RBF-Chebychev direct method for solving variational problems

A study is presented using a mesh-free approach and a radial basis function generated finite difference (RBF-FD) method for numerically modelling 3-D gravity data. The gravity responses, that is, vertical gravity and gravity gradients, are obtained by solving the partial differential equation (PDE), that is, the Poisson’s equation for gravitational potential. The mesh-free approach discretizes PDEs using exclusively a cloud of unconnected nodes, instead of traditional tessellated meshes as used by mesh-based numerical methods such as finite difference, finite element and finite volume. Thus, the potentially computationally expensive and unstable creation and manipulation of 3-D meshes can be entirely avoided. A new type of finite-smoothness radial basis functions (RBFs), namely, the quintic-order polyharmonic spline (PHS) RBF, is proposed here in the RBF-FD frame for solving the gravity problem. Previous geophysical data modelling studies using RBF-FD have employed the infinitely smooth RBFs, such as the popular Gaussian (GA) RBFs. Here, both GA and PHS RBFs were tested with different numbers of nodes per mesh-free subdomain and with various shape parameter values (only GA RBFs have a shape parameter). The test results show that the PHS RBF-FD method is more computationally efficient than the GA RBF-FD counterpart. To achieve more efficiency, unstructured node distributions are proposed in discretizing the density models. For both quasi-uniform and unstructured node distributions, numerical results from the proposed PHS RBF-FD demonstrate that the computed vertical gravity and gravitational potential values agree well with analytical solutions with a reasonable number of degrees of freedom. A comparison study of modelling a complex density model with the PHS RBF-FD scheme and nodal finite-element method shows that the RBF-FD scheme generates sparse, asymmetric, linear systems of equations, supports unstructured nodal discretization and local refinement, and can have nonlinear h-convergence under refinement. Finally, the proposed RBF-FD method was applied to obtain the vertical gravity and gravity gradients over a real-world density model, where the benefits of mesh-free discretization are clearly illustrated.

این مطالعه به منظور بررسی پیش بینی شاخص های عملکرد تولیدی در مرغان تخم گذار با استفاده از شبکه های عصبی مصنوعی و رگرسیون غیرخطی چندگانه انجام شد. بررسی بر روی اطلاعات چهار دوره متوالی پرورش در یک واحد پرورش مرغ تخم گذار صورت گرفت. روش های داده-کاوی شامل رگرسیون خطی و غیر خطی، شبکه عصبی پرسپترون سه لایه، شبکه عصبی پرسپترون چهار لایه و شبکه عصبی با تابع پایه ای شعاعی بود. در این مدل ها از متغیرهای سن گله، میزان خوراک مصرفی و فصل تولید به عنوان متغیر پیشگو و شاخص های عملکرد تولیدی شامل درصد تخم-گذاری، وزن توده ای تخم مرغ تولیدی و ضریب تبدیل غذایی به عنوان متغیر پاسخ استفاده شد. نتایج نهایی رگرسیون های خطی نشان داد که برای تمامی متغیرهای وابسته مورد مطالعه متغیر مستقل سن گله معنی دار می باشد. بنابراین رگرسیون غیر خطی شاخص های عملکرد تولیدی در مقابل سن برای مقایسه با شبکه های عصبی مختلف مورد بررسی قرار گرفت و برای مقایسه کلیه مدل ها از ضریب تعیین (R2) و میانگین قدر مطلق خطا (MAE) استفاده شد. نتایج نشان داد بین شبکه های عصبی مصنوعی مختلف مورد مطالعه، شبکه با تابع پایه ای شعاعی بهتر از سایر مدل های در پیش‌بینی شاخص های عملکرد تولیدی مرغان تخم گذار عمل می کند.

In this paper, a fractional order digital differentiator is designed by using Inverse multiquadric radial basis function (RBF). First, the RBF interpolation approach is described. Then, the non-integer delay sample estimation is derived by using RBF approach. Next, the Grunwald-Letnikov derivative and non-integer delay sample delay are applied to obtain the transfer function of the proposed method i.e. fractional order digital differentiator. The design accuracy of the proposed method is better then the conventional methods like examples Time domain least squares method, Fractional sample delay method and Frequency response approximation method.

Free vibration analysis of symmetric laminated composite plates by trigonometric shear deformation theory and inverse multiquadric RBF

In this paper, buckling analysis of isotropic, orthotropic, laminated composite and sandwich plates utilizing trigonometric shear deformation theory and meshless method based on the finite point formulation using thin plate, polynomial and inverse multiquadric radial basis function is presented. The convergence of the present method is studied for isotropic and laminated composite plates for different radial basis functions with optimal value of shape parameter. Numerical examples of laminated and sandwich plates subjected to various types of in-plane loads are solved to demonstrate accuracy and applicability of present method. Several new results for variety of composite and sandwich plates are presented. The present results are observed to be in good agreement with those available in literature. The effects of orthotropy ratio of material, span to thickness ratio, number of layers, core thickness and lamination scheme on the critical load of plates are also presented.

The design and simulation of ultrashort pulse shaping systems require pulse propagation methods that take the combined effects of dispersion, diffraction, and system aberrations into account. In the conventional pulse propagation methods based on the spectrum of plane wave, usually large number of sampling points are needed for the correct Fourier transform operations due to the fast oscillating phase of the complex pulse field. In this work, I have developed an alternative pulse propagation method, based on the Gaussian pulsed beam decomposition, as an extension of the monochromatic Gaussian beam propagation method. Methods for the decomposition of an input pulse, with arbitrary spatial and temporal (spectral) profiles, into a set of elementary Gaussian pulsed beams are proposed. Algorithms for computing the spatio-temporal and spatio-spectral profiles of the propagated pulse as the phase correct superposition of individual Gaussian pulsed beams are developed. The proposed decomposition method allows the elementary Gaussian pulsed beams to have different parameters depending on the local spatial and spectral phase of the given input pulse which reduces the number of Gaussian pulsed beams required to decompose an input pulsed beam with a given accuracy. Furthermore, a new kind of beam called the truncated Gaussian beam, is introduced and combined with the conventional Gaussian beam decomposition method to enable decomposition of fields after hard apertures. The analytical propagation equation of the truncated Gaussian beam through a paraxial optical system is derived. Additionally, the application of the Gaussian beam decomposition method is extended to handle the propagation of vectorial fields. Several example calculations are presented to validate the proposed methods and show their application in propagating fields through optical systems which are rather complicated to model using the conventional methods.

In this study, the prediction errors of various spatial interpolation methods used to model values at unmeasured locations was compared and the accuracy of these predictions was evaluated. The root mean square (RMS) was calculated by processing different parameters associated with spatial interpolation by using techniques such as inverse distance weighting, kriging, local polynomial interpolation and radial basis function to known elevation data of the east coastal area under the same condition. As a result, a circular model of simple kriging reached the smallest RMS value. Prediction map using the multiquadric method of a radial basis function was coincident with the spatial distribution obtained by constructing a triangulated irregular network of the study area through the raster mathematics. In addition, better interpolation results can be obtained by setting the optimal power value provided under the selected condition.

This doctoral thesis presents a framework for machine based interpretation of Malaysian Sign Language (MSL). The goal is to explore and develop necessary core algorithms that are capable of recognizing hand signs, based on the monocular/2D visual input of a low-cost hardware (Digital Webcam), without the assistance of visual-markers on hands. Successful hand sign interpretation with the aforementioned constrained visual system is challenging. Economical hardware devices often provide noisy/cluttered raw data with limited useful information. Non-involvement of visual markers imposes the requirement of additional strategies to disambiguate occlusions and background complexities. Natural variations in hand posture/gesture performances further convolute the recognition task. Addressing these challenges require computationally heavy algorithms in image processing, machine learning and pattern recognition. Thus vision-based sign language translator frameworks have to be multifaceted and versatile, in order to address innumerable practical concerns. In this research, hand postures interpretation is achieved by statistical projection methods. Analysis of high dimensional hand shape data is a complex task. Thus reducing dimensions via known projection methods aids in alleviating some of these complexities. Locality Preserving Projection (LPP) has been employed to accomplish this goal, while Principal Component Analysis (PCA) has been used as the benchmark method. Both methods were extensively tested against a hand posture database of 24 alphabet signs from MSL. As for the hand gesture interpretation, parameter-less Gaussian process based machine learning methods are proposed, as an alternative to current status quo. A variation of the Gaussian latent variable model – Gaussian Process Dynamic Model (GPDM) – has been employed for hand gesture interpretation. This has been comparatively studied against the established Hidden Markov Model (HMM). These machine learning methods were thoroughly tested against a hand gesture database of 64 signs from MSL. Grammatical sentence construction offers both intelligible sentences, and a mean of identifying erroneous sign classifications. In this thesis, a proof-of-concept on: use of Context Free Grammar (CFG) in successful parsing of meaningful sentences based on recognised gesture words, and how it can be extended in identifying (and correcting) erroneous sign classifications, is demonstrated with 92 sentences and the output of GPDM gesture classification. The novelty and contribution of this research: this is the first undertaking of markerless vision-based translation for MSL. Both LPP and GPDM are introduced to the sign language research field as an outcome of this investigation. The preliminary study and demonstration of grammatical sentence construction for translated gesture signs, is the first of its kind to the best of author's knowledge.

The human face has a unique shape and size, as well as a 3D character face model. During this process of animated facial expression of 3D virtual characters are mostly still done manually by moving the rig in each frame. The more characters used, the more production costs incurred. The absence of a cheap facial motion transfer system is also one of the reasons why not many studios are using motion capture technology in Indonesia. This study will evaluate the implementation of radial basis function (RBF) as a method of marker-transfer used as a reference to rig movement in the facial animation system. Testing is done by performing variations of radial function, namely: Gaussian, Inverse Quadratic, Inverse Multiquadric, and Multiquadric. The value of epsilon used is 0.01. The experimental results show that the range of feature point shifts generated by RBF Gaussian, Inverse Multiquadric, Inverse Quadratic, and Multiquadric have the same pattern with the difference in the distance of the marker rigging point shift on the target 3D model. The farthest range of differences is generated by RBF Gaussian. The resulting maximum range difference can reach 92.37% and a minimum of 2.47% compared to other methods. This appears on the Gaussian chart to have a sharper pattern. As with the concept of exaggeration, the Gaussian method which has the maximum range is the right method to apply the exaggeration principle in 3D face-expression animation.

Mathematical programming procedures to optimize the collector field subsystem of a power tower system

Beras Miskin (Raskin) Program is a program of social protection, as supporters of other programs such as nutrition improvement, healthy increase, education and productivity improvement of Poor Households. According to Badan Pusat Statistika, there were 14 criteria to determine a household is classified as poor households. Based on these criteria it will be classified of recipient households and non-recipient households of Beras Miskin (Raskin) Program by Support Vector Machine (SVM) method using LibSVM. The concept of classification by SVM is search for the best hyperplane which serves as a separator of two classes of data in the input space. Kernel function is used to convert the data into a higher dimensional space to allow a separation. LibSVM is a package program created by Chih-Chung Chang and Chih-Jen Lin from Department of Computer Science at National Taiwan University. The method used by LibSVM to obtain global solution of duality lagrange problem is decomposition method. To determine the best parameters of kernel function, used k-vold cross validation method and grid search algorithm. In this classification by SVM method using LibSVM, obtain the best accuracy value as 83,1933%, which is the kernel function Radial Basis Function (RBF). Keywords : Beras Miskin (Raskin) Program, Classification, Support Vector Machine (SVM), LibSVM, Kernel Function

Fast computation of RBF coefficients using FFT

This paper presented three disease diagnosis systems using pattern recognition based on genetic algorithm (GA) and neural networks. All systems dealt with feature selection and classification. GA chose subsets of features for the input of the classifier (neural network) and the accuracy of the classifier determined the percentage of effectiveness of each subset of features. The classifiers using in this paper were general regression neural network (GRNN), radial basis function (RBF) and radial basis network exact fit (RBEF). It uses breast cancer and hepatitis disease datasets taken from UCI machine learning database as medical dataset. The system performances were estimated by classification accuracy and they were compared with similar methods without feature selection. Key words: Pattern recognition, genetic algorithm, neural networks, classification.

Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval

The increased water demand and the increased capital construction costs of water resource development projects force engineers and water planners to utilize efficiently the existing and proposed water resources systems. Hence, it is considered necessary to find the optimum real time operating rules for systems of multiple reservoirs.Stochastic dynamic programming (SDP) has been used as the tool for deriving the real time operating rules for a system of multiple reservoirs, in preference to simulation analysis and linear programming. This is because the operation of the storages is considered as a sequential decision problem and dynamic programming is well suited to handle sequential, multi-period type decision problems. Further, the stochastic nature of streamflow is considered explicitly through a multivariate distribution for streamflow. The method theoretically produces the global optimum solution.The computational difficulties in terms of computer time and memory space have prohibited the realistic application of this method to systems of multiple reservoirs in the past. In this study, two methods have been introduced to reduce the computational difficulties of the method, thus making SDP more attractive to use in the derivation of the real time operating rules for a system of multiple reservoirs.The first method, the assumption of cross correlation of streamflow, reduces the number of states in the SDP method which reduces computer time and memory space. Further, it reduces the number of conditional probability estimates of streamflow which are used in recursive relation of the SDP algorithm. The second method, the “corridor” approach, reduces computer time involved in the SDP method by eliminating the computation of infeasible and/or inferior (suboptimal) solutions. These two methods have resulted in significant savings in the computer effort of the SDP method.The conditional probabilities of streamflow are computed by considering the hypervolume under the conditional probability density function between the integration limits using the computationally efficient Gaussian Legendre quadrature method. The conditional probability density function is derived from the historical streamflow data.Real time operating rules are expressed as a function of the storage volume(s) at the beginning of the current time interval and the forecast inflow into the storage(s) during the current time interval.The Melbourne water supply system is used as the example. The derived operating rules have been tested by operating a simulation model and the conclusion is made that the SDP method is a satisfactory technique for objectively deriving real time operating rules for a system of multiple reservoirs.Finally, a combined stochastic dynamic programming – statistical disaggregation approach is introduced to determine the real time operating rules for a system of multiple reservoirs where operational data are available. Releases from individual storages are a function of the total system storage volume and inflow. The method uses SDP to determine the release rules from the equivalent single reservoir of the multiple reservoir system; these releases are then disaggregated to individual releases using the statistical release disaggregation model whose parameters are derived from the historical operational data. The approach was used to derive real time operating rules for the Melbourne water supply system and the operating rules were validated using a simulation model of the system.