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GENERALIZED BOCHNER'S THEOREM FOR RADIAL FUNCTION 被引量:5
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作者 Wu Zongmin (Fudan University, China) 《Analysis in Theory and Applications》 1997年第3期47-57,共11页
A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is po... A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem. 展开更多
关键词 GENERALIZED BOCHNER’S THEOREM FOR radial function very
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Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion
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作者 Motohisa Osaka 《Applied Mathematics》 2024年第9期585-593,共9页
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the s... Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma. 展开更多
关键词 Electron Cloud radial Distribution function Nuclear Fusion TOKAMAK Laser
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Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation
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作者 Abdoulhafar Halassi Bacar Said Charriffaini Rawhoudine 《American Journal of Computational Mathematics》 2024年第3期318-332,共15页
Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes... Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management. 展开更多
关键词 Dam-Break Flows Numerical Simulation Shallow Water Equations radial Basis functions Urban Flood Inundation
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A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems
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作者 Scott A. Sarra Derek Musgrave +1 位作者 Marcus Stone Joseph I. Powell 《Journal of Applied Mathematics and Physics》 2024年第7期2559-2573,共15页
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with... Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used. 展开更多
关键词 Numerical Partial Differential Equations Boundary Value Problems radial Basis function Methods Ghost Points Variable Shape Parameter Least Squares
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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 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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A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification
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作者 S.Sathishkumar R.Devi Priya 《Intelligent Automation & Soft Computing》 SCIE 2023年第1期129-148,共20页
ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental ai... ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals. 展开更多
关键词 Electrocardiogram signal gaborfilter discrete cosine based discrete orthogonal stock well transform genetic algorithm radial basis function neural network
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Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms
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作者 Shehab Abdulhabib Alzaeemi Kim Gaik Tay +2 位作者 Audrey Huong Saratha Sathasivam Majid Khan bin Majahar Ali 《Computer Systems Science & Engineering》 SCIE EI 2023年第10期1163-1184,共22页
Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algor... Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT. 展开更多
关键词 Satisfiability logic programming symbolic radial basis function neural network evolutionary programming algorithm genetic algorithm evolution strategy algorithm differential evolution algorithm
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Local Radial Basis Function Methods: Comparison, Improvements, and Implementation
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作者 Scott A. Sarra 《Journal of Applied Mathematics and Physics》 2023年第12期3867-3886,共20页
Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented... Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox. 展开更多
关键词 radial Basis functions Shape Parameter Selection Quasi-Random Centers Numerical PDEs Scientific Computing Open Source Software Python Programming Language Reproducible Research
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A Numerical Method for Solving Ill-Conditioned Equation Systems Arising from Radial Basis Functions
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作者 Edward J. Kansa 《American Journal of Computational Mathematics》 2023年第2期356-370,共15页
Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are ... Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers. 展开更多
关键词 Continuously Differentiable radial Basis functions Global Maxima and Minima Solutions of Ill-Conditioned Linear Equations Block Gaussian Elimination Arbitrary Precision Arithmetic
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Analysis of radial basis function interpolation approach 被引量:4
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作者 邹友龙 胡法龙 +3 位作者 周灿灿 李潮流 李长喜 Keh-Jim Dunn 《Applied Geophysics》 SCIE CSCD 2013年第4期397-410,511,共15页
The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop... The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart. 展开更多
关键词 Inverse problems radial basis function interpolation new approach
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The essential rate of approximation for radial function manifold 被引量:1
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作者 LIN ShaoBo CAO FeiLong XU ZongBeni 《Science China Mathematics》 SCIE 2011年第9期1985-1994,共10页
In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r(B^d) be the usual Sobolev class of functions on the unit ball 54. We study the deviation fr... In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r(B^d) be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r(b^d). Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation. 展开更多
关键词 radial function rate of approximation Sobolev class ridge function
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An Evolutionary Programming Based on Hidden Neuron Modifiable Radial Basis Function Networks
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作者 陈向东 唐景山 宋爱国 《Journal of Southeast University(English Edition)》 EI CAS 2000年第2期36-41,共6页
In this paper, an improved radial basis function networks named hidden neuron modifiable radial basis function (HNMRBF) networks is proposed for target classification, and evolutionary programming (EP) is used as a le... In this paper, an improved radial basis function networks named hidden neuron modifiable radial basis function (HNMRBF) networks is proposed for target classification, and evolutionary programming (EP) is used as a learning algorithm to determine and modify the hidden neuron of HNMRBF nets. The result of passive sonar target classification shows that HNMRBF nets can effectively solve the problem of traditional neural networks, i. e. learning new target patterns on line will cause forgetting of the old patterns. 展开更多
关键词 target recognition radial basis function evolutionary programming
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Application of Radial Basis Function Network in Sensor Failure Detection
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作者 钮永胜 赵新民 《Journal of Beijing Institute of Technology》 EI CAS 1999年第2期70-76,共7页
Aim To detect sensor failure in control system using a single sensor signal. Methods A neural predictor was designed based on a radial basis function network(RBFN), and the neural predictor learned the sensor sig... Aim To detect sensor failure in control system using a single sensor signal. Methods A neural predictor was designed based on a radial basis function network(RBFN), and the neural predictor learned the sensor signal on line with a hybrid algorithm composed of n means clustering and Kalman filter and then gave the estimation of the sensor signal at the next step. If the difference between the estimation and the actural values of the sensor signal exceeded a threshold, the sensor could be declared to have a failure. The choice of the failure detection threshold depends on the noise variance and the possible prediction error of neural predictor. Results and Conclusion\ The computer simulation results show the proposed method can detect sensor failure correctly for a gyro in an automotive engine. 展开更多
关键词 sensor failure failure detection radial basis function network(BRFN) on line learning
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Comparison Between Radial Basis Function Neural Network and Regression Model for Estimation of Rice Biophysical Parameters Using Remote Sensing 被引量:10
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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 CSCD 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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SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS 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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Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization 被引量:16
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作者 ZHAO Min CUI Wei-cheng 《Journal of Marine Science and Application》 2007年第3期24-32,共9页
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
关键词 multidisciplinary design optimization (MDO) collaborative optimization (CO) optimal Latin hypercube design radial basis function network APPROXIMATION
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MESHLESS METHOD BASED ON COLLOCATION WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS 被引量:3
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作者 宋康祖 张雄 陆明万 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 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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Band structures of transverse waves in nanoscale multilayered phononic crystals with nonlocal interface imperfections by using the radial basis function method 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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Application of Near Infrared Diffuse Reflectance Spectroscopy with Radial Basis Function Neural Network to Determination of Rifampincin Isoniazid and Pyrazinamide Tablets 被引量:3
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作者 DU Lin-na WU Li-hang +5 位作者 LU Jia-hui GUO Wei-liang MENG Qing-fan JIANG Chao-jun SHEN Si-le TENG Li-rong 《Chemical Research in Chinese Universities》 SCIE CAS CSCD 2007年第5期518-523,共6页
Partial least squares(PLS),back-propagation neural network(BPNN)and radial basis function neural network(RBFNN)were respectively used for estalishing quantative analysis models with near infrared(NIR)diffuse r... Partial least squares(PLS),back-propagation neural network(BPNN)and radial basis function neural network(RBFNN)were respectively used for estalishing quantative analysis models with near infrared(NIR)diffuse reflectance spectra for determining the contents of rifampincin(RMP),isoniazid(INH)and pyrazinamide(PZA)in rifampicin isoniazid and pyrazinamide tablets.Savitzky-Golay smoothing,first derivative,second derivative,fast Fourier transform(FFT)and standard normal variate(SNV)transformation methods were applied to pretreating raw NIR diffuse reflectance spectra.The raw and pretreated spectra were divided into several regions,depending on the average spectrum and RSD spectrum.Principal component analysis(PCA)method was used for analyzing the raw and pretreated spectra in different regions in order to reduce the dimensions of input data.The optimum spectral regions and the models' parameters were chosen by comparing the root mean square error of cross-validation(RMSECV)values which were obtained by leave-one-out cross-validation method.The RMSECV values of the RBFNN models for determining the contents of RMP,INH and PZA were 0.00288,0.00226 and 0.00341,respectively.Using these models for predicting the contents of INH,RMP and PZA in prediction set,the RMSEP values were 0.00266,0.00227 and 0.00411,respectively.These results are better than those obtained from PLS models and BPNN models.With additional advantages of fast calculation speed and less dependence on the initial conditions,RBFNN is a suitable tool to model complex systems. 展开更多
关键词 Rifampicin isoniazid and pyrazinamide tablets NIR diffuse reflectance spectroscopy Partial least square Back-propagation neural network radial basis function neural network
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Synchronization of chaos using radial basis functions neural networks 被引量:2
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作者 Ren Haipeng Liu Ding 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第1期83-88,100,共7页
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
关键词 Chaos synchronization radial basis function neural networks Model error Parameter perturbation Measurement noise.
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