Search results for: real-coded genetic algorithm
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3635

Search results for: real-coded genetic algorithm

995 Automated Stereophotogrammetry Data Cleansing

Authors: Stuart Henry, Philip Morrow, John Winder, Bryan Scotney

Abstract:

The stereophotogrammetry modality is gaining more widespread use in the clinical setting. Registration and visualization of this data, in conjunction with conventional 3D volumetric image modalities, provides virtual human data with textured soft tissue and internal anatomical and structural information. In this investigation computed tomography (CT) and stereophotogrammetry data is acquired from 4 anatomical phantoms and registered using the trimmed iterative closest point (TrICP) algorithm. This paper fully addresses the issue of imaging artifacts around the stereophotogrammetry surface edge using the registered CT data as a reference. Several iterative algorithms are implemented to automatically identify and remove stereophotogrammetry surface edge outliers, improving the overall visualization of the combined stereophotogrammetry and CT data. This paper shows that outliers at the surface edge of stereophotogrammetry data can be successfully removed automatically.

Keywords: Data cleansing, stereophotogrammetry.

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994 Comparative Study between Classical P-Q Method and Modern Fuzzy Controller Method to Improve the Power Quality of an Electrical Network

Authors: A. Morsli, A.Tlemçani, N. Ould Cherchali, M. S. Boucherit

Abstract:

This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to a shunt Active Power Filter (sAPF) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: Fuzzy logic controller, P-Q method, Pulse Width Modulation (PWM), shunt Active Power Filter (sAPF), Total Harmonic Distortion (THD).

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993 A Hybrid Heuristic for the Team Orienteering Problem

Authors: Adel Bouchakhchoukha, Hakim Akeb

Abstract:

In this work, we propose a hybrid heuristic in order to solve the Team Orienteering Problem (TOP). Given a set of points (or customers), each with associated score (profit or benefit), and a team that has a fixed number of members, the problem to solve is to visit a subset of points in order to maximize the total collected score. Each member performs a tour starting at the start point, visiting distinct customers and the tour terminates at the arrival point. In addition, each point is visited at most once, and the total time in each tour cannot be greater than a given value. The proposed heuristic combines beam search and a local optimization strategy. The algorithm was tested on several sets of instances and encouraging results were obtained.

Keywords: Team Orienteering Problem, Vehicle Routing, Beam Search, Local Search.

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992 Intention Recognition using a Graph Representation

Authors: So-Jeong Youn, Kyung-Whan Oh

Abstract:

The human friendly interaction is the key function of a human-centered system. Over the years, it has received much attention to develop the convenient interaction through intention recognition. Intention recognition processes multimodal inputs including speech, face images, and body gestures. In this paper, we suggest a novel approach of intention recognition using a graph representation called Intention Graph. A concept of valid intention is proposed, as a target of intention recognition. Our approach has two phases: goal recognition phase and intention recognition phase. In the goal recognition phase, we generate an action graph based on the observed actions, and then the candidate goals and their plans are recognized. In the intention recognition phase, the intention is recognized with relevant goals and user profile. We show that the algorithm has polynomial time complexity. The intention graph is applied to a simple briefcase domain to test our model.

Keywords: Intention recognition, intention, graph, HCI.

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991 Flexible Heuristics for Project Scheduling with Limited Resources

Authors: Miloš Šeda

Abstract:

Resource-constrained project scheduling is an NPhard optimisation problem. There are many different heuristic strategies how to shift activities in time when resource requirements exceed their available amounts. These strategies are frequently based on priorities of activities. In this paper, we assume that a suitable heuristic has been chosen to decide which activities should be performed immediately and which should be postponed and investigate the resource-constrained project scheduling problem (RCPSP) from the implementation point of view. We propose an efficient routine that, instead of shifting the activities, extends their duration. It makes it possible to break down their duration into active and sleeping subintervals. Then we can apply the classical Critical Path Method that needs only polynomial running time. This algorithm can simply be adapted for multiproject scheduling with limited resources.

Keywords: Project management, resource-constrained scheduling, NP-hard problem, CPM, heuristic method.

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990 Simulation Method for Determining the Thermally Induced Displacement of Machine Tools – Experimental Validation and Utilization in the Design Process

Authors: G. Kehl, P. Wagner

Abstract:

A novel simulation method to determine the displacements of machine tools due to thermal factors is presented. The specific characteristic of this method is the employment of original CAD data from the design process chain, which is interpreted by an algorithm in terms of geometry-based allocation of convection and radiation parameters. Furthermore analogous models relating to the thermal behaviour of machine elements are automatically implemented, which were gained by extensive experimental testing with thermography imaging. With this a transient simulation of the thermal field and in series of the displacement of the machine tool is possible simultaneously during the design phase. This method was implemented and is already used industrially in the design of machining centres in order to improve the quality of herewith manufactured workpieces.

Keywords: Accuracy, design process, finite element analysis, machine tools, thermal simulation.

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989 Automatic Extraction of Water Bodies Using Whole-R Method

Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

Abstract:

Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R color component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: Chromaticity, Feature Extraction, Remote Sensing, Spectral library, Water Index.

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988 SMART: Solution Methods with Ants Running by Types

Authors: Nicolas Zufferey

Abstract:

Ant algorithms are well-known metaheuristics which have been widely used since two decades. In most of the literature, an ant is a constructive heuristic able to build a solution from scratch. However, other types of ant algorithms have recently emerged: the discussion is thus not limited by the common framework of the constructive ant algorithms. Generally, at each generation of an ant algorithm, each ant builds a solution step by step by adding an element to it. Each choice is based on the greedy force (also called the visibility, the short term profit or the heuristic information) and the trail system (central memory which collects historical information of the search process). Usually, all the ants of the population have the same characteristics and behaviors. In contrast in this paper, a new type of ant metaheuristic is proposed, namely SMART (for Solution Methods with Ants Running by Types). It relies on the use of different population of ants, where each population has its own personality.

Keywords: Optimization, Metaheuristics, Ant Algorithms, Evolutionary Procedures, Population-Based Methods.

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987 Using Multi-Objective Particle Swarm Optimization for Bi-objective Multi-Mode Resource-Constrained Project Scheduling Problem

Authors: Fatemeh Azimi, Razeeh Sadat Aboutalebi, Amir Abbas Najafi

Abstract:

In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.

Keywords: Evolutionary multi-objective optimization makespan, multi-mode, resource constraint, net present value.

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986 Grid-based Supervised Clustering - GBSC

Authors: Pornpimol Bungkomkhun, Surapong Auwatanamongkol

Abstract:

This paper presents a supervised clustering algorithm, namely Grid-Based Supervised Clustering (GBSC), which is able to identify clusters of any shapes and sizes without presuming any canonical form for data distribution. The GBSC needs no prespecified number of clusters, is insensitive to the order of the input data objects, and is capable of handling outliers. Built on the combination of grid-based clustering and density-based clustering, under the assistance of the downward closure property of density used in bottom-up subspace clustering, the GBSC can notably reduce its search space to avoid the memory confinement situation during its execution. On two-dimension synthetic datasets, the GBSC can identify clusters with different shapes and sizes correctly. The GBSC also outperforms other five supervised clustering algorithms when the experiments are performed on some UCI datasets.

Keywords: supervised clustering, grid-based clustering, subspace clustering

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985 Impairments Correction of Six-Port Based Millimeter-Wave Radar

Authors: Dan Ohev Zion, Alon Cohen

Abstract:

In recent years, the presence of short-range millimeter-wave radar in civil application has increased significantly. Autonomous driving, security, 3D imaging and high data rate communication systems are a few examples. The next challenge is the integration inside small form-factor devices, such as smartphones (e.g. gesture recognition). The main challenge is implementation of a truly low-power, low-complexity high-resolution radar. The most popular approach is the Frequency Modulated Continuous Wave (FMCW) radar, with an analog multiplication front-end. In this paper, we present an approach for adaptive estimation and correction of impairments of such front-end, specifically implemented using the Six-Port Device (SPD) as the multiplier element. The proposed algorithm was simulated and implemented on a 60 GHz radar lab prototype.

Keywords: Radar, millimeter-wave, six-port, FMCW Radar, IQ mismatch.

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984 Application and Limitation of Parallel Modelingin Multidimensional Sequential Pattern

Authors: Mahdi Esmaeili, Mansour Tarafdar

Abstract:

The goal of data mining algorithms is to discover useful information embedded in large databases. One of the most important data mining problems is discovery of frequently occurring patterns in sequential data. In a multidimensional sequence each event depends on more than one dimension. The search space is quite large and the serial algorithms are not scalable for very large datasets. To address this, it is necessary to study scalable parallel implementations of sequence mining algorithms. In this paper, we present a model for multidimensional sequence and describe a parallel algorithm based on data parallelism. Simulation experiments show good load balancing and scalable and acceptable speedup over different processors and problem sizes and demonstrate that our approach can works efficiently in a real parallel computing environment.

Keywords: Sequential Patterns, Data Mining, ParallelAlgorithm, Multidimensional Sequence Data

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983 Visual Hull with Imprecise Input

Authors: Peng He

Abstract:

Imprecision is a long-standing problem in CAD design and high accuracy image-based reconstruction applications. The visual hull which is the closed silhouette equivalent shape of the objects of interest is an important concept in image-based reconstruction. We extend the domain-theoretic framework, which is a robust and imprecision capturing geometric model, to analyze the imprecision in the output shape when the input vertices are given with imprecision. Under this framework, we show an efficient algorithm to generate the 2D partial visual hull which represents the exact information of the visual hull with only basic imprecision assumptions. We also show how the visual hull from polyhedra problem can be efficiently solved in the context of imprecise input.

Keywords: Geometric Domain, Computer Vision, Computational Geometry, Visual Hull, Image-Based reconstruction, Imprecise Input, CAD object

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982 Blind Source Separation Using Modified Gaussian FastICA

Authors: V. K. Ananthashayana, Jyothirmayi M.

Abstract:

This paper addresses the problem of source separation in images. We propose a FastICA algorithm employing a modified Gaussian contrast function for the Blind Source Separation. Experimental result shows that the proposed Modified Gaussian FastICA is effectively used for Blind Source Separation to obtain better quality images. In this paper, a comparative study has been made with other popular existing algorithms. The peak signal to noise ratio (PSNR) and improved signal to noise ratio (ISNR) are used as metrics for evaluating the quality of images. The ICA metric Amari error is also used to measure the quality of separation.

Keywords: Amari error, Blind Source Separation, Contrast function, Gaussian function, Independent Component Analysis.

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981 Computing a Time Based Effective Radius-of-Curvature for Roadways

Authors: Gary D. Cantrell, E. Alex Baylot

Abstract:

The radius-of-curvature (ROC) defines the degree of curvature along the centerline of a roadway whereby a travelling vehicle must follow. Roadway designs must encompass ROC in mitigating the cost of earthwork associated with construction while also allowing vehicles to travel at maximum allowable design speeds. Thus, a road will tend to follow natural topography where possible, but curvature must also be optimized to permit fast, but safe vehicle speeds. The more severe the curvature of the road, the slower the permissible vehicle speed. For route planning, whether for urban settings, emergency operations, or even parcel delivery, ROC is a necessary attribute of road arcs for computing travel time. It is extremely rare for a geo-spatial database to contain ROC. This paper will present a procedure and mathematical algorithm to calculate and assign ROC to a segment pair and/or polyline.

Keywords: linear features, radius-of-curvature, roads, routing, traffic, turning

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980 The Frequency Graph for the Traveling Salesman Problem

Authors: Y. Wang

Abstract:

Traveling salesman problem (TSP) is hard to resolve when the number of cities and routes become large. The frequency graph is constructed to tackle the problem. A frequency graph maintains the topological relationships of the original weighted graph. The numbers on the edges are the frequencies of the edges emulated from the local optimal Hamiltonian paths. The simplest kind of local optimal Hamiltonian paths are computed based on the four vertices and three lines inequality. The search algorithm is given to find the optimal Hamiltonian circuit based on the frequency graph. The experiments show that the method can find the optimal Hamiltonian circuit within several trials.

Keywords: Traveling salesman problem, frequency graph, local optimal Hamiltonian path, four vertices and three lines inequality.

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979 Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps

Authors: Moussa Yahia, Pascal Acco, Malek Benslama

Abstract:

Polynomial maps offer analytical properties used to obtain better performances in the scope of chaos synchronization under noisy channels. This paper presents a new method to simplify equations of the Exact Polynomial Kalman Filter (ExPKF) given in [1]. This faster algorithm is compared to other estimators showing that performances of all considered observers vanish rapidly with the channel noise making application of chaos synchronization intractable. Simulation of ExPKF shows that saturation drawn on the emitter to keep it stable impacts badly performances for low channel noise. Then we propose a particle filter that outperforms all other Kalman structured observers in the case of noisy channels.

Keywords: Chaos synchronization, Saturation, Fast ExPKF, Particlefilter, Polynomial maps.

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978 Improving Cache Memory Utilization

Authors: Sami I. Serhan, Hamed M. Abdel-Haq

Abstract:

In this paper, an efficient technique is proposed to manage the cache memory. The proposed technique introduces some modifications on the well-known set associative mapping technique. This modification requires a little alteration in the structure of the cache memory and on the way by which it can be referenced. The proposed alteration leads to increase the set size virtually and consequently to improve the performance and the utilization of the cache memory. The current mapping techniques have accomplished good results. In fact, there are still different cases in which cache memory lines are left empty and not used, whereas two or more processes overwrite the lines of each other, instead of using those empty lines. The proposed algorithm aims at finding an efficient way to deal with such problem.

Keywords: Modified Set Associative Mapping, Locality of Reference, Miss Ratio, Hit Ratio, Cache Memory, Clustered Behavior, Index Address, Tag Field, Status Field, and Complement of Index Address.

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977 Optimal Control of Viscoelastic Melt Spinning Processes

Authors: Shyam S.N. Perera

Abstract:

The optimal control problem for the viscoelastic melt spinning process has not been reported yet in the literature. In this study, an optimal control problem for a mathematical model of a viscoelastic melt spinning process is considered. Maxwell-Oldroyd model is used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and the temperature of the quench air and the fiber length serve as control variables. A constrained optimization problem is derived and the first–order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm. A computer program in MATLAB is developed for simulations.

Keywords: Fiber spinning, Maxwell-Oldroyd, Optimal control, First-order optimality system, Adjoint system

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976 Finding Viable Pollution Routes in an Urban Network under a Predefined Cost

Authors: Dimitra Alexiou, Stefanos Katsavounis, Ria Kalfakakou

Abstract:

In an urban area the determination of transportation routes should be planned so as to minimize the provoked pollution taking into account the cost of such routes. In the sequel these routes are cited as pollution routes.

The transportation network is expressed by a weighted graph G=(V,E,D,P) where every vertex represents a location to be served and contains unordered pairs (edges) of elements in V that indicate a simple road. The distances / cost and a weight that depict the provoked air pollution by a vehicle transition at every road are assigned to each road as well. These are the items of set D andrespectively.

Furthermore the investigated pollution routes must not exceed predefined corresponding values concerning the route cost and the route pollution level during the vehicle transition.

In this paper we present an algorithm that generates such routes in order that the decision maker selects the most appropriate one. 

Keywords: bi-criteria, pollution, shortest paths.

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975 Predicting Groundwater Areas Using Data Mining Techniques: Groundwater in Jordan as Case Study

Authors: Faisal Aburub, Wael Hadi

Abstract:

Data mining is the process of extracting useful or hidden information from a large database. Extracted information can be used to discover relationships among features, where data objects are grouped according to logical relationships; or to predict unseen objects to one of the predefined groups. In this paper, we aim to investigate four well-known data mining algorithms in order to predict groundwater areas in Jordan. These algorithms are Support Vector Machines (SVMs), Naïve Bayes (NB), K-Nearest Neighbor (kNN) and Classification Based on Association Rule (CBA). The experimental results indicate that the SVMs algorithm outperformed other algorithms in terms of classification accuracy, precision and F1 evaluation measures using the datasets of groundwater areas that were collected from Jordanian Ministry of Water and Irrigation.

Keywords: Classification, data mining, evaluation measures, groundwater.

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974 Optimal Trajectory Finding of IDP Ventilation Control with Outdoor Air Information and Indoor Health Risk Index

Authors: Minjeong Kim, Seungchul Lee, Iman Janghorban Esfahani, Jeong Tai Kim, Chang Kyoo Yoo

Abstract:

This study was carried out for an underground subway station at Seoul Metro, Korea. The optimal set-points of the ventilation control system are determined every 3 hours, then, the ventilation controller adjusts the ventilation fan speed according to the optimal set-point changes. Compared to manual ventilation system which is operated irrespective of the OAQ, the IDP-based ventilation control system saves 3.7% of the energy consumption. Compared to the fixed set-point controller which is operated irrespective of the IAQ diurnal variation, the IDP-based controller shows better performance with a 2% decrease in energy consumption, maintaining the comfortable IAQ range inside the station.

Keywords: Indoor air quality, iterative dynamic algorithm, outdoor air information, ventilation control system.

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973 A Recommender System Fusing Collaborative Filtering and User’s Review Mining

Authors: Seulbi Choi, Hyunchul Ahn

Abstract:

Collaborative filtering (CF) algorithm has been popularly used for recommender systems in both academic and practical applications. It basically generates recommendation results using users’ numeric ratings. However, the additional use of the information other than user ratings may lead to better accuracy of CF. Considering that a lot of people are likely to share their honest opinion on the items they purchased recently due to the advent of the Web 2.0, user's review can be regarded as the new informative source for identifying user's preference with accuracy. Under this background, this study presents a hybrid recommender system that fuses CF and user's review mining. Our system adopts conventional memory-based CF, but it is designed to use both user’s numeric ratings and his/her text reviews on the items when calculating similarities between users.

Keywords: Recommender system, collaborative filtering, text mining, review mining.

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972 Tuning of Thermal FEA Using Krylov Parametric MOR for Subsea Application

Authors: A. Suleng, T. Jelstad Olsen, J. Šindler, P. Bárta

Abstract:

A dead leg is a typical subsea production system component. CFD is required to model heat transfer within the dead leg. Unfortunately its solution is time demanding and thus not suitable for fast prediction or repeated simulations. Therefore there is a need to create a thermal FEA model, mimicking the heat flows and temperatures seen in CFD cool down simulations. This paper describes the conventional way of tuning and a new automated way using parametric model order reduction (PMOR) together with an optimization algorithm. The tuned FE analyses replicate the steady state CFD parameters within a maximum error in heat flow of 6 % and 3 % using manual and PMOR method respectively. During cool down, the relative error of the tuned FEA models with respect to temperature is below 5% comparing to the CFD. In addition, the PMOR method obtained the correct FEA setup five times faster than the manually tuned FEA.

Keywords: CFD, convective heat, FEA, model tuning, subseaproduction

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971 Development of Variable Stepsize Variable Order Block Method in Divided Difference Form for the Numerical Solution of Delay Differential Equations

Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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970 Review and Comparison of Associative Classification Data Mining Approaches

Authors: Suzan Wedyan

Abstract:

Associative classification (AC) is a data mining approach that combines association rule and classification to build classification models (classifiers). AC has attracted a significant attention from several researchers mainly because it derives accurate classifiers that contain simple yet effective rules. In the last decade, a number of associative classification algorithms have been proposed such as Classification based Association (CBA), Classification based on Multiple Association Rules (CMAR), Class based Associative Classification (CACA), and Classification based on Predicted Association Rule (CPAR). This paper surveys major AC algorithms and compares the steps and methods performed in each algorithm including: rule learning, rule sorting, rule pruning, classifier building, and class prediction.

Keywords: Associative Classification, Classification, Data Mining, Learning, Rule Ranking, Rule Pruning, Prediction.

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969 Multi-Font Farsi/Arabic Isolated Character Recognition Using Chain Codes

Authors: H. Izakian, S. A. Monadjemi, B. Tork Ladani, K. Zamanifar

Abstract:

Nowadays, OCR systems have got several applications and are increasingly employed in daily life. Much research has been done regarding the identification of Latin, Japanese, and Chinese characters. However, very little investigation has been performed regarding Farsi/Arabic characters recognition. Probably the reason is difficulty and complexity of those characters identification compared to the others and limitation of IT activities in Farsi and Arabic speaking countries. In this paper, a technique has been employed to identify isolated Farsi/Arabic characters. A chain code based algorithm along with other significant peculiarities such as number and location of dots and auxiliary parts, and the number of holes existing in the isolated character has been used in this study to identify Farsi/Arabic characters. Experimental results show the relatively high accuracy of the method developed when it is tested on several standard Farsi fonts.

Keywords: Farsi characters, OCR, feature extraction, chain code.

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968 A Molding Surface Auto-Inspection System

Authors: Ssu-Han Chen, Der-Baau Perng

Abstract:

Molding process in IC manufacturing secures chips against the harms done by hot, moisture or other external forces. While a chip was being molded,defects like cracks, dilapidation, or voids may be embedding on the molding surface. The molding surfaces the study poises to treat and the ones on the market, though, differ in the surface where texture similar to defects is everywhere. Manual inspection usually passes over low-contrast cracks or voids; hence an automatic optical inspection system for molding surface is necessary. The proposed system is consisted of a CCD, a coaxial light, a back light as well as a motion control unit. Based on the property of statistical textures of the molding surface, a series of digital image processing and classification procedure is carried out. After training of the parameter associated with above algorithm, result of the experiment suggests that the accuracy rate is up to 93.75%, contributing to the inspection quality of IC molding surface.

Keywords: Molding surface, machine vision, statistical texture, discrete Fourier transformation.

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967 Periodic Control of a Reverse Osmosis Water Desalination Unit

Authors: Ali Emad

Abstract:

Enhancement of the performance of a reverse osmosis (RO) unit through periodic control is studied. The periodic control manipulates the feed pressure and flow rate of the RO unit. To ensure the periodic behavior of the inputs, the manipulated variables (MV) are transformed into the form of sinusoidal functions. In this case, the amplitude and period of the sinusoidal functions become the surrogate MV and are thus regulated via nonlinear model predictive control algorithm. The simulation results indicated that the control system can generate cyclic inputs necessary to enhance the closedloop performance in the sense of increasing the permeate production and lowering the salt concentration. The proposed control system can attain its objective with arbitrary set point for the controlled outputs. Successful results were also obtained in the presence of modeling errors.

Keywords: Reverse osmosis, water desalination, periodic control, model predictive control.

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966 A Sociocybernetics Data Analysis Using Causality in Tourism Networks

Authors: M. Lloret-Climent, J. Nescolarde-Selva

Abstract:

The aim of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on a pre-designed algorithm and applying our interpretation of chaos theory developed in the context of General Systems Theory. This article sets out the causal relationships associated with tourist flows in order to enable the formulation of appropriate strategies. Our results can be applied to numerous cases. For example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups and to analyse tourist behaviour in terms of the most relevant variables. Unlike statistical analyses that merely provide information on current data, our method uses orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.

Keywords: Attractor, invariant set, orbits, tourist variables.

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