Search results for: Fuzzy number linear programming

Authors: Wann-Ming Wey

Abstract:

In recent years, the problems of global climate change and natural disasters have induced the concerns and attentions of environmental sustainability issues for the public. Aside from the environmental planning efforts done for human environment, Transit-Oriented Development (TOD) has been widely used as one of the future solutions for the sustainable city development. In order to be more consistent with the urban sustainable development, the development of the built environment planning based on the concept of Green TOD which combines both TOD and Green Urbanism is adapted here. The connotation of the urban development under the green TOD including the design toward environment protect, the maximum enhancement resources and the efficiency of energy use, use technology to construct green buildings and protected areas, natural ecosystems and communities linked, etc. Green TOD is not only to provide the solution to urban traffic problems, but to direct more sustainable and greener consideration for future urban development planning and design. In this study, we use both the TOD and Green Urbanism concepts to proceed to the study of the built environment planning and design. Fuzzy Delphi Technique (FDT) is utilized to screen suitable criteria of the green TOD. Furthermore, Fuzzy Analytic Network Process (FANP) and Quality Function Deployment (QFD) were then developed to evaluate the criteria and prioritize the alternatives. The study results can be regarded as the future guidelines of the built environment planning and designing under green TOD development in Taiwan.

Keywords: Green transit-oriented development, built environment, fuzzy Delphi technique, quality function deployment, fuzzy analytic network process.

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Authors: Noraziah Ahmad, Roslina Mohd Sidek, Mohd Affendy Omardin

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E-Appointment Scheduling (EAS) has been developed to handle appointment for UMP students, lecturers in Faculty of Computer Systems & Software Engineering (FCSSE) and Student Medical Center. The schedules are based on the timetable and university activities. Constraints Logic Programming (CLP) has been implemented to solve the scheduling problems by giving recommendation to the users in part of determining any available slots from the lecturers and doctors- timetable. By using this system, we can avoid wasting time and cost because this application will set an appointment by auto-generated. In addition, this system can be an alternative to the lecturers and doctors to make decisions whether to approve or reject the appointments.

Keywords: EAS, Constraint Logic Programming, PHP, Apache.

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Authors: R. Bhargava, Sonam Singh

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In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.

Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic

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Authors: Adam Czornik, Aleksander Nawrat

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This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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Authors: S. H. Sabzpoushan

Abstract:

In this research we show that the dynamics of an action potential in a cell can be modeled with a linear combination of the dynamics of the gating state variables. It is shown that the modeling error is negligible. Our findings can be used for simplifying cell models and reduction of computational burden i.e. it is useful for simulating action potential propagation in large scale computations like tissue modeling. We have verified our finding with the use of several cell models.

Keywords: Linear model, Action potential, gating dynamics.

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Authors: Siddhartha Bhattacharyya, Paramartha Dutta, Ujjwal Maulik, Prashanta Kumar Nandi

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The paper describes a self supervised parallel self organizing neural network (PSONN) architecture for true color image segmentation. The proposed architecture is a parallel extension of the standard single self organizing neural network architecture (SONN) and comprises an input (source) layer of image information, three single self organizing neural network architectures for segmentation of the different primary color components in a color image scene and one final output (sink) layer for fusion of the segmented color component images. Responses to the different shades of color components are induced in each of the three single network architectures (meant for component level processing) by applying a multilevel version of the characteristic activation function, which maps the input color information into different shades of color components, thereby yielding a processed component color image segmented on the basis of the different shades of component colors. The number of target classes in the segmented image corresponds to the number of levels in the multilevel activation function. Since the multilevel version of the activation function exhibits several subnormal responses to the input color image scene information, the system errors of the three component network architectures are computed from some subnormal linear index of fuzziness of the component color image scenes at the individual level. Several multilevel activation functions are employed for segmentation of the input color image scene using the proposed network architecture. Results of the application of the multilevel activation functions to the PSONN architecture are reported on three real life true color images. The results are substantiated empirically with the correlation coefficients between the segmented images and the original images.

Keywords: Colour image segmentation, fuzzy set theory, multi-level activation functions, parallel self-organizing neural network.

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Authors: Muhibul Haque Bhuyan, Quazi Deen Mohd Khosru

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This paper presents a threshold voltage model of pocket implanted sub-100 nm n-MOSFETs incorporating the drain and substrate bias effects using two linear pocket profiles. Two linear equations are used to simulate the pocket profiles along the channel at the surface from the source and drain edges towards the center of the n-MOSFET. Then the effective doping concentration is derived and is used in the threshold voltage equation that is obtained by solving the Poisson-s equation in the depletion region at the surface. Simulated threshold voltages for various gate lengths fit well with the experimental data already published in the literature. The simulated result is compared with the two other pocket profiles used to derive the threshold voltage models of n-MOSFETs. The comparison shows that the linear model has a simple compact form that can be utilized to study and characterize the pocket implanted advanced ULSI devices.

Keywords: Linear pocket profile, pocket implantation, nMOSFET, threshold voltage, short channel effect (SCE), reverse short channeleffect (RSCE).

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Authors: N. Mamode Khan, V. Jowaheer

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Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observations as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use quasi-likelihood estimation approach to estimate the parameters of the model. Under-dispersion parameter is estimated to be 2.14 justifying the appropriateness of Com-Poisson distribution in modelling under-dispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, quasi-likelihood estimation

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Authors: Nurul Liyana Abdul Aziz, Nur Aidya Hanum Aizam

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Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.

Keywords: University course timetabling problem, integer programming, preferences, constraints.

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Authors: Said Baadel, Fadi Thabtah, Joan Lu

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Clustering involves the partitioning of n objects into k clusters. Many clustering algorithms use hard-partitioning techniques where each object is assigned to one cluster. In this paper we propose an overlapping algorithm MCOKE which allows objects to belong to one or more clusters. The algorithm is different from fuzzy clustering techniques because objects that overlap are assigned a membership value of 1 (one) as opposed to a fuzzy membership degree. The algorithm is also different from other overlapping algorithms that require a similarity threshold be defined a priori which can be difficult to determine by novice users.

Keywords: Data mining, k-means, MCOKE, overlapping.

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Authors: Latifeh PourMohammadBagher

Abstract:

In this paper I have developed a system for evaluating the degree of fear emotion that the intelligent agent-based system may feel when it encounters to a persecuting event. In this paper I want to describe behaviors of emotional agents using human behavior in terms of the way their emotional states evolve over time. I have implemented a fuzzy inference system using Java environment. As the inputs of this system, I have considered three parameters related on human fear emotion. The system outputs can be used in agent decision making process or choosing a person for team working systems by combination the intensity of fear to other emotion intensities.

Keywords: Emotion simulation, Fear, Fuzzy intelligent agent

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Authors: Sanjeeb Kumar Kar

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The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: Siliang Wang, Minghui Wang, Jun Hu

Abstract:

A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: Kaveh Mollazade, Hojat Ahmadi, Mahmoud Omid, Reza Alimardani

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Recently, the issue of machine condition monitoring and fault diagnosis as a part of maintenance system became global due to the potential advantages to be gained from reduced maintenance costs, improved productivity and increased machine availability. The aim of this work is to investigate the effectiveness of a new fault diagnosis method based on power spectral density (PSD) of vibration signals in combination with decision trees and fuzzy inference system (FIS). To this end, a series of studies was conducted on an external gear hydraulic pump. After a test under normal condition, a number of different machine defect conditions were introduced for three working levels of pump speed (1000, 1500, and 2000 rpm), corresponding to (i) Journal-bearing with inner face wear (BIFW), (ii) Gear with tooth face wear (GTFW), and (iii) Journal-bearing with inner face wear plus Gear with tooth face wear (B&GW). The features of PSD values of vibration signal were extracted using descriptive statistical parameters. J48 algorithm is used as a feature selection procedure to select pertinent features from data set. The output of J48 algorithm was employed to produce the crisp if-then rule and membership function sets. The structure of FIS classifier was then defined based on the crisp sets. In order to evaluate the proposed PSD-J48-FIS model, the data sets obtained from vibration signals of the pump were used. Results showed that the total classification accuracy for 1000, 1500, and 2000 rpm conditions were 96.42%, 100%, and 96.42% respectively. The results indicate that the combined PSD-J48-FIS model has the potential for fault diagnosis of hydraulic pumps.

Keywords: Power Spectral Density, Machine ConditionMonitoring, Hydraulic Pump, Fuzzy Logic.

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Authors: Anselm L. Schüle, Thomas Rollmann, Reiner Anderl

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Within the collaborative research center 666 a new product development approach and the innovative manufacturing method of linear flow splitting are being developed. So far the design process is supported by 3D-CAD models utilizing User Defined Features in standard CAD-Systems. This paper now presents new functions for generating 3D-models of integral sheet metal products with bifurcations using Siemens PLM NX 6. The emphasis is placed on design and semi-automated insertion of User Defined Features. Therefore User Defined Features for both, linear flow splitting and its derivative linear bend splitting, were developed. In order to facilitate the modeling process, an application was developed that guides through the insertion process. Its usability and dialog layout adapt known standard features. The work presented here has significant implications on the quality, accurateness and efficiency of the product generation process of sheet metal products with higher order bifurcations.

Keywords: Linear Flow Splitting, CRC 666, User Defined Features.

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Authors: Loke Kean Koay, Horizon Gitano-Briggs, Mani Maran Ratnam

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Today air-core coils (ACC) are a viable alternative to ferrite-core coils in a range of applications due to their low induction effect. An analytical study was carried out and the results were used as a guide to understand the relationship between the magnet-coil distance and the resulting attractive magnetic force. Four different ACC models were fabricated for experimental study. The variation in the models included the dimensions, the number of coil turns and the current supply to the coil. Comparison between the analytical and experimental results for all the models shows an average discrepancy of less than 10%. An optimized ACC design was selected for the scanner which can provide maximum magnetic force.

Keywords: Air-Core Coils, Electromagnetic, Linear Optical Scanner

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Authors: Soltani Amir, Wang Xuan

Abstract:

The advantage of using non-linear passive damping  system in vibration control of two adjacent structures is investigated  under their base excitation. The base excitation is El Centro  earthquake record acceleration. The damping system is considered as  an optimum and effective non-linear viscous damper that is  connected between two adjacent structures. A MATLAB program is  developed to produce the stiffness and damping matrices and to  determine a time history analysis of the dynamic motion of the  system. One structure is assumed to be flexible while the other has a  rule as laterally supporting structure with rigid frames. The response  of the structure has been calculated and the non-linear damping  coefficient is determined using optimum LQR algorithm in an  optimum vibration control system. The non-linear parameter of  damping system is estimated and it has shown a significant advantage  of application of this system device for vibration control of two  adjacent tall building.

Keywords: Structural Control, Active and passive damping, Vibration control, Seismic isolation.

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Authors: Norbik Bashah, Idris Bharanidharan Shanmugam, Abdul Manan Ahmed

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Intrusion Detection Systems are increasingly a key part of systems defense. Various approaches to Intrusion Detection are currently being used, but they are relatively ineffective. Artificial Intelligence plays a driving role in security services. This paper proposes a dynamic model Intelligent Intrusion Detection System, based on specific AI approach for intrusion detection. The techniques that are being investigated includes neural networks and fuzzy logic with network profiling, that uses simple data mining techniques to process the network data. The proposed system is a hybrid system that combines anomaly, misuse and host based detection. Simple Fuzzy rules allow us to construct if-then rules that reflect common ways of describing security attacks. For host based intrusion detection we use neural-networks along with self organizing maps. Suspicious intrusions can be traced back to its original source path and any traffic from that particular source will be redirected back to them in future. Both network traffic and system audit data are used as inputs for both.

Keywords: Intrusion Detection, Network Security, Data mining, Fuzzy Logic.

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Authors: Njiri J. G., Ikua B. W., Nyakoe G. N.

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Optimization of cutting parameters important in precision machining in regards to efficiency and surface integrity of the machined part. Usually productivity and precision in machining is limited by the forces emanating from the cutting process. Due to the inherent varying nature of the workpiece in terms of geometry and material composition, the peak cutting forces vary from point to point during machining process. In order to increase productivity without compromising on machining accuracy, it is important to control these cutting forces. In this paper a fuzzy logic control algorithm is developed that can be applied in the control of peak cutting forces in milling of spherical surfaces using ball end mills. The controller can adaptively vary the feedrate to maintain allowable cutting force on the tool. This control algorithm is implemented in a computer numerical control (CNC) machine. It has been demonstrated that the controller can provide stable machining and improve the performance of the CNC milling process by varying feedrate.

Keywords: Ball-end mill, feedrate, fuzzy logic controller, machining optimization, spherical surface.

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Authors: M. Boudjerda, B. Touaibia, M. K. Mihoubi

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In Algeria agricultural irrigation is the primary water consuming sector followed by the domestic and industrial sectors. Economic development in the last decade has weighed heavily on water resources which are relatively limited and gradually decreasing to the detriment of agriculture. The research presented in this paper focuses on the optimization of irrigation water demand. Dynamic Programming-Neural Network (DPNN) method is applied to investigate reservoir optimization. The optimal operation rule is formulated to minimize the gap between water release and water irrigation demand. As a case study, Foum El-Gherza dam’s reservoir system in south of Algeria has been selected to examine our proposed optimization model. The application of DPNN method allowed increasing the satisfaction rate (SR) from 12.32% to 55%. In addition, the operation rule generated showed more reliable and resilience operation for the examined case study.

Keywords: ater management, agricultural demand, dam and reservoir operation, Foum el-Gherza dam, dynamic programming, artificial neural network.

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

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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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Authors: Noura Boudiaf, Allaoua Chaoui

Abstract:

One major difficulty that faces developers of concurrent and distributed software is analysis for concurrency based faults like deadlocks. Petri nets are used extensively in the verification of correctness of concurrent programs. ECATNets [2] are a category of algebraic Petri nets based on a sound combination of algebraic abstract types and high-level Petri nets. ECATNets have 'sound' and 'complete' semantics because of their integration in rewriting logic [12] and its programming language Maude [13]. Rewriting logic is considered as one of very powerful logics in terms of description, verification and programming of concurrent systems. We proposed in [4] a method for translating Ada-95 tasking programs to ECATNets formalism (Ada-ECATNet). In this paper, we show that ECATNets formalism provides a more compact translation for Ada programs compared to the other approaches based on simple Petri nets or Colored Petri nets (CPNs). Such translation doesn-t reduce only the size of program, but reduces also the number of program states. We show also, how this compact Ada-ECATNet may be reduced again by applying reduction rules on it. This double reduction of Ada-ECATNet permits a considerable minimization of the memory space and run time of corresponding Maude program.

Keywords: Ada tasking, ECATNets, Algebraic Petri Nets, Compact Representation, Analysis, Rewriting Logic, Maude.

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Authors: P. Subha Karuvelam, M. Rajaram

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Brushless DC motors (BLDC) are widely used in industrial areas. The BLDC motors are driven either by indirect ACAC converters or by direct AC-AC converters. Direct AC-AC converters i.e. matrix converters are used in this paper to drive the three phase BLDC motor and it eliminates the bulky DC link energy storage element. A matrix converter converts the AC power supply to an AC voltage of variable amplitude and variable frequency. A control technique is designed to generate the switching pulses for the three phase matrix converter. For the control of speed of the BLDC motor a separate PI controller and Fuzzy Logic Controller (FLC) are designed and a hysteresis current controller is also designed for the control of motor torque. The control schemes are designed and tested separately. The simulation results of both the schemes are compared and contrasted in this paper. The results show that the fuzzy logic control scheme outperforms the PI control scheme in terms of dynamic performance of the BLDC motor. Simulation results are validated with the experimental results.

Keywords: Fuzzy logic controller, matrix converter, permanent magnet brushless DC motor, PI controller.

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Authors: Sung-Hun Lee, Yun-Seong Lee, Jin-O Kim

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Reliability Centered Maintenance(RCM) is one of most widely used methods in the modern power system to schedule a maintenance cycle and determine the priority of inspection. In order to apply the RCM method to the Smart Grid, a precedence study for the new structure of rearranged system should be performed due to introduction of additional installation such as renewable and sustainable energy resources, energy storage devices and advanced metering infrastructure. This paper proposes a new method to evaluate the priority of maintenance and inspection of the power system facilities in the Smart Grid using the Risk Priority Number. In order to calculate that risk index, it is required that the reliability block diagram should be analyzed for the Smart Grid system. Finally, the feasible technical method is discussed to estimate the risk potential as part of the RCM procedure.

Keywords: Expert System, FMECA, Fuzzy Theory, Reliability Centered Maintenance, Risk Priority Number

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Authors: Lukas Mocek, Alexandros Markopoulos

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The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

Keywords: Linear elasticity, fictitious domain method, Total-FETI, domain decomposition, saddle-point system.

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: Single-degree-of-freedom system, linear acceleration method, nonlinear excited system, equivalent displacement method.

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Authors: Rami N. Khushaba, Adel Al-Jumaily

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The myoelectric signal (MES) is one of the Biosignals utilized in helping humans to control equipments. Recent approaches in MES classification to control prosthetic devices employing pattern recognition techniques revealed two problems, first, the classification performance of the system starts degrading when the number of motion classes to be classified increases, second, in order to solve the first problem, additional complicated methods were utilized which increase the computational cost of a multifunction myoelectric control system. In an effort to solve these problems and to achieve a feasible design for real time implementation with high overall accuracy, this paper presents a new method for feature extraction in MES recognition systems. The method works by extracting features using Wavelet Packet Transform (WPT) applied on the MES from multiple channels, and then employs Fuzzy c-means (FCM) algorithm to generate a measure that judges on features suitability for classification. Finally, Principle Component Analysis (PCA) is utilized to reduce the size of the data before computing the classification accuracy with a multilayer perceptron neural network. The proposed system produces powerful classification results (99% accuracy) by using only a small portion of the original feature set.

Keywords: Biomedical Signal Processing, Data mining andInformation Extraction, Machine Learning, Rehabilitation.

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Authors: Natarajan Vijayarangan, Prasanna S. Bidare

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Cryptography, Image watermarking and E-banking are filled with apparent oxymora and paradoxes. Random sequences are used as keys to encrypt information to be used as watermark during embedding the watermark and also to extract the watermark during detection. Also, the keys are very much utilized for 24x7x365 banking operations. Therefore a deterministic random sequence is very much useful for online applications. In order to obtain the same random sequence, we need to supply the same seed to the generator. Many researchers have used Deterministic Random Number Generators (DRNGs) for cryptographic applications and Pseudo Noise Random sequences (PNs) for watermarking. Even though, there are some weaknesses in PN due to attacks, the research community used it mostly in digital watermarking. On the other hand, DRNGs have not been widely used in online watermarking due to its computational complexity and non-robustness. Therefore, we have invented a new design of generating DRNG using Pi-series to make it useful for online Cryptographic, Digital watermarking and Banking applications.

Keywords: E-tokens, LFSR, non-linear, Pi series, pseudo random number.

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Authors: Lilac Al Safadi, Rana Abu Nafesa, Regina Garcia

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Motivated by Microsoft Co. Academic Program initiative, the department of Information Technology in King Saud University has adopted Microsoft products in three courses. The initiative aimed at enhancing the abilities of the university graduates and equipping them with skills that would help them in the job market. A number of methods of collecting assessment data were used to evaluate the course adoption initiative. Assessment data indicated that the goal of the course adoption is being achieved and that the students were much better prepared to design applications and administrate networks.

Keywords: course adoption, assessment, programming, technologies

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Authors: Takashi Mitsuishi, Koji Saigusa

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This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: Defuzzification, periodic membership function, polar coordinates transformation.

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