Search results for: Software Engineering Methods

Authors: Winsy P.S. Dissanayake, Chandana P. W. Prasad, Ashutosh K. Singh

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The rapid pace of technological advancement and its consequential widening digital divide has resulted in the marginalization of the disabled especially the communication challenged. The dearth of suitable technologies for the development of assistive technologies has served to further marginalize the communications challenged user population and widen this chasm even further. Given the varying levels of disability there and its associated requirement for customized solution based. This paper explains the use of a Software Development Kits (SDK) for the bridging of this communications divide through the use of industry poplar communications SDKs towards identification of requirements for communications challenged users as well as identification of appropriate frameworks for future development initiatives.

Keywords: Assistive Technology, Communication, Disability, Marginalization, Software Development Kit, Waveform and Wideband

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Authors: Vinod Kumar, Navin Kumar, Surjit Angra, Prince Sharma

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This paper presents the design analysis of saddle support of a horizontal pressure vessel. Since saddle have the vital role to support the pressure vessel and to maintain its stability, it should be designed in such a way that it can afford the vessel load and internal pressure of the vessel due to liquid contained in the vessel. A model of horizontal pressure vessel and saddle support is created in ANSYS. Stresses are calculated using mathematical approach and ANSYS software. The analysis reveals the zone of high localized stress at the junction part of the pressure vessel and saddle support due to operating conditions. The results obtained by both the methods are compared with allowable stress value for safe designing.

Keywords: ANSYS, Pressure Vessel, Saddle, Support.

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Authors: Rouaz Idriss, Bourahla Nour-Eddine, Kahlouche Farah, Rafa Sid Ali

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The stability of structures made of light-gauge steel depends highly on the contribution of Shear Wall Panel (SWP) systems under horizontal forces due to wind or earthquake loads. Steel plate sheathing is often used with these panels made of cold formed steel (CFS) to improve its shear strength. In order to predict the shear strength resistance, two methods are presented in this paper. In the first method, the steel plate sheathing is modeled with plats strip taking into account only the tension and compression force due to the horizontal load, where both track and stud are modeled according to the geometrical and mechanical characteristics of the specimen used in the experiments. The theoretical background and empirical formulations of this method are presented in this paper. However, the second method is based on a micro modeling of the cold formed steel Shear Wall Panel “CFS-SWP” using Abaqus software. A nonlinear analysis was carried out with an in-plan monotonic load. Finally, the comparison between these two methods shows that the micro modeling with Abaqus gives better prediction of shear resistance of SWP than strips method. However, the latter is easier and less time consuming than the micro modeling method.

Keywords: Cold Formed Steel Shear Wall Panel, CFS-SWP, micro modeling, nonlinear analysis, strip method.

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Authors: Guangbin Wang, Fuping Tan

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In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.

Keywords: Nonsingular H-matrix, parallel alternating method, convergence.

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Authors: Morteza Kazemi Torbaghan, Seyed Mehran Kazemi, Rahele Zhiani, Fakhriye Hamed

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Truss optimization problem has been vastly studied during the past 30 years and many different methods have been proposed for this problem. Even though most of these methods assume that the design variables are continuously valued, in reality, the design variables of optimization problems such as cross-sectional areas are discretely valued. In this paper, an improved hill climbing and an improved simulated annealing algorithm have been proposed to solve the truss optimization problem with discrete values for crosssectional areas. Obtained results have been compared to other methods in the literature and the comparison represents that the proposed methods can be used more efficiently than other proposed methods

Keywords: Size Optimization of Trusses, Hill Climbing, Simulated Annealing.

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Authors: N. Samarinas, C. Evangelides, C. Vrekos

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The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: Classification, fuzzy logic, tolerance relations, rainfall data.

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Authors: P. G. F. Siqueira, N. G. S. Almeida, P. M. A. Stemler, P. R. Cetlin, M. T. P. Aguilar

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The processing of metals through Equal Channel Angular Pressing (ECAP) leads to their remarkable strengthening. The ECAP dies control the amount of strain imposed on the material through its geometry, especially through the angle between the die channels, and thus the microstructural and mechanical properties evolution of the material. The present study describes the design of an ECAP die whose utilization and maintenance are facilitated, and that also controls the eventual undesired flow of the material during processing. The proposed design was validated through numerical simulations procedures using commercial software. The die was manufactured according to the present design and tested. Tests using aluminum alloys also indicated to be suitable for the processing of higher strength alloys.

Keywords: ECAP, mechanical design, numerical methods, SPD.

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Authors: J. Menčík

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Actual load, material characteristics and other quantities often differ from the design values. This can cause worse function, shorter life or failure of a civil engineering structure, a machine, vehicle or another appliance. The paper shows main causes of the uncertainties and deviations and presents a systematic approach and efficient tools for their elimination or mitigation of consequences. Emphasis is put on the design stage, which is most important for reliability ensuring. Principles of robust design and important tools are explained, including FMEA, sensitivity analysis and probabilistic simulation methods. The lifetime prediction of long-life objects can be improved by long-term monitoring of the load response and damage accumulation in operation. The condition evaluation of engineering structures, such as bridges, is often based on visual inspection and verbal description. Here, methods based on fuzzy logic can reduce the subjective influences.

Keywords: Design, fuzzy methods, Monte Carlo, reliability, robust design, sensitivity analysis, simulation, uncertainties.

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Authors: N. Nacereddine, L. Hamami, M. Tridi, N. Oucief

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In non destructive testing by radiography, a perfect knowledge of the weld defect shape is an essential step to appreciate the quality of the weld and make decision on its acceptability or rejection. Because of the complex nature of the considered images, and in order that the detected defect region represents the most accurately possible the real defect, the choice of thresholding methods must be done judiciously. In this paper, performance criteria are used to conduct a comparative study of four non parametric histogram thresholding methods for automatic extraction of weld defect in radiographic images.

Keywords: Radiographic images, non parametric methods, histogram thresholding, performance criteria.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

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Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Sangsuree Vasupongayya, Kittisak Keawneam, Kittipong Sengloilaun, Patt Emmawat

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Library management systems are commonly used in all educational related institutes. Many commercial products are available. However, many institutions may not be able to afford the cost of using commercial products. Therefore, an alternative solution in such situations would be open source software. This paper is focusing on reviewing open source library management system packages currently available. The review will focus on the abilities to perform four basic components which are traditional services, interlibrary load management, managing electronic materials and basic common management system such as security, alert system and statistical reports. In addition, environment, basic requirement and supporting aspects of each open source package are also mentioned.

Keywords: open source, library management, review.

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Authors: S. Manaseer, F. A. Masooud, A. A. Sharieh

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Fault tolerance is critical in many of today's large computer systems. This paper focuses on improving fault tolerance through testing. Moreover, it concentrates on the memory faults: how to access the editable part of a process memory space and how this part is affected. A special Software Fault Injection Technique (SFIT) is proposed for this purpose. This is done by sequentially scanning the memory of the target process, and trying to edit maximum number of bytes inside that memory. The technique was implemented and tested on a group of programs in software packages such as jet-audio, Notepad, Microsoft Word, Microsoft Excel, and Microsoft Outlook. The results from the test sample process indicate that the size of the scanned area depends on several factors. These factors are: process size, process type, and virtual memory size of the machine under test. The results show that increasing the process size will increase the scanned memory space. They also show that input-output processes have more scanned area size than other processes. Increasing the virtual memory size will also affect the size of the scanned area but to a certain limit.

Keywords: Complex software systems, Error detection, Fault tolerance, Injection and testing methodology, Memory faults, Process and virtual memory.

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Authors: M. Samaka

Abstract:

This paper presents the development of a software application for Off-line robot task programming and simulation. Such application is designed to assist in robot task planning and to direct manipulator motion on sensor based programmed motion. The concept of the designed programming application is to use the power of the knowledge base for task accumulation. In support of the programming means, an interactive graphical simulation for manipulator kinematics was also developed and integrated into the application as the complimentary factor to the robot programming media. The simulation provides the designer with useful, inexpensive, off-line tools for retain and testing robotics work cells and automated assembly lines for various industrial applications.

Keywords: Robot programming, task-level programming, robot languages, robot simulation, robotics software.

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Authors: S. Houssaini, L. Bahi

Abstract:

The motorway segment between Tangier and Oued R’mel has experienced, since the beginning of building works, significant instability and landslides linked to a number of geological, hydrogeological and geothermic factors affecting the different formations. The landslides observed are not fully understood, despite many studies conducted on this segment. This study aims at producing new methods to better explain the phenomena behind the landslides, taking into account the geotechnical and geothermic contexts. This analysis builds up on previous studies and geotechnical data collected in the field. The final body of data collected shall be processed through the Plaxis software for a better and customizable view of the landslide problems in the area, which will help tofind solutions and stabilize land in the area.

Keywords: Landslides, modeling, risk, stabilization.

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Authors: Md. Athar Imtiaz, Abduljalil S. Al-Mudhary, Md. Taha Mirhashemi, Roslina Ibrahim

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Information Technology (IT) is being used by almost all organizations throughout the world. However its success at supporting and improving business is debatable. There is always the risk of IT project failure and studies have proven that a large number of IT projects indeed do fail. There are many components that further the success of IT projects; these have been studied in previous studies. Studies have found the most necessary components for success in software development projects, executive information systems etc. In this study previous literatures that have looked into these success promoting factors have been critically reviewed and analyzed. 15 Critical Success Factors (CSF) of IT projects were enlisted and examined. These factors can be applied to all IT projects and is not specific to a particular type of IT/IS project. A hypothesis was also generated after the evaluation of the factors.

Keywords: Critical Success Factors, CSF, IT Projects, IS Projects, Software Development Projects.

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Authors: A. H. Sajedi Pour, N. Hedayat, Z. Yazdi

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Sediment loads transfer in hydraulic installations and their consequences for the O&M of modern canal systems is emerging as one of the most important considerations in hydraulic engineering projects apriticularly those which are inteded to feed the irrigation and draiange schemes of large command areas such as the Dez and Mogahn in Iran.. The aim of this paper is to investigate the applicability of the vortex tube as a viable means of extracting sediment loads entering the canal systems in general and the water inatke structures in particulars. The Western conveyance canal of the Dez Diversion weir which feeds the Karkheh Flood Plain in Sothwestern Dezful has been used as the case study using the data from the Dastmashan Hydrometric Station. The SHARC software has been used as an analytical framework to interprete the data. Results show that given the grain size D50 and the canal turbulence the adaption length from the beginning of the canal and after the diversion dam is estimated at 477 m, a point which is suitable for laying the vortex tube.

Keywords: Vortex tube, sediments, western canal, SHARCmodel

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Authors: C. Malça, N. Alves, A. Mateus

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This work was one of the tasks of the Manufacturing2Client project, whose objective was to develop a frontal deflector to be commercialized in the automotive industry, using new project and manufacturing methods. In this task, in particular, it was proposed to develop the ability to predict computationally the aerodynamic influence of flow in vehicles, in an effort to reduce fuel consumption in vehicles from class 3 to 8. With this aim, two deflector models were developed and their aerodynamic performance analyzed. The aerodynamic study was done using the Computational Fluid Dynamics (CFD) software Ansys CFX and allowed the calculation of the drag coefficient caused by the vehicle motion for the different configurations considered. Moreover, the reduction of diesel consumption and carbon dioxide (CO2) emissions associated with the optimized deflector geometry could be assessed.

Keywords: Aerodynamic analysis, CFD, CO2 emissions, Drag coefficient, Frontal deflector, Fuel consumption.

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Authors: Muhibul Haque Bhuyan

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Inclusion of any design project in an undergraduate electrical and electronic engineering curriculum and producing creative ideas in the final year capstone design projects have received numerous comments at the Board of Accreditation for Engineering and Technical Education (BAETE) several times by the mentors and visiting program evaluator team members at different public and private universities in Bangladesh. To eradicate this deficiency which is needed for getting the program accreditation, a thorough change was required in the Department of Electrical and Electronic Engineering (EEE) for its BSc in EEE program at Southeast University, Dhaka, Bangladesh. We suggested making changes in the course curriculum titles and contents, emphasizing to include capstone design projects, question setting, examining students through other standard methods, selecting and retaining Outcome-Based Education (OBE)-oriented engineering faculty members, improving laboratories through purchasing new equipment and software as well as developing new experiments for each laboratory courses, and engaging the students to practical designs in various courses and final year projects. This paper reports on capstone design project course objectives, course outcomes, mapping with the program outcomes, cognitive domain of learning, assessment schemes, guidelines, suggestions and recommendations for supervision processes, assessment strategy, and rubric setting, etc. It is expected that this will substantially improve the capstone design projects offering, supervision, and assessment in the undergraduate EEE program to fulfill the arduous requirements of BAETE accreditation based on OBE.

Keywords: Course outcome, capstone design project, assessment and evaluation, electrical and electronic engineering.

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Authors: T. Hui Teo, Wee Tiong Tan, Pradeep K. Gopalakrishnan, Victor K. H. Phay, Ma Su M. M. Shwe

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A healthcare monitoring system is presented in this paper. This system is based on ultra-low power sensor nodes and a personal server, which is based on hardware and software extensions to a Personal Digital Assistant (PDA)/Smartphone. The sensor node collects data from the body of a patient and sends it to the personal server where the data is processed, displayed and made ready to be sent to a healthcare network, if necessary. The personal server consists of a compact low power receiver module and equipped with a Smartphone software. The receiver module takes less than 30 × 30 mm board size and consumes approximately 25 mA in active mode.

Keywords: healthcare monitoring, sensor node, personal server, wireless.

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Authors: A. A. Shafie, Fadhlan Hafiz, M. H. Ali

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Motion detection is very important in image processing. One way of detecting motion is using optical flow. Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. The method used for finding the optical flow in this project is assuming that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. This technique is later used in developing software for motion detection which has the capability to carry out four types of motion detection. The motion detection software presented in this project also can highlight motion region, count motion level as well as counting object numbers. Many objects such as vehicles and human from video streams can be recognized by applying optical flow technique.

Keywords: Background modeling, Motion detection, Optical flow, Velocity smoothness constant, motion trajectories.

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Authors: Neil Bar, Andrew Heweston

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Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

Keywords: Probability of failure, point estimate method, Monte-Carlo simulations, sensitivity analysis, slope stability.

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Authors: Mohamed Amine Ouddan, Hassane Essafi

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Source code retrieval is of immense importance in the software engineering field. The complex tasks of retrieving and extracting information from source code documents is vital in the development cycle of the large software systems. The two main subtasks which result from these activities are code duplication prevention and plagiarism detection. In this paper, we propose a Mohamed Amine Ouddan, and Hassane Essafi source code retrieval system based on two-level fingerprint representation, respectively the structural and the semantic information within a source code. A sequence alignment technique is applied on these fingerprints in order to quantify the similarity between source code portions. The specific purpose of the system is to detect plagiarism and duplicated code between programs written in different programming languages belonging to the same class, such as C, Cµ, Java and CSharp. These four languages are supported by the actual version of the system which is designed such that it may be easily adapted for any programming language.

Keywords: Source code retrieval, plagiarism detection, clonedetection, sequence alignment.

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: R. Tlili Yaakoubi, H. Nakouri, O. Blanpain, S. Lallahem

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The current tools for real time management of sewer systems are based on two software tools: the software of weather forecast and the software of hydraulic simulation. The use of the first ones is an important cause of imprecision and uncertainty, the use of the second requires temporal important steps of decision because of their need in times of calculation. This way of proceeding fact that the obtained results are generally different from those waited. The major idea of this project is to change the basic paradigm by approaching the problem by the "automatic" face rather than by that "hydrology". The objective is to make possible the realization of a large number of simulations at very short times (a few seconds) allowing to take place weather forecasts by using directly the real time meditative pluviometric data. The aim is to reach a system where the decision-making is realized from reliable data and where the correction of the error is permanent. A first model of control laws was realized and tested with different return-period rainfalls. The gains obtained in rejecting volume vary from 19 to 100 %. The development of a new algorithm was then used to optimize calculation time and thus to overcome the subsequent combinatorial problem in our first approach. Finally, this new algorithm was tested with 16- year-rainfall series. The obtained gains are 40 % of total volume rejected to the natural environment and of 65 % in the number of discharges.

Keywords: Automation, optimization, paradigm, RTC.

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Authors: Alicia Y. C. Tang, Rukaini Hj. Abdullah, Sharifuddin M. Zain

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This paper discusses the development of a qualitative simulator (abbreviated QRiOM) for predicting the behaviour of organic chemical reactions. The simulation technique is based on the qualitative process theory (QPT) ontology. The modelling constructs of QPT embody notions of causality which can be used to explain the behaviour of a chemical system. The major theme of this work is that, in a qualitative simulation environment, students are able to articulate his/her knowledge through the inspection of explanations generated by software. The implementation languages are Java and Prolog. The software produces explanation in various forms that stresses on the causal theories in the chemical system which can be effectively used to support learning.

Keywords: Chemical reactions, explanation, qualitative processtheory, simulation

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Authors: Rim Bouhaouel, Naoufel Kraïem, Zuhoor Al Khanjari

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Unified Modeling Language (UML) is considered as one of the widespread modeling language standardized by the Object Management Group (OMG). Therefore, the model driving engineering (MDE) community attempts to provide reuse of UML diagrams, and do not construct it from scratch. The UML model appears according to a specific software development process. The existing method generation models focused on the different techniques of transformation without considering the development process. Our work aims to construct an UML component from fragments of UML diagram basing on an agile method. We define UML fragment as a portion of a UML diagram, which express a business target. To guide the generation of fragments of UML models using an agile process, we need a flexible approach, which adapts to the agile changes and covers all its activities. We use the software product line (SPL) to derive a fragment of process agile method. This paper explains our approach, named RECUP, to generate UML fragments following an agile process, and overviews the different aspects. In this paper, we present the approach and we define the different phases and artifacts.

Keywords: UML, component, fragment, agile, SPL.

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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: Toshihiko Sasama, Kentaro Kishida, Kazunori Sugahara, Hiroshi Masuyama

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A mobile ad hoc network is a network of mobile nodes without any notion of centralized administration. In such a network, each mobile node behaves not only as a host which runs applications but also as a router to forward packets on behalf of others. Clustering has been applied to routing protocols to achieve efficient communications. A CH network expresses the connected relationship among cluster-heads. This paper discusses the methods for constructing a CH network, and produces the following results: (1) The required running costs of 3 traditional methods for constructing a CH network are not so different from each other in the static circumstance, or in the dynamic circumstance. Their running costs in the static circumstance do not differ from their costs in the dynamic circumstance. Meanwhile, although the routing costs required for the above 3 methods are not so different in the static circumstance, the costs are considerably different from each other in the dynamic circumstance. Their routing costs in the static circumstance are also very different from their costs in the dynamic circumstance, and the former is one tenths of the latter. The routing cost in the dynamic circumstance is mostly the cost for re-routing. (2) On the strength of the above results, we discuss new 2 methods regarding whether they are tolerable or not in the dynamic circumstance, that is, whether the times of re-routing are small or not. These new methods are revised methods that are based on the traditional methods. We recommended the method which produces the smallest routing cost in the dynamic circumstance, therefore producing the smallest total cost.

Keywords: cluster, mobile ad hoc network, re-routing cost, simulation

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Authors: Guangbin Wang, Xue Li

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In this paper, we present parallel alternating two-stage methods for solving linear system Ax=b, where A is a symmetric positive definite matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: alternating two-stage, convergence, linear system, parallel.

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