Search results for: nonlinear partial differential equation.

Authors: Ammar Anwar Khan, Nissar R. Wani, Nazar Malik, Abdulrehman Al-Arainy, and Saad Alghuwainem

Abstract:

Power cables are vulnerable to failure due to aging or defects that occur with the passage of time under continuous operation and loading stresses. PD detection and characterization provide information on the location, nature, form and extent of the degradation. As a result, PD monitoring has become an important part of condition based maintenance (CBM) program among power utilities. Online partial discharge (PD) localization of defect sources in power cable system is possible using the time of flight method. The information regarding the time difference between the main and reflected pulses and cable length can help in locating the partial discharge source along the cable length. However, if the length of the cable is not known and the defect source is located at the extreme ends of the cable or in the middle of the cable, then double ended measurement is required to indicate the location of PD source. Use of multiple sensors can also help in discriminating the cable PD or local/ external PD. This paper presents the experience and results from online partial discharge measurements conducted in the laboratory and the challenges in partial discharge source localization.

Keywords: Power cables, partial discharge localization, HFCT, condition based monitoring.

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Ch. Surawut, D. Sukawat

Abstract:

In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. This equation provides downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: Dynamic Equation, Downscaling, Inverse distance weight interpolation.

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Authors: Kyoung Hoon Kim

Abstract:

A thermodynamic analysis of a partial evaporating Rankine cycle with regeneration using zeotropic ammonia-water mixture as a working fluid is presented in this paper. The thermodynamic laws were applied to evaluate the system performance. Based on the thermodynamic model, the effects of the vapor quality and the ammonia mass fraction on the system performance were extensively investigated. The results showed that thermal efficiency has a peak value with respect to the vapor quality as well as the ammonia mass fraction. The partial evaporating ammonia based Rankine cycle has a potential to improve recovery of low-grade finite heat source.

Keywords: Ammonia-water, Rankine cycle, partial evaporating, thermodynamic performance.

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

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This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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Authors: Leila Vafajoo, Farhad Khorasheh, Mehrnoosh Hamzezadeh Nakhjavani, Moslem Fattahi

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In the present study, a procedure was developed to determine the optimum reaction rate constants in generalized Arrhenius form and optimized through the Nelder-Mead method. For this purpose, a comprehensive mathematical model of a fixed bed reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3 catalyst was developed. Utilizing appropriate kinetic rate expressions for the main dehydrogenation reaction as well as side reactions and catalyst deactivation, a detailed model for the radial flow reactor was obtained. The reactor model composed of a set of partial differential equations (PDE), ordinary differential equations (ODE) as well as algebraic equations all of which were solved numerically to determine variations in components- concentrations in term of mole percents as a function of time and reactor radius. It was demonstrated that most significant variations observed at the entrance of the bed and the initial olefin production obtained was rather high. The aforementioned method utilized a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method was demonstrated by comparing the predicted values of the kinetic constants using the proposed method with a series of experimental values reported in the literature for different systems.

Keywords: Dehydrogenation, Pt-Sn/Al2O3 Catalyst, Modeling, Nelder-Mead, Optimization

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

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In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: M.V Rajesh, Archana R, A Unnikrishnan, R Gopikakumari, Jeevamma Jacob

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The System Identification problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a performance function based on error between the given process output and identified process output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems. The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5]. The work reported here is an attempt to implement few of the well known algorithms in the context of modeling of nonlinear systems, and to make a performance comparison to establish the relative merits and demerits.

Keywords: Multilayer neural networks, Radial Basis Functions, Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.

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Authors: B. Mukanova, N. Glazyrina, S. Glazyrin

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The formulated problem of optimization of the technological process of water treatment for thermal power plants is considered in this article. The problem is of multiparametric nature. To optimize the process, namely, reduce the amount of waste water, a new technology was developed to reuse such water. A mathematical model of the technology of wastewater reuse was developed. Optimization parameters were determined. The model consists of a material balance equation, an equation describing the kinetics of ion exchange for the non-equilibrium case and an equation for the ion exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion exchange. A direct problem of calculating the impurity concentration at the outlet of the water treatment plant was numerically solved. The direct problem was approximated by an implicit point-to-point computation difference scheme. The inverse problem was formulated as relates to determination of the parameters of the mathematical model of the water treatment plant operating in non-equilibrium conditions. The formulated inverse problem was solved. Following the results of calculation the time of start of the filter regeneration process was determined, as well as the period of regeneration process and the amount of regeneration and wash water. Multi-parameter optimization of water treatment process for thermal power plants allowed decreasing the amount of wastewater by 15%.

Keywords: Direct problem, multiparametric optimization, optimization parameters, water treatment.

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Authors: Marzieh Dosti, Alireza Nazemi

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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: Meng Hu, Lili Wang

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In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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Authors: Guang Zeng, Jin Huang, Zicai Li

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In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

Keywords: Finite-difference equation, computational stability, hirt method.

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Authors: Hafiz Muhammad Obaid, Umais Tayyab, Shabbir Majeed Ch.

Abstract:

In this paper, a CMOS differential operational transresistance amplifier (OTRA) is presented. The amplifier is designed and implemented in a standard umc90-nm CMOS technology. The differential OTRA provides wider bandwidth at high gain. It also shows much better rise and fall time and exhibits a very good input current dynamic range of 50 to 50 μA. The OTRA can be used in many analog VLSI applications. The presented amplifier has high gain bandwidth product of 617.6 THz Ω. The total power dissipation of the presented amplifier is also very low and it is 0.21 mW.

Keywords: CMOS, differential, operational transresistance amplifier, OTRA, 90 nm, VLSI.

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Authors: C. Sinescu, M. Negrutiu, M. Romînu, C. Haiduc, E. Petrescu, M. Leretter, A.G. Podoleanu

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Optical Coherence Tomography (OCT) combined with the Confocal Microscopy, as a noninvasive method, permits the determinations of materials defects in the ceramic layers depth. For this study 256 anterior and posterior metal and integral ceramic fixed partial dentures were used, made with Empress (Ivoclar), Wollceram and CAD/CAM (Wieland) technology. For each investigate area 350 slices were obtain and a 3D reconstruction was perform from each stuck. The Optical Coherent Tomography, as a noninvasive method, can be used as a control technique in integral ceramic technology, before placing those fixed partial dentures in the oral cavity. The purpose of this study is to evaluate the capability of En face Optical Coherence Tomography (OCT) combined with a fluorescent method in detection and analysis of possible material defects in metalceramic and integral ceramic fixed partial dentures. As a conclusion, it is important to have a non invasive method to investigate fixed partial prostheses before their insertion in the oral cavity in order to satisfy the high stress requirements and the esthetic function.

Keywords: Ceramic Fixed Partial Dentures, Material Defects, En face Optical Coherence Tomography, Fluorescence.

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Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang

Abstract:

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: KLMS, online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS.

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Authors: G. Zahedi, H. Yaghoobi

Abstract:

Modeling of a heterogeneous industrial fixed bed reactor for selective dehydrogenation of heavy paraffin with Pt-Sn- Al2O3 catalyst has been the subject of current study. By applying mass balance, momentum balance for appropriate element of reactor and using pressure drop, rate and deactivation equations, a detailed model of the reactor has been obtained. Mass balance equations have been written for five different components. In order to estimate reactor production by the passage of time, the reactor model which is a set of partial differential equations, ordinary differential equations and algebraic equations has been solved numerically. Paraffins, olefins, dienes, aromatics and hydrogen mole percent as a function of time and reactor radius have been found by numerical solution of the model. Results of model have been compared with industrial reactor data at different operation times. The comparison successfully confirms validity of proposed model.

Keywords: Dehydrogenation, fixed bed reactor, modeling, linear alkyl benzene.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

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Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: R.Marsalek

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (ν ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ν <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: ferro-precipitate, adsorption, SDS, zeta potential

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: Channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow.

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Authors: Prasanta Kundu, N.K. Kishore, A.K. Sinha

Abstract:

Insulation used in transformer is mostly oil pressboard insulation. Insulation failure is one of the major causes of catastrophic failure of transformers. It is established that partial discharges (PD) cause insulation degradation and premature failure of insulation. Online monitoring of PDs can reduce the risk of catastrophic failure of transformers. There are different techniques of partial discharge measurement like, electrical, optical, acoustic, opto-acoustic and ultra high frequency (UHF). Being non invasive and non interference prone, acoustic emission technique is advantageous for online PD measurement. Acoustic detection of p.d. is based on the retrieval and analysis of mechanical or pressure signals produced by partial discharges. Partial discharges are classified according to the origin of discharges. Their effects on insulation deterioration are different for different types. This paper reports experimental results and analysis for classification of partial discharges using acoustic emission signal of laboratory simulated partial discharges in oil pressboard insulation system using three different electrode systems. Acoustic emission signal produced by PD are detected by sensors mounted on the experimental tank surface, stored on an oscilloscope and fed to computer for further analysis. The measured AE signals are analyzed using discrete wavelet transform analysis and wavelet packet analysis. Energy distribution in different frequency bands of discrete wavelet decomposed signal and wavelet packet decomposed signal is calculated. These analyses show a distinct feature useful for PD classification. Wavelet packet analysis can sort out any misclassification arising out of DWT in most cases.

Keywords: Acoustic emission, discrete wavelet transform, partial discharge, wavelet packet analysis.

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Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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Authors: Şaban Çetin, Özgür Demir

Abstract:

In this study, Fuzzy PID Control scheme is designed for an active suspension system. The main goal of an active suspension system for using in a vehicle model is reducing body deflections and handling high comfort for a passenger car. The present system was modelled as a two-degree-of-freedom (2-DOF) nonlinear vehicle model.

Keywords: Active suspension system, Fuzzy PID controller, a nonlinear quarter car model.

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Authors: Sewon Kim, Changyeop Lee, Minjun Kwon

Abstract:

A noble low NOx combustion technology, based on partial oxidation combustion concept in a fuel rich combustion zone, is successfully applied in this research. The burner is designed such that a portion of fuel is heated and pre-vaporized in the furnace then injected into a fuel rich combustion zone so that a partial oxidation reaction occurs. The effects of equivalence ratio, thermal load, and fuel distribution ratio on the emissions of NOx and CO are experimentally investigated. This newly developed combustion technology showed very low NOx emission level, about 12 ppm, when light oil is used as a fuel.

Keywords: Burner, low NOx, liquid fuel, partial oxidation, fuel rich.

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Authors: Fadi Awawdeh, H.M. Jaradat

Abstract:

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

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