Search results for: adomian decomposition method.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8258

Search results for: adomian decomposition method.

8048 A New Definition of the Intrinsic Mode Function

Authors: Zhihua Yang, Lihua Yang

Abstract:

This paper makes a detailed analysis regarding the definition of the intrinsic mode function and proves that Condition 1 of the intrinsic mode function can really be deduced from Condition 2. Finally, an improved definition of the intrinsic mode function is given.

Keywords: Empirical Mode Decomposition (EMD), Hilbert-Huang transform(HHT), Intrinsic Mode Function(IMF).

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8047 Catalytic Pyrolysis of Sewage Sludge for Upgrading Bio-Oil Quality Using Sludge-Based Activated Char as an Alternative to HZSM5

Authors: Ali Zaker, Zhi Chen

Abstract:

Due to the concerns about the depletion of fossil fuel sources and the deteriorating environment, the attempt to investigate the production of renewable energy will play a crucial role as a potential to alleviate the dependency on mineral fuels. One particular area of interest is generation of bio-oil through sewage sludge (SS) pyrolysis. SS can be a potential candidate in contrast to other types of biomasses due to its availability and low cost. However, the presence of high molecular weight hydrocarbons and oxygenated compounds in the SS bio-oil hinders some of its fuel applications. In this context, catalytic pyrolysis is another attainable route to upgrade bio-oil quality. Among different catalysts (i.e., zeolites) studied for SS pyrolysis, activated chars (AC) are eco-friendly alternatives. The beneficial features of AC derived from SS comprise the comparatively large surface area, porosity, enriched surface functional groups and presence of a high amount of metal species that can improve the catalytic activity. Hence, a sludge-based AC catalyst was fabricated in a single-step pyrolysis reaction with NaOH as the activation agent and was compared with HZSM5 zeolite in this study. The thermal decomposition and kinetics were invested via thermogravimetric analysis (TGA) for guidance and control of pyrolysis and catalytic pyrolysis and the design of the pyrolysis setup. The results indicated that the pyrolysis and catalytic pyrolysis contain four obvious stages and the main decomposition reaction occurred in the range of 200-600 °C. Coats-Redfern method was applied in the 2nd and 3rd devolatilization stages to estimate the reaction order and activation energy (E) from the mass loss data. The average activation energy (Em) values for the reaction orders n = 1, 2 and 3 were in the range of 6.67-20.37 kJ/mol for SS; 1.51-6.87 kJ/mol for HZSM5; and 2.29-9.17 kJ/mol for AC, respectively. According to the results, AC and HZSM5 both were able to improve the reaction rate of SS pyrolysis by abridging the Em value. Moreover, to generate and examine the effect of the catalysts on the quality of bio-oil, a fixed-bed pyrolysis system was designed and implemented. The composition analysis of the produced bio-oil was carried out via gas chromatography/mass spectrometry (GC/MS). The selected SS to catalyst ratios were 1:1, 2:1 and 4:1. The optimum ratio in terms of cracking the long-chain hydrocarbons and removing oxygen-containing compounds was 1:1 for both catalysts. The upgraded bio-oils with HZSM5 and AC were in the total range of C4-C17 with around 72% in the range of C4-C9. The bio-oil from pyrolysis of SS contained 49.27% oxygenated compounds while the presence of HZSM5 and AC dropped to 7.3% and 13.02%, respectively. Meanwhile, generation of value-added chemicals such as light aromatic compounds were significantly improved in the catalytic process. Furthermore, the fabricated AC catalyst was characterized by BET, SEM-EDX, FT-IR and TGA techniques. Overall, this research demonstrated that AC is an efficient catalyst in the pyrolysis of SS and can be used as a cost-competitive catalyst in contrast to HZSM5.

Keywords: Activated char, bio-oil, catalytic pyrolysis, HZSM5, sewage sludge.

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8046 The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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8045 Seat Assignment Problem Optimization

Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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8044 Structuring and Visualizing Healthcare Claims Data Using Systems Architecture Methodology

Authors: Inas S. Khayal, Weiping Zhou, Jonathan Skinner

Abstract:

Healthcare delivery systems around the world are in crisis. The need to improve health outcomes while decreasing healthcare costs have led to an imminent call to action to transform the healthcare delivery system. While Bioinformatics and Biomedical Engineering have primarily focused on biological level data and biomedical technology, there is clear evidence of the importance of the delivery of care on patient outcomes. Classic singular decomposition approaches from reductionist science are not capable of explaining complex systems. Approaches and methods from systems science and systems engineering are utilized to structure healthcare delivery system data. Specifically, systems architecture is used to develop a multi-scale and multi-dimensional characterization of the healthcare delivery system, defined here as the Healthcare Delivery System Knowledge Base. This paper is the first to contribute a new method of structuring and visualizing a multi-dimensional and multi-scale healthcare delivery system using systems architecture in order to better understand healthcare delivery.

Keywords: Health informatics, systems thinking, systems architecture, healthcare delivery system, data analytics.

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8043 Development of a Nano-Alumina-Zirconia Composite Catalyst as an Active Thin Film in Biodiesel Production

Authors: N. Marzban, J. K. Heydarzadeh M. Pourmohammadbagher, M. H. Hatami, A. Samia

Abstract:

A nano-alumina-zirconia composite catalyst was synthesized by a simple aqueous sol-gel method using AlCl3.6H2O and ZrCl4 as precursors. Thermal decomposition of the precursor and subsequent formation of γ-Al2O3 and t-Zr were investigated by thermal analysis. XRD analysis showed that γ-Al2O3 and t-ZrO2 phases were formed at 700 °C. FT-IR analysis also indicated that the phase transition to γ-Al2O3 occurred in corroboration with X-ray studies. TEM analysis of the calcined powder revealed that spherical particles were in the range of 8-12 nm. The nano-alumina-zirconia composite particles were mesoporous and uniformly distributed in their crystalline phase. In order to measure the catalytic activity, esterification reaction was carried out. Biodiesel, as a renewable fuel, was formed in a continuous packed column reactor. Free fatty acid (FFA) was esterified with ethanol in a heterogeneous catalytic reactor. It was found that the synthesized γ-Al2O3/ZrO2 composite had the potential to be used as a heterogeneous base catalyst for biodiesel production processes.

Keywords: Nano-alumina-zirconia, composite catalyst, thin film, biodiesel.

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8042 Light Harvesting Titanium Nanocatalyst for Remediation of Methyl Orange

Authors: Brajesh Kumar, Luis Cumbal

Abstract:

An ecofriendly Citrus paradisipeel extract mediated synthesis of TiO2 nanoparticles is reported under sonication. U.V.-vis, Transmission electron microscopy, Dynamic light scattering, and X-ray analyses are performed to characterize the formation of TiO2 nanoparticles. It is almost spherical in shape, having a size of 60–140 nm and the XRD peaks at 2θ = 25.363° confirm the characteristic facets for anatase form. The synthesized nanocatalyst is highly active in the decomposition of methyl orange (64 mg/L) in sunlight (~73%) for 2.5h.

Keywords: Ecofriendly, TiO2 nanoparticles, Citrusparadisi, TEM.

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8041 Fabrication and Characterization of CdS Nanoparticles Annealed by using Different Radiations

Authors: Aneeqa Sabah, Saadat Anwar Siddiqi, Salamat Ali

Abstract:

The systematic manipulations of shapes and sizes of inorganic compounds greatly benefit the various application fields including optics, magnetic, electronics, catalysis and medicine. However shape control has been much more difficult to achieve. Hence exploration of novel method for the preparation of differently shaped nanoparticles is challenging research area. II-VI group of semiconductor cadmium sulphide (CdS) nanostructure with different morphologies (such as, acicular like, mesoporous, spherical shapes) and of crystallite sizes vary from 11 to 16 nm were successfully synthesized by chemical aqueous precipitation of Cd2+ ions with homogeneously released S2- ions from decomposition of cadmium sulphate (CdSO4) and thioacetamide (CH3CSNH2) by annealing at different radiations (microwave, ultrasonic and sunlight) with matter and systematic research has been done for various factors affecting the controlled growth rate of CdS nanoparticles. The obtained nanomaterials have been characterized by X-ray Diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR), Thermogravometric (DSC-TGA) analysis and Scanning Electron Microscopy (SEM). The result indicates that on increasing the reaction time particle size increases but on increasing the molar ratios grain size decreases.

Keywords: CdS nanoparticles, Morphology, Oxidation, Radiations

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8040 Convex Restrictions for Outage Constrained MU-MISO Downlink under Imperfect Channel State Information

Authors: A. Preetha Priyadharshini, S. B. M. Priya

Abstract:

In this paper, we consider the MU-MISO downlink scenario, under imperfect channel state information (CSI). The main issue in imperfect CSI is to keep the probability of each user achievable outage rate below the given threshold level. Such a rate outage constraints present significant and analytical challenges. There are many probabilistic methods are used to minimize the transmit optimization problem under imperfect CSI. Here, decomposition based large deviation inequality and Bernstein type inequality convex restriction methods are used to perform the optimization problem under imperfect CSI. These methods are used for achieving improved output quality and lower complexity. They provide a safe tractable approximation of the original rate outage constraints. Based on these method implementations, performance has been evaluated in the terms of feasible rate and average transmission power. The simulation results are shown that all the two methods offer significantly improved outage quality and lower computational complexity.

Keywords: Imperfect channel state information, outage probability, multiuser- multi input single output.

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8039 A New Method to Solve a Non Linear Differential System

Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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8038 Characterization of Acetogenic and Methanogenic Leachates Generated from a Sanitary Landfill Site

Authors: Aik Heng Lee, Hamid Nikraz, Yung Tse Hung

Abstract:

Decomposition processes take place in landfill generate leachates that can be categorized mainly of acetogenic and methanogenic in nature. BOD:COD ratio computed in this study for a landfill site over a 3 years duration revealed as a good indicator to identify acetogenic leachate from methanogenic leachate. Correlation relationships to predict pollutant level taking into consideration of climatic condition are derived.

Keywords: Acetogenic Leachate, Methanogenic Leachate, BOD:COD Ratio.

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8037 Speckle Reducing Contourlet Transform for Medical Ultrasound Images

Authors: P.S. Hiremath, Prema T. Akkasaligar, Sharan Badiger

Abstract:

Speckle noise affects all coherent imaging systems including medical ultrasound. In medical images, noise suppression is a particularly delicate and difficult task. A tradeoff between noise reduction and the preservation of actual image features has to be made in a way that enhances the diagnostically relevant image content. Even though wavelets have been extensively used for denoising speckle images, we have found that denoising using contourlets gives much better performance in terms of SNR, PSNR, MSE, variance and correlation coefficient. The objective of the paper is to determine the number of levels of Laplacian pyramidal decomposition, the number of directional decompositions to perform on each pyramidal level and thresholding schemes which yields optimal despeckling of medical ultrasound images, in particular. The proposed method consists of the log transformed original ultrasound image being subjected to contourlet transform, to obtain contourlet coefficients. The transformed image is denoised by applying thresholding techniques on individual band pass sub bands using a Bayes shrinkage rule. We quantify the achieved performance improvement.

Keywords: Contourlet transform, Despeckling, Pyramidal directionalfilter bank, Thresholding.

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8036 Quadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation

Authors: Maharavo Randrianarivony

Abstract:

The objective is to split a simply connected polygon into a set of convex quadrilaterals without inserting new boundary nodes. The presented approach consists in repeatedly removing quadrilaterals from the polygon. Theoretical results pertaining to quadrangulation of simply connected polygons are derived from the usual 2-ear theorem. It produces a quadrangulation technique with O(n) number of quadrilaterals. The theoretical methodology is supplemented by practical results and CAD surface segmentation.

Keywords: Quadrangulation, simply connected, two-ear theorem.

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8035 An Efficient Method for Solving Multipoint Equation Boundary Value Problems

Authors: Ampon Dhamacharoen, Kanittha Chompuvised

Abstract:

In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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8034 The Differential Transform Method for Advection-Diffusion Problems

Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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8033 HPL-TE Method for Determination of Coatings Relative Total Emissivity Sensitivity Analysis of the Influences of Method Parameters

Authors: Z. Veselý, M. Honner

Abstract:

High power laser – total emissivity method (HPL-TE method) for determination of coatings relative total emissivity dependent on the temperature is introduced. Method principle, experimental and evaluation parts of the method are described. Computer model of HPL-TE method is employed to perform the sensitivity analysis of the effect of method parameters on the sample surface temperature in the positions where the surface temperature and radiation heat flux are measured.

Keywords: High temperature laser testing, measurement ofthermal properties, emissivity, coatings.

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8032 A New Iterative Method for Solving Nonlinear Equations

Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

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8031 Distributed Multi-Agent Based Approach on an Intelligent Transportation Network

Authors: Xiao Yihong, Yu Kexin, Burra Venkata Durga Kumar

Abstract:

With the accelerating process of urbanization, the problem of urban road congestion is becoming more and more serious. Intelligent transportation system combining distributed and artificial intelligence has become a research hotspot. As the core development direction of the intelligent transportation system, Cooperative Intelligent Transportation System (C-ITS) integrates advanced information technology and communication methods and realizes the integration of human, vehicle, roadside infrastructure and other elements through the multi-agent distributed system. By analyzing the system architecture and technical characteristics of C-ITS, the paper proposes a distributed multi-agent C-ITS. The system consists of Roadside Subsystem, Vehicle Subsystem and Personal Subsystem. At the same time, we explore the scalability of the C-ITS and put forward incorporating local rewards in the centralized training decentralized execution paradigm, hoping to add a scalable value decomposition method. In addition, we also suggest introducing blockchain to improve the safety of the traffic information transmission process. The system is expected to improve vehicle capacity and traffic safety.

Keywords: Distributed system, artificial intelligence, multi-agent, Cooperative Intelligent Transportation System.

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8030 Multi-level Metadata Integration System: XML, RDF and RuleML

Authors: Messaouda Fareh, Omar Boussaid, Rachid Challal

Abstract:

Our work is part of the heterogeneous data integration, with the definition of a structural and semantic mediation model. Our aim is to propose architecture for the heterogeneous sources metadata mediation, represented by XML, RDF and RuleML models, providing to the user the metadata transparency. This, by including data structures, of natures fundamentally different, and allowing the decomposition of a query involving multiple sources, to queries specific to these sources, then recompose the result.

Keywords: Mediator, Metadata, Query, RDF, RuleML, XML, Xquery.

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8029 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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8028 Spread Spectrum Image Watermarking for Secured Multimedia Data Communication

Authors: Tirtha S. Das, Ayan K. Sau, Subir K. Sarkar

Abstract:

Digital watermarking is a way to provide the facility of secure multimedia data communication besides its copyright protection approach. The Spread Spectrum modulation principle is widely used in digital watermarking to satisfy the robustness of multimedia signals against various signal-processing operations. Several SS watermarking algorithms have been proposed for multimedia signals but very few works have discussed on the issues responsible for secure data communication and its robustness improvement. The current paper has critically analyzed few such factors namely properties of spreading codes, proper signal decomposition suitable for data embedding, security provided by the key, successive bit cancellation method applied at decoder which have greater impact on the detection reliability, secure communication of significant signal under camouflage of insignificant signals etc. Based on the analysis, robust SS watermarking scheme for secure data communication is proposed in wavelet domain and improvement in secure communication and robustness performance is reported through experimental results. The reported result also shows improvement in visual and statistical invisibility of the hidden data.

Keywords: Spread spectrum modulation, spreading code, signaldecomposition, security, successive bit cancellation

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8027 Application of Seismic Wave Method in Early Estimation of Wencheng Earthquake

Authors: Wenlong Liu, Yucheng Liu

Abstract:

This paper introduces the application of seismic wave method in earthquake prediction and early estimation. The advantages of the seismic wave method over the traditional earthquake prediction method are demonstrated. An example is presented in this study to show the accuracy and efficiency of using the seismic wave method in predicting a medium-sized earthquake swarm occurred in Wencheng, Zhejiang, China. By applying this method, correct predictions were made on the day after this earthquake swarm started and the day the maximum earthquake occurred, which provided scientific bases for governmental decision-making.

Keywords: earthquake prediction, earthquake swarm, seismicactivity method, seismic wave method, Wencheng earthquake

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8026 Analytical Solutions of Kortweg-de Vries(KdV) Equation

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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8025 Some Results on Preconditioned Modified Accelerated Overrelaxation Method

Authors: Guangbin Wang, Deyu Sun, Fuping Tan

Abstract:

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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8024 An Active Set Method in Image Inpainting

Authors: Marrick Neri, Esmeraldo Ronnie Rey Zara

Abstract:

In this paper, we apply a semismooth active set method to image inpainting. The method exploits primal and dual features of a proposed regularized total variation model, following after the technique presented in [4]. Numerical results show that the method is fast and efficient in inpainting sufficiently thin domains.

Keywords: Active set method, image inpainting, total variation model.

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8023 Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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8022 Application of He’s Parameter-Expansion Method to a Coupled Van Der Pol oscillators with Two Kinds of Time-delay Coupling

Authors: Mohammad Taghi Darvishi, Samad Kheybari

Abstract:

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.

Keywords: Parameter-expansion method, coupled van der pol oscillator, time-delay system.

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8021 Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method

Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: Dynamical diffraction, hologram, object image, X-ray holography.

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8020 Gas Turbine Optimal PID Tuning by Genetic Algorithm using MSE

Authors: R. Oonsivilai, A. Oonsivilai

Abstract:

Realistic systems generally are systems with various inputs and outputs also known as Multiple Input Multiple Output (MIMO). Such systems usually prove to be complex and difficult to model and control purposes. Therefore, decomposition was used to separate individual inputs and outputs. A PID is assigned to each individual pair to regulate desired settling time. Suitable parameters of PIDs obtained from Genetic Algorithm (GA), using Mean of Squared Error (MSE) objective function.

Keywords: Gas Turbine, PID, Genetic Algorithm, Transfer function.Mean of Squared Error

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8019 Steepest Descent Method with New Step Sizes

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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