspended Matter Concentration in Hangzhou Bay 认领 引用
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作者 CHEN Wanqian GAO Jinpeng +5 位作者 XU Minjie LIU Zezheng LI Bingtian LV Jing LI Shujiang SUN Junchuan 《Journal of Ocean University of China》 SCIE CAS CSCD 2025年第3期557-568,共12页
Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of thes... Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of these missing data is highly valuable for engineering and scientific research.In this study,the radial basis function(RBF)method is used to estimate the spatial distribution of total suspended matter(TSM)concentration in Hangzhou Bay using remote sensing data with severe data gaps.The estimation precision is validated by comparing the results with those of other commonly used interpolation methods,such as the Kriging method and the basic spline(B-spline)method.In addition,the applicability of the RBF method is explored.Results show that the estimation of the RBF method is significantly close to the observation in Hangzhou Bay.The average of the mean absolute error,mean relative error,and root mean square error in all the experiments is evidently smaller than those of the Kriging and B-spline interpolations,indicating that the proposed method is more appropriate for estimating the spatial distribution of the TSM in Hangzhou Bay.Finally,the TSM distribution in the blank observational area is predicted.This study can provide some reference values for handling watercolor remote sensing data. 展开更多
关键词 ocean remote sensing satellite total suspended matter concentration interpolation radial basis function Kriging method basic spline method
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Radial Basis Function Neural Network Adaptive Controller for Wearable Upper-Limb Exoskeleton with Disturbance Observer 认领 引用
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作者 Mohammad Soleimani Amiri Sahbi Boubaker +1 位作者 Rizauddin Ramli Souad Kamel 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第9期3113-3133,共21页
Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled pe... Disability is defined as a condition that makes it difficult for a person to perform certain vital activities.In recent years,the integration of the concepts of intelligence in solving various problems for disabled persons has become more frequent.However,controlling an exoskeleton for rehabilitation presents challenges due to their nonlinear characteristics and external disturbances caused by the structure itself or the patient wearing the exoskeleton.To remedy these problems,this paper presents a novel adaptive control strategy for upper-limb rehabilitation exoskeletons,addressing the challenges of nonlinear dynamics and external disturbances.The proposed controller integrated a Radial Basis Function Neural Network(RBFNN)with a disturbance observer and employed a high-dimensional integral Lyapunov function to guarantee system stability and trajectory tracking performance.In the control system,the role of the RBFNN was to estimate uncertain signals in the dynamic model,while the disturbance observer tackled external disturbances during trajectory tracking.Artificially created scenarios for Human-Robot interactive experiments and periodically repeated reference trajectory experiments validated the controller’s performance,demonstrating efficient tracking.The proposed controller is found to achieve superior tracking accuracy with Root-Mean-Squared(RMS)errors of 0.022-0.026 rad for all joints,outperforming conventional Proportional-Integral-Derivative(PID)by 73%and Neural-Fuzzy Adaptive Control(NFAC)by 389.47%lower error.These results suggested that the RBFNN adaptive controller,coupled with disturbance compensation,could serve as an effective rehabilitation tool for upper-limb exoskeletons.These results demonstrate the superiority of the proposed method in enhancing rehabilitation accuracy and robustness,offering a promising solution for the control of upper-limb assistive devices.Based on the obtained results and due to their high robustness,the proposed control schemes can be extended to other motor disabilities,including lower limb exoskeletons. 展开更多
关键词 Adaptive neural network controller disturbance observer upper-limb exoskeleton rehabilitation robotics Lyapunov stability radial basis function network
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Transient analysis of functionally graded curved shells using a nonuniform shape parameter integrated radial basis function approach 认领 引用
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作者 Vay Siu Lo Andrzej Katunin Thien Tich Truong 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2025年第3期296-308,共13页
In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/dmax,where dmaxis the max... In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/dmax,where dmaxis the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated. 展开更多
关键词 Integrated radial basis function Shape parameter Functionally graded material Curved shell Transient analysis
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A Basis Function Generation Based Digital Predistortion Concurrent Neural Network Model for RF Power Amplifiers 认领 引用
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作者 SHAO Jianfeng HONG Xi +2 位作者 WANG Wenjie LIN Zeyu LI Yunhua 《ZTE Communications》 2025年第1期71-77,共7页
This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a f... This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a feedforward neural network(FNN)and a convolutional neural network(CNN).The proposed model takes the basic elements that form the bases as input,defined by the generalized memory polynomial(GMP)and dynamic deviation reduction(DDR)models.The FNN generates the basis function and its output represents the basis values,while the CNN generates weights for the corresponding bases.Through the concurrent training of FNN and CNN,the hidden layer coefficients are updated,and the complex multiplication of their outputs yields the trained in-phase/quadrature(I/Q)signals.The proposed model was trained and tested using 300 MHz and 400 MHz broadband data in an orthogonal frequency division multiplexing(OFDM)communication system.The results show that the model achieves an adjacent channel power ratio(ACPR)of less than-48 d B within a 100 MHz integral bandwidth for both the training and test datasets. 展开更多
关键词 basis function generation digital predistortion generalized memory polynomial dynamic deviation reduction neural network
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Comparison Between Radial Basis Function Neural Network and Regression Model for Estimation of Rice Biophysical Parameters Using Remote Sensing 认领 引用 被引量：11
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作者 YANG Xiao-Hua WANG Fu-Min +4 位作者 HUANG Jing-Feng WANG Jian-Wen WANG Ren-Chao SHEN Zhang-Quan WANG Xiu-Zhen 《Pedosphere》 SCIE CAS 2009年第2期176-188,共13页
The radial basis function （RBF） emerged as a variant of artificial neural network. Generalized regression neural network （GRNN） is one type of RBF, and its principal advantages are that it can quickly learn and ra... The radial basis function （RBF） emerged as a variant of artificial neural network. Generalized regression neural network （GRNN） is one type of RBF, and its principal advantages are that it can quickly learn and rapidly converge to the optimal regression surface with large number of data sets. Hyperspectral reflectance （350 to 2500 nm） data were recorded at two different rice sites in two experiment fields with two cultivars, three nitrogen treatments and one plant density （45 plants m^-2）. Stepwise multivariable regression model （SMR） and RBF were used to compare their predictability for the leaf area index （LAI） and green leaf chlorophyll density （GLCD） of rice based on reflectance （R） and its three different transformations, the first derivative reflectance （D1）, the second derivative reflectance （D2） and the log-transformed reflectance （LOG）. GRNN based on D1 was the best model for the prediction of rice LAI and CLCD. The relationships between different transformations of reflectance and rice parameters could be further improved when RBF was employed. Owing to its strong capacity for nonlinear mapping and good robustness, GRNN could maximize the sensitivity to chlorophyll content using D1. It is concluded that RBF may provide a useful exploratory and predictive tool for the estimation of rice biophysical parameters. 展开更多
关键词 biophysical parameters radial basis function regression model remote sensing rice
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An efficient large-scale mesh deformation method based on MPI/Open MP hybrid parallel radial basis function interpolation 认领 引用 被引量：9
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作者 Zhong ZHAO Rong MA +2 位作者 Lei HE Xinghua CHANG Laiping ZHANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2020年第5期1392-1404,共13页
An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlik... An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points. 展开更多
关键词 Mesh deformation Moving mesh generation MPI/Open MP hybrid parallel computing Parallel radial basis function interpolation Unstructured hybrid grid
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Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow 认领 引用 被引量：7
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作者 Qinghua Jiang Lailai Zhu +1 位作者 Chang Shu Vinothkumar Sekar 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2021年第12期1757-1772,共16页
To improve the performance of multilayer perceptron(MLP)neural networks activated by conventional activation functions,this paper presents a new MLP activated by univariate Gaussian radial basis functions(RBFs)with ad... To improve the performance of multilayer perceptron(MLP)neural networks activated by conventional activation functions,this paper presents a new MLP activated by univariate Gaussian radial basis functions(RBFs)with adaptive centers and widths,which is composed of more than one hidden layer.In the hidden layer of the RBF-activated MLP network(MLPRBF),the outputs of the preceding layer are first linearly transformed and then fed into the univariate Gaussian RBF,which exploits the highly nonlinear property of RBF.Adaptive RBFs might address the issues of saturated outputs,low sensitivity,and vanishing gradients in MLPs activated by other prevailing nonlinear functions.Finally,we apply four MLP networks with the rectified linear unit(ReLU),sigmoid function(sigmoid),hyperbolic tangent function(tanh),and Gaussian RBF as the activation functions to approximate the one-dimensional(1D)sinusoidal function,the analytical solution of viscous Burgers’equation,and the two-dimensional(2D)steady lid-driven cavity flows.Using the same network structure,MLP-RBF generally predicts more accurately and converges faster than the other threeMLPs.MLP-RBF using less hidden layers and/or neurons per layer can yield comparable or even higher approximation accuracy than other MLPs equipped with more layers or neurons. 展开更多
关键词 Multilayer perceptron neural network Activation function Radial basis function Numerical approximation
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Mesh deformation on 3D complex configurations using multistep radial basis functions interpolation 认领 引用 被引量：9
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作者 Gang WANG Xin CHEN Zhikan LIU 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第4期660-671,共12页
The Radial Basis Function（RBF） method with data reduction is an effective way to perform mesh deformation. However, for large deformations on meshes of complex aerodynamic configurations, the efficiency of the RBF m... The Radial Basis Function（RBF） method with data reduction is an effective way to perform mesh deformation. However, for large deformations on meshes of complex aerodynamic configurations, the efficiency of the RBF mesh deformation method still needs to be further improved to fulfill the demand of practical application. To achieve this goal, a multistep RBF method based on a multilevel subspace RBF algorithm is presented to further improve the efficiency of the mesh deformation method in this research. A whole deformation is divided into a series of steps, and the supporting radius is adjusted in accordance with the maximal displacement error. Furthermore, parallel computing is applied to the interpolation to enhance the efficiency. Typical deformation problems of the NASA Common Research Model（CRM） configuration, the DLR-F6 wing-body-nacellepylon configuration, and the DLR-F11 high-lift configuration are tested to verify the feasibility of this method. Test results show that the presented multistep RBF mesh deformation method is efficient and robust in dealing with large deformation problems over complex geometries. 展开更多
关键词 Data reduction Greedy method Mesh deformation Radial basis function Unstructured mesh
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Estimation of vegetation biophysical parameters by remote sensing using radial basis function neural network 认领 引用 被引量：3
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作者 YANG Xiao-hua HUANG Jing-feng +2 位作者 WANG Jian-wen WANG Xiu-zhen LIU Zhan-yu 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2007年第6期883-895,共13页
Hyperspectral reflectance (350~2500 nm) data were recorded at two different sites of rice in two experiment fields including two cultivars, and three levels of nitrogen (N) application. Twenty-five Vegetation Indices ... Hyperspectral reflectance (350~2500 nm) data were recorded at two different sites of rice in two experiment fields including two cultivars, and three levels of nitrogen (N) application. Twenty-five Vegetation Indices (VIs) were used to predict the rice agronomic parameters including Leaf Area Index (LAI, m2 green leaf/m2 soil) and Green Leaf Chlorophyll Density (GLCD, mg chlorophyll/m2 soil) by the traditional regression models and Radial Basis Function Neural Network (RBF). RBF emerged as a variant of Artificial Neural Networks (ANNs) in the late 1980’s. A large variety of training algorithms has been tested for training RBF networks. In this study, Original RBF (ORBF), Gradient Descent RBF (GDRBF), and Generalized Regression Neural Network (GRNN) were employed. Results showed that green waveband Normalized Difference Vegetation Index (NDVIgreen) and TCARI/OSAVI have the best prediction power for LAI by exponent model and ORBF respectively, and that TCARI/OSAVI has the best prediction power for GLCD by exponent model and GDRBF. The best performances of RBF are compared with the traditional models, showing that the relationship between VIs and agronomic variables are further improved when RBF is used. Compared with the best traditional models, ORBF using TCARI/OSAVI improves the prediction power for LAI by lowering the Root Mean Square Error (RMSE) for 0.1119, and GDRBF using TCARI/OSAVI improves the prediction power for GLCD by lowering the RMSE for 26.7853. It is concluded that RBF provides a useful exploratory and predictive tool when applied to the sensitive VIs. 展开更多
关键词 Artificial neural network （ANN） Radial basis function （RBF） Remote sensing Rice Vegetation index （VI）
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SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS 认领 引用 被引量：9
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作者 Wang Hui Qin Qinghua 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第1期21-29,共9页
The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and ... The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference. 展开更多
关键词 meshless method analog equation method method of fundamental solution radial basis function singular value decomposition Helmholtz equation
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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 认领 引用 被引量：2
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作者 Yuhong Jin Lei Hou +1 位作者 Zhenyong Lu Yushu Chen 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2023年第2期180-197,共18页
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 cause... 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. 展开更多
关键词 Hollow shaft rotor Breathing crack Radial basis function network Pattern recognition neural network Machine learning
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MESHLESS METHOD BASED ON COLLOCATION WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS 认领 引用 被引量：3
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作者 宋康祖 张雄 陆明万 《Acta Mechanica Sinica》 SCIE EI CAS 2004年第5期551-557,共7页
Based on our previous study,the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs)are used,so that it could re... Based on our previous study,the accuracy of derivatives of interpolating functions are usually very poor near the boundary of domain when Compactly Supported Radial Basis Functions (CSRBFs)are used,so that it could result in significant error in solving partial differential equations with Neumann boundary conditions.To overcome this drawback,the Consistent Compactly Supported Radial Basis Functions(CCSRBFs)are developed,which satisfy the predetermined consistency con- ditions.Meshless method based on point collocation with CCSRBFs is developed for solving partial differential equations.Numerical studies show that the proposed method improves the accuracy of approximation significantly. 展开更多
关键词 radial basis function collocation meshless
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Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions 认领 引用 被引量：3
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作者 Yihao Wu Bo Zhong Zhicai Luo 《Journal of Earth Science》 SCIE CAS CSCD 2018年第6期1349-1358,共10页
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri... The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling. 展开更多
关键词 regional gravity field modeling Poisson wavelets radial basis functions Tikhonov regularization method L-curve variance component estimation（VCE）
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Band structures of transverse waves in nanoscale multilayered phononic crystals with nonlocal interface imperfections by using the radial basis function method 认领 引用 被引量：2
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作者 Zhizhong Yan Chunqiu Wei Chuanzeng Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2017年第2期415-428,共14页
A radial basis function collocation method based on the nonlocal elastic continuum theory is developed to compute the band structures of nanoscale multilayered phononic crystals. The effects of nonlocal imperfect inte... A radial basis function collocation method based on the nonlocal elastic continuum theory is developed to compute the band structures of nanoscale multilayered phononic crystals. The effects of nonlocal imperfect interfaces on band structures of transverse waves propagating obliquely or vertically in the system are studied. The correctness of the present method is verified by comparing the numerical results with those obtained by applying the transfer matrix method in the case of nonlocal perfect interface. Furthermore, the influences of the nanoscale size, the impedance ratio and the incident angle on the cut-off frequency and band structures are investigated and discussed in detail. Numerical results show that the nonlocal interface imperfections have significant effects on the band structures in the macroscopic and microscopic scale. 展开更多
关键词 Radial basis function Phononic crystal Nanoscale Band structure Nonlocal imperfect interface
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A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients 认领 引用 被引量：3
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作者 W.T.ANG X.WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第4期551-566,共16页
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 ... 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. 展开更多
关键词 elliptic partial differential equation variable coefficient boundary element method radial basis function anisotropic thermoelastostatics
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High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake 认领 引用 被引量：1
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作者 Guocheng Hao Juan Guo +2 位作者 Wei Zhang Yunliang Chen David AYuen 《Geoscience Frontiers》 SCIE CAS CSCD 2022年第1期364-373,共10页
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... 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. 展开更多
关键词 Earth’s natural pulse electromagnetic field Chaos theory Radial Basis Function neural network Forecasting model
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Rough set and radial basis function neural network based insulation data mining fault diagnosis for power transformer 认领 引用 被引量：2
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作者 董立新 肖登明 刘奕路 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2007年第2期263-268,共6页
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... 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. 展开更多
关键词 rough set （RS） radial basis function neural network （RBFNN） data mining fault diagnosis
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Electrode Wear Prediction in Milling Electrical Discharge Machining Based on Radial Basis Function Neural Network 认领 引用 被引量：2
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作者 黄河 白基成 +1 位作者 卢泽生 郭永丰 《Journal of Shanghai Jiaotong university(Science)》 EI 2009年第6期736-741,共6页
Milling electrical discharge machining(EDM) enables the machining of complex cavities using cylindrical or tubular electrodes.To ensure acceptable machining accuracy the process requires some methods of compensating f... Milling electrical discharge machining(EDM) enables the machining of complex cavities using cylindrical or tubular electrodes.To ensure acceptable machining accuracy the process requires some methods of compensating for electrode wear.Due to the complexity and random nature of the process,existing methods of compensating for such wear usually involve off-line prediction.This paper discusses an innovative model of electrode wear prediction for milling EDM based upon a radial basis function(RBF) network.Data gained from an orthogonal experiment were used to provide training samples for the RBF network.The model established was used to forecast the electrode wear,making it possible to calculate the real-time tool wear in the milling EDM process and,to lay the foundations for dynamic compensation of the electrode wear on-line.This paper demonstrates that by using this model prediction errors can be controlled within 8%. 展开更多
关键词 milling electrical discharge machining （EDM） electrode wear prediction radial basis function （RBF） neural network
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Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation 认领 引用 被引量：1
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作者 Hossein Mirinejad Tamer Inanc Jacek M.Zurada 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第8期1380-1388,共9页
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to... This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency. 展开更多
关键词 Costate estimation direct trajectory optimization Galerkin projection numerical optimal control radial basis function interpolation
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