Search results for: Complex technical system

Authors: Ye Wei, Sitalakshmi Venkatraman, Fahri Benli, Fiona Wahr

Abstract:

The present digital world poses many challenges to various stakeholders in the education sector. In particular, lecturers of higher education (HE) are faced with the problem of ensuring that students are able to achieve the required learning outcomes despite rapid changes taking place worldwide. Different strategies are adopted to retain student engagement and commitment in classrooms to address the differences in learning habits, preferences and styles of the digital generation of students recently. Further, with the onset of coronavirus disease (COVID-19) pandemic, online classroom has become the most suitable alternate mode of teaching environment to cope with lockdown restrictions. These changes have compounded the problems in the learning engagement and short attention span of HE students. New Agile methodologies that have been successfully employed to manage projects in different fields are gaining prominence in the education domain. In this paper, we present the application of Scrum as an agile methodology to enhance student learning and engagement in an online smart classroom environment. We demonstrate the use of our proposed approach using a case study to teach key topics in information technology that require students to gain technical and business-related data analytics skills.

Keywords: Agile methodology, Scrum, online learning, smart classroom environment, student engagement, active learning.

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Authors: Jinn-Yi Yeh, Tai-Hsi Wu

Abstract:

Hemodialysis patients might suffer from unhealthy care behaviors or long-term dialysis treatments. Ultimately they need to be hospitalized. If the hospitalization rate of a hemodialysis center is high, its quality of service would be low. Therefore, how to decrease hospitalization rate is a crucial problem for health care. In this study we combined temporal abstraction with data mining techniques for analyzing the dialysis patients' biochemical data to develop a decision support system. The mined temporal patterns are helpful for clinicians to predict hospitalization of hemodialysis patients and to suggest them some treatments immediately to avoid hospitalization.

Keywords: Hemodialysis, Temporal abstract, Data mining, Healthcare quality.

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Authors: M. Abdullah-Al-Wadud

Abstract:

Sensor-based Activity Recognition systems usually accounts which sensors have been activated to perform an activity. The system then combines the conditional probabilities of those sensors to represent different activities and takes the decision based on that. However, the information about the sensors which are not activated may also be of great help in deciding which activity has been performed. This paper proposes an approach where the sensory data related to both usage and non-usage of objects are utilized to make the classification of activities. Experimental results also show the promising performance of the proposed method.

Keywords: Naïve Bayesian-based classification, Activity recognition, sensor data, object-usage model.

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Authors: Kwok Tak Kit

Abstract:

The government and community have raised their awareness of the benefits of water reuse. Deforestation has a significant effect to climate change as it causes the drying out of the tropical rainforest and hence increases the chance of natural threaten the storage and supply of clean water. This paper focuses on discussion of the relationship of the natural water collection system, afforestation and country parks towards environmental sustainability and circular economy, with a case study of water conservation policy and strategy in Hong Kong and Singapore for further research.

Keywords: Afforestation, environmental sustainability, water conservation, circular economy, climate change.

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Authors: Chih-Hui Chiu, Chun-Hsien Lin

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In this study, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive output recurrent cerebellar model articulation control (AORCMAC) and H∞ control technique is proposed for wheeled inverted pendulums (WIPs) real-time control with exact system dynamics unknown. Moreover, a robust H∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. The experimental results indicate that the WIPs can stand upright stably when using the proposed RIBTC.

Keywords: Wheeled inverted pendulum, backsteppingtracking control, H∞ control, adaptive output recurrentcerebellar model articulation control.

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Authors: T. Denkçeken, M. Canpolat, Đ. Bassorgun, S. Yücel, M.A. Çiftçioğlu, M. Baykara Murat Canpolat , Tuba Denkçeken , Đbrahim Bassorgun , Selçuk Yücel , M. Akif Çiftçioğlu , Mehmet Baykara

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Elastic light single-scattering spectroscopy system with a single optical fiber probe was employed to differentiate cancerous prostate tissue from non-cancerous prostate tissue ex-vivo just after radical prostatectomy. First, ELSSS spectra were acquired from cancerous prostate tissue to define its spectral features. Then, spectra were acquired from normal prostate tissue to define difference in spectral features between the cancerous and normal prostate tissues. Of the total 66 tissue samples were evaluated from nine patients by ELSSS system. Comparing of histopathology results and ELSSS measurements revealed that sign of the spectral slopes of cancerous prostate tissue is negative and non-cancerous tissue is positive in the wavelength range from 450 to 750 nm. Based on the correlation between histopathology results and sign of the spectral slopes, ELSSS system differentiates cancerous prostate tissue from non- cancerous with a sensitivity of 0.95 and a specificity of 0.94.

Keywords: Diagnosis, prostatic neoplasm, prostatectomy, spectrum analysis

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Authors: Jameson McFarlane, Thorne J. McFarlane, Leon Bernard

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Social network sites (SNS) is an emerging phenomenon that is here to stay. The popularity and the ubiquity of the SNS technology are undeniable. Because most SNS are free and easy to use people from all walks of life and from almost any age are attracted to that technology. College age students are by far the largest segment of the population using SNS. Since most SNS have been adapted for mobile devices, not only do you find students using this technology in their study, while working on labs or on projects, a substantial number of students have been found to use SNS even while listening to lectures. This study found that SNS use has a significant negative impact on the grade point average of college students particularly in the first semester. However, this negative impact is greatly diminished by the end of the third semester partly because the students have adjusted satisfactorily to the challenges of college or because they have learned how to adequately manage their time. It was established that the kinds of activities the students are engaged in during the SNS use are the leading factor affecting academic performance. Of those activities, using SNS during a lecture or while studying is the foremost contributing factor to lower academic performance. This is due to “cognitive” or “information” bottleneck, a condition in which the students find it very difficult to multitask or to switch between resources leading to inefficiency in information retention and thus, educational performance.

Keywords: Social network sites, social network analysis, regression coefficient, psychological engagement.

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Authors: Mohammed Z. Khedher, Gheith A. Abandah, Ahmed M. Al-Khawaldeh

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Recognition of characters greatly depends upon the features used. Several features of the handwritten Arabic characters are selected and discussed. An off-line recognition system based on the selected features was built. The system was trained and tested with realistic samples of handwritten Arabic characters. Evaluation of the importance and accuracy of the selected features is made. The recognition based on the selected features give average accuracies of 88% and 70% for the numbers and letters, respectively. Further improvements are achieved by using feature weights based on insights gained from the accuracies of individual features.

Keywords: Arabic handwritten characters, Feature extraction, Off-line recognition, Optical character recognition.

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Authors: JooHyung Oh, Dongwan Kang, Sekwon Kim, ChaeTae Im

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Currently, there has been a 3G mobile networks data traffic explosion due to the large increase in the number of smartphone users. Unlike a traditional wired infrastructure, 3G mobile networks have limited wireless resources and signaling procedures for complex wireless resource management. And mobile network security for various abnormal and malicious traffic technologies was not ready. So Malicious or potentially malicious traffic originating from mobile malware infected smart devices can cause serious problems to the 3G mobile networks, such as DoS and scanning attack in wired networks. This paper describes the DoS security threat in the 3G mobile network and proposes a detection technology.

Keywords: 3G, WCDMA, DoS, Security Threat

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Authors: Pairaya J., Buddhagarn R., Sukree S., Punthumadee K.

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Application of Information Technology (IT) has revolutionized the functioning of business all over the world. Its impact has been felt mostly among the information of dependent industries. Tourism is one of such industry. The conceptual framework in this study represents an innovation of travel information searching system on mobile devices which is used as tools to deliver travel information (such as hotels, restaurants, tourist attractions and souvenir shops) for each user by travelers segmentation based on data mining technique to segment the tourists- behavior patterns then match them with tourism products and services. This system innovation is designed to be a knowledge incremental learning. It is a marketing strategy to support business to respond traveler-s demand effectively.

Keywords: Tourism, Innovation, Information Searching, Data Mining.

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Authors: Chaimaa Messaoudi, Rachida Fissoune, Hassan Badir

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Technological advances of computer science and data analysis are helping to provide continuously huge volumes of biological data, which are available on the web. Such advances involve and require powerful techniques for data integration to extract pertinent knowledge and information for a specific question. Biomedical exploration of these big data often requires the use of complex queries across multiple autonomous, heterogeneous and distributed data sources. Semantic integration is an active area of research in several disciplines, such as databases, information-integration, and ontology. We provide a survey of some approaches and techniques for integrating biological data, we focus on those developed in the ontology community.

Keywords: Semantic data integration, biological ontology, linked data, semantic web, OWL, RDF.

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Authors: Dilusha Weeraddana, Ashanie Gunathillake, Samiru Gayan

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In an emergency, combining Wireless Sensor Network's data with the knowledge gathered from various other information sources and navigation algorithms, could help safely guide people to a building exit while avoiding the risky areas. This paper presents an emergency response and navigation support architecture for data gathering, knowledge manipulation, and navigational support in an emergency situation. At normal state, the system monitors the environment. When an emergency event detects, the system sends messages to first responders and immediately identifies the risky areas from safe areas to establishing escape paths. The main functionalities of the system include, gathering data from a wireless sensor network which is deployed in a multi-story indoor environment, processing it with information available in a knowledge base, and sharing the decisions made, with first responders and people in the building. The proposed architecture will act to reduce risk of losing human lives by evacuating people much faster with least congestion in an emergency environment. 

Keywords: Emergency response, Firefighters, Navigation, Wireless sensor network.

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Authors: Ali Dinarveis

Abstract:

This paper compares the energy and exergy efficiency of a vapour compression refrigeration system using refrigerants of different groups. In this study, five different refrigerants including R507A, R134a, R114, R22 and R717 have been studied. EES Program is used to solve the thermodynamic equations. The results of this analysis are shown graphically. Based on the results, energy and exergy efficiencies for R717 are higher than the other refrigerants. Also, the energy and exergy efficiencies will be decreased with increasing the condensing temperature and decreasing the evaporating temperature.

Keywords: Energy, exergy, refrigeration, temperature, thermodynamic.

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Authors: Y.B.Gandole

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Compaction testing methods allow at-speed detecting of errors while possessing low cost of implementation. Owing to this distinctive feature, compaction methods have been widely used for built-in testing, as well as external testing. In the latter case, the bandwidth requirements to the automated test equipment employed are relaxed which reduces the overall cost of testing. Concurrent compaction testing methods use operational signals to detect misbehavior of the device under test and do not require input test stimuli. These methods have been employed for digital systems only. In the present work, we extend the use of compaction methods for concurrent testing of analog-to-digital converters. We estimate tolerance bounds for the result of compaction and evaluate the aliasing rate.

Keywords: Analog-to Digital Converter, Embedded system, Concurrent Testing

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Authors: M. Tarafdar Haque, A. Taheri

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Application of neural networks in execution of programmed pulse width modulation (PPWM) of a voltage source inverter (VSI) is studied in this paper. Using the proposed method it is possible to cancel out the desired harmonics in output of VSI in addition to control the magnitude of fundamental harmonic, contineously. By checking the non-trained values and a performance index, the most appropriate neural network is proposed. It is shown that neural networks may solve the custom difficulties of practical utilization of PPWM such as large size of memory, complex digital circuits and controlling the magnitude of output voltage in a discrete manner.

Keywords: Neural Network, Inverter, PPWM.

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Authors: Hongmin Deng, Qionghua Wang

Abstract:

A modified two dimensional (2D) logistic map based on cross feedback control is proposed. This 2D map exhibits more random chaotic dynamical properties than the classic one dimensional (1D) logistic map in the statistical characteristics analysis. So it is utilized as the pseudo-random (PN) sequence generator, where the obtained real-valued PN sequence is quantized at first, then applied to radio frequency identification (RFID) communication system in this paper. This system is experimentally validated on a cortex-M₀ development board, which shows the effectiveness in key generation, the size of key space and security. At last, further cryptanalysis is studied through the test suite in the National Institute of Standards and Technology (NIST).

Keywords: Chaos encryption, logistic map, pseudo-random sequence, RFID.

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Authors: Mohammad Ali Tabarzad, Caro Lucas, Nassim Jafarzadeh Eslami

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After the development of the Internet a suitable discipline for trading goods electronically has been emerged. However, this type of markets is not still mature enough in order to become independent and get closer to seller/buyer-s needs. Furthermore, the buyable and sellable goods in these markets still don-t have essential standards for being well-defined. In this paper, we will present a model for development of a market which can contain goods with variable definitions and we will also investigate its characteristics. Besides, by noticing the fact that people have different discriminations, it-s figured out that the significance of each attribute of a specific product may vary from different people-s view points. Consequently we-ll present a model for weighting and accordingly different people-s view points could be satisfied. These two aspects will be discussed completely throughout this paper.

Keywords: Electronic markets, selection of multi attributegoods, data infusion.

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Authors: Qian-Ping Guo, Hou-Biao Li

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The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords: CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.

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Authors: R. Keerativittatayut, B. Kaewkamnerdpong, J. Laothamatas, W. Sungkarat

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Dynamic Causal Modeling (DCM) functional Magnetic Resonance Imaging (fMRI) is a promising technique to study the connectivity among brain regions and effects of stimuli through modeling neuronal interactions from time-series neuroimaging. The aim of this study is to study characteristics of a mirror neuron system (MNS) in elderly group (age: 60-70 years old). Twenty volunteers were MRI scanned with visual stimuli to study a functional brain network. DCM was employed to determine the mechanism of mirror neuron effects. The results revealed major activated areas including precentral gyrus, inferior parietal lobule, inferior occipital gyrus, and supplementary motor area. When visual stimuli were presented, the feed-forward connectivity from visual area to conjunction area was increased and forwarded to motor area. Moreover, the connectivity from the conjunction areas to premotor area was also increased. Such findings can be useful for future diagnostic process for elderly with diseases such as Parkinson-s and Alzheimer-s.

Keywords: Mirror Neuron System (MNS), Dynamic Causal Modeling (DCM), Functional Magnetic Resonance Imaging (fMRI)

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Authors: M. Susithra, R. Gnanadass

Abstract:

Ancillary services are support services which are essential for humanizing and enhancing the reliability and security of the electric power system. Reactive power ancillary service is one of the important ancillary services in a restructured electricity market which determines the cost of supplying ancillary services and finding of how this cost would change with respect to operating decisions. This paper presents a new formation that can be used to minimize the Independent System Operator (ISO)’s total payment for reactive power ancillary service. The modified power flow tracing algorithm estimates the availability of reserve reactive power for ancillary service. In order to find optimum reactive power dispatch, Biogeography based optimization method (BPO) is proposed. Market Reactive Clearing Price (MRCP) is then estimated and it encourages generator companies (GENCOs) to participate in an ancillary service. Finally, optimal weighting factor and real time utilization factor of reactive power give the minimum ISO’s total payment. The effectiveness of proposed design is verified using IEEE 30 bus system.

Keywords: Biogeography based optimization method, Power flow tracing method, Reactive generation capability curve and Reactive power ancillary service.

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Authors: Reza Ziaie Moayed, Ehsan Azini

Abstract:

Jet grouting (JG) is one of the methods of improving and increasing the strength and bearing of soil in which the high pressure water or grout is injected through the nozzles into the soil. During this process, a part of the soil and grout particles comes out of the drill borehole, and the other part is mixed up with the grout in place, as a result of this process, a mass of modified soil is created. The purpose of this method is to change the soil into a mixture of soil and cement, commonly known as "soil-cement". In this paper, first, the principles of high pressure injection and then the effective parameters in the JG method are described. Then, the tests on the samples taken from the columns formed from the excavation around the soil-cement columns, as well as the static loading test on the created column, are discussed. In the other part of this paper, the soil behavior models for numerical modeling in PLAXIS software are mentioned. The purpose of this paper is to evaluate the results of numerical modeling based on in-situ static loading tests. The results indicate an acceptable agreement between the results of the tests mentioned and the modeling results. Also, modeling with this software as an appropriate option for technical feasibility can be used to soil improvement using JG.

Keywords: Jet grouting column, Soil improvement, Numerical modeling, In-situ loading test.

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Authors: Zaw Tun, Aung Htein Maw

Abstract:

The nature of wireless ad hoc and sensor networks make them very attractive to attackers. One of the most popular and serious attacks in wireless ad hoc networks is wormhole attack and most proposed protocols to defend against this attack used positioning devices, synchronized clocks, or directional antennas. This paper analyzes the nature of wormhole attack and existing methods of defending mechanism and then proposes round trip time (RTT) and neighbor numbers based wormhole detection mechanism. The consideration of proposed mechanism is the RTT between two successive nodes and those nodes- neighbor number which is needed to compare those values of other successive nodes. The identification of wormhole attacks is based on the two faces. The first consideration is that the transmission time between two wormhole attack affected nodes is considerable higher than that between two normal neighbor nodes. The second detection mechanism is based on the fact that by introducing new links into the network, the adversary increases the number of neighbors of the nodes within its radius. This system does not require any specific hardware, has good performance and little overhead and also does not consume extra energy. The proposed system is designed in ad hoc on-demand distance vector (AODV) routing protocol and analysis and simulations of the proposed system are performed in network simulator (ns-2).

Keywords: AODV, Wormhole attacks, Wireless ad hoc andsensor networks

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Authors: Dae-ho Won, Jong-wook Hong, Yeon-Mo Yang, Jinung An

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To reduce accidents in the industry, WSNs(Wireless Sensor networks)- sensor data is used. WSNs- sensor data has the persistence and continuity. therefore, we design and exploit the buffer management system that has the persistence and continuity to avoid and delivery data conflicts. To develop modules, we use the multi buffers and design the buffer management modules that transfer sensor data through the context-aware methods.

Keywords: safe management system, buffer management, context-aware, input data stream

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Authors: Pelaez Verdet, Antonio, Loscertales Sanchez, Pilar

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One of the mayor problems of programming a cruise circuit is to decide which destinations to include and which don-t. Thus a decision problem emerges, that might be solved using a linear and goal programming approach. The problem becomes more complex if several boats in the fleet must be programmed in a limited schedule, trying their capacity matches best a seasonal demand and also attempting to minimize the operation costs. Moreover, the programmer of the company should consider the time of the passenger as a limited asset, and would like to maximize its usage. The aim of this work is to design a method in which, using linear and goal programming techniques, a model to design circuits for the cruise company decision maker can achieve an optimal solution within the fleet schedule.

Keywords: Itinerary design, cruise programming, goalprogramming, linear programming

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Authors: P. Abhishesh, B. S. Ryuh, Y. S. Oh, H. J. Moon, R. Akanksha

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This paper discusses about the conceptual design and development of the control system software using Programmable logic controller (PLC) for autonomous driving and agricultural operations of Multipurpose Agricultural Robot Platform (MARP). Based on given initial conditions by field analysis and desired agricultural operations, the structural design development of MARP is done using modelling and analysis tool. PLC, being robust and easy to use, has been used to design the autonomous control system of robot platform for desired parameters. The robot is capable of performing autonomous driving and three automatic agricultural operations, viz. hilling, mulching, and sowing of seeds in the respective order. The input received from various sensors on the field is later transmitted to the controller via ZigBee network to make the changes in the control program to get desired field output. The research is conducted to provide assistance to farmers by reducing labor hours for agricultural activities by implementing automation. This study will provide an alternative to the existing systems with machineries attached behind tractors and rigorous manual operations on agricultural field at effective cost.

Keywords: Agricultural operations, autonomous driving, MARP, PLC.

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Authors: Mehmet Nefes, Selman Demirel, Hasan H. Ertok, Cenk Sen

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A typical reliability engineering problem regarding communication satellites has been considered to determine redundancy allocation scheme of power amplifiers within payload transponder module, whose dominant function is to amplify power levels of the received signals from the Earth, through maximizing reliability against mass, power, and other technical limitations. Adding each redundant power amplifier component increases not only reliability but also hardware, testing, and launch cost of a satellite. This study investigates a multi-objective approach used in order to solve Redundancy Allocation Problem (RAP) for a communication satellite payload transponder, focusing on design cost due to redundancy and reliability factors. The main purpose is to find the optimum power amplifier redundancy configuration satisfying reliability and capacity thresholds simultaneously instead of analyzing respectively or independently. A mathematical model and calculation approach are instituted including objective function definitions, and then, the problem is solved analytically with different input parameters in MATLAB environment. Example results showed that payload capacity and failure rate of power amplifiers have remarkable effects on the solution and also processing time.

Keywords: Communication satellite payload, multi-objective optimization, redundancy allocation problem, reliability, transponder.

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Authors: Konstantza Tonova, Ivan Svinyarov, Milen G. Bogdanov

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Ionic liquids consisting of a phosphonium cationic moiety and a saccharinate anion are synthesized and compared with their precursors, phosphonium chlorides, in reference to their extraction efficiency towards L-lactic acid. On the base of measurements of the acid and the water partitioning in the equilibrium biphasic systems, the molar ratios between acid, water and ionic liquid are estimated which allows to deduce the lactic acid extractive pathway. The effect of a salting-out addition that strengthens hydrophobicity in both phases is studied in view to reveal the best biphasic system with respect to IL low toxicity and high extraction efficiency.

Keywords: Biphasic system, Extraction, Ionic liquids, Lactic acid.

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Authors: Seon-Ho Yoon, Jin-Young Choi, Dong-Jun Won

Abstract:

This paper presents hierarchical operation strategies which are minimizing operation error between day ahead operation plan and real time operation. Operating power systems between centralized and decentralized approaches can be represented as hierarchical control scheme, featured as primary control, secondary control and tertiary control. Primary control is known as local control, featuring fast response. Secondary control is referred to as microgrid Energy Management System (EMS). Tertiary control is responsible of coordinating the operations of multi-microgrids. In this paper, we formulated 3 stage microgrid operation strategies which are similar to hierarchical control scheme. First stage is to set a day ahead scheduled output power of Battery Energy Storage System (BESS) which is only controllable source in microgrid and it is optimized to minimize cost of exchanged power with main grid using Particle Swarm Optimization (PSO) method. Second stage is to control the active and reactive power of BESS to be operated in day ahead scheduled plan in case that State of Charge (SOC) error occurs between real time and scheduled plan. The third is rescheduling the system when the predicted error is over the limited value. The first stage can be compared with the secondary control in that it adjusts the active power. The second stage is comparable to the primary control in that it controls the error in local manner. The third stage is compared with the secondary control in that it manages power balancing. The proposed strategies will be applied to one of the buildings in Electronics and Telecommunication Research Institute (ETRI). The building microgrid is composed of Photovoltaic (PV) generation, BESS and load and it will be interconnected with the main grid. Main purpose of that is minimizing operation cost and to be operated in scheduled plan. Simulation results support validation of proposed strategies.

Keywords: Battery energy storage system, energy management system, microgrid, particle swarm optimization.

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Authors: A. Jamekhorshid, G. Karimi, I. Noshadi, A. Jahangiri

Abstract:

Non-uniform current distribution in polymer electrolyte membrane fuel cells results in local over-heating, accelerated ageing, and lower power output than expected. This issue is very critical when fuel cell experiences water flooding. In this work, the performance of a PEM fuel cell is investigated under cathode flooding conditions. Two-dimensional partially flooded GDL models based on the conservation laws and electrochemical relations are proposed to study local current density distributions along flow fields over a wide range of cell operating conditions. The model results show a direct association between cathode inlet humidity increases and that of average current density but the system becomes more sensitive to flooding. The anode inlet relative humidity shows a similar effect. Operating the cell at higher temperatures would lead to higher average current densities and the chance of system being flooded is reduced. In addition, higher cathode stoichiometries prevent system flooding but the average current density remains almost constant. The higher anode stoichiometry leads to higher average current density and higher sensitivity to cathode flooding.

Keywords: Current distribution, Flooding, Hydrogen energysystem, PEM fuel cell.

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Authors: Gil-Eon Jeong, Sung-Kie Youn, K. C. Park

Abstract:

Treatment for the non-matching interface is an important computational issue. To handle this problem, the method of Lagrange multipliers including classical and localized versions are the most popular technique. It essentially imposes the interface compatibility conditions by introducing Lagrange multipliers. However, the numerical system becomes unstable and inefficient due to the Lagrange multipliers. The interface element-independent formulation that does not include the Lagrange multipliers can be obtained by modifying the independent variables mathematically. Through this modification, more efficient and stable system can be achieved while involving equivalent accuracy comparing with the conventional method. A numerical example is conducted to verify the validity of the presented method.

Keywords: Element-independent formulation, non-matching interface, interface coupling, methods of Lagrange multipliers.

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