Search results for: modal expansion approach

Authors: Chunshien Li, Jhao-Wun Hu, Tai-Wei Chiang, Tsunghan Wu

Abstract:

Time series forecasting is an important and widely popular topic in the research of system modeling. This paper describes how to use the hybrid PSO-RLSE neuro-fuzzy learning approach to the problem of time series forecasting. The PSO algorithm is used to update the premise parameters of the proposed prediction system, and the RLSE is used to update the consequence parameters. Thanks to the hybrid learning (HL) approach for the neuro-fuzzy system, the prediction performance is excellent and the speed of learning convergence is much faster than other compared approaches. In the experiments, we use the well-known Mackey-Glass chaos time series. According to the experimental results, the prediction performance and accuracy in time series forecasting by the proposed approach is much better than other compared approaches, as shown in Table IV. Excellent prediction performance by the proposed approach has been observed.

Keywords: forecasting, hybrid learning (HL), Neuro-FuzzySystem (NFS), particle swarm optimization (PSO), recursiveleast-squares estimator (RLSE), time series

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Authors: S. S. Bendib, L. W. Mouss, S. Kalla

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This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: Embedded real-time systems design, makespan, reliability, self-organization, compromises.

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Authors: Cherif Haddad, Faouzi Ben Charrada

Abstract:

On a such wide-area environment as a Grid, data placement is an important aspect of distributed database systems. In this paper, we address the problem of initial placement of database no-replicated fragments in Grid architecture. We propose a graph based approach that considers resource restrictions. The goal is to optimize the use of computing, storage and communication resources. The proposed approach is developed in two phases: in the first phase, we perform fragment grouping using knowledge about fragments dependency and, in the second phase, we determine an efficient placement of the fragment groups on the Grid. We also show, via experimental analysis that our approach gives solutions that are close to being optimal for different databases and Grid configurations.

Keywords: Grid computing, Distributed systems, Data resourcesmanagement, Database systems, Database placement.

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Authors: Naveen Virmani, Rajeev Saha, Rajeshwar Sahai

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There is drastic change in manufacturing era in last two decades. It has become mandatory for the industries to become aware of latest and advanced manufacturing technologies and strategies. Leagile manufacturing focuses on minimizing the wastes and meeting customers’ requirements in minimum time possible. However, it becomes difficult to implement all leagile tools simultaneously in industry. In this paper, 17 main criteria of leagile manufacturing have been found and DEMATEL (Decision Making Trial and Evaluation Laboratory) approach has been applied to analyze importance of criteria and casual relations among these criteria.

Keywords: Agile, DEMATEL approach, lean, leagile manufacturing.

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Authors: N. W. U. D. Chathurani, Shlomo Geva, Vinod Chandran, Proboda Rajapaksha

Abstract:

Selecting an appropriate image representation is the most important factor in implementing an effective Content-Based Image Retrieval (CBIR) system. This paper presents a multi-feature fusion approach for efficient CBIR, based on the distance distribution of features and relative feature weights at the time of query processing. It is a simple yet effective approach, which is free from the effect of features' dimensions, ranges, internal feature normalization and the distance measure. This approach can easily be adopted in any feature combination to improve retrieval quality. The proposed approach is empirically evaluated using two benchmark datasets for image classification (a subset of the Corel dataset and Oliva and Torralba) and compared with existing approaches. The performance of the proposed approach is confirmed with the significantly improved performance in comparison with the independently evaluated baseline of the previously proposed feature fusion approaches.

Keywords: Feature fusion, image retrieval, membership function, normalization.

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Authors: Philippe A. Martin

Abstract:

This article first summarizes reasons why current approaches supporting Open Learning and Distance Education need to be complemented by tools permitting lecturers, researchers and students to cooperatively organize the semantic content of Learning related materials (courses, discussions, etc.) into a fine-grained shared semantic network. This first part of the article also quickly describes the approach adopted to permit such a collaborative work. Then, examples of such semantic networks are presented. Finally, an evaluation of the approach by students is provided and analyzed.

Keywords: knowledge sharing, knowledge evaluation, e-learning

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Authors: Hadj Bourdoucen, Adel Gastli

Abstract:

In this paper, an approach for finding optimized layouts for connecting PV units delivering maximum array output power is suggested. The approach is based on considering the different varying parameters of PV units that might be extracted from a general two-diode model. These are mainly, solar irradiation, reverse saturation currents, ideality factors, series and shunt resistances in addition to operating temperature. The approach has been tested on 19 possible 2×3 configurations and allowed to determine the optimized configurations as well as examine the effects of the different units- parameters on the maximum output power. Thus, using this approach, standard arrays with n×m units can be configured for maximum generated power and allows designing PV based systems having reduced surfaces to fit specific required power, as it is the case for solar cars and other mobile systems.

Keywords: Photovoltaic, PV unit, optimum configuration, maximum power, Orcad.

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Authors: Sang-Rak Kim, Jea-Yong Park, Won-Goo Lee, Jin-Shik Yu, Seog-Young Han

Abstract:

This paper presents a Reliability-Based Topology Optimization (RBTO) based on Evolutionary Structural Optimization (ESO). An actual design involves uncertain conditions such as material property, operational load and dimensional variation. Deterministic Topology Optimization (DTO) is obtained without considering of the uncertainties related to the uncertainty parameters. However, RBTO involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). Limit state function is approximated using Monte Carlo Simulation and Central Composite Design for reliability analysis. ESO, one of the topology optimization techniques, is adopted for topology optimization. Numerical examples are presented to compare the DTO with RBTO.

Keywords: Evolutionary Structural Optimization, PerformanceMeasure Approach, Reliability-Based Topology Optimization, Reliability Index Approach.

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Authors: Ramandeep S. Sidhu, Sunil Khullar, Parvinder S. Sandhu, R. P. S. Bedi, Kiranbir Kaur

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In this paper, subtractive clustering based fuzzy inference system approach is used for early detection of faults in the function oriented software systems. This approach has been tested with real time defect datasets of NASA software projects named as PC1 and CM1. Both the code based model and joined model (combination of the requirement and code based metrics) of the datasets are used for training and testing of the proposed approach. The performance of the models is recorded in terms of Accuracy, MAE and RMSE values. The performance of the proposed approach is better in case of Joined Model. As evidenced from the results obtained it can be concluded that Clustering and fuzzy logic together provide a simple yet powerful means to model the earlier detection of faults in the function oriented software systems.

Keywords: Subtractive clustering, fuzzy inference system, fault proneness.

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Authors: Siyanda S. Biyela, Willie A. Cronje

Abstract:

This paper presents a desktop study of comparing two different wave energy to electricity technologies (WECs) using a techno-economic approach. This techno-economic approach forms basis of a framework for rapid comparison of current and future technologies. The approach also seeks to assist in investment and strategic decision making expediting future deployment of wave energy harvesting in South Africa.

Keywords: Cost of energy, tool, wave energy converter, WEC-Sim.

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Authors: Ramaswamy Palaniappan

Abstract:

This paper reports a new approach on identifying the individuality of persons by using parametric classification of multiple mental thoughts. In the approach, electroencephalogram (EEG) signals were recorded when the subjects were thinking of one or more (up to five) mental thoughts. Autoregressive features were computed from these EEG signals and classified by Linear Discriminant classifier. The results here indicate that near perfect identification of 400 test EEG patterns from four subjects was possible, thereby opening up a new avenue in biometrics.

Keywords: Autoregressive, Biometrics, Electroencephalogram, Linear discrimination, Mental thoughts.

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Authors: Tijani Delleji, Mourad Zribi, Ahmed Ben Hamida

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This paper discusses EM algorithm and Bootstrap approach combination applied for the improvement of the satellite image fusion process. This novel satellite image fusion method based on estimation theory EM algorithm and reinforced by Bootstrap approach was successfully implemented and tested. The sensor images are firstly split by a Bayesian segmentation method to determine a joint region map for the fused image. Then, we use the EM algorithm in conjunction with the Bootstrap approach to develop the bootstrap EM fusion algorithm, hence producing the fused targeted image. We proposed in this research to estimate the statistical parameters from some iterative equations of the EM algorithm relying on a reference of representative Bootstrap samples of images. Sizes of those samples are determined from a new criterion called 'hybrid criterion'. Consequently, the obtained results of our work show that using the Bootstrap EM (BEM) in image fusion improve performances of estimated parameters which involve amelioration of the fused image quality; and reduce the computing time during the fusion process.

Keywords: Satellite image fusion, Bayesian segmentation, Bootstrap approach, EM algorithm.

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Authors: Leon Fu, Xiangyang Xue

Abstract:

In this paper, we propose a new approach to query-by-humming, focusing on MP3 songs database. Since MP3 songs are much more difficult in melody representation than symbolic performance data, we adopt to extract feature descriptors from the vocal sounds part of the songs. Our approach is based on signal filtering, sub-band spectral processing, MDCT coefficients analysis and peak energy detection by ignorance of the background music as much as possible. Finally, we apply dual dynamic programming algorithm for feature similarity matching. Experiments will show us its online performance in precision and efficiency.

Keywords: DP, MDCT, MP3, QBH.

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Authors: Sara Ansari, Mohammad Hadi Sadreddini

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The increasing importance of data stream arising in a wide range of advanced applications has led to the extensive study of mining frequent patterns. Mining data streams poses many new challenges amongst which are the one-scan nature, the unbounded memory requirement and the high arrival rate of data streams. In this paper, we propose a new approach for mining itemsets on data stream. Our approach SFIDS has been developed based on FIDS algorithm. The main attempts were to keep some advantages of the previous approach and resolve some of its drawbacks, and consequently to improve run time and memory consumption. Our approach has the following advantages: using a data structure similar to lattice for keeping frequent itemsets, separating regions from each other with deleting common nodes that results in a decrease in search space, memory consumption and run time; and Finally, considering CPU constraint, with increasing arrival rate of data that result in overloading system, SFIDS automatically detect this situation and discard some of unprocessing data. We guarantee that error of results is bounded to user pre-specified threshold, based on a probability technique. Final results show that SFIDS algorithm could attain about 50% run time improvement than FIDS approach.

Keywords: Data stream, frequent itemset, stream mining.

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Authors: Sourabh Agrawal, Ashok K. Jain

Abstract:

Stick models are widely used in studying the behaviour of straight as well as skew bridges and viaducts subjected to earthquakes while carrying out preliminary studies. The application of such models to highly curved bridges continues to pose challenging problems. A viaduct proposed in the foothills of the Himalayas in Northern India is chosen for the study. It is having 8 simply supported spans @ 30 m c/c. It is doubly curved in horizontal plane with 20 m radius. It is inclined in vertical plane as well. The superstructure consists of a box section. Three models have been used: a conventional stick model, an improved stick model and a 3D finite element model. The improved stick model is employed by making use of body constraints in order to study its capabilities. The first 8 frequencies are about 9.71% away in the latter two models. Later the difference increases to 80% in 50th mode. The viaduct was subjected to all three components of the El Centro earthquake of May 1940. The numerical integration was carried out using the Hilber- Hughes-Taylor method as implemented in SAP2000. Axial forces and moments in the bridge piers as well as lateral displacements at the bearing levels are compared for the three models. The maximum difference in the axial forces and bending moments and displacements vary by 25% between the improved and finite element model. Whereas, the maximum difference in the axial forces, moments, and displacements in various sections vary by 35% between the improved stick model and equivalent straight stick model. The difference for torsional moment was as high as 75%. It is concluded that the stick model with body constraints to model the bearings and expansion joints is not desirable in very sharp S curved viaducts even for preliminary analysis. This model can be used only to determine first 10 frequency and mode shapes but not for member forces. A 3D finite element analysis must be carried out for meaningful results.

Keywords: Bearing, body constraint, box girder, curved viaduct, expansion joint, finite element, link element, seismic, stick model, time history analysis.

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Authors: Shahram Mohammadi, Ali Frajzadeh

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A lot of matching algorithms with different characteristics have been introduced in recent years. For real time systems these algorithms are usually based on minutiae features. In this paper we introduce a novel approach for feature extraction in which the extracted features are independent of shift and rotation of the fingerprint and at the meantime the matching operation is performed much more easily and with higher speed and accuracy. In this new approach first for any fingerprint a reference point and a reference orientation is determined and then based on this information features are converted into polar coordinates. Due to high speed and accuracy of this approach and small volume of extracted features and easily execution of matching operation this approach is the most appropriate for real time applications.

Keywords: Matching, Minutiae, Reference point, Reference orientation

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Authors: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

Abstract:

Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I₁, I₂, … I_n at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: Multi-temporal satellite image, urban growth, Non-stationarity, stochastic modeling.

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Authors: S. Raja Balachandar, K.Kannan

Abstract:

This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: Combinatorial Optimization Problem, Generalized Assignment Problem, Intercept Matrix, Heuristic, Computational Complexity, NP-Hard Problems.

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Authors: Sahil, Rajeev Saha, Sanjeev Kumar

Abstract:

Material selection is one of the key issues for the production of reliable and quality products in industries. A number of materials are available for a single product due to which material selection become a difficult task. The aim of this paper is to select appropriate material for gear used in fuel pump by using Graph Theory and Matrix Approach (GTMA). GTMA is a logical and systematic approach that can be used to model and analyze various engineering systems. In present work, four alternative material and their seven attributes are used to identify the best material for given product.

Keywords: Material, GTMA, MADM, digraph, decision making.

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Authors: M. Bouri, L. Chraïbi, N. Sefiani

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Currently, industries endeavor to align their environmental management system with the ISO 14001:2015 international standard, while preserving competitiveness and sustainability. Then, a key driver for these industries is to develop a skilled workforce that is able to implement, continuously improve and audit the environmental management system. The purpose of this paper is to provide an environmental competency framework that aims to identify, rank and categorize the competencies required by both the environmental managers and auditors. This competency framework is expected to be useful during competency assessment, recruitment, and training processes. To achieve this end, a modified 2-tuple Delphi approach is here proposed based on a combination of the modified Delphi approach and the 2-tuple linguistic representation model. The adopted approach is presented as numerous questionnaires that are spread over multiple rounds in order to obtain a consensus among the different Moroccan experts participating to this study.

Keywords: Competency framework, Delphi, environmental competency, 2-tuple.

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Authors: Samy Sadek, Ayoub Al-Hamadi, Axel Panning, Bernd Michaelis, Usama Sayed

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In this paper, we propose a novel approach for image segmentation via fuzzification of Rènyi Entropy of Generalized Distributions (REGD). The fuzzy REGD is used to precisely measure the structural information of image and to locate the optimal threshold desired by segmentation. The proposed approach draws upon the postulation that the optimal threshold concurs with maximum information content of the distribution. The contributions in the paper are as follow: Initially, the fuzzy REGD as a measure of the spatial structure of image is introduced. Then, we propose an efficient entropic segmentation approach using fuzzy REGD. However the proposed approach belongs to entropic segmentation approaches (i.e. these approaches are commonly applied to grayscale images), it is adapted to be viable for segmenting color images. Lastly, diverse experiments on real images that show the superior performance of the proposed method are carried out.

Keywords: Entropy of generalized distributions, entropy fuzzification, entropic image segmentation.

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Authors: Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine

Abstract:

This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Keywords: Gauss-Legendre, Clenshaw-Curtis, quadrature, Peano kernel, irregular sampling.

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Authors: Zviad Ghadua, Biswa Bhattacharya

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The Flash Flood Guidance (FFG) provides the rainfall amount of a given duration necessary to cause flooding. The approach is based on the development of rainfall-runoff curves, which helps us to find out the rainfall amount that would cause flooding. An alternative approach, mostly experimented with Italian Alpine catchments, is based on determining threshold discharges from past events and on finding whether or not an oncoming flood has its magnitude more than some critical discharge thresholds found beforehand. Both approaches suffer from large uncertainties in forecasting flash floods as, due to the simplistic approach followed, the same rainfall amount may or may not cause flooding. This uncertainty leads to the question whether a probabilistic model is preferable over a deterministic one in forecasting flash floods. We propose the use of a Bayesian probabilistic approach in flash flood forecasting. A prior probability of flooding is derived based on historical data. Additional information, such as antecedent moisture condition (AMC) and rainfall amount over any rainfall thresholds are used in computing the likelihood of observing these conditions given a flash flood has occurred. Finally, the posterior probability of flooding is computed using the prior probability and the likelihood. The variation of the computed posterior probability with rainfall amount and AMC presents the suitability of the approach in decision making in an uncertain environment. The methodology has been applied to the Posina basin in Italy. From the promising results obtained, we can conclude that the Bayesian approach in flash flood forecasting provides more realistic forecasting over the FFG.

Keywords: Flash flood, Bayesian, flash flood guidance, FFG, forecasting, Posina.

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Authors: Ramin Halavati, Mansour Jamzad, Mahdieh Soleymani

Abstract:

Persian (Farsi) script is totally cursive and each character is written in several different forms depending on its former and later characters in the word. These complexities make automatic handwriting recognition of Persian a very hard problem and there are few contributions trying to work it out. This paper presents a novel practical approach to online recognition of Persian handwriting which is based on representation of inputs and patterns with very simple visual features and comparison of these simple terms. This recognition approach is tested over a set of Persian words and the results have been quite acceptable when the possible words where unknown and they were almost all correct in cases that the words where chosen from a prespecified list.

Keywords: Image Processing, Pattern Recognition.

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Authors: Heung Seok Chae, Jaegeol Park

Abstract:

Recently, there have been an increasing interest in RFID system and RFID systems have been applied to various applications. Load balancing is a fundamental technique for providing scalability of systems by moving workload from overloaded nodes to under-loaded nodes. This paper presents an approach to adaptive load balancing for RFID middlewares. Workloads of RFID middlewares can have a considerable variation according to the location of the connected RFID readers and can abruptly change at a particular instance. The proposed approach considers those characteristics of RFID middle- wares to provide an efficient load balancing.

Keywords: RFID middleware, Adaptive load balancing.

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Authors: Abdur Rosyid, Mohamed El-Madany, Mohanad Alata

Abstract:

Due to simplicity and low cost, rotordynamic system is often modeled by using lumped parameters. Recently, finite elements have been used to model rotordynamic system as it offers higher accuracy. However, it involves high degrees of freedom. In some applications such as control design, this requires higher cost. For this reason, various model reduction methods have been proposed. This work demonstrates the quality of model reduction of rotor-bearing-support system through substructuring. The quality of the model reduction is evaluated by comparing some first natural frequencies, modal damping ratio, critical speeds, and response of both the full system and the reduced system. The simulation shows that the substructuring is proven adequate to reduce finite element rotor model in the frequency range of interest as long as the number and the location of master nodes are determined appropriately. However, the reduction is less accurate in an unstable or nearly-unstable system.

Keywords: Finite element model, rotordynamic system, model reduction, substructuring.

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Authors: Mohamed Mahmoud Hasan, Hoda M. O. Mokhtar

Abstract:

With the gigantic increment in portable applications use and the spread of positioning and location-aware technologies that we are seeing today, new procedures and methodologies for location-based strategies are required. Location recommendation is one of the highly demanded location-aware applications uniquely with the wide accessibility of social network applications that are location-aware including Facebook check-ins, Foursquare, and others. In this paper, we aim to present a new methodology for location recommendation. The proposed approach coordinates customary spatial traits alongside other essential components including shortest distance, and user interests. We also present another idea namely, "activity trajectory" that represents trajectory that fulfills the set of activities that the user is intrigued to do. The approach dispatched acquaints the related distance value to select trajectory(ies) with minimum cost value (distance) and spatial-area to prune unneeded directions. The proposed calculation utilizes the idea of movement direction to prescribe most comparable N-trajectory(ies) that matches the client's required action design with least voyaging separation. To upgrade the execution of the proposed approach, parallel handling is applied through the employment of a MapReduce based approach. Experiments taking into account genuine information sets were built up and tested for assessing the proposed approach. The exhibited tests indicate how the proposed approach beets different strategies giving better precision and run time.

Keywords: Location-based recommendation, map-reduce, recommendation system, trajectory search.

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Authors: N. Z. A. Hamid, M. S. M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.

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Authors: Kyrre M Begnum, Matthew Disney

Abstract:

Virtualization and high performance computing have been discussed from a performance perspective in recent publications. We present and discuss a flexible and efficient approach to the management of virtual clusters. A virtual machine management tool is extended to function as a fabric for cluster deployment and management. We show how features such as saving the state of a running cluster can be used to avoid disruption. We also compare our approach to the traditional methods of cluster deployment and present benchmarks which illustrate the efficiency of our approach.

Keywords: Cluster management, clusters, high-performance, virtual machines, Xen

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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