Search results for: Fuzzy Goal Programming.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2215

Search results for: Fuzzy Goal Programming.

1015 Implementation of the Recursive Formula for Evaluation of the Strength of Daniels’ Model

Authors: Václav Sadílek, Miroslav Vořechovský

Abstract:

The paper deals with the classical fiber bundle model of equal load sharing, sometimes referred to as the Daniels’ bundle or the democratic bundle. Daniels formulated a multidimensional integral and also a recursive formula for evaluation of the strength cumulative distribution function. This paper describes three algorithms for evaluation of the recursive formula and also their implementations with source codes in the Python high-level programming language. A comparison of the algorithms are provided with respect to execution time. Analysis of orders of magnitudes of addends in the recursion is also provided.

Keywords: Daniels bundle model, equal load sharing, Python, mpmath.

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1014 CAD Based Predictive Models of the Undeformed Chip Geometry in Drilling

Authors: Panagiotis Kyratsis, Dr. Ing. Nikolaos Bilalis, Dr. Ing. Aristomenis Antoniadis

Abstract:

Twist drills are geometrical complex tools and thus various researchers have adopted different mathematical and experimental approaches for their simulation. The present paper acknowledges the increasing use of modern CAD systems and using the API (Application Programming Interface) of a CAD system, drilling simulations are carried out. The developed DRILL3D software routine, creates parametrically controlled tool geometries and using different cutting conditions, achieves the generation of solid models for all the relevant data involved (drilling tool, cut workpiece, undeformed chip). The final data derived, consist a platform for further direct simulations regarding the determination of cutting forces, tool wear, drilling optimizations etc.

Keywords: Drilling, CAD based simulation, 3D-modelling.

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1013 Determining the Minimum Threshold for the Functional Relatedness of Inner-Outer Class

Authors: Sim Hui Tee, Rodziah Atan, Abdul Azim Abd Ghani

Abstract:

Inner class is a specialized class that defined within a regular outer class. It is used in some programming languages such as Java to carry out the task which is related to its outer class. The functional relatedness between inner class and outer class is always the main concern of defining an inner class. However, excessive use of inner class could sabotage the class cohesiveness. In addition, excessive inner class leads to the difficulty of software maintenance and comprehension. Our research aims at determining the minimum threshold for the functional relatedness of inner-outer class. Such minimum threshold is a guideline for removing or relocating the excessive inner class. Our research provides a feasible way for software developers to define inner classes which are functionally related to the outer class.

Keywords: Cohesion, functional relatedness of inner-outer class, inner class.

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1012 Performance Evaluation of Qos Parameters in Cognitive Radio Using Genetic Algorithm

Authors: Maninder Jeet Kaur, Moin Uddin, Harsh K. Verma

Abstract:

The efficient use of available licensed spectrum is becoming more and more critical with increasing demand and usage of the radio spectrum. This paper shows how the use of spectrum as well as dynamic spectrum management can be effectively managed and spectrum allocation schemes in the wireless communication systems be implemented and used, in future. This paper would be an attempt towards better utilization of the spectrum. This research will focus on the decision-making process mainly, with an assumption that the radio environment has already been sensed and the QoS requirements for the application have been specified either by the sensed radio environment or by the secondary user itself. We identify and study the characteristic parameters of Cognitive Radio and use Genetic Algorithm for spectrum allocation. Performance evaluation is done using MATLAB toolboxes.

Keywords: Cognitive Radio, Fitness Functions, Fuzzy Logic, Quality of Service (QoS)

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1011 Modeling of the Process Parameters using Soft Computing Techniques

Authors: Miodrag T. Manić, Dejan I. Tanikić, Miloš S. Stojković, Dalibor M. ðenadić

Abstract:

The design of technological procedures for manufacturing certain products demands the definition and optimization of technological process parameters. Their determination depends on the model of the process itself and its complexity. Certain processes do not have an adequate mathematical model, thus they are modeled using heuristic methods. First part of this paper presents a state of the art of using soft computing techniques in manufacturing processes from the perspective of applicability in modern CAx systems. Methods of artificial intelligence which can be used for this purpose are analyzed. The second part of this paper shows some of the developed models of certain processes, as well as their applicability in the actual calculation of parameters of some technological processes within the design system from the viewpoint of productivity.

Keywords: fuzzy logic, manufacturing, neural networks

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1010 Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method

Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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1009 Entrepreneur Universal Education System: Future Evolution

Authors: Khaled Elbehiery, Hussam Elbehiery

Abstract:

The success of education is dependent on evolution and adaptation, while the traditional system has worked before, one type of education evolved with the digital age is virtual education that has influenced efficiency in today’s learning environments. Virtual learning has indeed proved its efficiency to overcome the drawbacks of the physical environment such as time, facilities, location, etc., but despite what it had accomplished, the educational system over all is not adequate for being a productive system yet. Earning a degree is not anymore enough to obtain a career job; it is simply missing the skills and creativity. There are always two sides of a coin; a college degree or a specialized certificate, each has its own merits, but having both can put you on a successful IT career path. For many of job-seeking individuals across world to have a clear meaningful goal for work and education and positively contribute the community, a productive correlation and cooperation among employers, universities alongside with the individual technical skills is a must for generations to come. Fortunately, the proposed research “Entrepreneur Universal Education System” is an evolution to meet the needs of both employers and students, in addition to gaining vital and real-world experience in the chosen fields is easier than ever. The new vision is to empower the education to improve organizations’ needs which means improving the world as its primary goal, adopting universal skills of effective thinking, effective action, effective relationships, preparing the students through real-world accomplishment and encouraging them to better serve their organization and their communities faster and more efficiently.

Keywords: Virtual education, academic degree, certificates, internship, amazon web services, Microsoft Azure, Google cloud platform, hybrid models.

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1008 Highly Accurate Tennis Ball Throwing Machine with Intelligent Control

Authors: Ferenc Kovács, Gábor Hosszú

Abstract:

The paper presents an advanced control system for tennis ball throwing machines to improve their accuracy according to the ball impact points. A further advantage of the system is the much easier calibration process involving the intelligent solution of the automatic adjustment of the stroking parameters according to the ball elasticity, the self-calibration, the use of the safety margin at very flat strokes and the possibility to placing the machine to any position of the half court. The system applies mathematical methods to determine the exact ball trajectories and special approximating processes to access all points on the aimed half court.

Keywords: Control system, robot programming, robot control, sports equipment, throwing machine.

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1007 Evolutionary Search Techniques to Solve Set Covering Problems

Authors: Darwin Gouwanda, S. G. Ponnambalam

Abstract:

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.

Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.

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1006 Some Solid Transportation Models with Crisp and Rough Costs

Authors: Pradip Kundu, Samarjit Kar, Manoranjan Maiti

Abstract:

In this paper, some practical solid transportation models are formulated considering per trip capacity of each type of conveyances with crisp and rough unit transportation costs. This is applicable for the system in which full vehicles, e.g. trucks, rail coaches are to be booked for transportation of products so that transportation cost is determined on the full of the conveyances. The models with unit transportation costs as rough variables are transformed into deterministic forms using rough chance constrained programming with the help of trust measure. Numerical examples are provided to illustrate the proposed models in crisp environment as well as with unit transportation costs as rough variables.

Keywords: Solid transportation problem, Rough set, Rough variable, Trust measure.

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1005 Decision Support System for Suppliers

Authors: Babak Tashakori Bafghi, Laleh Tashakori, Reza Allahyari Soeini, Mohammad Mokhtari

Abstract:

Supplier selection is a multi criteria decision-making process that comprises tangible and intangible factors. The majority of previous supplier selection techniques do not consider strategic perspective. Besides, uncertainty is one of the most important obstacles in supplier selection. For the first, time in this paper, the idea of the algorithm " Knapsack " is used to select suppliers Moreover, an attempt has to be made to take the advantage of a simple numerical method for solving model .This is an innovation to resolve any ambiguity in choosing suppliers. This model has been tried in the suppliers selected in a competitive environment and according to all desired standards of quality and quantity to show the efficiency of the model, an industry sample has been uses.

Keywords: Knapsack, linear programming, supplier select, supply chain management.

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1004 Intelligent Vision System for Human-Robot Interface

Authors: Al-Amin Bhuiyan, Chang Hong Liu

Abstract:

This paper addresses the development of an intelligent vision system for human-robot interaction. The two novel contributions of this paper are 1) Detection of human faces and 2) Localizing the eye. The method is based on visual attributes of human skin colors and geometrical analysis of face skeleton. This paper introduces a spatial domain filtering method named ?Fuzzily skewed filter' which incorporates Fuzzy rules for deciding the gray level of pixels in the image in their neighborhoods and takes advantages of both the median and averaging filters. The effectiveness of the method has been justified over implementing the eye tracking commands to an entertainment robot, named ''AIBO''.

Keywords: Fuzzily skewed filter, human-robot interface, rmscontrast, skin color segmentation.

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1003 GSM Based Smart Patient Monitoring System

Authors: Ayman M. Mansour

Abstract:

In this paper, we propose an intelligent system that is used for monitoring the health conditions of patients. Monitoring the health condition of patients is a complex problem that involves different medical units and requires continuous monitoring especially in rural areas because of inadequate number of available specialized physicians. The proposed system will improve patient care and drive costs down comparing to the existing system in Jordan. The proposed system will be the start point to faster and improve the communication between different units in the health system in Jordan. Connecting patients and their physicians beyond hospital doors regarding their geographical area is an important issue in developing the health system in Jordan. The ability of making medical decisions, the quality of medical is expected to be improved.

Keywords: GSM, SMS, Patient, Monitoring system, Fuzzy Logic, Multi-agent system.

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1002 An Integrated Mixed-Integer Programming Model to Address Concurrent Project Scheduling and Material Ordering

Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of project scheduling and material ordering can provide more flexibility to the project scheduling problem, as the project execution costs can be enhanced. Hence, the issue has been taken into account in this paper. To do so, a mixed-integer mathematical model is developed which considers the aforementioned flexibility, in addition to the materials quantity discount and space availability restrictions. Moreover, the activities duration has been treated as decision variables. Finally, the efficiency of the proposed model is tested by different instances. Additionally, the influence of the aforementioned parameters is investigated on the model performance.

Keywords: Material ordering, project scheduling, quantity discount, space availability.

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1001 Automated Segmentation of ECG Signals using Piecewise Derivative Dynamic Time Warping

Authors: Ali Zifan, Mohammad Hassan Moradi, Sohrab Saberi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG-s. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna-s two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna-s method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise DerivativeDynamic Time Warping.

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1000 Web Service Providing Using Web Service Transformation

Authors: Youngmee Shin, Hyunjoo Bae

Abstract:

In order to provide existing SOAP (Simple Object Access Protocol)-based Web services with users who are familiar with REST (REpresentational State Transfer)-style Web services, this paper proposes Web service providing method using Web service transformation. This enables SOAP-based service providers to define rules for mapping from RESTful Web services to SOAP-based ones. Using these mapping rules, HTTP request messages for RESTful services are converted automatically into SOAP-based service invocations. Web service providers need not develop duplicate RESTful services and they can avoid programming mediation modules per service. Furthermore, they need not equip mediation middleware like ESB (Enterprise Service Bus) only for the purpose of transformation of two different Web service styles.

Keywords: REST, SOAP, Web Services, Web ServiceTransformation.

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999 Survey of Key Management Algorithms in WiMAX

Authors: R. Chithra, B. Kalavathi, J. Christy Lavanya

Abstract:

WiMAX is a telecommunications technology and it is specified by the Institute of Electrical and Electronics Engineers Inc., as the IEEE 802.16 standard. The goal of this technology is to provide a wireless data over long distances in a variety of ways. IEEE 802.16 is a recent standard for mobile communication. In this paper, we provide an overview of various key management algorithms to provide security for WiMAX.

Keywords: Broadcast, Rekeying, Scalability, Secrecy, Unicast, WiMAX.

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998 Role of GIS in Distribution Power Systems

Authors: N. Rezaee, M Nayeripour, A. Roosta, T. Niknam

Abstract:

With the prevalence of computer and development of information technology, Geographic Information Systems (GIS) have long used for a variety of applications in electrical engineering. GIS are designed to support the analysis, management, manipulation and mapping of spatial data. This paper presents several usages of GIS in power utilities such as automated route selection for the construction of new power lines which uses a dynamic programming model for route optimization, load forecasting and optimizing planning of substation-s location and capacity with comprehensive algorithm which involves an accurate small-area electric load forecasting procedure and simulates the different cost functions of substations.

Keywords: Geographic information systems (GIS), optimallocation and capacity, power distribution planning, route selection, spatial load forecasting.

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997 Multi Objective Micro Genetic Algorithm for Combine and Reroute Problem

Authors: Soottipoom Yaowiwat, Manoj Lohatepanont, Proadpran Punyabukkana

Abstract:

Several approaches such as linear programming, network modeling, greedy heuristic and decision support system are well-known approaches in solving irregular airline operation problem. This paper presents an alternative approach based on Multi Objective Micro Genetic Algorithm. The aim of this research is to introduce the concept of Multi Objective Micro Genetic Algorithm as a tool to solve irregular airline operation, combine and reroute problem. The experiment result indicated that the model could obtain optimal solutions within a few second.

Keywords: Irregular Airline Operation, Combine and RerouteRoutine, Genetic Algorithm, Micro Genetic Algorithm, Multi ObjectiveOptimization, Evolutionary Algorithm.

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996 A Heuristic Based Conceptual Framework for Product Innovation

Authors: Amalia Suzianti

Abstract:

This research elaborates decision models for product innovation in the early phases, focusing on one of the most widely implemented method in marketing research: conjoint analysis and the related conjoint-based models with special focus on heuristics programming techniques for the development of optimal product innovation. The concept, potential, requirements and limitations of conjoint analysis and its conjoint-based heuristics successors are analysed and the development of conceptual framework of Genetic Algorithm (GA) as one of the most widely implemented heuristic methods for developing product innovations are discussed.

Keywords: Product Innovation, Conjoint Analysis, Heuristic Model, Genetic Algorithm

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995 The Labeled Classification and its Application

Authors: M. Nemissi, H. Seridi, H. Akdag

Abstract:

This paper presents and evaluates a new classification method that aims to improve classifiers performances and speed up their training process. The proposed approach, called labeled classification, seeks to improve convergence of the BP (Back propagation) algorithm through the addition of an extra feature (labels) to all training examples. To classify every new example, tests will be carried out each label. The simplicity of implementation is the main advantage of this approach because no modifications are required in the training algorithms. Therefore, it can be used with others techniques of acceleration and stabilization. In this work, two models of the labeled classification are proposed: the LMLP (Labeled Multi Layered Perceptron) and the LNFC (Labeled Neuro Fuzzy Classifier). These models are tested using Iris, wine, texture and human thigh databases to evaluate their performances.

Keywords: Artificial neural networks, Fusion of neural networkfuzzysystems, Learning theory, Pattern recognition.

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994 Vibration Control of MDOF Structure under Earthquake Excitation using Passive Control and Active Control

Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

Abstract:

In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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993 Automated ECG Segmentation Using Piecewise Derivative Dynamic Time Warping

Authors: Ali Zifan, Sohrab Saberi, Mohammad Hassan Moradi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG's. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna's two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna's method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise Derivative Dynamic Time Warping.

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992 An Engineering Approach to Forecast Volatility of Financial Indices

Authors: Irwin Ma, Tony Wong, Thiagas Sankar

Abstract:

By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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991 Improving RBF Networks Classification Performance by using K-Harmonic Means

Authors: Z. Zainuddin, W. K. Lye

Abstract:

In this paper, a clustering algorithm named KHarmonic means (KHM) was employed in the training of Radial Basis Function Networks (RBFNs). KHM organized the data in clusters and determined the centres of the basis function. The popular clustering algorithms, namely K-means (KM) and Fuzzy c-means (FCM), are highly dependent on the initial identification of elements that represent the cluster well. In KHM, the problem can be avoided. This leads to improvement in the classification performance when compared to other clustering algorithms. A comparison of the classification accuracy was performed between KM, FCM and KHM. The classification performance is based on the benchmark data sets: Iris Plant, Diabetes and Breast Cancer. RBFN training with the KHM algorithm shows better accuracy in classification problem.

Keywords: Neural networks, Radial basis functions, Clusteringmethod, K-harmonic means.

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990 Surface Roughness Analysis, Modelling and Prediction in Fused Deposition Modelling Additive Manufacturing Technology

Authors: Yusuf S. Dambatta, Ahmed A. D. Sarhan

Abstract:

Fused deposition modelling (FDM) is one of the most prominent rapid prototyping (RP) technologies which is being used to efficiently fabricate CAD 3D geometric models. However, the process is coupled with many drawbacks, of which the surface quality of the manufactured RP parts is among. Hence, studies relating to improving the surface roughness have been a key issue in the field of RP research. In this work, a technique of modelling the surface roughness in FDM is presented. Using experimentally measured surface roughness response of the FDM parts, an ANFIS prediction model was developed to obtain the surface roughness in the FDM parts using the main critical process parameters that affects the surface quality. The ANFIS model was validated and compared with experimental test results.

Keywords: Surface roughness, fused deposition modelling, adaptive neuro fuzzy inference system, ANFIS, orientation.

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989 Implementing a Database from a Requirement Specification

Authors: M. Omer, D. Wilson

Abstract:

Creating a database scheme is essentially a manual process. From a requirement specification the information contained within has to be analyzed and reduced into a set of tables, attributes and relationships. This is a time consuming process that has to go through several stages before an acceptable database schema is achieved. The purpose of this paper is to implement a Natural Language Processing (NLP) based tool to produce a relational database from a requirement specification. The Stanford CoreNLP version 3.3.1 and the Java programming were used to implement the proposed model. The outcome of this study indicates that a first draft of a relational database schema can be extracted from a requirement specification by using NLP tools and techniques with minimum user intervention. Therefore this method is a step forward in finding a solution that requires little or no user intervention.

Keywords: Information Extraction, Natural Language Processing, Relation Extraction.

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988 Urban Roads of Bhopal City

Authors: Anshu Gupta

Abstract:

Quality evaluation of urban environment is an integral part of efficient urban environment planning and management. The development of fuzzy set theory (FST) and the introduction of FST to the urban study field attempts to incorporate the gradual variation and avoid loss of information. Urban environmental quality assessment pertain to interpretation and forecast of the urban environmental quality according to the national regulation about the permitted content of contamination for the sake of protecting human health and subsistence environment . A strategic motor vehicle control strategy has to be proposed to mitigate the air pollution in the city. There is no well defined guideline for the assessment of urban air pollution and no systematic study has been reported so far for Indian cities. The methodology adopted may be useful in similar cities of India. Remote sensing & GIS can play significant role in mapping air pollution.

Keywords: GIS, Pollution, Remote Sensing, Urban.

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987 An Application for Web Mining Systems with Services Oriented Architecture

Authors: Thiago M. R. Dias, Gray F. Moita, Paulo E. M. Almeida

Abstract:

Although the World Wide Web is considered the largest source of information there exists nowadays, due to its inherent dynamic characteristics, the task of finding useful and qualified information can become a very frustrating experience. This study presents a research on the information mining systems in the Web; and proposes an implementation of these systems by means of components that can be built using the technology of Web services. This implies that they can encompass features offered by a services oriented architecture (SOA) and specific components may be used by other tools, independent of platforms or programming languages. Hence, the main objective of this work is to provide an architecture to Web mining systems, divided into stages, where each step is a component that will incorporate the characteristics of SOA. The separation of these steps was designed based upon the existing literature. Interesting results were obtained and are shown here.

Keywords: Web Mining, Service Oriented Architecture, WebServices.

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986 Evaluation of Linear and Geometrically Nonlinear Static and Dynamic Analysis of Thin Shells by Flat Shell Finite Elements

Authors: Djamel Boutagouga, Kamel Djeghaba

Abstract:

The choice of finite element to use in order to predict nonlinear static or dynamic response of complex structures becomes an important factor. Then, the main goal of this research work is to focus a study on the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements. In this purpose: First, simple triangular and quadrilateral flat shell finite elements are implemented in an incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear analysis. The triangular element is a combination of DKT and CST elements, while the quadrilateral is a combination of DKQ and the bilinear quadrilateral membrane element. In both elements, the sixth degree of freedom is handled via introducing fictitious stiffness. Secondly, in the same code, the sixth degrees of freedom in these elements is handled differently where the in-plane rotational d.o.f is considered as an effective d.o.f in the in-plane filed interpolation. Our goal is to compare resulting shell elements. Third, the analysis is enlarged to dynamic linear analysis by direct integration using Newmark-s implicit method. Finally, the linear dynamic analysis is extended to geometrically nonlinear dynamic analysis where Newmark-s method is used to integrate equations of motion and the Newton-Raphson method is employed for iterating within each time step increment until equilibrium is achieved. The obtained results demonstrate the effectiveness and robustness of the interpolation of the in-plane rotational d.o.f. and present deficiencies of using fictitious stiffness in dynamic linear and nonlinear analysis.

Keywords: Flat shell, dynamic analysis, nonlinear, Newmark, drilling rotation.

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