Search results for: Adaptive method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8588

Search results for: Adaptive method

8048 Dynamic Background Updating for Lightweight Moving Object Detection

Authors: Kelemewerk Destalem, Jungjae Cho, Jaeseong Lee, Ju H. Park, Joonhyuk Yoo

Abstract:

Background subtraction and temporal difference are often used for moving object detection in video. Both approaches are computationally simple and easy to be deployed in real-time image processing. However, while the background subtraction is highly sensitive to dynamic background and illumination changes, the temporal difference approach is poor at extracting relevant pixels of the moving object and at detecting the stopped or slowly moving objects in the scene. In this paper, we propose a simple moving object detection scheme based on adaptive background subtraction and temporal difference exploiting dynamic background updates. The proposed technique consists of histogram equalization, a linear combination of background and temporal difference, followed by the novel frame-based and pixel-based background updating techniques. Finally, morphological operations are applied to the output images. Experimental results show that the proposed algorithm can solve the drawbacks of both background subtraction and temporal difference methods and can provide better performance than that of each method.

Keywords: Background subtraction, background updating, real time and lightweight algorithm, temporal difference.

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8047 An Intelligent Cascaded Fuzzy Logic Based Controller for Controlling the Room Temperature in Hydronic Heating System

Authors: Vikram Jeganathan, A. V. Sai Balasubramanian, N. Ravi Shankar, S. Subbaraman, R. Rengaraj

Abstract:

Heating systems are a necessity for regions which brace extreme cold weather throughout the year. To maintain a comfortable temperature inside a given place, heating systems making use of- Hydronic boilers- are used. The principle of a single pipe system serves as a base for their working. It is mandatory for these heating systems to control the room temperature, thus maintaining a warm environment. In this paper, the concept of regulation of the room temperature over a wide range is established by using an Adaptive Fuzzy Controller (AFC). This fuzzy controller automatically detects the changes in the outside temperatures and correspondingly maintains the inside temperature to a palatial value. Two separate AFC's are put to use to carry out this function: one to determine the quantity of heat needed to reach the prospective temperature required and to set the desired temperature; the other to control the position of the valve, which is directly proportional to the error between the present room temperature and the user desired temperature. The fuzzy logic controls the position of the valve as per the requirement of the heat. The amount by which the valve opens or closes is controlled by 5 knob positions, which vary from minimum to maximum, thereby regulating the amount of heat flowing through the valve. For the given test system data, different de-fuzzifier methods have been implemented and the results are compared. In order to validate the effectiveness of the proposed approach, a fuzzy controller has been designed by obtaining a test data from a real time system. The simulations are performed in MATLAB and are verified with standard system data. The proposed approach can be implemented for real time applications.

Keywords: Adaptive fuzzy controller, Hydronic heating system

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8046 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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8045 Quality Classification and Monitoring Using Adaptive Metric Distance and Neural Networks: Application in Pickling Process

Authors: S. Bouhouche, M. Lahreche, S. Ziani, J. Bast

Abstract:

Modern manufacturing facilities are large scale, highly complex, and operate with large number of variables under closed loop control. Early and accurate fault detection and diagnosis for these plants can minimise down time, increase the safety of plant operations, and reduce manufacturing costs. Fault detection and isolation is more complex particularly in the case of the faulty analog control systems. Analog control systems are not equipped with monitoring function where the process parameters are continually visualised. In this situation, It is very difficult to find the relationship between the fault importance and its consequences on the product failure. We consider in this paper an approach to fault detection and analysis of its effect on the production quality using an adaptive centring and scaling in the pickling process in cold rolling. The fault appeared on one of the power unit driving a rotary machine, this machine can not track a reference speed given by another machine. The length of metal loop is then in continuous oscillation, this affects the product quality. Using a computerised data acquisition system, the main machine parameters have been monitored. The fault has been detected and isolated on basis of analysis of monitored data. Normal and faulty situation have been obtained by an artificial neural network (ANN) model which is implemented to simulate the normal and faulty status of rotary machine. Correlation between the product quality defined by an index and the residual is used to quality classification.

Keywords: Modeling, fault detection and diagnosis, parameters estimation, neural networks, Fault Detection and Diagnosis (FDD), pickling process.

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8044 The Homotopy Analysis Method for Solving Discontinued Problems Arising in Nanotechnology

Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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8043 Adomian Method for Second-order Fuzzy Differential Equation

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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8042 An Image Segmentation Algorithm for Gradient Target Based on Mean-Shift and Dictionary Learning

Authors: Yanwen Li, Shuguo Xie

Abstract:

In electromagnetic imaging, because of the diffraction limited system, the pixel values could change slowly near the edge of the image targets and they also change with the location in the same target. Using traditional digital image segmentation methods to segment electromagnetic gradient images could result in lots of errors because of this change in pixel values. To address this issue, this paper proposes a novel image segmentation and extraction algorithm based on Mean-Shift and dictionary learning. Firstly, the preliminary segmentation results from adaptive bandwidth Mean-Shift algorithm are expanded, merged and extracted. Then the overlap rate of the extracted image block is detected before determining a segmentation region with a single complete target. Last, the gradient edge of the extracted targets is recovered and reconstructed by using a dictionary-learning algorithm, while the final segmentation results are obtained which are very close to the gradient target in the original image. Both the experimental results and the simulated results show that the segmentation results are very accurate. The Dice coefficients are improved by 70% to 80% compared with the Mean-Shift only method.

Keywords: Gradient image, segmentation and extract, mean-shift algorithm, dictionary learning.

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8041 Multilevel Arnoldi-Tikhonov Regularization Methods for Large-Scale Linear Ill-Posed Systems

Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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8040 Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities

Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: structured variational inequalities, proximal point method, global convergence

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8039 A Method for Improving Dental Crown Fit-Increasing the Robustness

Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

Abstract:

The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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8038 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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8037 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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8036 Robust Statistics Based Algorithm to Remove Salt and Pepper Noise in Images

Authors: V.R.Vijaykumar, P.T.Vanathi, P.Kanagasabapathy, D.Ebenezer

Abstract:

In this paper, a robust statistics based filter to remove salt and pepper noise in digital images is presented. The function of the algorithm is to detect the corrupted pixels first since the impulse noise only affect certain pixels in the image and the remaining pixels are uncorrupted. The corrupted pixels are replaced by an estimated value using the proposed robust statistics based filter. The proposed method perform well in removing low to medium density impulse noise with detail preservation upto a noise density of 70% compared to standard median filter, weighted median filter, recursive weighted median filter, progressive switching median filter, signal dependent rank ordered mean filter, adaptive median filter and recently proposed decision based algorithm. The visual and quantitative results show the proposed algorithm outperforms in restoring the original image with superior preservation of edges and better suppression of impulse noise

Keywords: Image denoising, Nonlinear filter, Robust Statistics, and Salt and Pepper Noise.

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8035 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method

Authors: Caihong Su

Abstract:

Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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8034 Review of Strategies for Hybrid Energy Storage Management System in Electric Vehicle Application

Authors: Kayode A. Olaniyi, Adeola A. Ogunleye, Tola M. Osifeko

Abstract:

Electric Vehicles (EV) appear to be gaining increasing patronage as a feasible alternative to Internal Combustion Engine Vehicles (ICEVs) for having low emission and high operation efficiency. The EV energy storage systems are required to handle high energy and power density capacity constrained by limited space, operating temperature, weight and cost. The choice of strategies for energy storage evaluation, monitoring and control remains a challenging task. This paper presents review of various energy storage technologies and recent researches in battery evaluation techniques used in EV applications. It also underscores strategies for the hybrid energy storage management and control schemes for the improvement of EV stability and reliability. The study reveals that despite the advances recorded in battery technologies there is still no cell which possess both the optimum power and energy densities among other requirements, for EV application. However combination of two or more energy storages as hybrid and allowing the advantageous attributes from each device to be utilized is a promising solution. The review also reveals that State-of-Charge (SoC) is the most crucial method for battery estimation. The conventional method of SoC measurement is however questioned in the literature and adaptive algorithms that include all model of disturbances are being proposed. The review further suggests that heuristic-based approach is commonly adopted in the development of strategies for hybrid energy storage system management. The alternative approach which is optimization-based is found to be more accurate but is memory and computational intensive and as such not recommended in most real-time applications.

Keywords: Hybrid electric vehicle, hybrid energy storage, battery state estimation, ate of charge, state of health.

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8033 Variational Iteration Method for the Solution of Boundary Value Problems

Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.

Abstract:

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.

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8032 A Normalization-based Robust Image Watermarking Scheme Using SVD and DCT

Authors: Say Wei Foo, Qi Dong

Abstract:

Digital watermarking is one of the techniques for copyright protection. In this paper, a normalization-based robust image watermarking scheme which encompasses singular value decomposition (SVD) and discrete cosine transform (DCT) techniques is proposed. For the proposed scheme, the host image is first normalized to a standard form and divided into non-overlapping image blocks. SVD is applied to each block. By concatenating the first singular values (SV) of adjacent blocks of the normalized image, a SV block is obtained. DCT is then carried out on the SV blocks to produce SVD-DCT blocks. A watermark bit is embedded in the highfrequency band of a SVD-DCT block by imposing a particular relationship between two pseudo-randomly selected DCT coefficients. An adaptive frequency mask is used to adjust local watermark embedding strength. Watermark extraction involves mainly the inverse process. The watermark extracting method is blind and efficient. Experimental results show that the quality degradation of watermarked image caused by the embedded watermark is visually transparent. Results also show that the proposed scheme is robust against various image processing operations and geometric attacks.

Keywords: Image watermarking, Image normalization, Singularvalue decomposition, Discrete cosine transform, Robustness.

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8031 Role and Relative Effectiveness of Immune System for Combating Small Pox and AIDS

Authors: A. Taqaddas

Abstract:

The human body has a complex system of innate and adaptive mechanisms for combating infection. This article discusses the role and relative effectiveness of these mechanisms in relation to small pox and AIDS.

Keywords: AIDS, Immune System, Small Pox, Viral Infections.

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8030 Adaptive Responses of Carum copticum to in vitro Salt Stress

Authors: R. Razavizadeh, F. Adabavazeh, M. Rezaee Chermahini

Abstract:

Salinity is one of the most widespread agricultural problems in arid and semi-arid areas that limits the plant growth and crop productivity. In this study, the salt stress effects on protein, reducing sugar, proline contents and antioxidant enzymes activities of Carum copticum L. under in vitro conditions were studied. Seeds of C. copticum were cultured in Murashige and Skoog (MS) medium containing 0, 25, 50, 100 and 150 mM NaCl and calli were cultured in MS medium containing 1 μM 2, 4-dichlorophenoxyacetic acid, 4 μM benzyl amino purine and different levels of NaCl (0, 25, 50, 100 and 150 mM). After NaCl treatment for 28 days, the proline and reducing sugar contents of shoots, roots and calli increased significantly in relation to the severity of the salt stress. The highest amount of proline and carbohydrate were observed at 150 and 100 mM NaCl, respectively. The reducing sugar accumulation in shoots was the highest as compared to roots, whereas, proline contents did not show any significant difference in roots and shoots under salt stress. The results showed significant reduction of protein contents in seedlings and calli. Based on these results, proteins extracted from the shoots, roots and calli of C. copticum treated with 150 mM NaCl showed the lowest contents. The positive relationships were observed between activity of antioxidant enzymes and the increase in stress levels. Catalase, ascorbate peroxidase and superoxide dismutase activity increased significantly under salt concentrations in comparison to the control. These results suggest that the accumulation of proline and sugars, and activation of antioxidant enzymes play adaptive roles in the adaptation of seedlings and callus of C. copticum to saline conditions.

Keywords: Antioxidant enzymes, Carum copticum, organic solutes, salt stress.

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8029 Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation

Authors: G.Hariharan, K.Kannan

Abstract:

In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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8028 Robust Adaptive ELS-QR Algorithm for Linear Discrete Time Stochastic Systems Identification

Authors: Ginalber L. O. Serra

Abstract:

This work proposes a recursive weighted ELS algorithm for system identification by applying numerically robust orthogonal Householder transformations. The properties of the proposed algorithm show it obtains acceptable results in a noisy environment: fast convergence and asymptotically unbiased estimates. Comparative analysis with others robust methods well known from literature are also presented.

Keywords: Stochastic Systems, Robust Identification, Parameter Estimation, Systems Identification.

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8027 A Method for Measurement and Evaluation of Drape of Textiles

Authors: L. Fridrichova, R. Knížek, V. Bajzík

Abstract:

Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: Drape, drape shape, automated drape meter.

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8026 Seat Assignment Model for Student Admissions Process at Saudi Higher Education Institutions

Authors: Mohammed Salem Alzahrani

Abstract:

In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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8025 A Dual Method for Solving General Convex Quadratic Programs

Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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8024 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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8023 Selection Initial modes for Belief K-modes Method

Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

Abstract:

The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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8022 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations

Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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8021 Comparison of Finite-Element and IEC Methods for Cable Thermal Analysis under Various Operating Environments

Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

Abstract:

In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method. 

Keywords: Cable ampacity, Finite element method, underground cable, thermal rating.

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8020 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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8019 Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media

Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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