The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific com...The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.展开更多
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
In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and autom...In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.展开更多
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
To improve the nonlinear approximating ability of cerebellar model articulation controller(CMAC), by introducing the Gauss basis functions and the similarity measure based addressing scheme, a new kind of fuzzy CMAC...To improve the nonlinear approximating ability of cerebellar model articulation controller(CMAC), by introducing the Gauss basis functions and the similarity measure based addressing scheme, a new kind of fuzzy CMAC with Gauss basis functions(GFCMAC) was presented. Moreover, based upon the improvement of the self organizing feature map algorithm of Kohonen, the structural self organizing algorithm for GFCMAC(SOGFCMAC) was proposed. Simulation results show that adopting the Gauss basis functions and fuzzy techniques can remarkably improve the nonlinear approximating capacity of CMAC. Compared with the traditional CMAC,CMAC with general basis functions and fuzzy CMAC(FCMAC), SOGFCMAC has the obvious advantages in the aspects of the convergent speed, approximating accuracy and structural self organizing.展开更多
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/d_(max),where d_(max)is 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/d_(max),where d_(max)is 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
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
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
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
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
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
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
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 syst...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.展开更多
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
For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon'...For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.展开更多
In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to in...In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.展开更多
We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improveme...We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.展开更多
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
This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equat...This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.展开更多
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 difficult...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.展开更多
文摘The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.
基金Supported by the National Basic Research Program of China(2012CB025904)Zhengzhou Shengda University of Economics,Business and Management(SD-YB2025085)。
文摘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.
基金Supported by Science and Technology of Development Fund of Macao (042/2007/A3)
文摘In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
文摘To improve the nonlinear approximating ability of cerebellar model articulation controller(CMAC), by introducing the Gauss basis functions and the similarity measure based addressing scheme, a new kind of fuzzy CMAC with Gauss basis functions(GFCMAC) was presented. Moreover, based upon the improvement of the self organizing feature map algorithm of Kohonen, the structural self organizing algorithm for GFCMAC(SOGFCMAC) was proposed. Simulation results show that adopting the Gauss basis functions and fuzzy techniques can remarkably improve the nonlinear approximating capacity of CMAC. Compared with the traditional CMAC,CMAC with general basis functions and fuzzy CMAC(FCMAC), SOGFCMAC has the obvious advantages in the aspects of the convergent speed, approximating accuracy and structural self organizing.
基金Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study
文摘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/d_(max),where d_(max)is 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.
基金co-supported by the ‘‘111" Project of China (No. B17037)the National Natural Science Foundation of China (No. 11772265)
文摘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.
基金supported by ZTE Industry-University-Institute Cooperation Funds under Grant No.HC-CN-20220722010。
文摘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.
文摘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.
基金funded by the King Salman Center For Disability Research,through Research Group No.KSRG-2024-468。
文摘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.
基金supported by the Open Funds for Hubei Key Laboratory of Marine Geological Resources,China University of Geosciences(No.MGR202308)the Natural Science Foundation of Shandong Province(No.ZR2020MD085)+3 种基金the National Natural Science Foundation of China(No.41821004)the Taishan Scholar Program(No.tstp2022114)the Shandong Provincial Natural Science Foundation(No.DKXZZ202206)the National Key Research and Development Program of China(No.2016YFC1402404).
文摘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.
基金The project supported by the National Natural Science Foundation of China (10172052)
文摘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.
基金This project was supported in part by the Science Foundation of Shanxi Province (2003F028)China Postdoctoral Science Foundation (20060390318).
文摘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.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘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.
文摘For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.
基金Project supported by the National Natural Science Foundation of China (Grant No.11101454)the Educational Commission Foundation of Chongqing City,China (Grant No.KJ130626)the Program of Innovation Team Project in University of Chongqing City,China (Grant No.KJTD201308)
文摘In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.
文摘We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.
文摘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.
基金supported by PRIN-MIUR-Cofin 2006by University of Bologna"Funds for selected research topics"
文摘This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.
基金Supported by National Natural Science Youth Foundation (10401021).
文摘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.
