Search results for: dynamic programming algorithms
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3757

Search results for: dynamic programming algorithms

1837 Proposal of a Model Supporting Decision-Making Based On Multi-Objective Optimization Analysis on Information Security Risk Treatment

Authors: Ritsuko Kawasaki (Aiba), Takeshi Hiromatsu

Abstract:

Management is required to understand all information security risks within an organization, and to make decisions on which information security risks should be treated in what level by allocating how much amount of cost. However, such decision-making is not usually easy, because various measures for risk treatment must be selected with the suitable application levels. In addition, some measures may have objectives conflicting with each other. It also makes the selection difficult. Moreover, risks generally have trends and it also should be considered in risk treatment. Therefore, this paper provides the extension of the model proposed in the previous study. The original model supports the selection of measures by applying a combination of weighted average method and goal programming method for multi-objective analysis to find an optimal solution. The extended model includes the notion of weights to the risks, and the larger weight means the priority of the risk.

Keywords: Information security risk treatment, Selection of risk measures, Risk acceptanceand Multi-objective optimization.

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1836 A Hybrid Feature Subset Selection Approach based on SVM and Binary ACO. Application to Industrial Diagnosis

Authors: O. Kadri, M. D. Mouss, L.H. Mouss, F. Merah

Abstract:

This paper proposes a novel hybrid algorithm for feature selection based on a binary ant colony and SVM. The final subset selection is attained through the elimination of the features that produce noise or, are strictly correlated with other already selected features. Our algorithm can improve classification accuracy with a small and appropriate feature subset. Proposed algorithm is easily implemented and because of use of a simple filter in that, its computational complexity is very low. The performance of the proposed algorithm is evaluated through a real Rotary Cement kiln dataset. The results show that our algorithm outperforms existing algorithms.

Keywords: Binary Ant Colony algorithm, Support VectorMachine, feature selection, classification.

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1835 Advanced Image Analysis Tools Development for the Early Stage Bronchial Cancer Detection

Authors: P. Bountris, E. Farantatos, N. Apostolou

Abstract:

Autofluorescence (AF) bronchoscopy is an established method to detect dysplasia and carcinoma in situ (CIS). For this reason the “Sotiria" Hospital uses the Karl Storz D-light system. However, in early tumor stages the visualization is not that obvious. With the help of a PC, we analyzed the color images we captured by developing certain tools in Matlab®. We used statistical methods based on texture analysis, signal processing methods based on Gabor models and conversion algorithms between devicedependent color spaces. Our belief is that we reduced the error made by the naked eye. The tools we implemented improve the quality of patients' life.

Keywords: Bronchoscopy, digital image processing, lung cancer, texture analysis.

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1834 Detection of Sags, Swells, and Transients Using Windowing Technique Based On Continuous S-Transform (CST)

Authors: K. Daud, A. F. Abidin, N. Hamzah, H. S. Nagindar Singh

Abstract:

This paper produces a new approach for power quality analysis using a windowing technique based on Continuous S-transform (CST). This half-cycle window technique approach can detect almost correctly for initial detection of disturbances i.e. voltage sags, swells, and transients. Samples in half cycle window has been analyzed based continuous S-transform for entire disturbance waveform. The modified parameter has been produced by MATLAB programming m-file based on continuous s-transform. CST has better time frequency and localization property than traditional and also has ability to detect the disturbance under noisy condition correctly. The excellent time-frequency resolution characteristic of the CST makes it the most an attractive candidate for analysis of power system disturbances signals.

Keywords: Power quality disturbances, initial detection, half cycle windowing, continuous S-transform.

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1833 Mining News Sites to Create Special Domain News Collections

Authors: David B. Bracewell, Fuji Ren, Shingo Kuroiwa

Abstract:

We present a method to create special domain collections from news sites. The method only requires a single sample article as a seed. No prior corpus statistics are needed and the method is applicable to multiple languages. We examine various similarity measures and the creation of document collections for English and Japanese. The main contributions are as follows. First, the algorithm can build special domain collections from as little as one sample document. Second, unlike other algorithms it does not require a second “general" corpus to compute statistics. Third, in our testing the algorithm outperformed others in creating collections made up of highly relevant articles.

Keywords: Information Retrieval, News, Special DomainCollections,

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1832 The Investigation of the Role of Institutions in the Process of Growth and Development of Economy

Authors: Seyed Mohammad Reza Hosseini

Abstract:

The new institutional Economics helps generalization and expansion of new classic by adding the institution theories to Economic. It is clear that the appropriate institution is among the factors that lead to success in Economic programs. If the institutional are appropriate, the society will save the source and when we make use of time to apply the program, there will be welfare and average revenue product will also increase. In Economy, one should not expect the real manifestation of Economic programs only with a model for estimating and predicting rather institutions of the same purpose and along with production are needed to form the process of growth and development costs. In this research, the institution role in transaction costs, financial markets, distribution of revenue and capital and its influence on the process of growth and development are investigated so that handicaps and problems of Iran Economic Institutions can be recognized. In other words, incapability, non productivity and ambiguity of the institution in Iran Economic are some of the factors that handicap Economic growth and development. For example, Iran government as an important institution while having 20 ministries,83 organizations and 60 years of programming could not go along the growth and development but why?

Keywords: Institution, New institutional economics, Transaction costs.

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1831 Comprehensive Analysis of Data Mining Tools

Authors: S. Sarumathi, N. Shanthi

Abstract:

Due to the fast and flawless technological innovation there is a tremendous amount of data dumping all over the world in every domain such as Pattern Recognition, Machine Learning, Spatial Data Mining, Image Analysis, Fraudulent Analysis, World Wide Web etc., This issue turns to be more essential for developing several tools for data mining functionalities. The major aim of this paper is to analyze various tools which are used to build a resourceful analytical or descriptive model for handling large amount of information more efficiently and user friendly. In this survey the diverse tools are illustrated with their extensive technical paradigm, outstanding graphical interface and inbuilt multipath algorithms in which it is very useful for handling significant amount of data more indeed.

Keywords: Classification, Clustering, Data Mining, Machine learning, Visualization.

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1830 Assessment of Multi-Domain Energy Systems Modelling Methods

Authors: M. Stewart, Ameer Al-Khaykan, J. M. Counsell

Abstract:

Emissions are a consequence of electricity generation. A major option for low carbon generation, local energy systems featuring Combined Heat and Power with solar PV (CHPV) has significant potential to increase energy performance, increase resilience, and offer greater control of local energy prices while complementing the UK’s emissions standards and targets. Recent advances in dynamic modelling and simulation of buildings and clusters of buildings using the IDEAS framework have successfully validated a novel multi-vector (simultaneous control of both heat and electricity) approach to integrating the wide range of primary and secondary plant typical of local energy systems designs including CHP, solar PV, gas boilers, absorption chillers and thermal energy storage, and associated electrical and hot water networks, all operating under a single unified control strategy. Results from this work indicate through simulation that integrated control of thermal storage can have a pivotal role in optimizing system performance well beyond the present expectations. Environmental impact analysis and reporting of all energy systems including CHPV LES presently employ a static annual average carbon emissions intensity for grid supplied electricity. This paper focuses on establishing and validating CHPV environmental performance against conventional emissions values and assessment benchmarks to analyze emissions performance without and with an active thermal store in a notional group of non-domestic buildings. Results of this analysis are presented and discussed in context of performance validation and quantifying the reduced environmental impact of CHPV systems with active energy storage in comparison with conventional LES designs.

Keywords: CHPV, thermal storage, control, dynamic simulation.

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1829 Magnetic Field Analysis for a Distribution Transformer with Unbalanced Load Conditions by using 3-D Finite Element Method

Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

Abstract:

This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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1828 A Scalable Media Job Framework for an Open Source Search Engine

Authors: Pooja Mishra, Chris Pollett

Abstract:

This paper explores efficient ways to implement various media-updating features like news aggregation, video conversion, and bulk email handling. All of these jobs share the property that they are periodic in nature, and they all benefit from being handled in a distributed fashion. The data for these jobs also often comes from a social or collaborative source. We isolate the class of periodic, one round map reduce jobs as a useful setting to describe and handle media updating tasks. As such tasks are simpler than general map reduce jobs, programming them in a general map reduce platform could easily become tedious. This paper presents a MediaUpdater module of the Yioop Open Source Search Engine Web Portal designed to handle such jobs via an extension of a PHP class. We describe how to implement various media-updating tasks in our system as well as experiments carried out using these implementations on an Amazon Web Services cluster.

Keywords: Distributed jobs framework, news aggregation, video conversion, email.

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1827 Iterative Clustering Algorithm for Analyzing Temporal Patterns of Gene Expression

Authors: Seo Young Kim, Jae Won Lee, Jong Sung Bae

Abstract:

Microarray experiments are information rich; however, extensive data mining is required to identify the patterns that characterize the underlying mechanisms of action. For biologists, a key aim when analyzing microarray data is to group genes based on the temporal patterns of their expression levels. In this paper, we used an iterative clustering method to find temporal patterns of gene expression. We evaluated the performance of this method by applying it to real sporulation data and simulated data. The patterns obtained using the iterative clustering were found to be superior to those obtained using existing clustering algorithms.

Keywords: Clustering, microarray experiment, temporal pattern of gene expression data.

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1826 Energy Efficient Resource Allocation in Distributed Computing Systems

Authors: Samee Ullah Khan, C. Ardil

Abstract:

The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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1825 A High Bitrate Information Hiding Algorithm for Video in Video

Authors: Wang Shou-Dao, Xiao Chuang-Bai, Lin Yu

Abstract:

In high bitrate information hiding techniques, 1 bit is embedded within each 4 x 4 Discrete Cosine Transform (DCT) coefficient block by means of vector quantization, then the hidden bit can be effectively extracted in terminal end. In this paper high bitrate information hiding algorithms are summarized, and the scheme of video in video is implemented. Experimental result shows that the host video which is embedded numerous auxiliary information have little visually quality decline. Peak Signal to Noise Ratio (PSNR)Y of host video only degrades 0.22dB in average, while the hidden information has a high percentage of survives and keeps a high robustness in H.264/AVC compression, the average Bit Error Rate(BER) of hiding information is 0.015%.

Keywords: Information Hiding, Embed, Quantification, Extract

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1824 Visual Search Based Indoor Localization in Low Light via RGB-D Camera

Authors: Yali Zheng, Peipei Luo, Shinan Chen, Jiasheng Hao, Hong Cheng

Abstract:

Most of traditional visual indoor navigation algorithms and methods only consider the localization in ordinary daytime, while we focus on the indoor re-localization in low light in the paper. As RGB images are degraded in low light, less discriminative infrared and depth image pairs are taken, as the input, by RGB-D cameras, the most similar candidates, as the output, are searched from databases which is built in the bag-of-word framework. Epipolar constraints can be used to relocalize the query infrared and depth image sequence. We evaluate our method in two datasets captured by Kinect2. The results demonstrate very promising re-localization results for indoor navigation system in low light environments.

Keywords: Indoor navigation, low light, RGB-D camera, vision based.

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1823 Solving Machine Loading Problem in Flexible Manufacturing Systems Using Particle Swarm Optimization

Authors: S. G. Ponnambalam, Low Seng Kiat

Abstract:

In this paper, a particle swarm optimization (PSO) algorithm is proposed to solve machine loading problem in flexible manufacturing system (FMS), with bicriterion objectives of minimizing system unbalance and maximizing system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools. The performance of the PSO is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The results support that the proposed PSO is comparable with the algorithms reported in the literature.

Keywords: Machine loading problem, FMS, Particle Swarm Optimization.

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1822 Elimination of Redundant Links in Web Pages– Mathematical Approach

Authors: G. Poonkuzhali, K.Thiagarajan, K.Sarukesi

Abstract:

With the enormous growth on the web, users get easily lost in the rich hyper structure. Thus developing user friendly and automated tools for providing relevant information without any redundant links to the users to cater to their needs is the primary task for the website owners. Most of the existing web mining algorithms have concentrated on finding frequent patterns while neglecting the less frequent one that are likely to contain the outlying data such as noise, irrelevant and redundant data. This paper proposes new algorithm for mining the web content by detecting the redundant links from the web documents using set theoretical(classical mathematics) such as subset, union, intersection etc,. Then the redundant links is removed from the original web content to get the required information by the user..

Keywords: Web documents, Web content mining, redundantlink, outliers, set theory.

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1821 Delay-Independent Closed-Loop Stabilization of Neutral System with Infinite Delays

Authors: I. Davies, O. L. C. Haas

Abstract:

In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.

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1820 An Optimal Algorithm for HTML Page Building Process

Authors: Maryam Jasim Abdullah, Bassim. H. Graimed, Jalal. S. Hameed

Abstract:

Demand over web services is in growing with increases number of Web users. Web service is applied by Web application. Web application size is affected by its user-s requirements and interests. Differential in requirements and interests lead to growing of Web application size. The efficient way to save store spaces for more data and information is achieved by implementing algorithms to compress the contents of Web application documents. This paper introduces an algorithm to reduce Web application size based on reduction of the contents of HTML files. It removes unimportant contents regardless of the HTML file size. The removing is not ignored any character that is predicted in the HTML building process.

Keywords: HTML code, HTML tag, WEB applications, Document compression, DOM tree.

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1819 Morphological Description of Cervical Cell Images for the Pathological Recognition

Authors: N. Lassouaoui, L. Hamami, N. Nouali

Abstract:

The tracking allows to detect the tumor affections of cervical cancer, it is particularly complex and consuming time, because it consists in seeking some abnormal cells among a cluster of normal cells. In this paper, we present our proposed computer system for helping the doctors in tracking the cervical cancer. Knowing that the diagnosis of the malignancy is based in the set of atypical morphological details of all cells, herein, we present an unsupervised genetic algorithm for the separation of cell components since the diagnosis is doing by analysis of the core and the cytoplasm. We give also the various algorithms used for computing the morphological characteristics of cells (Ratio core/cytoplasm, cellular deformity, ...) necessary for the recognition of illness.

Keywords: Cervical cell, morphological analysis, recognition, segmentation.

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1818 Data Placement in Heterogeneous Storage of Short Videos

Authors: W. Jaipahkdee, C. Srinilta

Abstract:

The overall service performance of I/O intensive system depends mainly on workload on its storage system. In heterogeneous storage environment where storage elements from different vendors with different capacity and performance are put together, workload should be distributed according to storage capability. This paper addresses data placement issue in short video sharing website. Workload contributed by a video is estimated by the number of views and life time span of existing videos in same category. Experiment was conducted on 42,000 video titles in six weeks. Result showed that the proposed algorithm distributed workload and maintained balance better than round robin and random algorithms.

Keywords: data placement, heterogeneous storage system, YouTube, short videos

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1817 Effect of Tethers Tension Force in the Behavior of a Tension Leg Platform Subjected to Hydrodynamic Force

Authors: Amr R. El-Gamal, Ashraf Essa, Ayman Ismail

Abstract:

The tension leg platform (TLP) is one of the compliant structures which are generally used for deep water oil exploration. With respect to the horizontal degrees of freedom, it behaves like a floating structure moored by vertical tethers which are pretension due to the excess buoyancy of the platform, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. In the current study, a numerical study for square TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy’s linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP's, the dynamic behavior of TLP's; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmark’s beta integration method. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether tension force, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations that is significantly dependent on wave height, and that special attention should be given to tethers fatigue because of their high tensile static and dynamic stress.

Keywords: Tethers tension, tension leg platforms, hydrodynamic wave forces, wave characteristic.

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1816 Impulsive Noise-Resilient Subband Adaptive Filter

Authors: Young-Seok Choi

Abstract:

We present a new subband adaptive filter (R-SAF) which is robust against impulsive noise in system identification. To address the vulnerability of adaptive filters based on the L2-norm optimization criterion against impulsive noise, the R-SAF comes from the L1-norm optimization criterion with a constraint on the energy of the weight update. Minimizing L1-norm of the a posteriori error in each subband with a constraint on minimum disturbance gives rise to the robustness against the impulsive noise and the capable convergence performance. Experimental results clearly demonstrate that the proposed R-SAF outperforms the classical adaptive filtering algorithms when impulsive noise as well as background noise exist.

Keywords: Subband adaptive filter, L1-norm, system identification, robustness, impulsive interference.

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1815 Multiobjective Optimal Power Flow Using Hybrid Evolutionary Algorithm

Authors: Alawode Kehinde O., Jubril Abimbola M. Komolafe Olusola A.

Abstract:

This paper solves the environmental/ economic dispatch power system problem using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and its hybrid with a Convergence Accelerator Operator (CAO), called the NSGA-II/CAO. These multiobjective evolutionary algorithms were applied to the standard IEEE 30-bus six-generator test system. Several optimization runs were carried out on different cases of problem complexity. Different quality measure which compare the performance of the two solution techniques were considered. The results demonstrated that the inclusion of the CAO in the original NSGA-II improves its convergence while preserving the diversity properties of the solution set.

Keywords: optimal power flow, multiobjective power dispatch, evolutionary algorithm

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1814 Wavelet-Based Data Compression Technique for Wireless Sensor Networks

Authors: P. Kumsawat, N. Pimpru, K. Attakitmongcol, A.Srikaew

Abstract:

In this paper, we proposed an efficient data compression strategy exploiting the multi-resolution characteristic of the wavelet transform. We have developed a sensor node called “Smart Sensor Node; SSN". The main goals of the SSN design are lightweight, minimal power consumption, modular design and robust circuitry. The SSN is made up of four basic components which are a sensing unit, a processing unit, a transceiver unit and a power unit. FiOStd evaluation board is chosen as the main controller of the SSN for its low costs and high performance. The software coding of the implementation was done using Simulink model and MATLAB programming language. The experimental results show that the proposed data compression technique yields recover signal with good quality. This technique can be applied to compress the collected data to reduce the data communication as well as the energy consumption of the sensor and so the lifetime of sensor node can be extended.

Keywords: Wireless sensor network, wavelet transform, data compression, ZigBee, skipped high-pass sub-band.

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1813 Impact of Fair Share and its Configurations on Parallel Job Scheduling Algorithms

Authors: Sangsuree Vasupongayya

Abstract:

To provide a better understanding of fair share policies supported by current production schedulers and their impact on scheduling performance, A relative fair share policy supported in four well-known production job schedulers is evaluated in this study. The experimental results show that fair share indeed reduces heavy-demand users from dominating the system resources. However, the detailed per-user performance analysis show that some types of users may suffer unfairness under fair share, possibly due to priority mechanisms used by the current production schedulers. These users typically are not heavy-demands users but they have mixture of jobs that do not spread out.

Keywords: Fair share, Parallel job scheduler, Backfill, Measures

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1812 Harmony Search-based K-Coverage Enhancement in Wireless Sensor Networks

Authors: Shaimaa M. Mohamed, Haitham S. Hamza, Imane A. Saroit

Abstract:

Many wireless sensor network applications require K-coverage of the monitored area. In this paper, we propose a scalable harmony search based algorithm in terms of execution time, K-Coverage Enhancement Algorithm (KCEA), it attempts to enhance initial coverage, and achieve the required K-coverage degree for a specific application efficiently. Simulation results show that the proposed algorithm achieves coverage improvement of 5.34% compared to K-Coverage Rate Deployment (K-CRD), which achieves 1.31% when deploying one additional sensor. Moreover, the proposed algorithm is more time efficient.

Keywords: Wireless Sensor Networks (WSN), Harmony Search Algorithms, K-Coverage, Mobile WSN.

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1811 Stabilization of a New Configurable Two- Wheeled Machine Using a PD-PID and a Hybrid FL Control Strategies: A Comparative Study

Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

Abstract:

A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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1810 Classification of Fuzzy Petri Nets, and Their Applications

Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha

Abstract:

Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.

Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.

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1809 Universal Method for Timetable Construction based on Evolutionary Approach

Authors: Maciej Norberciak

Abstract:

Timetabling problems are often hard and timeconsuming to solve. Most of the methods of solving them concern only one problem instance or class. This paper describes a universal method for solving large, highly constrained timetabling problems from different domains. The solution is based on evolutionary algorithm-s framework and operates on two levels – first-level evolutionary algorithm tries to find a solution basing on given set of operating parameters, second-level algorithm is used to establish those parameters. Tabu search is employed to speed up the solution finding process on first level. The method has been used to solve three different timetabling problems with promising results.

Keywords: Evolutionary algorithms, tabu search, timetabling.

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1808 A Qualitative Description of the Dynamics in the Interactions between Three Populations: Pollinators, Plants, and Herbivores

Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.

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