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
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
It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method wide...It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.展开更多
A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained wi...A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained widespread attention,while the modelling precision is primarily influenced by the base function network.In this study,we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise(HDBSCAN)algorithm,and the performance of the algorithm is verified by the observed gravity data in the Auvergne area.Furthermore,the turning point method is used to optimize the bandwidth of the basis function spectrum,which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously.Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model.Compared to the existing methods,the number of SRBFs used for modelling has been reduced by 15.8%,and the time cost to determine the centre positions of SRBFs has been saved by 12.5%.Hence,the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.展开更多
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
Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collabora...Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collaborative Optimization （CO） is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.展开更多
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
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 ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27...The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27),finite-range droplet model(FRDM12)and Weizsäcker-Skyrme(WS4)mass models.It is found that when the RBF approach is employed with a simple linear basis function,different mass models have different performances in extrapolating nuclear masses in the same region,and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions.The WS4 and FRDM12 models(two macroscopic–microscopic mass models),combined with the RBF approach,may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.展开更多
In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results fo...In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.展开更多
A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership fu...A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.展开更多
基金Project supported by the National Natural Science Foundation of China (No.40571115)the National High Tech-nology Research and Development Program (863 Program) of China (Nos.2006AA120101 and 2007AA10Z205)
文摘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.
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.
基金provided by China Geological Survey with the project(Nos.DD20190707,DD20190012)the Fundamental Research Funds for China Central public research Institutes with the project(No.JKY202014)
文摘It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.
基金funded by The Fundamental Research Funds for Chinese Academy of surveying and mapping(AR2402)Open Fund of Wuhan,Gravitation and Solid Earth Tides,National Observation and Research Station(No.WHYWZ202213)。
文摘A high-precision regional gravity field model is significant in various geodesy applications.In the field of modelling regional gravity fields,the spherical radial basis functions(SRBFs)approach has recently gained widespread attention,while the modelling precision is primarily influenced by the base function network.In this study,we propose a method for constructing a data-adaptive network of SRBFs using a modified Hierarchical Density-Based Spatial Clustering of Applications with Noise(HDBSCAN)algorithm,and the performance of the algorithm is verified by the observed gravity data in the Auvergne area.Furthermore,the turning point method is used to optimize the bandwidth of the basis function spectrum,which satisfies the demand for both high-precision gravity field and quasi-geoid modelling simultaneously.Numerical experimental results indicate that our algorithm has an accuracy of about 1.58 mGal in constructing the gravity field model and about 0.03 m in the regional quasi-geoid model.Compared to the existing methods,the number of SRBFs used for modelling has been reduced by 15.8%,and the time cost to determine the centre positions of SRBFs has been saved by 12.5%.Hence,the modified HDBSCAN algorithm presented here is a suitable design method for constructing the SRBF data adaptive network.
基金sponsored by the National Natural Science Foundation of China(61333002)Open Research Foundation of the State Key Laboratory of Geodesy and Earth’s Dynamics(SKLGED2018-5-4-E)+5 种基金Foundation of the Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems(ACIA2017002)111 projects under Grant(B17040)Open Research Project of the Hubei Key Laboratory of Intelligent Geo-Information Processing(KLIGIP-2017A02)supported by the Three Gorges Research Center for geo-hazardMinistry of Education cooperation agreements of Krasnoyarsk Science Center and Technology BureauRussian Academy of Sciences。
文摘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.
文摘Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization （MDO） is a more promising approach. For this reason, Collaborative Optimization （CO） is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.
基金This work was partially supported by the research grant of the National University of Singapore(NUS),Ministry of Education(MOE Tier 1).
文摘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.
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(Grant No.U1867212,12047567)the Natural Science Foundation of Guangxi(Grant NO.2017GXNSFGA198001)the Middle-aged and Young Teachers’Basic Ability Promotion Project of Guangxi(CN)(Grant No.2019KY0061)。
文摘The ability of the radial basis function(RBF)approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31),Hartree–Fock-Bogoliubov(HFB27),finite-range droplet model(FRDM12)and Weizsäcker-Skyrme(WS4)mass models.It is found that when the RBF approach is employed with a simple linear basis function,different mass models have different performances in extrapolating nuclear masses in the same region,and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions.The WS4 and FRDM12 models(two macroscopic–microscopic mass models),combined with the RBF approach,may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.
基金supported, in part, by the GNAMPA and the GNFM of the Italian INdAM
文摘In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.
基金The National Natural Science Foundation of China(No.51106025,51106027,51036002)Specialized Research Fund for the Doctoral Program of Higher Education(No.20130092110061)the Youth Foundation of Nanjing Institute of Technology(No.QKJA201303)
文摘A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.
