Search results for: multi- grounded

Authors: Jean Berger, Nassirou Lo, Martin Noel

Abstract:

Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: Search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization.

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Authors: A. Zanj, F. He

Abstract:

In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: Multi-physical domain, conduction model, port-based modeling, dynamic interaction, physical modeling.

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Authors: Danping Lin, C.K.M. Lee

Abstract:

Re-entrant scheduling is an important search problem with many constraints in the flow shop. In the literature, a number of approaches have been investigated from exact methods to meta-heuristics. This paper presents a genetic algorithm that encodes the problem as multi-level chromosomes to reflect the dependent relationship of the re-entrant possibility and resource consumption. The novel encoding way conserves the intact information of the data and fastens the convergence to the near optimal solutions. To test the effectiveness of the method, it has been applied to the resource-constrained re-entrant flow shop scheduling problem. Computational results show that the proposed GA performs better than the simulated annealing algorithm in the measure of the makespan

Keywords: Resource-constrained, re-entrant, genetic algorithm (GA), multi-level encoding

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Authors: Hanan Rizk

Abstract:

Heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques, and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed the proportional–integral–derivative (PID) controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: Seyed Fazel Ziaei Asl, Ali Karami, Gholamreza Ashari, Azam Behrang, Arezoo Assareh, N.Hedayat

Abstract:

Predict daily global solar radiation (GSR) based on meteorological variables, using Multi-layer perceptron (MLP) neural networks is the main objective of this study. Daily mean air temperature, relative humidity, sunshine hours, evaporation, wind speed, and soil temperature values between 2002 and 2006 for Dezful city in Iran (32° 16' N, 48° 25' E), are used in this study. The measured data between 2002 and 2005 are used to train the neural networks while the data for 214 days from 2006 are used as testing data.

Keywords: Multi-layer Perceptron (MLP) Neural Networks;Global Solar Radiation (GSR), Meteorological Parameters, Prediction.

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Authors: Hla Hla Khaing, Yit Jian Liang, Nant Nyein Moe Htay, Jiang Fan

Abstract:

Partial shadowing is one of the problems that are always faced in terrestrial applications of solar photovoltaic (PV). The effects of partial shadow on the energy yield of conventional mono-crystalline and multi-crystalline PV modules have been researched for a long time. With deployment of new thin-film solar PV modules in the market, it is important to understand the performance of new PV modules operating under the partial shadow in the tropical zone. This paper addresses the impacts of different partial shadowing on the operating characteristics of four different types of solar PV modules that include multi-crystalline, amorphous thin-film, CdTe thin-film and CIGS thin-film PV modules.

Keywords: Partial shade, CdTe, CIGS, multi-crystalline (mc-Si), amorphous silicon (a-Si), bypass diode.

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Authors: J. Lin, T. C. Kuo, C. -Y. Gau, K. C. Liu, Y. J. Huang, J. D. Yu, Y. W. Lin

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A multi-agent type robot for disaster response in calamity scene is proposed in this paper. The proposed grouped rescue robots can perform cooperative reconnaissance and surveillance to achieve a given rescue mission. The multi-agent rescue of dual set robot consists of one master set and three slave units. The research for this rescue robot system is going to detect at harmful environment where human is unreachable, such as the building is infected with virus or the factory has hazardous liquid in effluent. As a dual set robot, with Bluetooth and communication network, the master set can connect with slave units and send information back to computer by wireless and monitor. Therefore, rescuer can be informed the real-time information in a calamity area. Furthermore, each slave robot is able to obstacle avoidance by ultrasonic sensors, and encodes distance and location by compass. The master robot can integrate every devices information to increase the efficiency of prospected and research unknown area.

Keywords: Designing of multi-agent rescue robot, development and basic experiments of master-slave type rescue robots.

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Josef Wolfartsberger, Michael Heiml, Georg Schwarz, Sabrina Egger

Abstract:

Growing individualization and higher numbers of variants in industrial assembly products raise the complexity of manufacturing processes. Technical assistance systems considering both procedural and human factors allow for an increase in product quality and a decrease in required learning times by supporting workers with precise working instructions. Due to varying needs of workers, the presentation of working instructions leads to several challenges. This paper presents an approach for a multi-modal visualization application to support assembly work of complex parts. Our approach is integrated within an interconnected assistance system network and supports the presentation of cloud-streamed textual instructions, images, videos, 3D animations and audio files along with multi-modal user interaction, customizable UI, multi-platform support (e.g. tablet-PC, TV screen, smartphone or Augmented Reality devices), automated text translation and speech synthesis. The worker benefits from more accessible and up-to-date instructions presented in an easy-to-read way.

Keywords: Assembly, assistive technologies, augmented reality, manufacturing, visualization.

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Authors: Dawit Mengistu, Lars Lundberg, Paul Davidsson

Abstract:

A major requirement for Grid application developers is ensuring performance and scalability of their applications. Predicting the performance of an application demands understanding its specific features. This paper discusses performance modeling and prediction of multi-agent based simulation (MABS) applications on the Grid. An experiment conducted using a synthetic MABS workload explains the key features to be included in the performance model. The results obtained from the experiment show that the prediction model developed for the synthetic workload can be used as a guideline to understand to estimate the performance characteristics of real world simulation applications.

Keywords: Grid computing, Performance modeling, Performance prediction, Multi-agent simulation.

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Authors: Yoshiaki Shikata, Nobutane Hanayama

Abstract:

We present a prioritized, limited multi-server processor sharing (PS) system where each server has various capacities, and N (≥2) priority classes are allowed in each PS server. In each prioritized, limited server, different service ratio is assigned to each class request, and the number of requests to be processed is limited to less than a certain number. Routing strategies of such prioritized, limited multi-server PS systems that take into account the capacity of each server are also presented, and a performance evaluation procedure for these strategies is discussed. Practical performance measures of these strategies, such as loss probability, mean waiting time, and mean sojourn time, are evaluated via simulation. In the PS server, at the arrival (or departure) of a request, the extension (shortening) of the remaining sojourn time of each request receiving service can be calculated by using the number of requests of each class and the priority ratio. Utilising a simulation program which executes these events and calculations, the performance of the proposed prioritized, limited multi-server PS rule can be analyzed. From the evaluation results, most suitable routing strategy for the loss or waiting system is clarified.

Keywords: Processor sharing, multi-server, various capacity, N priority classes, routing strategy, loss probability, mean sojourn time, mean waiting time, simulation.

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Authors: Pushpendra S. Bharti, S. Maheshwari

Abstract:

Electric discharge machining (EDM) is one of the most widely used non-conventional manufacturing process to shape difficult-to-cut materials. The process yield, in terms of material removal rate, surface roughness and tool wear rate, of EDM may considerably be improved by selecting the optimal combination(s) of process parameters. This paper employs Multi-response signal-to-noise (MRSN) ratio technique to find the optimal combination(s) of the process parameters during EDM of Inconel 718. Three cases v.i.z. high cutting efficiency, high surface finish, and normal machining have been taken and the optimal combinations of input parameters have been obtained for each case. Analysis of variance (ANOVA) has been employed to find the dominant parameter(s) in all three cases. The experimental verification of the obtained results has also been made. MRSN ratio technique found to be a simple and effective multi-objective optimization technique.

Keywords: EDM, material removal rate, multi-response signal-to-noise ratio, optimization, surface roughness.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

We model the process of a data center as a multi- objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consump¬tion and response time (makespan) subject to the constraints of deadlines and architectural requirements. A simple technique based on multi-objective goal programming is proposed that guarantees Pareto optimal solution with excellence in convergence process. The proposed technique also is compared with other traditional approach. The simulation results show that the proposed technique achieves superior performance compared to the min-min heuristics, and com¬petitive performance relative to the optimal solution implemented in UNDO for small-scale problems.

Keywords: Energy-efficient computing, distributed systems, multi-objective optimization.

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Authors: Sonia Rebai, Mohamed Naceur Azaiez, Dhafer Saidane

Abstract:

In this study, we develop a performance evaluation model based on a multi-attribute utility approach aiming at reaching the sustainable banking (SB) status. This model is built accounting for various banks’ stakeholders in a win-win paradigm. In addition, it offers the opportunity for adopting a global measure of performance as an indication of a bank’s sustainability degree. This measure is referred to as banking sustainability performance index (BSPI). This index may constitute a basis for ranking banks. Moreover, it may constitute a bridge between the assessment types of financial and extra-financial rating agencies. A real application is performed on three French banks.

Keywords: Multi-attribute utility theory, Performance, Sustainable banking.

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Authors: Properties, Approximation Distribution Reductions in Multigranulation Rough Set Model

Abstract:

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

Keywords: Incomplete information system, maximal compatible class, multi-granulation rough set model, reduction.

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Authors: Parviz Fattahi

Abstract:

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it quit difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. In this paper, a Pareto approach to solve the multi objective flexible job shop scheduling problems is proposed. The objectives considered are to minimize the overall completion time (makespan) and total weighted tardiness (TWT). An effective simulated annealing algorithm based on the proposed approach is presented to solve multi objective flexible job shop scheduling problem. An external memory of non-dominated solutions is considered to save and update the non-dominated solutions during the solution process. Numerical examples are used to evaluate and study the performance of the proposed algorithm. The proposed algorithm can be applied easily in real factory conditions and for large size problems. It should thus be useful to both practitioners and researchers.

Keywords: Flexible job shop, Scheduling, Hierarchical approach, simulated annealing, tabu search, multi objective.

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Authors: Bijaya Krushna Mangaraj, Deepak Kumar Das

Abstract:

Sustainability in rural production system can only be achieved if it can suitably satisfy the local requirement as well as the outside demand with the changing time. With the increased pressure from the food sector in a globalised world, the agrarian economy needs to re-organise its cultivable land system to be compatible with new management practices as well as the multiple needs of various stakeholders and the changing resource scenario. An attempt has been made to transform this problem into a multi-objective decisionmaking problem considering various objectives, resource constraints and conditional constraints. An interactive fuzzy multi-objective programming approach has been used for such a purpose taking a case study in Indian context to demonstrate the validity of the method.

Keywords: Land re-organisation, Crop planning, Multiobjective Decision-Making, Fuzzy Goal Programming.

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Authors: Xiao Yihong, Yu Kexin, Burra Venkata Durga Kumar

Abstract:

With the accelerating process of urbanization, the problem of urban road congestion is becoming more and more serious. Intelligent transportation system combining distributed and artificial intelligence has become a research hotspot. As the core development direction of the intelligent transportation system, Cooperative Intelligent Transportation System (C-ITS) integrates advanced information technology and communication methods and realizes the integration of human, vehicle, roadside infrastructure and other elements through the multi-agent distributed system. By analyzing the system architecture and technical characteristics of C-ITS, the paper proposes a distributed multi-agent C-ITS. The system consists of Roadside Subsystem, Vehicle Subsystem and Personal Subsystem. At the same time, we explore the scalability of the C-ITS and put forward incorporating local rewards in the centralized training decentralized execution paradigm, hoping to add a scalable value decomposition method. In addition, we also suggest introducing blockchain to improve the safety of the traffic information transmission process. The system is expected to improve vehicle capacity and traffic safety.

Keywords: Distributed system, artificial intelligence, multi-agent, Cooperative Intelligent Transportation System.

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Authors: Do-Jin Jang, Sung-Ah Kim

Abstract:

A kinetic façade responds to user requirements and environmental conditions.  In designing a kinetic façade, kinetic patterns play a key role in determining its performance. This paper proposes a biomimetic method for the multi-objective optimization for kinetic façade design. The autonomous decentralized control system is combined with flocking algorithm. The flocking agents are autonomously reacting to sensor values and bring about kinetic patterns changing over time. A series of experiments were conducted to verify the potential and limitations of the flocking based decentralized control. As a result, it could show the highest performance balancing multiple objectives such as solar radiation and openness among the comparison group.

Keywords: Biomimicry, flocking algorithm, autonomous decentralized control, multi-objective optimization.

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Authors: S. Chatterji, S. L. Shimi

Abstract:

As wind, solar and other clean and green energy sources gain popularity worldwide, engineers are seeking ways to make renewable energy systems more affordable and to integrate them with existing ac power grids. In the present paper an attempt has been made for integrating the PV arrays to the smart nano grid using an artificial intelligent (AI) based solar powered cascade multilevel inverter. The AI based controller switching scheme has been used for improving the power quality by reducing the Total Harmonic Distortion (THD) of the multi-level inverter output voltage.

Keywords: Artificial Intelligent (AI), Solar Powered Multi-level Inverter, Smart nano grid, Total Harmonic Distortion (THD).

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Authors: Joumana Farah, François Marx, Clovis Francis

Abstract:

The aim of this paper is to emphasize and alleviate the effect of phase noise due to imperfect local oscillators on the performances of a Multi-Carrier CDMA system. After the cancellation of Common Phase Error (CPE), an iterative approach is introduced which iteratively estimates Inter-Carrier Interference (ICI) components in the frequency domain and cancels their contribution in the time domain. Simulation are conducted in order to investigate the achievable performances for several parameters, such as the spreading factor, the modulation order, the phase noise power and the transmission Signal-to-Noise Ratio.

Keywords: Inter-carrier Interference, Multi-Carrier Code DivisionMultiple Access, Orthogonal Frequency Division Multiplexing, Phase noise.

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Authors: Shuangquan Liu, Jinwen Wang, Dada Wang

Abstract:

A case study of the generation scheduling optimization of the multi-hydroplants on the Yuan River Basin in China is reported in this paper. Concerning the uncertainty of the inflows, the long/mid-term generation scheduling (LMTGS) problem is solved by a stochastic model in which the inflows are considered as stochastic variables. For the short-term generation scheduling (STGS) problem, a constraint violation priority is defined in case not all constraints are satisfied. Provided the stage-wise separable condition and low dimensions, the hydroplant-based operational region schedules (HBORS) problem is solved by dynamic programming (DP). The coordination of LMTGS and STGS is presented as well. The feasibility and the effectiveness of the models and solution methods are verified by the numerical results.

Keywords: generation scheduling, multi-hydroplants, optimization.

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Authors: Gyumin Hwang, Jihong Lee

Abstract:

This paper studied the CSS-based indoor localization system which is easy to implement, inexpensive to compose the systems, additionally CSS-based indoor localization system covers larger area than other system. However, this system has problem which is affected by reflected distance data. This problem in localization is caused by the multi-path effect. Error caused by multi-path is difficult to be corrected because the indoor environment cannot be described. In this paper, in order to solve the problem by multi-path, we have supplemented the localization system by using pattern matching method based on extended database. Thereby, this method improves precision of estimated. Also this method is verified by experiments in gymnasium. Database was constructed by 1m intervals, and 16 sample data were collected from random position inside the region of DB points. As a result, this paper shows higher accuracy than existing method through graph and table.

Keywords: Chirp Spread Spectrum (CSS), Indoor Localization, Pattern-Matching, Time of Arrival (ToA), Multi-Path, Mahalanobis Distance, Reception Rate, Simultaneous Localization and Mapping (SLAM), Laser Range Finder (LRF).

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Authors: Sagir M. Yusuf, Chris Baber

Abstract:

In this paper, we describe how Bayesian inferential reasoning will contributes in obtaining a well-satisfied prediction for Distributed Constraint Optimization Problems (DCOPs) with uncertainties. We also demonstrate how DCOPs could be merged to multi-agent knowledge understand and prediction (i.e. Situation Awareness). The DCOPs functions were merged with Bayesian Belief Network (BBN) in the form of situation, awareness, and utility nodes. We describe how the uncertainties can be represented to the BBN and make an effective prediction using the expectation-maximization algorithm or conjugate gradient descent algorithm. The idea of variable prediction using Bayesian inference may reduce the number of variables in agents’ sampling domain and also allow missing variables estimations. Experiment results proved that the BBN perform compelling predictions with samples containing uncertainties than the perfect samples. That is, Bayesian inference can help in handling uncertainties and dynamism of DCOPs, which is the current issue in the DCOPs community. We show how Bayesian inference could be formalized with Distributed Situation Awareness (DSA) using uncertain and missing agents’ data. The whole framework was tested on multi-UAV mission for forest fire searching. Future work focuses on augmenting existing architecture to deal with dynamic DCOPs algorithms and multi-agent information merging.

Keywords: DCOP, multi-agent reasoning, Bayesian reasoning, swarm intelligence.

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Authors: Masood Karamoozian, Zhang Hong

Abstract:

The necessity and complexity of the decision-making process and the interference of the various factors to make decisions and consider all the relevant factors in a problem are very obvious nowadays. Hence, researchers show their interest in multi-criteria decision-making methods. In this research, the Analytical Hierarchy Process (AHP), Simple Additive Weighting (SAW), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods of multi-criteria decision-making have been used to solve the problem of optimal construction systems. Systems being evaluated in this problem include; Light Steel Frames (LSF), a case study of designs by Zhang Hong studio in the Southeast University of Nanjing, Insulating Concrete Form (ICF), Ordinary Construction System (OCS), and Precast Concrete System (PRCS) as another case study designs in Zhang Hong studio in the Southeast University of Nanjing. Crowdsourcing was done by using a questionnaire at the sample level (200 people). Questionnaires were distributed among experts in university centers and conferences. According to the results of the research, the use of different methods of decision-making led to relatively the same results. In this way, with the use of all three multi-criteria decision-making methods mentioned above, the PRCS was in the first rank, and the LSF system ranked second. Also, the PRCS, in terms of performance standards and economics, was ranked first, and the LSF system was allocated the first rank in terms of environmental standards.

Keywords: Multi-criteria decision making, AHP, SAW, TOPSIS.

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Authors: H. Bouhamed, A. Rebai, T. Lecroq, M. Jaoua

Abstract:

The objective of our work is to develop a new approach for discovering knowledge from a large mass of data, the result of applying this approach will be an expert system that will serve as diagnostic tools of a phenomenon related to a huge information system. We first recall the general problem of learning Bayesian network structure from data and suggest a solution for optimizing the complexity by using organizational and optimization methods of data. Afterward we proposed a new heuristic of learning a Multi-Entities Bayesian Networks structures. We have applied our approach to biological facts concerning hereditary complex illnesses where the literatures in biology identify the responsible variables for those diseases. Finally we conclude on the limits arched by this work.

Keywords: Data-organization, data-optimization, automatic knowledge discovery, Multi-Entities Bayesian networks, score merging.

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Authors: Ali Farhaninejad, Rizal Zahari, Ehsan Rasooliyazdi

Abstract:

Increasing energy absorption is a significant parameter in vehicle design. Absorbing more energy results in decreasing occupant damage. Limitation of the deflection in a side impact results in decreased energy absorption (SEA) and increased peak load (PL). Hence a high crash force jeopardizes passenger safety and vehicle integrity. The aims of this paper are to determine suitable dimensions and material of a square beam subjected to side impact, in order to maximize SEA and minimize PL. To achieve this novel goal, the geometric parameters of a square beam are optimized using the response surface method (RSM).multi-objective optimization is performed, and the optimum design for different response features is obtained.

Keywords: Crashworthiness, side impact, energy absorption, multi-objective optimization, Square beam, SEA

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Authors: Wafa Labib

Abstract:

Teaching methods include lectures, workshops and tutorials for the presentation and discussion of ideas have become out of date; were developed outside the discipline of architecture from the college of engineering and do not satisfy the architectural students’ needs and causes them many difficulties in integrating structure into their design. In an attempt to improve structure teaching methods, this paper focused upon proposing a supportive teaching/learning tool using multi-media applications which seeks to better meet the architecture student’s needs and capabilities and improve the understanding and application of basic and intermediate structural engineering and technology principles. Before introducing the use of multi-media as a supportive teaching tool, a questionnaire was distributed to third year students of a structural design course who were selected as a sample to be surveyed forming a sample of 90 cases. The primary aim of the questionnaire was to identify the students’ learning style and to investigate whether the selected method of teaching could make the teaching and learning process more efficient. Students’ reaction on the use of this method was measured using three key elements indicating that this method is an appropriate teaching method for the nature of the students and the course as well.

Keywords: Teaching Method, Architecture, Learning style, Multi-Media.

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Authors: Djamel Saba, Fatima Zohra Laallam, Brahim Berbaoui

Abstract:

This paper presents a contribution to the design of a multi-agent for the energy management system in a hybrid energy system (SEH). The multi-agent-based energy-coordination management system (MA-ECMS) is based mainly on coordination between agents. The agents share the tasks and exchange information through communications protocols to achieve the main goal. This intelligent system can fully manage the consumption and production or simply to make proposals for action he thinks is best. The initial step is to give a presentation for the system that we want to model in order to understand all the details as much as possible. In our case, it is to implement a system for simulating a process control of energy management.

Keywords: Multi agents system, hybrid energy system, communications protocols, modelization, simulation, control process, energy management.

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Authors: Pasayev, A., C. Askerov, R. Sadiqov, C. Ardil

Abstract:

In contrast to existing of calculation of temperature field of a profile part a blade with convective cooling which are not taking into account multi connective in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM AND FDM) numerical methods from the point of view of a realization on the PC. The theoretical substantiation of these methods is proved by the appropriate theorems.

Keywords: multi coherent systems, method of the boundary integrated equations, singular operators, gas turbines

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