Search results for: direct power control

Authors: U. Amin, A. Talib, S. A. Qureshi, M. J. Hossain, G. Ahmad

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The choice evaluation between oil-immersed and dry-type transformers is often controlled by cost, location, and application. This paper compares the electrical performance of liquid- filled and dry-type transformers, which will assist the customer to choose the right and efficient ones for particular applications. An accurate assessment of the time-average flux density, electric field intensity and voltage distribution in an oil-insulated and a dry-type transformer have been computed and investigated. The detailed transformer modeling and analysis has been carried out to determine electrical parameter distributions. The models of oil-immersed and dry-type transformers are developed and solved by using the finite element method (FEM) to compare the electrical parameters. The effects of non-uniform and non-coherent voltage gradient, flux density and electric field distribution on the power losses and insulation properties of transformers are studied in detail. The results show that, for the same voltage and kilo-volt-ampere (kVA) rating, oil-immersed transformers have better insulation properties and less hysteresis losses than the dry-type.

Keywords: Finite element method, flux density, transformer, voltage gradient.

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Authors: José R. G. Braga, Joice B. Mendes, Guilherme H. Caponetto, Alexandre C. B. Ramos

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With major technological advances and to reduce the cost of training apprentices for real-time critical systems, it was necessary the development of Intelligent Tutoring Systems for training apprentices in these systems. These systems, in general, have interactive features so that the learning is actually more efficient, making the learner more familiar with the mechanism in question. In the home stage of learning, tests are performed to obtain the student's income, a measure on their use. The aim of this paper is to present a framework to model an Intelligent Tutoring Systems using the UML language. The various steps of the analysis are considered the diagrams required to build a general model, whose purpose is to present the different perspectives of its development.

Keywords: Computer based training, Hypermedia, Software modeling.

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Authors: Houda Najeh, Stéphane Ploix, Mahendra Pratap Singh, Karim Chabir, Mohamed Naceur Abdelkrim

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Building systems are highly vulnerable to different kinds of faults and failures. In fact, various faults, failures and human behaviors could affect the building performance. This paper tackles the detection of unreliable sensors in buildings. Different literature surveys on diagnosis techniques for sensor grids in buildings have been published but all of them treat only bias and outliers. Occurences of data gaps have also not been given an adequate span of attention in the academia. The proposed methodology comprises the automatic thresholding for data gap detection for a set of heterogeneous sensors in instrumented buildings. Sensor measurements are considered to be regular time series. However, in reality, sensor values are not uniformly sampled. So, the issue to solve is from which delay each sensor become faulty? The use of time series is required for detection of abnormalities on the delays. The efficiency of the method is evaluated on measurements obtained from a real power plant: an office at Grenoble Institute of technology equipped by 30 sensors.

Keywords: Building system, time series, diagnosis, outliers, delay, data gap.

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Authors: M.Pourmahmoud, M.Salmanzadeh, M.Mehrani, M.R.Isvandzibaei

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In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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Authors: A. A. Shafie, M. F. Alias, M. H. Ali

Abstract:

The main objective of this project is to build an autonomous microcontroller-based mobile robot for a local robot soccer competition. The black competition field is equipped with white lines to serve as the guidance path for competing robots. Two prototypes of soccer robot embedded with the Basic Stamp II microcontroller have been developed. Two servo motors are used as the drive train for the first prototype whereas the second prototype uses two DC motors as its drive train. To sense the lines, lightdependent resistors (LDRs) supply the analog inputs for the microcontroller. The performances of both prototypes are evaluated. The DC motor-driven robot has produced better trajectory control over the one using servo motors and has brought the team into the final round.

Keywords: Soccer robot, Obstacle detection, Differential drive, Line following.

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Authors: S. Visetpotjanakit, N. Nakkaew

Abstract:

Determination of low level ⁹⁰Sr in seawater has been widely developed for the purpose of environmental monitoring and radiological research because ⁹⁰Sr is one of the most hazardous radionuclides released from atmospheric during the testing of nuclear weapons, waste discharge from the generation nuclear energy and nuclear accident occurring at power plants. A liquid extraction technique using bis-2-etylhexyl-phosphoric acid to separate and purify yttrium followed by Cherenkov counting using a liquid scintillation counter to determine ⁹⁰Y in secular equilibrium to ⁹⁰Sr was developed to monitor ⁹⁰Sr in the Asia Pacific Ocean. The analytical performance was validated for the accuracy, precision, and trueness criteria. Sr-90 determination in seawater using various low concentrations in a range of 0.01 – 1 Bq/L of 30 liters spiked seawater samples and 0.5 liters of IAEA-RML-2015-01 proficiency test sample was performed for statistical evaluation. The results had a relative bias in the range from 3.41% to 12.28%, which is below accepted relative bias of ± 25% and passed the criteria confirming that our analytical approach for determination of low levels of ⁹⁰Sr in seawater was acceptable. Moreover, the approach is economical, non-laborious and fast.

Keywords: Proficiency test, radiation monitoring, seawater, strontium determination.

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Authors: Bambang Ariantara, Nandy Putra, Rangga Aji Pamungkas

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The development of electric vehicle batteries have resulted in very high energy density lithium-ion batteries. However, this progress is accompanied by the risk of thermal runaway, which can result in serious accidents. Heat pipes are heat exchangers that are suitable to be applied in electric vehicle battery thermal management for their lightweight, compact size and do not require external power supply. This paper aims to examine experimentally a Flat Plate Loop Heat Pipe (FPLHP) performance as a heat exchanger in thermal management system of lithium-ion battery for electric vehicle application. The heat generation of the battery was simulated using a cartridge heater. Stainless steel screen mesh was used as the capillary wick. Distilled water, alcohol and acetone were used as working fluids with a filling ratio of 60%. It was found that acetone gives the best performance that produces thermal resistance of 0.22 W/°C with 50°C evaporator temperature at heat flux load of 1.61 W/cm2.

Keywords: Electric vehicle, flat plate loop heat pipe, lithium-ion battery, thermal management system.

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Authors: Sarit Rashkovits, Yael Livne

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The study investigates the relationship between education level, workplace learning behaviors, psychological empowerment and burnout in a sample of 191 teachers. We hypothesized that education level will positively affect psychological state of increased empowerment and decreased burnout, and we purposed that these effects will be mediated by workplace learning behaviors. We used multiple regression analyses to test the model that included also the 6 following control variables: The teachers' age, gender, and teaching tenure; the schools' religious level, the pupils' needs: regular/ special needs, and the class level: elementary/ high school. The results support the purposed mediating model.

Keywords: Education level, Learning behaviors, Psychological empowerment, Burnout.

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Authors: M. Salmanpour, O. Nourani Zonouz

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In this research, a numerical simulation of an Electrohydrodynamic (EHD) actuator’s effects on the flow around a square cylinder by using a finite volume method has been investigated. This is one of the newest ways for controlling the fluid flows. Two plate electrodes are flush-mounted on the surface of the cylinder and one wire electrode is placed on the line with zero angle of attack relative to the stagnation point and excited with DC power supply. The discharge produces an electric force and changes the local momentum behaviors in the fluid layers. For this purpose, after selecting proper domain and boundary conditions, the electric field relating to the problem has been analyzed and then the results in the form of electrical body force have been entered in the governing equations of fluid field (Navier-Stokes equations). The effect of ionic wind resulted from the Electrohydrodynamic actuator, on the velocity, pressure and the wake behind cylinder has been considered. According to the results, it is observed that the fluid flow accelerates in the nearest wall of the frontal half of the cylinder and the pressure difference between frontal and hinder cylinder is increased.

Keywords: CFD, corona discharge, electro hydrodynamics, flow around square cylinders.

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Authors: N. Phattanakulkaewmorie, T. Paseephol, A.Moongngarm

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This study investigated the effect of germination on chemical compositions, physio-chemical properties of malted (germinated) red sorghum flours and evaluated characteristics of gluten free breads from sorghum flour. Results showed that germinated sorghum flour had higher amylase activity, swelling power and solubility at 95°C, but lower in the peak, break down, final and set back viscosities than ungerminated sample (p≤0.05). Five gluten free breads made from sorghum flour blends, with different ratios of ungerminated and germinated sorghum flour, were compared for the physical properties with those made from wheat flour. Crumb hardness, cohesiveness, gumminess and chewiness of sorghum breads were found significantly higher than those of wheat bread. With increasing of ungerminated flour proportion, the bread hardness increased while the cohesiveness declined. Sorghum breads appeared red to human eyes with a*values of 10.41-15.77.Their crust and crumb colors differed significantly from those of wheat bread.

Keywords: Flour, germination, gluten free bread, sorghum.

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Authors: Tomi Roinila, Aki Taskinen, Matti Vilkko

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Switched-mode converters play now a significant role in modern society. Their operation are often crucial in various electrical applications affecting the every day life. Therefore, the quality of the converters needs to be reliably verified. Recent studies have shown that the converters can be fully characterized by a set of frequency responses which can be efficiently used to validate the proper operation of the converters. Consequently, several methods have been proposed to measure the frequency responses fast and accurately. Most often correlation-based techniques have been applied. The presented measurement methods are highly sensitive to external errors and system nonlinearities. This fact has been often forgotten and the necessary uncertainty analysis of the measured responses has been neglected. This paper presents a simple approach to analyze the noise and nonlinearities in the frequency-response measurements of switched-mode converters. Coherence analysis is applied to form a confidence interval characterizing the noise and nonlinearities involved in the measurements. The presented method is verified by practical measurements from a high-frequency switchedmode converter.

Keywords: Switched-mode converters, Frequency analysis, CoherenceAnalysis.

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Authors: L. Al-Mulla, N. R. Bhat, M. Khalil

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A study was conducted in greenhouse environment to determine the response of five tissue-cultured date palm cultivars, Al- Ahamad, Nabusaif, Barhee, Khalas, and Kasab to irrigation water salinity of 1.6, 5, 10, or 20 dS/ m. The salinity level of 1.6dS/m, was used as a control. The effects of high salinity on plant survival were manifested at 360 days after planting (DAP) onwards. Three cultivars, Khalas, Kasab and Barhee were able to tolerate 10 dS/m salinity level at 24 months after the start of study. Khalas tolerated the highest salinity level of 20 dS/ m and 'Nabusaif' was found to be the least tolerant cv. The average heights of palms and the number of fronds were decreased with increasing salinity levels as time progressed.

Keywords: Acclimatization, Irrigation water salinity, Kuwait, Land degradation.

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Authors: K. Benamrane, T. Abdelkrim, T. Benslimane, Aeh. Benkhelifa, B. Bezza

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This paper presents a comparison between two Pulse Width Modulation (PWM) algorithms applied to a three-level Neutral Point Clamped (NPC) Voltage Source Inverter (VSI). The first algorithm applied is the triangular-sinusoidal strategy; the second is the Space Vector Pulse Width Modulation (SVPWM) strategy. In the first part, we present a topology of three-level NCP VSI. After that, we develop the two PWM strategies to control this converter. At the end the experimental results are presented.

Keywords: Multilevel inverter, Space vector pulse width modulation (SVPWM), triangular-sinusoidal strategy.

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Authors: Jianbo Hu, Hongbao Wang

Abstract:

The widely used Total Variation de-noising algorithm can preserve sharp edge, while removing noise. However, since fixed regularization parameter over entire image, small details and textures are often lost in the process. In this paper, we propose a modified Total Variation algorithm to better preserve smaller-scaled features. This is done by allowing an adaptive regularization parameter to control the amount of de-noising in any region of image, according to relative information of local feature scale. Experimental results demonstrate the efficient of the proposed algorithm. Compared with standard Total Variation, our algorithm can better preserve smaller-scaled features and show better performance.

Keywords: Adaptive, de-noising, feature scale, regularizationparameter, Total Variation.

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Authors: Ane Larrea, Victor Sebastian, Manuel Arruebo, Jesus Santamaria

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We present a gas-liquid microfluidic system as a reactor to obtain magnetite nanoparticles with an excellent degree of control regarding their crystalline phase, shape and size. Several types of microflow approaches were selected to prevent nanomaterial aggregation and to promote homogenous size distribution. The selected reactor consists of a mixer stage aided by ultrasound waves and a reaction stage using a N2-liquid segmented flow to prevent magnetite oxidation to non-magnetic phases. A milli-fluidic reactor was developed to increase the production rate where a magnetite throughput close to 450 mg/h in a continuous fashion was obtained.

Keywords: Microfluidics, magnetic nanoparticles, continuous production, nanomaterials.

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Authors: Eric Kojo Wu Aikins

Abstract:

This paper contributes to the debate on the proximate causes of climate change. Also, it discusses the impact of the global temperature increases since the beginning of the twentieth century and the effectiveness of climate change models in isolating the primary cause (anthropogenic influences or natural variability in temperature) of the observed temperature increases that occurred within this period. The paper argues that if climate scientist and policymakers ignore the anthropogenic influence (greenhouse gases) on global warming on the pretense of lack of agreement among various climate models and their inability to account for all the necessary factors of global warming at all levels the current efforts of greenhouse emissions control and global warming as a whole could be exacerbated.

Keywords: Anthropogenic Effects, Arctic, Climate Change, Natural Variability.

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Authors: Moon-Tak Oh, Kyung-Min Park, Tae-Eun Yoon, Hoon Choi, Chil-Woo Lee

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This paper is about middleware which enables group-user applications on mobile devices in physical proximity to interact with other devices without intervention of a central server. Requirements of the middleware are identified from service usage scenarios, and the functional architecture of the middleware is specified. These requirements include Group Management, Synchronization, and Resource Management. Group Management needs to provide various capabilities to such applications with respect to managing multiple users (e.g., creation of groups, discovery of group or individual users, member join/leave, election of a group manager and service-group association) using D2D communication technology. We designed the middleware for the above requirements on the Android platform.

Keywords: Group user, middleware, mobile service, physical proximity.

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Authors: Helena Vomackova

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This contribution examines the relationship between the family environment and the level of young pupils’ scholastic success. It comments on the partial results of a research probe carried out in the year 2012 on a sample of 412 Czech Republic primary school pupils of the fourth, fifth and sixths forms within the Project IGA 43 201 15 0004 01. The key links of this project were monitored in relation to the highest education level achieved by the learners´ parents, as well as to the type of family it is (in particular its ability to function), to component factors specific to the family climate (their willingness to share information, communication, parental control) and, finally, to the number of children in the family as an important socialization constituent.

Keywords: Family environment factors, scholastic success, parents’ education, family type, family climate.

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Authors: Sumit Kumar, Sunil Kumar, Chandan Deep Singh

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This paper presents modeling and simulation of flexible robot in an underwater environment. The underwater environment completely contrasts with ground or space environment. The robot in an underwater situation is subjected to various dynamic forces like buoyancy forces, hydrostatic and hydrodynamic forces. The underwater robot is modeled as Rayleigh beam. The developed model further allows estimating the deflection of tip in two directions. The complete dynamics of the underwater robot is analyzed, which is the main focus of this investigation. The control of robot trajectory is not discussed in this paper. Simulation is performed using Symbol Shakti software.

Keywords: Bond graph modeling, dynamics. modeling, Rayleigh beam, underwater robot.

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Authors: Gabriele Cecchetti, Anna Lina Ruscelli, Filippo Cugini, Piero Castoldi

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European Rail Traffic Management System (ERTMS) is the European reference for interoperable and safer signaling systems to efficiently manage trains running. If implemented, it allows trains cross seamlessly intra-European national borders. ERTMS has defined a secure communication protocol, EURORADIO, based on open communication networks. Its RadioInfill function can improve the reaction of the signaling system to changes in line conditions, avoiding unnecessary braking: its advantages in terms of power saving and travel time has been analyzed. In this paper a software implementation of the EURORADIO protocol with RadioInfill for ERTMS Level 1 using GSM-R is illustrated as part of the SR-Secure Italian project. In this building-blocks architecture the EURORADIO layers communicates together through modular Application Programm Interfaces. Security coding rules and railway industry requirements specified by EN 50128 standard have been respected. The proposed implementation has successfully passed conformity tests and has been tested on a computer-based simulator.

Keywords: ERTMS, ETCS signalling, EURORADIO protocol, radio infill function.

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Authors: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim

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In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.

Keywords: Smart Hybrid Powerpack (SHP), Electro Hydraulic Actuator (EHA), Permanent Sensor fault tolerance, Sliding mode observer (SMO), Graphic User Interface (GUI).

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Authors: F. Sarabchi, A. H. Darvishan, H. Yeganeh, H. Ahmadian

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Next generation networks with the idea of convergence of service and control layer in existing networks (fixed, mobile and data) and with the intention of providing services in an integrated network, has opened new horizon for telecom operators. On the other hand, economic problems have caused operators to look for new source of income including consider new services, subscription of more users and their promotion in using morenetwork resources and easy participation of service providers or 3rd party operators in utilizing networks. With this requirement, an architecture based on next generation objectives for service layer is necessary. In this paper, a new architecture based on IMS model explains participation of 3rd party operators in creation and implementation of services on an integrated telecom network.

Keywords: Service model, IMS, API, Scripting language, JAIN, Parlay.

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Authors: Ali Roozbahani, Aref Mardani, Roohollah Jokar, Hamid Taghavifar

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Evaluating and measuring the performance parameters of wheels and tillage equipments under controlled conditions obligates the use of soil bin facility. In this research designing, constructing and evaluating a single-wheel tester has been studied inside a soil bin. The tested wheel was directly driven by the electric motor. Vertical load was applied by a power bolt on wheel. This tester can measure required draft force, the depth of tire sinkage, contact area between wheel and soil, and soil stress at different depths and in the both alongside and perpendicular to the direction of traversing. In order to evaluate the system preparation, traction force was measured by the connected S-shaped load cell as arms between the wheel-tester and carriage. Treatments of forward speed, slip, and vertical load at a constant pressure were investigated in a complete randomized block design. The results indicated that the traction force increased at constant wheel load. The results revealed that the maximum traction force was observed within the %15 of slip.

Keywords: Slip, single wheel-tester, soil bin, soil–machine, speed, traction.

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Authors: Clark Van Dam, Gagan Mirchandani

Abstract:

The Continuously Adaptive Mean-Shift (CamShift) algorithm, incorporating scene depth information is combined with the l1-minimization sparse representation based method to form a hybrid kernel and state space-based tracking algorithm. We take advantage of the increased efficiency of the former with the robustness to occlusion property of the latter. A simple interchange scheme transfers control between algorithms based upon drift and occlusion likelihood. It is quantified by the projection of target candidates onto a depth map of the 2D scene obtained with a low cost stereo vision webcam. Results are improved tracking in terms of drift over each algorithm individually, in a challenging practical outdoor multiple occlusion test case.

Keywords: CamShift, l1-minimization, particle filter, stereo vision, video tracking.

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Authors: Hen Friman

Abstract:

Various categories of aqueous solutions are discharged within residential, institutional, commercial, and industrial structures. To safeguard public health and preserve the environment, it is imperative to subject wastewater to treatment processes that eliminate pathogens (such as bacteria and viruses), nutrients (such as nitrogen and phosphorus), and other compounds. Failure to address untreated sewage accumulation can result in an array of adverse consequences. Israel exemplifies a special case in wastewater management. Appropriate wastewater treatment significantly benefits sectors such as agriculture, tourism, horticulture, and industry. Nevertheless, untreated sewage in settlements lacking proper sewage collection or transportation networks remains an ongoing and substantial threat. Notably, the process of wastewater treatment entails substantial energy consumption. Consequently, this study explores the integration of solar energy as a renewable power source within the wastewater treatment framework. By incorporating renewable energy sources into the process, costs can be minimized, and decentralized facilities can be established even in areas lacking adequate infrastructure for traditional treatment methods.

Keywords: Renewable energy, solar energy, decentralized facilities, wastewater treatment.

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Authors: S. P. Sharma, Som Nath Saha

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This paper presents the performance, based on exergy analysis of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater based on energy balance equations has been presented and the results obtained have been compared with that of a conventional flat-plate solar air heater. The double flow corrugated absorber solar air heater performs thermally better than the flat plate double flow and conventional flat-plate solar air heater under same operating conditions. However, the corrugated absorber leads to higher pressure drop thereby increasing pumping power. The results revealed that the energy and exergy efficiencies of double flow corrugated absorber solar air heater is much higher than conventional solar air heater with the concept involving of increase in heat transfer surface area and turbulence in air flow. The results indicate that the energy efficiency increases, however, exergy efficiency decreases with increase in mass flow rate.

Keywords: Corrugated absorber, double flow, exergy efficiency, solar air heater.

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Authors: Mahamed G.H. Omran, Andries P Engelbrecht, Ayed Salman

Abstract:

An end-member selection method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed in this paper. The algorithm uses the K-means clustering algorithm and a method of dynamic selection of end-members subsets to find the appropriate set of end-members for a given set of multispectral images. The proposed algorithm has been successfully applied to test image sets from various platforms such as LANDSAT 5 MSS and NOAA's AVHRR. The experimental results of the proposed algorithm are encouraging. The influence of different values of the algorithm control parameters on performance is studied. Furthermore, the performance of different versions of PSO is also investigated.

Keywords: End-members selection, multispectral satellite imagery, particle swarm optimization, spectral unmixing.

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Authors: A. R. Seifi

Abstract:

This work presents a new algorithm based on a combination of fuzzy (FUZ), Dynamic Programming (DP), and Genetic Algorithm (GA) approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The novel formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses fuzzy reasoning for sitting of capacitors in radial distribution feeders, DP for sizing and finally GA for finding the optimum shape of membership functions which are used in fuzzy reasoning stage. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem.

Keywords: Capacitor planning, Fuzzy logic method, Genetic Algorithm, Dynamic programming, Radial Distribution feeder

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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