Search results for: Low VoltageImpulse Method

Authors: Yan Lyu, Yiqun Pan, Zhizhong Huang

Abstract:

In the design stage of a new building, the energy model of this building is often required for the analysis of the performance on energy efficiency. In practice, a certain degree of geometric simplification should be done in the establishment of building energy models, since the detailed geometric features of a real building are hard to be described perfectly in most energy simulation engine, such as ESP-r, eQuest or EnergyPlus. Actually, the detailed description is not necessary when the result with extremely high accuracy is not demanded. Therefore, this paper analyzed the relationship between the error of the simulation result from building energy models and the geometric simplification of the models. Finally, the following two parameters are selected as the indices to characterize the geometric feature of in building energy simulation: the southward projected area and total side surface area of the building. Based on the parameterization method, the simplification from an arbitrary column building to a typical shape (a cuboid) building can be made for energy modeling. The result in this study indicates that no more than 7% prediction error of annual cooling/heating load will be caused by the geometric simplification for those buildings with the ratio of southward projection length to total perimeter of the bottom of 0.25~0.35, which means this method is applicable for building performance simulation.

Keywords: building energy model, simulation, geometric simplification, design, regression

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Authors: Khalid Al-Tahat, Khaled Zuhair Mahmoud, Ahmad Al-Mughrabi

Abstract:

This paper proposes a novel methodology for enabling debugging and tracing of production web applications without affecting its normal flow and functionality. This method of debugging enables developers and maintenance engineers to replace a set of existing resources such as images, server side scripts, cascading style sheets with another set of resources per web session. The new resources will only be active in the debug session and other sessions will not be affected. This methodology will help developers in tracing defects, especially those that appear only in production environments and in exploring the behaviour of the system. A realization of the proposed methodology has been implemented in Java.

Keywords: Live debugging, web application, web resources, inconsistent bugs, tracing.

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Authors: B. Marungsri, W. Onchantuek, A. Oonsivilai, T. Kulworawanichpong

Abstract:

This paper presents the simulation results of electric field and potential distributions along surface of silicone rubber polymer insulators under clean and various contamination conditions with/without water droplets. Straight sheds insulator having leakage distance 290 mm was used in this study. Two type of contaminants, playwood dust and cement dust, have been studied the effect of contamination on the insulator surface. The objective of this work is to comparison the effect of contamination on potential and electric field distributions along the insulator surface when water droplets exist on the insulator surface. Finite element method (FEM) is adopted for this work. The simulation results show that contaminations have no effect on potential distribution along the insulator surface while electric field distributions are obviously depended on contamination conditions.

Keywords: electric field distribution, potential distribution, silicone rubber polymer insulator, finite element method

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Authors: Nebi Gedik

Abstract:

Electroencephalography (EEG) investigations of the brain computer interfaces are based on the electrical signals resulting from neural activities in the brain. In this paper, it is offered a method for classifying motor imagery EEG signals. The suggested method classifies EEG signals into two classes using the wave atom transform, and the transform coefficients are assessed, creating the feature set. Classification is done with SVM and k-NN algorithms with and without feature selection. For feature selection t-test approaches are utilized. A test of the approach is performed on the BCI competition III dataset IIIa.

Keywords: motor imagery, EEG, wave atom transform, SVM, k-NN, t-test

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Authors: Yuichi Masukake, Yoshihisa Ishida

Abstract:

In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: Ilona I. Iatcheva, Rumena D. Stancheva, Mario Metodiev

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The paper deals with determination of electromagnetic and temperature field distribution of induction heating system used for pipe brazing. The problem is considered as coupled – time harmonic electromagnetic and transient thermal field. It has been solved using finite element method. The detailed maps of electromagnetic and thermal field distribution have been obtained. The good understanding of the processes in the considered system ensures possibilities for control, management and increasing the efficiency of the welding process.

Keywords: Electromagnetic field, temperature field, finiteelement method, induction heating, pipe brazing.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

In the real application of active control systems to mitigate the response of structures subjected to sever external excitations such as earthquake and wind induced vibrations, since the capacity of actuators is limited then the actuators saturate. Hence, in designing controllers for linear and nonlinear structures under sever earthquakes, the actuator saturation should be considered as a constraint. In this paper optimal design of active controllers for nonlinear structures by considering the actuator saturation has been studied. To this end a method has been proposed based on defining an optimization problem which considers the minimizing of the maximum displacement of the structure as objective when a limited capacity for actuator has been used as a constraint in optimization problem. To evaluate the effectiveness of the proposed method, a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of pre-stressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used as active control mechanism and algorithm. To enhance the efficiency of the controllers, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been found by using the Distributed Genetic Algorithm (DGA). According to the results it has been concluded that the proposed method has been effective in considering the actuator saturation in designing optimal controllers for nonlinear frames. Also it has been shown that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers for considering the actuator saturation.

Keywords: Active control, Actuator Saturation, Nonlinear, Optimization.

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Authors: S. Venkateswaran, C. Mallika Parveen

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The fluid flow and the properties of the hydraulic fluid inside a torque converter are the main topics of interest in this research. The primary goal is to investigate the applicability of various viscous fluids inside the torque converter. The Taguchi optimization method is adopted to analyse the fluid flow in a torque converter from a design perspective. Calculations are conducted in maximizing the pressure since greater the pressure, greater the torque developed. Using the values of the S/N ratios obtained, graphs are plotted. Computational Fluid Dynamics (CFD) analysis is also conducted.

Keywords: Hydraulic fluid, Taguchi's method, optimization, pressure, torque.

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Authors: Hussain Syed Asad, Richard Kwok Kit Yuen, Gongsheng Huang

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Real-time optimization has been considered an effective approach for improving energy efficient operation of heating, ventilation, and air-conditioning (HVAC) systems. In model-based real-time optimization, model mismatches cannot be avoided. When model mismatches are significant, the performance of the real-time optimization will be impaired and hence the expected energy saving will be reduced. In this paper, the model mismatches for chiller plant on real-time optimization are considered. In the real-time optimization of the chiller plant, simplified semi-physical or grey box model of chiller is always used, which should be identified using available operation data. To overcome the model mismatches associated with the chiller model, hybrid Genetic Algorithms (HGAs) method is used for online real-time training of the chiller model. HGAs combines Genetic Algorithms (GAs) method (for global search) and traditional optimization method (i.e. faster and more efficient for local search) to avoid conventional hit and trial process of GAs. The identification of model parameters is synthesized as an optimization problem; and the objective function is the Least Square Error between the output from the model and the actual output from the chiller plant. A case study is used to illustrate the implementation of the proposed method. It has been shown that the proposed approach is able to provide reliability in decision making, enhance the robustness of the real-time optimization strategy and improve on energy performance.

Keywords: Energy performance, hybrid adaptive modeling, hybrid genetic algorithms, real-time optimization, heating, ventilation, and air-conditioning.

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Authors: Seyed Hossein Iranmanesh, Zahra Mokhtari

Abstract:

Estimation time and cost of work completion in a project and follow up them during execution are contributors to success or fail of a project, and is very important for project management team. Delivering on time and within budgeted cost needs to well managing and controlling the projects. To dealing with complex task of controlling and modifying the baseline project schedule during execution, earned value management systems have been set up and widely used to measure and communicate the real physical progress of a project. But it often fails to predict the total duration of the project. In this paper data mining techniques is used predicting the total project duration in term of Time Estimate At Completion-EAC (t). For this purpose, we have used a project with 90 activities, it has updated day by day. Then, it is used regular indexes in literature and applied Earned Duration Method to calculate time estimate at completion and set these as input data for prediction and specifying the major parameters among them using Clem software. By using data mining, the effective parameters on EAC and the relationship between them could be extracted and it is very useful to manage a project with minimum delay risks. As we state, this could be a simple, safe and applicable method in prediction the completion time of a project during execution.

Keywords: Data Mining Techniques, Earned Duration Method, Earned Value, Estimate At Completion.

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Authors: F. Barzegar, M. H. Sheikhi

Abstract:

In the present work we model a Multiquantum Well structure Separate Absorption and Charge Multiplication Avalanche Photodiode (MQW-SACM-APD), while the Absorption region coincide with the MQW. We consider the nonuniformity of electric field using split-step method in active region. This model is based on the carrier rate equations in the different regions of the device. Using the model we obtain the photocurrent, and dark current. As an example, InGaAs/InP SACM-APD and MQW-SACM-APD are simulated. There is a good agreement between the simulation and experimental results.

Keywords: Avalanche Photodiode, Physical Model, MultiquantumWell, Split Step Method.

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Authors: Mehrnaz Najafi, Hassan Haghighi

Abstract:

Morgan-s refinement calculus (MRC) is one of the well-known methods allowing the formality presented in the program specification to be continued all the way to code. On the other hand, Object-Z (OZ) is an extension of Z adding support for classes and objects. There are a number of methods for obtaining code from OZ specifications that can be categorized into refinement and animation methods. As far as we know, only one refinement method exists which refines OZ specifications into code. However, this method does not have fine-grained refinement rules and thus cannot be automated. On the other hand, existing animation methods do not present mapping rules formally and do not support the mapping of several important constructs of OZ, such as all cases of operation expressions and most of constructs in global paragraph. In this paper, with the aim of providing an automatic path from OZ specifications to code, we propose an approach to map OZ specifications into their counterparts in MRC in order to use fine-grained refinement rules of MRC. In this way, having counterparts of our specifications in MRC, we can refine them into code automatically using MRC tools such as RED. Other advantages of our work pertain to proposing mapping rules formally, supporting the mapping of all important constructs of Object-Z, and considering dynamic instantiation of objects while OZ itself does not cover this facility.

Keywords: Formal method, Formal specification, Formalprogram development, Morgan's Refinement Calculus, Object-Z

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Authors: Jonghyun Park, Toan Nguyen Dinh, Gueesang Lee

Abstract:

In this paper, we present a novel approach to accurately detect text regions including shop name in signboard images with complex background for mobile system applications. The proposed method is based on the combination of text detection using edge profile and region segmentation using fuzzy c-means method. In the first step, we perform an elaborate canny edge operator to extract all possible object edges. Then, edge profile analysis with vertical and horizontal direction is performed on these edge pixels to detect potential text region existing shop name in a signboard. The edge profile and geometrical characteristics of each object contour are carefully examined to construct candidate text regions and classify the main text region from background. Finally, the fuzzy c-means algorithm is performed to segment and detected binarize text region. Experimental results show that our proposed method is robust in text detection with respect to different character size and color and can provide reliable text binarization result.

Keywords: Text detection, edge profile, signboard image, fuzzy clustering.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

Abstract:

Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Apurv Kulkarni, Shreyas Badave, B. Rajiv

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Non-parametric reliability technique is useful for assessment of reliability of systems for which failure rates are not available. This is useful when detection of malfunctioning of any component is the key purpose during ongoing operation of the system. The main purpose of the Heat Exchanger Cycle discussed in this paper is to provide hot water at a constant temperature for longer periods of time. In such a cycle, certain components play a crucial role and this paper presents an effective way to predict the malfunctioning of the components by determination of system reliability. The method discussed in the paper is feasible and this is clarified with the help of various test cases.

Keywords: Heat exchanger cycle, K-statistics, PID controller, system reliability.

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Authors: Wenhui Tang, Daorong Wang, Xia Huang, Xianwen Ran

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Based on the thermodynamic theory, the dependence of sublimation energy of metal on temperature and pressure is discussed, and the results indicate that the sublimation energy decreases linearly with the increase of temperature and pressure. Combined with this result, the blow-off impulse of aluminum induced by pulsed X-ray is simulated by smoothed particle hydrodynamics (SPH) method. The numerical results show that, while the change of sublimation energy with temperature and pressure is considered, the blow-off impulse of aluminum is larger than the case that the sublimation energy is assumed to be a constant.

Keywords: sublimation energy, blow-off impulse, pulsed X-ray, SPH method.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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Authors: Bao Thach Nguyen, Abbas Mohajerani

Abstract:

A typical flexible pavement structure consists of the surface, base, sub-base and subgrade soil. The loading traffic is transferred from the top layer with higher stiffness to the layer below with less stiffness. Under normal traffic loading, the behaviour of flexible pavement is very complex and can be predicted by using the repeated load triaxial test equipment in the laboratory. However, the nature of the repeated load triaxial testing procedure is considered time-consuming, complicated and expensive, and it is a challenge to carry out as a routine test in the laboratory. Therefore, the current paper proposes a numerical approach to simulate the repeated load triaxial test by employing the discrete element method. A sample with particle size ranging from 2.36mm to 19.0mm was constructed. Material properties, which included normal stiffness, shear stiffness, coefficient of friction, maximum dry density and particle density, were used as the input for the simulation. The sample was then subjected to a combination of deviator and confining stress and it was found that the discrete element method is able to simulate the repeated load triaxial test in the laboratory.

Keywords: Discrete element method, repeated load triaxial, pavement materials.

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Authors: Tohru Kawabe

Abstract:

In this paper, a 2DOF (two degrees of freedom) PID (Proportional-Integral-Derivative) controller based on MPC (Model predictive control) algorithm fo slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method aims to improve the safety and the stability of EVs under braking by controlling the wheel slip ration. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Model predictive control, PID controller, Two degrees of freedom, Electric Vehicle, Slip suppression.

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Authors: Vitalice K. Oduol, C. Ardil

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A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.

Keywords: bit error rate, block codes, code correlation matrix, eigenstructure, soft-decision decoding, weight vector.

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Authors: Ming-Hsiang Shih, Wen-Pei Sung, Shih-Heng Tung

Abstract:

The purposes of hydraulic gate are to maintain the functions of storing and draining water. It bears long-term hydraulic pressure and earthquake force and is very important for reservoir and waterpower plant. The high tensile strength of steel plate is used as constructional material of hydraulic gate. The cracks and rusts, induced by the defects of material, bad construction and seismic excitation and under water respectively, thus, the mechanics phenomena of gate with crack are probing into the cause of stress concentration, induced high crack increase rate, affect the safety and usage of hydroelectric power plant. Stress distribution analysis is a very important and essential surveying technique to analyze bi-material and singular point problems. The finite difference infinitely small element method has been demonstrated, suitable for analyzing the buckling phenomena of welding seam and steel plate with crack. Especially, this method can easily analyze the singularity of kink crack. Nevertheless, the construction form and deformation shape of some gates are three-dimensional system. Therefore, the three-dimensional Digital Image Correlation (DIC) has been developed and applied to analyze the strain variation of steel plate with crack at weld joint. The proposed Digital image correlation (DIC) technique is an only non-contact method for measuring the variation of test object. According to rapid development of digital camera, the cost of this digital image correlation technique has been reduced. Otherwise, this DIC method provides with the advantages of widely practical application of indoor test and field test without the restriction on the size of test object. Thus, the research purpose of this research is to develop and apply this technique to monitor mechanics crack variations of weld steel hydraulic gate and its conformation under action of loading. The imagines can be picked from real time monitoring process to analyze the strain change of each loading stage. The proposed 3-Dimensional digital image correlation method, developed in the study, is applied to analyze the post-buckling phenomenon and buckling tendency of welded steel plate with crack. Then, the stress intensity of 3-dimensional analysis of different materials and enhanced materials in steel plate has been analyzed in this paper. The test results show that this proposed three-dimensional DIC method can precisely detect the crack variation of welded steel plate under different loading stages. Especially, this proposed DIC method can detect and identify the crack position and the other flaws of the welded steel plate that the traditional test methods hardly detect these kind phenomena. Therefore, this proposed three-dimensional DIC method can apply to observe the mechanics phenomena of composite materials subjected to loading and operating.

Keywords: Welded steel plate, crack variation, three-dimensional Digital Image Correlation (DIC).

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Authors: Mohsen Ebrahimi, Milad M. Rabieh

Abstract:

In this paper, two very different optimization algorithms, Genetic and DIRECT algorithms, are used to history match a bottomhole pressure response for a reservoir with wellbore storage and skin with the best possible analytical model. No initial guesses are available for reservoir parameters. The results show that the matching process is much faster and more accurate for DIRECT method in comparison with Genetic algorithm. It is furthermore concluded that the DIRECT algorithm does not need any initial guesses, whereas Genetic algorithm needs to be tuned according to initial guesses.

Keywords: DIRECT algorithm, Genetic algorithm, Analytical modeling, History match

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Authors: Nataša Živić, Christoph Ruland

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Method of Parallel Joint Channel Coding and Cryptography has been analyzed and simulated in this paper. The method is an extension of Soft Input Decryption with feedback, which is used for improvement of channel decoding of secured messages. Parallel Joint Channel Coding and Cryptography results in improved coding gain of channel decoding, which achieves more than 2 dB. Such results are an implication of a combination of receiver components and their interoperability.

Keywords: Block length, Coding gain, Feedback, L-values, Parallel Joint Channel Coding and Cryptography, Soft Input Decryption.

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Authors: Kentaro Miyoko, Yoshihiko Mori, Yugo Ikeda, Yoshihiro Nishino, Yong-Bok Choi, Hiromi Okada

Abstract:

Optical burst switching (OBS) has been proposed to realize the next generation Internet based on the wavelength division multiplexing (WDM) network technologies. In the OBS, the burst contention is one of the major problems. The deflection routing has been designed for resolving the problem. However, the deflection routing becomes difficult to prevent from the burst contentions as the network load becomes high. In this paper, we introduce a flow rate control methods to reduce burst contentions. We propose new flow rate control methods based on the leaky bucket algorithm and deflection routing, i.e. separate leaky bucket deflection method, and dynamic leaky bucket deflection method. In proposed methods, edge nodes which generate data bursts carry out the flow rate control protocols. In order to verify the effectiveness of the flow rate control in OBS networks, we show that the proposed methods improve the network utilization and reduce the burst loss probability through computer simulations.

Keywords: Optical burst switching, OBS, flow rate control.

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Authors: T. Li, J.Y. Zhang, W.H. Zhang, M.H. Zhu

Abstract:

A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.

Keywords: Fluid-structure interaction, Navier-Stokes equation, Space-time finite element method, vortex-induced vibration.

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Authors: K. G. Firouzjah, A. Sheikholeslami

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The perfect operation of common Active Filters is depended on accuracy of identification system distortion. Also, using a suitable method in current injection and reactive power compensation, leads to increased filter performance. Due to this fact, this paper presents a method based on predictive current control theory in shunt active filter applications. The harmonics of the load current is identified by using o–d–q reference frame on load current and eliminating the DC part of d–q components. Then, the rest of these components deliver to predictive current controller as a Threephase reference current by using Park inverse transformation. System is modeled in discreet time domain. The proposed method has been tested using MATLAB model for a nonlinear load (with Total Harmonic Distortion=20%). The simulation results indicate that the proposed filter leads to flowing a sinusoidal current (THD=0.15%) through the source. In addition, the results show that the filter tracks the reference current accurately.

Keywords: Active filter, predictive current control, low pass filter, harmonic omitting, o–d–q reference frame.

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Authors: Takashi Sakai, Yuri Shimomura

Abstract:

The crystal orientation is a factor that affects the microscopic material properties. Crystal orientation determines the anisotropy of the polycrystalline material. And it is closely related to the mechanical properties of the material. In this paper, for pure copper polycrystalline material, two different methods; X-Ray Diffraction (XRD) and Electron Backscatter Diffraction (EBSD); and the crystal orientation were analyzed. In the latter method, it is possible that the X-ray beam diameter is thicker as compared to the former, to measure the crystal orientation macroscopically relatively. By measurement of the above, we investigated the change in crystal orientation and internal tissues of pure copper.

Keywords: Bending, electron backscatter diffraction, X-ray diffraction, microstructure, IPF map, orientation distribution function.

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Authors: Y. Galerkin, L. Marenina

Abstract:

Stator elements «Vane diffuser + crossover + return channel» of stages with different specific speed were investigated by CFD calculations. The regime parameter was introduced to present efficiency and loss coefficient performance of all elements together. Flow structure demonstrated advantages and disadvantages of design. Flow separation in crossovers was eliminated by its shape modification. Efficiency increased visibly. Calculated CFD performances are in acceptable correlation with predicted ones by engineering design method. The information obtained is useful for design method better calibration.

Keywords: Vane diffuser, return channel, crossover, efficiency, loss coefficient, inlet flow angle.

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Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani

Abstract:

A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.

Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam

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Authors: Irina Eglite, Andrei A. Kolyshkin

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The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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