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Basis Functions (basis + function)
Kinds of Basis Functions Terms modified by Basis Functions Selected AbstractsDeformation by examples: a density flow approachCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2 2007Hoi-Chau Leung Abstract In this article, a shape transformation technique is introduced for deforming objects based on a given deformation example. The example consists of two reference shapes representing two different states of an object. The reference shapes are assumed to morph from one state to the other. The evolution between the two reference shapes determines the shape transformation function. Any given objects can then be deformed by the same transformation. A continuous 4D Radial Basis Function is used to construct a density flow field (an extension of the optical flow in computer vision) representing the shape transformation of the example in 3-space. Objects embedded in the density flow field are deformed by moving vertices of the objects along the density flow vectors. Additional parameters are introduced to control the process of the deformation. This provides explicit control on the shape of the object obtained in the deformation process. Copyright © 2007 John Wiley & Sons, Ltd. [source] Tuning for shape dimensions in macaque inferior temporal cortexEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 1 2005Greet Kayaert Abstract It is widely assumed that distributed bell-shaped tuning (e.g. Radial Basis functions) characterizes the shape selectivity of macaque inferior temporal (IT) neurons, analogous to the orientation or spatial frequency tuning found in early visual cortex. Demonstrating such tuning properties requires testing the responses of neurons for different values along dimensions of shape. We recorded the responses of single macaque IT neurons to variations of a rectangle and a triangle along simple shape dimensions, such as taper and axis curvature. The neurons showed systematic response modulation along these dimensions, with the greatest response, on average, to the highest values on the dimensions, e.g. to the most curved shapes. Within the range of values tested, the response functions were monotonic rather than bell-shaped. Multi-dimensional scaling of the neural responses showed that these simple shape dimensions were coded orthogonally by IT neurons: the degree and direction of responses modulation (i.e. the increase or decrease of responses along a dimension) was independent for the different dimensions. Furthermore, for combinations of curvature-related and other simple shape dimensions, the joint tuning was separable, that is well predicted by the product of the tuning for each of the dimensions. The independence of dimensional tuning may provide the neural basis for the independence of psychophysical judgements of multidimensional stimuli. [source] Basis functions for the consistent and accurate representation of surface mass loadingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007Peter J. Clarke SUMMARY Inversion of geodetic site displacement data to infer surface mass loads has previously been demonstrated using a spherical harmonic representation of the load. This method suffers from the continent-rich, ocean-poor distribution of geodetic data, coupled with the predominance of the continental load (water storage and atmospheric pressure) compared with the ocean bottom pressure (including the inverse barometer response). Finer-scale inversion becomes unstable due to the rapidly increasing number of parameters which are poorly constrained by the data geometry. Several approaches have previously been tried to mitigate this, including the adoption of constraints over the oceanic domain derived from ocean circulation models, the use of smoothness constraints for the oceanic load, and the incorporation of GRACE gravity field data. However, these methods do not provide appropriate treatment of mass conservation and of the ocean's equilibrium-tide response to the total gravitational field. Instead, we propose a modified set of basis functions as an alternative to standard spherical harmonics. Our basis functions allow variability of the load over continental regions, but impose global mass conservation and equilibrium tidal behaviour of the oceans. We test our basis functions first for the efficiency of fitting to realistic modelled surface loads, and then for accuracy of the estimates of the inferred load compared with the known model load, using synthetic geodetic displacements with real GPS network geometry. Compared to standard spherical harmonics, our basis functions yield a better fit to the model loads over the period 1997,2005, for an equivalent number of parameters, and provide a more accurate and stable fit using the synthetic geodetic displacements. In particular, recovery of the low-degree coefficients is greatly improved. Using a nine-parameter fit we are able to model 58 per cent of the variance in the synthetic degree-1 zonal coefficient time-series, 38,41 per cent of the degree-1 non-zonal coefficients, and 80 per cent of the degree-2 zonal coefficient. An equivalent spherical harmonic estimate truncated at degree 2 is able to model the degree-1 zonal coefficient similarly (56 per cent of variance), but only models 59 per cent of the degree-2 zonal coefficient variance and is unable to model the degree-1 non-zonal coefficients. [source] Short-term load forecasting using informative vector machineELECTRICAL ENGINEERING IN JAPAN, Issue 2 2009Eitaro Kurata Abstract In this paper, a novel method is proposed for short-term load forecasting, which is one of the important tasks in power system operation and planning. The load behavior is so complicated that it is hard to predict the load. The deregulated power market is faced with the new problem of an increase in the degree of uncertainty. Thus, power system operators are concerned with the significant level of load forecasting. Namely, probabilistic load forecasting is required to smooth power system operation and planning. In this paper, an IVM (Informative Vector Machine) based method is proposed for short-term load forecasting. IVM is one of the kernel machine techniques that are derived from an SVM (Support Vector Machine). The Gaussian process (GP) satisfies the requirements that the prediction results are expressed as a distribution rather than as points. However, it is inclined to be overtrained for noise due to the basis function with N2 elements for N data. To overcome this problem, this paper makes use of IVM that selects necessary data for the model approximation with a posteriori distribution of entropy. That has a useful function to suppress the excess training. The proposed method is tested using real data for short-term load forecasting. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(2): 23, 31, 2009; Published online in Wiley InterScience (www. interscience.wiley.com). DOI 10.1002/eej.20693 [source] Financial decision support using neural networks and support vector machinesEXPERT SYSTEMS, Issue 4 2008Chih-Fong Tsai Abstract: Bankruptcy prediction and credit scoring are the two important problems facing financial decision support. The multilayer perceptron (MLP) network has shown its applicability to these problems and its performance is usually superior to those of other traditional statistical models. Support vector machines (SVMs) are the core machine learning techniques and have been used to compare with MLP as the benchmark. However, the performance of SVMs is not fully understood in the literature because an insufficient number of data sets is considered and different kernel functions are used to train the SVMs. In this paper, four public data sets are used. In particular, three different sizes of training and testing data in each of the four data sets are considered (i.e. 3:7, 1:1 and 7:3) in order to examine and fully understand the performance of SVMs. For SVM model construction, the linear, radial basis function and polynomial kernel functions are used to construct the SVMs. Using MLP as the benchmark, the SVM classifier only performs better in one of the four data sets. On the other hand, the prediction results of the MLP and SVM classifiers are not significantly different for the three different sizes of training and testing data. [source] Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001M. Elansari Abstract In the solution of Poisson's equation using either the dual reciprocity boundary element method or the method of fundamental solution, radial basis functions (RBFs) are used to approximate the right-hand side of the governing partial differential equation to eliminate the domain integration. This paper shows that if the RBF interpolation is collocated on the Gaussian quadrature nodes, we seem to observe superconvergence behaviour. This behaviour is demonstrated using a series of numerical examples. Copyright © 2001 John Wiley & Sons, Ltd. [source] On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximantsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010Adrian Rosolen Abstract We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd. [source] Complex variable moving least-squares method: a meshless approximation techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007K. M. Liew Abstract Based on the moving least-squares (MLS) approximation, we propose a new approximation method,the complex variable moving least-squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two-dimensional elasticity problems,the complex variable meshless method (CVMM),and the formulae of the CVMM for two-dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM. Copyright © 2006 John Wiley & Sons, Ltd. [source] A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Jie Shen Abstract In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox,de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd. [source] An enriched meshless method for non-linear fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004B. N. Rao Abstract This paper presents an enriched meshless method for fracture analysis of cracks in homogeneous, isotropic, non-linear-elastic, two-dimensional solids, subject to mode-I loading conditions. The method involves an element-free Galerkin formulation and two new enriched basis functions (Types I and II) to capture the Hutchinson,Rice,Rosengren singularity field in non-linear fracture mechanics. The Type I enriched basis function can be viewed as a generalized enriched basis function, which degenerates to the linear-elastic basis function when the material hardening exponent is unity. The Type II enriched basis function entails further improvements of the Type I basis function by adding trigonometric functions. Four numerical examples are presented to illustrate the proposed method. The boundary layer analysis indicates that the crack-tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered, whether for the near-tip asymptotic field or for the far-tip elastic field. Numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the J -integral for the applied load intensities and material properties considered. Also, the crack-mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results. Furthermore, the meshless results show excellent agreement with the experimental measurements, indicating that the new basis functions are also capable of capturing elastic,plastic deformations at a stress concentration effectively. Copyright © 2003 John Wiley & Sons, Ltd. [source] A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuliINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008N. Mai-Duy Abstract This paper reports a radial basis function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of higher-order derivatives. The method is applied to simulate thermally driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleigh number solutions are achieved and they are in good agreement with previously published numerical data. Copyright © 2007 John Wiley & Sons, Ltd. [source] A novel compact piecewise-linear representation,INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 1 2005Chengtao Wen Abstract A new compact MAX representation for 2-D continuous piecewise-linear (PWL) functions is developed in this paper. The representation is promising since it can be easily generalized into higher dimensions. We also establish the explicit functional form of basis function and demonstrate that the proposed basis function is the elementary ,building block' from which a fully general 2-D PWL function can be constructed. In addition, we reveal the relationship of basis function with minimal degenerate intersection and Hinging Hyperplane, which shows that the MAX model can unify Chua's canonical expression, Li's representation, lattice PWL function and Bremann's Hinging Finding Algorithm into one common theoretical framework. Copyright © 2005 John Wiley & Sons, Ltd. [source] Neural networks,a new approach to model vapour-compression heat pumpsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 7 2001H. Bechtler Abstract The aim of this paper is to model the steady-state performance of a vapour-compression liquid heat pump with the use of neural networks. The model uses a generalized radial basis function (GRBF) neural network. Its input vector consists only of parameters that are easily measurable, i.e. the chilled water outlet temperature from the evaporator, the cooling water inlet temperature to the condenser and the evaporator capacity. The model then predicts relevant performance parameters of the heat pump, especially the coefficient of performance (COP). Models are developed for three different refrigerants, namely LPG, R22 and R290. It is found that not every model achieves the same accuracy. Predicted COP values, when LPG or R22 are used as refrigerant, are usually accurate to within 2 per cent, whereas many predictions for R290 deviate more than ±10 per cent. Copyright © 2001 John Wiley & Sons, Ltd. [source] Matching pursuit-based shape representation and recognition using scale-spaceINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2006François Mendels Abstract In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, namely the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invariant dictionary of basis function (BFs). This description is used to recognize multiple objects in images. In the learning phase, a template object is decomposed, and the extracted subset of BFs, called meta-atom, gives the description of the object. This description is then naturally extended into the linear scale-space using the definition of our BFs, and thus providing a more general representation of the object. We use this enhanced description as a predefined dictionary of the object to conduct an MP-based shape recognition task into the linear scale-space. The introduction of the scale-space approach improves the robustness of our method: we avoid local minima issues encountered when minimizing a nonconvex energy function. We show results for the detection of complex synthetic shapes, as well as real world (aerial and medical) images. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 162,180, 2006 [source] Reformulated radial basis function neural networks with adjustable weighted normsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 10 2003Mary M. Randolph-Gips This article presents a new family of reformulated radial basis function (RBF) neural networks that employ adjustable weighted norms to measure the distance between the training vectors and the centers of the radial basis functions. The reformulated RBF model introduced in this article incorporates norm weights that can be updated during learning to facilitate the implementation of the desired input-output mapping. Experiments involving classification and function approximation tasks verify that the proposed RBF neural networks outperform conventional RBF neural networks and reformulated RBF neural networks employing fixed Euclidean norms. Reformulated RBF neural networks with adjustable weighted norms are also strong competitors to conventional feedforward neural networks in terms of performance, implementation simplicity, and training speed. © 2003 Wiley Periodicals, Inc. [source] Nonlinear wave function expansions: A progress reportINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2007Ron Shepard Abstract Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one- and two-particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy-based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed-form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Generic representation and evaluation of properties as a function of position in reciprocal spaceJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2002Kevin Cowtan A generalized approach is described for evaluating arbitrary functions of position in reciprocal space. This is a generalization which subsumes a whole range of calculations that form a part of almost every crystallographic software application. Examples include scaling of structure factors, the calculation of structure-factor statistics, and some simple likelihood calculations for a single parameter. The generalized approach has a number of advantages: all these calculations may now be performed by a single software routine which need only be debugged and optimized once; the existing approach of dividing reciprocal space into resolution shells with discontinuities at the boundaries is no longer necessary; the implementation provided makes employing the new functionality extremely simple and concise. The calculation is split into three standard components, for which a number of implementations are provided for different tasks. A `basis function' describes some function of position in reciprocal space, the shape of which is determined by a small number of parameters. A `target function' describes the property for which a functional representation is required, for example . An `evaluator' takes a basis and target function and optimizes the parameters of the basis function to fit the target function. Ideally the components should be usable in any combination. [source] One class classifiers for process monitoring illustrated by the application to online HPLC of a continuous processJOURNAL OF CHEMOMETRICS, Issue 3-4 2010Sila Kittiwachana Abstract In process monitoring, a representative out-of-control class of samples cannot be generated. Here, it is assumed that it is possible to obtain a representative subset of samples from a single ,in-control class' and one class classifiers namely Q and D statistics (respectively the residual distance to the disjoint PC model and the Mahalanobis distance to the centre of the QDA model in the projected PC space), as well as support vector domain description (SVDD) are applied to disjoint PC models of the normal operating conditions (NOC) region, to categorise whether the process is in-control or out-of-control. To define the NOC region, the cumulative relative standard deviation (CRSD) and a test of multivariate normality are described and used as joint criteria. These calculations were based on the application of window principal components analysis (WPCA) which can be used to define a NOC region. The D and Q statistics and SVDD models were calculated for the NOC region and percentage predictive ability (%PA), percentage model stability (%MS) and percentage correctly classified (%CC) obtained to determine the quality of models from 100 training/test set splits. Q, D and SVDD control charts were obtained, and 90% confidence limits set up based on multivariate normality (D and Q) or SVDD D value (which does not require assumptions of normality). We introduce a method for finding an optimal radial basis function for the SVDD model and two new indices of percentage classification index (%CI) and percentage predictive index (%PI) for non-NOC samples are also defined. The methods in this paper are exemplified by a continuous process studied over 105.11,h using online HPLC. Copyright © 2010 John Wiley & Sons, Ltd. [source] Optimizing the tuning parameters of least squares support vector machines regression for NIR spectraJOURNAL OF CHEMOMETRICS, Issue 5 2006T. Coen Abstract Partial least squares (PLS) is one of the most used tools in chemometrics. Other data analysis techniques such as artificial neural networks and least squares support vector machines (LS-SVMs) have however made their entry in the field of chemometrics. These techniques can also model nonlinear relations, but the presence of tuning parameters is a serious drawback. These parameters balance the risk of overfitting with the possibility to model the underlying nonlinear relation. In this work a methodology is proposed to initialize and optimize those tuning parameters for LS-SVMs with radial basis function (RBF)-kernel based on a statistical interpretation. In this way, these methods become much more appealing for new users. The presented methods are applied on manure spectra. Although this dataset is only slightly nonlinear, good results were obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical instabilities in the computation of pseudopotential matrix elementsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2006Christoph van Wüllen Abstract Steep high angular momentum Gaussian basis functions in the vicinity of a nucleus whose inner electrons are replaced by an effective core potential may lead to numerical instabilities when calculating matrix elements of the core potential. Numerical roundoff errors may be amplified to an extent that spoils any result obtained in such a calculation. Effective core potential matrix elements for a model problem are computed with high numerical accuracy using the standard algorithm used in quantum chemical codes and compared to results of the MOLPRO program. Thus, it is demonstrated how the relative and absolute errors depend an basis function angular momenta, basis function exponents and the distance between the off-center basis function and the center carrying the effective core potential. Then, the problem is analyzed and closed expressions are derived for the expected numerical error in the limit of large basis function exponents. It is briefly discussed how other algorithms would behave in the critical case, and they are found to have problems as well. The numerical stability could be increased a little bit if the type 1 matrix elements were computed without making use of a partial wave expansion. © 2005 Wiley Periodicals, Inc., J Comput Chem 27: 135,141 2006 [source] Applications of neural network analyses to in vivo 1H magnetic resonance spectroscopy of Parkinson disease patientsJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 1 2002David Axelson PhD Abstract Purpose To apply neural network analyses to in vivo magnetic resonance spectra of controls and Parkinson disease (PD) patients for the purpose of classification. Materials and Methods Ninety-seven in vivo proton magnetic resonance spectra of the basal ganglia were recorded from 31 patients with (PD) and 14 age-matched healthy volunteers on a 1.5-T imager. The PD patients were grouped as follows: probable PD (N = 15), possible PD (N = 11), and atypical PD (N = 5). Total acquisition times of approximately five minutes were achieved with a TE (echo time) of 135 msec, a TR (repetition time) of 2000 msec, and 128 scan averages. Neural network (back propagation, Kohonen, probabilistic, and radial basis function) and related (generative topographic mapping) data analyses were performed. Results Conventional data analysis showed no statistically significant differences in metabolite ratios based on measuring signal intensities. The trained networks could distinguish control from PD with considerable accuracy (true positive fraction 0.971, true negative fraction 0.933). When four classes were defined, approximately 88% of the predictions were correct. The multivariate analysis indicated metabolic changes in the basal ganglia in PD. Conclusion A variety of neural network and related approaches can be successfully applied to both qualitative visualization and classification of in vivo spectra of PD patients. J. Magn. Reson. Imaging 2002;16:13,20. © 2002 Wiley -Liss, Inc. [source] Factorized approach to nonlinear MPC using a radial basis function modelAICHE JOURNAL, Issue 2 2001Sharad Bhartiya A new computationally efficient approach for nonlinear model predictive control (NMPC) presented here uses the factorability of radial basis function (RBF) process models in a traditional model predictive control (MPC) framework. The key to the approach is to formulate the RBF process model that can make nonlinear predictions across a p-step horizon without using future unknown process measurements. The RBF model avoids error propagation from use of model predictions us input in a recursive or iterative manner. The resulting NMPC formulation using the RBF model provides analytic expressions for the gradient and Hessian of the controller's objective function in terms of RBF network parameters. Solution of the NMPC optimization problem is simplifed significantly by factorization of the RBF model output into terms containing only known and unknown parts of the process. [source] Application of an Artificial Neural Network for Simulating Robust Plasma-Sprayed Zirconia CoatingsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 5 2008Ming-Der Jean This article presents the application of the artificial neural network (ANN) of a statistically designed experiment for developing a robust wear-resistant zirconia coating. In this research, experimental design with orthogonal arrays efficiently provides enough information with the least number of experiments, reducing the cost and time. A radial basis function (RBF) network for the wear behavior is adopted. The friction and tribological properties of zirconia coatings were investigated. The microstructural feature of the coatings is also addressed in this study. It is found that the worn volumes of plasma-sprayed zirconia coatings after wear tests are greatly improved by the optimal parameters. The relationships between the microstructure of the worn surface and their properties are examined, and the results reveal a higher wear resistance and a lower worn surface roughness with a large amount of plastic deformations. These wear resistant structures formed as a result of a dense lamellar formation during sprayed zirconia coatings. The RBF network can be established efficiently. A comparison of the predicted results with that of the RBF network and the Taguchi method predictor shows average errors of 2.735% and 9.191% for the RBF network and the Taguchi method, respectively. It is experimentally confirmed that the RBF network predictions are in agreement with the experiments, and it can be reliably used for the prediction of wear for plasma sprayings. The experimental results demonstrate that the RBF network used for a statistically designed experiment is an effective, efficient, and intelligent approach for developing a robust, high efficiency, and high-quality zirconia coating process. [source] Use of wavelet transform to the method-of-moments matrix arising from electromagnetic scattering problems of 2D objects due to oblique plane-wave incidenceMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2002Jin Yu Abstract An efficient method is presented for transforming the matrix of the method of moments obtained by the expansion of the unknown surface currents with pulse basis function and the use of point match testing to a matrix with wavelet basis and testing functions. When the electromagnetic scattering object is a dielectric or object under oblique plane-wave incidence, more than one equivalent surface current component exists at the object surface. When these currents are connected into one current vector in the method of moments, there must be some discontinuities between the current components. These discontinuities make the direct wavelet transform to the whole MoM matrix inefficient and not equivalent to the use of the wavelet functions in the expansion of the unknown currents and the testing. Therefore, the wavelet transform must be constructed in a different way to avoid these discontinuities. Here, the proper wavelet transform that is equivalent to the use of the wavelet functions in the MoM, which avoids such discontinuities, is presented. This transform is referred to as wavelet subtransform. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 130,134, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10394 [source] A basis function for approximation and the solutions of partial differential equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2008H. Y. Tian Abstract In this article, we introduce a type of basis functions to approximate a set of scattered data. Each of the basis functions is in the form of a truncated series over some orthogonal system of eigenfunctions. In particular, the trigonometric eigenfunctions are used. We test our basis functions on recovering the well-known Franke's and Peaks functions given by scattered data, and on the extension of a singular function from an irregular domain onto a square. These basis functions are further used in Kansa's method for solving Helmholtz-type equations on arbitrary domains. Proper one level and two level approximation techniques are discussed. A comparison of numerical with analytic solutions is given. The numerical results show that our approach is accurate and efficient. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Scott A. Sarra Abstract Differentiation matrices associated with radial basis function (RBF) collocation methods often have eigenvalues with positive real parts of significant magnitude. This prevents the use of the methods for time-dependent problems, particulary if explicit time integration schemes are employed. In this work, accuracy and eigenvalue stability of symmetric and asymmetric RBF collocation methods are numerically explored for some model hyperbolic initial boundary value problems in one and two dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] Online identification of nonlinear multivariable processes using self-generating RBF neural networksASIAN JOURNAL OF CONTROL, Issue 5 2010Karim Salahshoor Abstract This paper addresses the problem of online model identification for multivariable processes with nonlinear and time-varying dynamic characteristics. For this purpose, two online multivariable identification approaches with self-organizing neural network model structures will be presented. The two adaptive radial basis function (RBF) neural networks are called as the growing and pruning radial basis function (GAP-RBF) and minimal resource allocation network (MRAN). The resulting identification algorithms start without a predefined model structure and the dynamic model is generated autonomously using the sequential input-output data pairs in real-time applications. The extended Kalman filter (EKF) learning algorithm has been extended for both of the adaptive RBF-based neural network approaches to estimate the free parameters of the identified multivariable model. The unscented Kalman filter (UKF) has been proposed as an alternative learning algorithm to enhance the accuracy and robustness of nonlinear multivariable processes in both the GAP-RBF and MRAN based approaches. In addition, this paper intends to study comparatively the general applicability of the particle filter (PF)-based approaches for the case of non-Gaussian noisy environments. For this purpose, the Unscented Particle Filter (UPF) is employed to be used as alternative to the EKF and UKF for online parameter estimation of self-generating RBF neural networks. The performance of the proposed online identification approaches is evaluated on a highly nonlinear time-varying multivariable non-isothermal continuous stirred tank reactor (CSTR) benchmark problem. Simulation results demonstrate the good performances of all identification approaches, especially the GAP-RBF approach incorporated with the UKF and UPF learning algorithms. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Artificial neural network modeling of O2 separation from air in a hollow fiber membrane moduleASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2008S. S. Madaeni Abstract In this study artificial neural network (ANN) modeling of a hollow fiber membrane module for separation of oxygen from air was conducted. Feed rates, transmembrane pressure, membrane surface area, and membrane permeability for the present constituents in the feed were network input data. Output data were rate of permeate from the membrane, the amount of N2 in the remaining flow, and the amount of O2 in the permeate flow. Experimental data were obtained from software developed by Research Institute of Petroleum Industry (RIPI). A part of the data generated by this software was confirmed by experimental results available in literature. Two third of the data were employed for training ANNs. Based on different training algorithms, radial basis function (RBF) was found as the best network with minimum training error. Generalization capability of best RBF networks was checked by one third of unseen data. The network was able to properly predict new data that incorporate excellent performance of the network. The developed model can be used for optimization and online control. Copyright © 2008 Curtin University of Technology and John Wiley & Sons, Ltd. [source] 3D virtual simulator for breast plastic surgeryCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2008Youngjun Kim Abstract We have proposed novel 3D virtual simulation software for breast plastic surgery. Our software comprises two processes: a 3D torso modeling and a virtual simulation of the surgery result. First, image-based modeling is performed in order to obtain a female subject's 3D torso data. Our image-based modeling method utilizes a template model, and this is deformed according to the patient's photographs. For the deformation, we applied procrustes analysis and radial basis functions (RBF). In order to enhance reality, the subject's photographs are mapped onto a mesh. Second, from the modeled subject data, we simulate the subject's virtual appearance after the plastic surgery by morphing the shape of the breasts. We solve the simulation problem by an example-based approach. The subject's virtual shape is obtained from the relations between the pair sets of feature points from previous patients' photographs obtained before and after the surgery. Copyright © 2008 John Wiley & Sons, Ltd. [source] Implicit Surface Modelling with a Globally Regularised Basis of Compact SupportCOMPUTER GRAPHICS FORUM, Issue 3 2006C. Walder We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations [source] | ||||||||||||||||||||||||||||||||||||||||||||||