Search results for: variational spline.

Authors: Rongli Gai, Zhiyuan Chang, Xiaohong Wang, Jingyu Liu

Abstract:

In view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC (Computerized Numerical Control) machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: Adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Anastasiia Yu. Timofeeva

Abstract:

Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: Grade point average, orthogonal regression, penalized regression spline, locally weighted regression.

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Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

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Authors: Lina Yan, Jingjing Di, Ke Wang

Abstract:

A new basis function neural network algorithm is proposed for numerical integration. The main idea is to construct neural network model based on spline basis functions, which is used to approximate the integrand by training neural network weights. The convergence theorem of the neural network algorithm, the theorem for numerical integration and one corollary are presented and proved. The numerical examples, compared with other methods, show that the algorithm is effective and has the characteristics such as high precision and the integrand not required known. Thus, the algorithm presented in this paper can be widely applied in many engineering fields.

Keywords: Numerical integration, Spline basis function, Neural network algorithm

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Authors: Sarun Phibanchon, Michael A. Allen

Abstract:

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.

Keywords: Soliton, instability, variational method, spectral method.

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Authors: Marwan Abukhaled, Ibrahim Sadek

Abstract:

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.

Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach

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Authors: Hanita Daud, Noorhana Yahya, Vijanth Sagayan, Muizuddin Talib

Abstract:

This paper discusses on the use of Spline Interpolation and Mean Square Error (MSE) as tools to process data acquired from the developed simulator that shall replicate sea bed logging environment. Sea bed logging (SBL) is a new technique that uses marine controlled source electromagnetic (CSEM) sounding technique and is proven to be very successful in detecting and characterizing hydrocarbon reservoirs in deep water area by using resistivity contrasts. It uses very low frequency of 0.1Hz to 10 Hz to obtain greater wavelength. In this work the in house built simulator was used and was provided with predefined parameters and the transmitted frequency was varied for sediment thickness of 1000m to 4000m for environment with and without hydrocarbon. From series of simulations, synthetics data were generated. These data were interpolated using Spline interpolation technique (degree of three) and mean square error (MSE) were calculated between original data and interpolated data. Comparisons were made by studying the trends and relationship between frequency and sediment thickness based on the MSE calculated. It was found that the MSE was on increasing trends in the set up that has the presence of hydrocarbon in the setting than the one without. The MSE was also on decreasing trends as sediment thickness was increased and with higher transmitted frequency.

Keywords: Spline Interpolation, Mean Square Error, Sea Bed Logging, Controlled Source Electromagnetic

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: Human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, Prior distribution and approximate posterior distribution, KTH dataset.

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Authors: Carine Moussaed, Stephen Wornom, Bruno Koobus, Maria Vittoria Salvetti, Alain Dervieux,

Abstract:

The effects of dynamic subgrid scale (SGS) models are investigated in variational multiscale (VMS) LES simulations of bluff body flows. The spatial discretization is based on a mixed finite element/finite volume formulation on unstructured grids. In the VMS approach used in this work, the separation between the largest and the smallest resolved scales is obtained through a variational projection operator and a finite volume cell agglomeration. The dynamic version of Smagorinsky and WALE SGS models are used to account for the effects of the unresolved scales. In the VMS approach, these effects are only modeled in the smallest resolved scales. The dynamic VMS-LES approach is applied to the simulation of the flow around a circular cylinder at Reynolds numbers 3900 and 20000 and to the flow around a square cylinder at Reynolds numbers 22000 and 175000. It is observed as in previous studies that the dynamic SGS procedure has a smaller impact on the results within the VMS approach than in LES. But improvements are demonstrated for important feature like recirculating part of the flow. The global prediction is improved for a small computational extra cost.

Keywords: variational multiscale LES, dynamic SGS model, unstructured grids, circular cylinder, square cylinder.

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Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi

Abstract:

The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.

Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

Abstract:

Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model.

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

Abstract:

In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: Deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab

Abstract:

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.

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Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park

Abstract:

In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.

Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: Bayesian rule, Gaussian process classification model with multiclass, Gaussian process prior, human action classification, laplace approximation, variational EM algorithm.

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Authors: M.Asif, M.R.Arshad, P.A.Wilson

Abstract:

In this paper, a simple active contour based visual tracking algorithm is presented for outdoor AGV application which is currently under development at the USM robotic research group (URRG) lab. The presented algorithm is computationally low cost and able to track road boundaries in an image sequence and can easily be implemented on available low cost hardware. The proposed algorithm used an active shape modeling using the B-spline deformable template and recursive curve fitting method to track the current orientation of the road.

Keywords: Active contour, B-spline, recursive curve fitting.

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Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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Authors: Adam Rabcewicz

Abstract:

Variational methods for optical flow estimation are known for their excellent performance. The method proposed by Brox et al. [5] exemplifies the strength of that framework. It combines several concepts into single energy functional that is then minimized according to clear numerical procedure. In this paper we propose a modification of that algorithm starting from the spatiotemporal gradient constancy assumption. The numerical scheme allows to establish the connection between our model and the CLG(H) method introduced in [18]. Experimental evaluation carried out on synthetic sequences shows the significant superiority of the spatial variant of the proposed method. The comparison between methods for the realworld sequence is also enclosed.

Keywords: optical flow, variational methods, gradient constancy assumption.

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Authors: S. Benchelha, H. C. Aoudjehane, M. Hakdaoui, R. El Hamdouni, H. Mansouri, T. Benchelha, M. Layelmam, M. Alaoui

Abstract:

The logistic regression (LR) and multivariate adaptive regression spline (MarSpline) are applied and verified for analysis of landslide susceptibility map in Oudka, Morocco, using geographical information system. From spatial database containing data such as landslide mapping, topography, soil, hydrology and lithology, the eight factors related to landslides such as elevation, slope, aspect, distance to streams, distance to road, distance to faults, lithology map and Normalized Difference Vegetation Index (NDVI) were calculated or extracted. Using these factors, landslide susceptibility indexes were calculated by the two mentioned methods. Before the calculation, this database was divided into two parts, the first for the formation of the model and the second for the validation. The results of the landslide susceptibility analysis were verified using success and prediction rates to evaluate the quality of these probabilistic models. The result of this verification was that the MarSpline model is the best model with a success rate (AUC = 0.963) and a prediction rate (AUC = 0.951) higher than the LR model (success rate AUC = 0.918, rate prediction AUC = 0.901).

Keywords: Landslide susceptibility mapping, regression logistic, multivariate adaptive regression spline, Oudka, Taounate, Morocco.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen

Abstract:

Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.

Keywords: Natural Language Inference, explanation generation, variational auto-encoder, generative model.

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Authors: R. Mirabdollah Yani, E. Darabi

Abstract:

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.

Keywords: variational iteration method (VIM), cable vibration, closed-form solution

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Rossella Arcucci, Luisa D’Amore, Simone Celestino, Giuseppe Scotti, Giuliano Laccetti

Abstract:

This work is the first dowel in a rather wide research activity in collaboration with Euro Mediterranean Center for Climate Changes, aimed at introducing scalable approaches in Ocean Circulation Models. We discuss designing and implementation of a parallel algorithm for solving the Variational Data Assimilation (DA) problem on Graphics Processing Units (GPUs). The algorithm is based on the fully scalable 3DVar DA model, previously proposed by the authors, which uses a Domain Decomposition approach (we refer to this model as the DD-DA model). We proceed with an incremental porting process consisting of 3 distinct stages: requirements and source code analysis, incremental development of CUDA kernels, testing and optimization. Experiments confirm the theoretic performance analysis based on the so-called scale up factor demonstrating that the DD-DA model can be suitably mapped on GPU architectures.

Keywords: Data Assimilation, Parallel Algorithm, GPU architectures, Ocean Models.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

Abstract:

To minimize power losses, it is important to determine the location and size of local generators to be placed in unbalanced power distribution systems. On account of some inherent features of unbalanced distribution systems, such as radial structure, large number of nodes, a wide range of X/R ratios, the conventional techniques developed for the transmission systems generally fail on the determination of optimum size and location of distributed generators (DGs). This paper presents a simple method for investigating the problem of contemporaneously choosing best location and size of DG in three-phase unbalanced radial distribution system (URDS) for power loss minimization and to improve the voltage profile of the system. Best location of the DG is determined by using voltage index analysis and size of DG is computed by variational technique algorithm according to available standard size of DGs. This paper presents the results of simulations for 25-bus and IEEE 37- bus Unbalanced Radial Distribution system.

Keywords: Distributed generator, unbalanced radial distributionsystem, voltage index analysis, variational algorithm.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: Multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, Importance sampling, approximate posterior distribution, Marginal likelihood evidence.

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Authors: K. Bommanna Raja, M.Madheswaran, K.Thyagarajah

Abstract:

A higher order spline interpolated contour obtained with up-sampling of homogenously distributed coordinates for segmentation of kidney region in different classes of ultrasound kidney images has been developed and presented in this paper. The performance of the proposed method is measured and compared with modified snake model contour, Markov random field contour and expert outlined contour. The validation of the method is made in correspondence with expert outlined contour using maximum coordinate distance, Hausdorff distance and mean radial distance metrics. The results obtained reveal that proposed scheme provides optimum contour that agrees well with expert outlined contour. Moreover this technique helps to preserve the pixels-of-interest which in specific defines the functional characteristic of kidney. This explores various possibilities in implementing computer-aided diagnosis system exclusively for US kidney images.

Keywords: Ultrasound Kidney Image – Kidney Segmentation –Active Contour – Markov Random Field – Higher Order SplineInterpolation

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Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

Abstract:

This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.

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