Search results for: Static Analysis.

Authors: Riad S. Jabri

Abstract:

Pattern matching based on regular tree grammars have been widely used in many areas of computer science. In this paper, we propose a pattern matcher within the framework of code generation, based on a generic and a formalized approach. According to this approach, parsers for regular tree grammars are adapted to a general pattern matching solution, rather than adapting the pattern matching according to their parsing behavior. Hence, we first formalize the construction of the pattern matches respective to input trees drawn from a regular tree grammar in a form of the so-called match trees. Then, we adopt a recently developed generic parser and tightly couple its parsing behavior with such construction. In addition to its generality, the resulting pattern matcher is characterized by its soundness and efficient implementation. This is demonstrated by the proposed theory and by the derived algorithms for its implementation. A comparison with similar and well-known approaches, such as the ones based on tree automata and LR parsers, has shown that our pattern matcher can be applied to a broader class of grammars, and achieves better approximation of pattern matches in one pass. Furthermore, its use as a machine code selector is characterized by a minimized overhead, due to the balanced distribution of the cost computations into static ones, during parser generation time, and into dynamic ones, during parsing time.

Keywords: Bottom-up automata, Code selection, Pattern matching, Regular tree grammars, Match trees.

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Authors: A. Hossein Sahoolizadeh, B. Zargham Heidari, C. Hamid Dehghani

Abstract:

In this paper, a new face recognition method based on PCA (principal Component Analysis), LDA (Linear Discriminant Analysis) and neural networks is proposed. This method consists of four steps: i) Preprocessing, ii) Dimension reduction using PCA, iii) feature extraction using LDA and iv) classification using neural network. Combination of PCA and LDA is used for improving the capability of LDA when a few samples of images are available and neural classifier is used to reduce number misclassification caused by not-linearly separable classes. The proposed method was tested on Yale face database. Experimental results on this database demonstrated the effectiveness of the proposed method for face recognition with less misclassification in comparison with previous methods.

Keywords: Face recognition Principal component analysis, Linear discriminant analysis, Neural networks.

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Authors: Mohammad Mashud, S. M. Nahid Hasan

Abstract:

The aim of the research work is to modify the NACA 4215 airfoil with flap and rotary cylinder at the leading edge of the airfoil and experimentally study the static pressure distribution over the airfoil completed with flap and leading-edge vortex generator. In this research, NACA 4215 wing model has been constructed by generating the profile geometry using the standard equations and design software such as AutoCAD and SolidWorks. To perform the experiment, three wooden models are prepared and tested in subsonic wind tunnel. The experiments were carried out in various angles of attack. Flap angle and momentum injection rate are changed to observe the characteristics of pressure distribution. In this research, a new concept of flow separation control mechanism has been introduced to improve the aerodynamic characteristics of airfoil. Control of flow separation over airfoil which experiences a vortex generator (rotating cylinder) at the leading edge of airfoil is experimentally simulated under the effects of momentum injection. The experimental results show that the flow separation control is possible by the proposed mechanism, and benefits can be achieved by momentum injection technique. The wing performance is significantly improved due to control of flow separation by momentum injection method.

Keywords: Airfoil, momentum injection, flap and pressure distribution.

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Authors: Alexandra Oliveros, Miguel Sotaquirá

Abstract:

DNA microarray technology is widely used by geneticists to diagnose or treat diseases through gene expression. This technology is based on the hybridization of a tissue-s DNA sequence into a substrate and the further analysis of the image formed by the thousands of genes in the DNA as green, red or yellow spots. The process of DNA microarray image analysis involves finding the location of the spots and the quantification of the expression level of these. In this paper, a tool to perform DNA microarray image analysis is presented, including a spot addressing method based on the image projections, the spot segmentation through contour based segmentation and the extraction of relevant information due to gene expression.

Keywords: Contour segmentation, DNA microarrays, edge detection, image processing, segmentation, spot addressing.

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Authors: Aumnad Phdungsilp, Teeradej Wuttipornpun

Abstract:

Decision support based upon risk analysis into comparison of the electricity generation from different renewable energy technologies can provide information about their effects on the environment and society. The aim of this paper is to develop the assessment framework regarding risks to health and environment, and the society-s benefits of the electric power plant generation from different renewable sources. The multicriteria framework to multiattribute risk analysis technique and the decision analysis interview technique are applied in order to support the decisionmaking process for the implementing renewable energy projects to the Bangkok case study. Having analyses the local conditions and appropriate technologies, five renewable power plants are postulated as options. As this work demonstrates, the analysis can provide a tool to aid decision-makers for achieving targets related to promote sustainable energy system.

Keywords: Analytic Hierarchy Process, Bangkok, MultiattributeRisk Analysis, Renewable Energy Technology.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch size B as the generalizing parameter. Results for the case of single-packet arrivals are obtained first. The similarities between the two families of functions are then used to obtain results for the general case of batch arrival queue with a batch size larger than one.

Keywords: batch arrivals, generalized Bessel functions, queuetransient analysis, time-varying probabilities.

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Authors: N. Karunakaran, V. Balasubramanian

Abstract:

This paper presents the results of a study aimed at establishing the temperature distribution during the welding of aluminum alloy plates by Pulsed Current Gas Tungsten Arc Welding (PCGTAW) and Constant Current Gas Tungsten Arc Welding (CCGTAW) processes. Pulsing of the GTA welding current influences the dimensions and solidification rate of the fused zone, it also reduces the weld pool volume hence a narrower bead. In this investigation, the base material considered was aluminum alloy AA 6351 T6, which is finding use in aircraft, automobile and high-speed train components. A finite element analysis was carried out using ANSYS, and the results of the FEA were compared with the experimental results. It is evident from the study that the finite element analysis using ANSYS can be effectively used to model PCGTAW process for finding temperature distribution.

Keywords: Gas tungsten arc welding, pulsed current, finite element analysis, thermal analysis, aluminum alloy.

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Authors: Miloje S. Radenkovic, Tamal Bose

Abstract:

This paper presents the convergence analysis of a prediction based blind equalizer for IIR channels. Predictor parameters are estimated by using the recursive least squares algorithm. It is shown that the prediction error converges almost surely (a.s.) toward a scalar multiple of the unknown input symbol sequence. It is also proved that the convergence rate of the parameter estimation error is of the same order as that in the iterated logarithm law.

Keywords: Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.

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Authors: A. H. Fatah, A. H. Ahmed

Abstract:

Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Keywords: Gamma-Ray, Spectrum analysis, Non-linear leastsquare fitting.

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Authors: Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang

Abstract:

One good analysis method in seismic response analysis is direct time integration, which widely adopts Rayleigh damping. An approach is presented for selection of Rayleigh damping coefficients to be used in seismic analyses to produce a response that is consistent with Modal damping response. In the presented approach, the expression of the error of peak response, acquired through complete quadratic combination method, and Rayleigh damping coefficients was set up and then the coefficients were produced by minimizing the error. Two finite element modes of soil layers, excited by 28 seismic waves, were used to demonstrate the feasibility and validity.

Keywords: Rayleigh damping, modal damping, damping coefficients, seismic response analysis.

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Authors: M. H. Nagrial, J. Rizk, A. Hellany

Abstract:

This paper presents the design, analysis and development of permanent magnet (PM) torque couplers. These couplers employ rare-earth magnets. Based on finite element analysis and earlier analytical works both concentric and face-type synchronous type couplers have been designed and fabricated. The experimental performance has good correlation with finite element calculations.

Keywords: Finite Element Analysis, Synchronous TorqueCouplers, Permanent Magnet Torque Couplers

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

Abstract:

An analytical 4-DOF nonlinear model of a de Laval rotor-stator system based on Energy Principles has been used theoretically and experimentally to investigate fault symptoms in a rotating system. The faults, namely rotor-stator-rub, crack and unbalance are modeled as excitations on the rotor shaft. Mayes steering function is used to simulate the breathing behaviour of the crack. The fault analysis technique is based on waveform signal, orbits and Fast Fourier Transform (FFT) derived from simulated and real measured signals. Simulated and experimental results manifest considerable mutual resemblance of elliptic-shaped orbits and FFT for a same range of test data.

Keywords: A breathing crack, fault, FFT, nonlinear, orbit, rotorstator rub, vibration analysis.

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Authors: Asha Hasnimy Mohd Hashim, Lee Ai Choo

Abstract:

We investigated the effects of modified preprogrammed training mode Chase Trainer from Balance Trainer (BT3, HurLab, Tampere, Finland) on athlete who experienced unilateral Patellofemoral Pain Syndrome (PFPS). Twenty-seven athletes with mean age= 14.23 ±1.31 years, height = 164.89 ± 7.85 cm, weight = 56.94 ± 9.28 kg were randomly assigned to two groups: experiment (EG; n = 14) and injured (IG; n = 13). EG performed a series of Chase Trainer program which required them to shift their body weight at different directions, speeds and angle of leaning twice a week for duration of 8 weeks. The static postural control and perceived pain level measures were taken at baseline, after 6 weeks and 8 weeks of training. There was no significant difference in any of tested variables between EG and IG before and after 6-week the intervention period. However, after 8-week of training, the postural control (eyes open) and perceived pain level of EG improved compared to IG (p<0.05). The postural control with eyes closed of EG improved (p<0.05) but the values were not significantly different compared to IG after training. The results suggest that using Chase Trainer exercise program it is possible to improve individual postural control and decreased perceived pain level in athlete with unilateral Patellofemoral Pain Syndrome (PFPS).

Keywords: Patellofemoral Pain Syndrome, perceived pain level, postural control.

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Authors: Yurii Bloshko, Oksana Olar

Abstract:

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: Fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms.

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Authors: M. Heikkinen, A. Sarpola, H. Hellman, J. Rämö, Y. Hiltunen

Abstract:

Independent component analysis (ICA) is a computational method for finding underlying signals or components from multivariate statistical data. The ICA method has been successfully applied in many fields, e.g. in vision research, brain imaging, geological signals and telecommunications. In this paper, we apply the ICA method to an analysis of mass spectra of oligomeric species emerged from aluminium sulphate. Mass spectra are typically complex, because they are linear combinations of spectra from different types of oligomeric species. The results show that ICA can decomposite the spectral components for useful information. This information is essential in developing coagulation phases of water treatment processes.

Keywords: Independent component analysis, massspectroscopy, water treatment, aluminium sulphate.

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Authors: Emre Kara, Metehan Demir, Şura Karakuzu, Kadir Koç, Ahmet F. Geylan, Halil Aykul

Abstract:

While the polymeric foam cored sandwiches have been realized for many years, recently there is a growing and outstanding interest on the use of sandwiches consisting of aluminum foam core because of their some of the distinct mechanical properties such as high bending stiffness, high load carrying and energy absorption capacities. These properties make them very useful in the transportation industry (automotive, aerospace, shipbuilding industry), where the "lightweight design" philosophy and the safety of vehicles are very important aspects. Therefore, in this study, the sandwich panels with aluminum alloy foam core and various types and thicknesses of glass fiber reinforced polymer (GFRP) skins produced via Vacuum Assisted Resin Transfer Molding (VARTM) technique were obtained by using a commercial toughened epoxy based adhesive with two components. The aim of this contribution was the analysis of the bending response of sandwiches with various glass fiber reinforced polymer skins. The three point bending tests were performed on sandwich panels at different values of support span distance using a universal static testing machine in order to clarify the effects of the type and thickness of the GFRP skins in terms of peak load, energy efficiency and absorbed energy values. The GFRP skins were easily bonded to the aluminum alloy foam core under press machine with a very low pressure. The main results of the bending tests are: force-displacement curves, peak force values, absorbed energy, collapse mechanisms and the influence of the support span length and GFRP skins. The obtained results of the experimental investigation presented that the sandwich with the skin made of thicker S-Glass fabric failed at the highest load and absorbed the highest amount of energy compared to the other sandwich specimens. The increment of the support span distance made the decrease of the peak force and absorbed energy values for each type of panels. The common collapse mechanism of the panels was obtained as core shear failure which was not affected by the skin materials and the support span distance.

Keywords: Aluminum foam, collapse mechanisms, light-weight structures, transport application

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Authors: Estela Macedo Alves

Abstract:

This paper is an overview on public policy analysis focused on the study of Brazilian public policy making process. The methodology is based on the review of some theories on the subject, linking them to Brazilian reality. The study presents basic policy analysis concepts, such as policy, polity and politics. It is emphasized John Kingdon's Multiple Stream Model, because of its clarifying aspects concerning public policies formulation process in democratic countries. In this path it was possible to establish interpretations on environmental public policies in Brazil and understand its methods, instead of presenting only a case study. At the end, it is possible to connect theory with Brazilian reality, identifying negative and positive points of its political processes and structure.

Keywords: Brazilian policies, environmental public policy, multiple stream model, public policy analysis.

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Authors: S. L. Tulasi Devi, R. N. Rao

Abstract:

This paper focuses attention on specific aspects of entrepreneurial decisions relating to investment, both in the total fixed investments and plant & machinery (separately). Demand and financial factors, internal and external, are considered in the investment analysis. Finally the influence of determinants of fixed investment and investment plans are examined in Electric Power industry in India.

Keywords: Determinants, Electric Power Industry, Fixed Assets, Econometric Analysis.

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Authors: Hatem A. Khater, A. Baith Mohamed, Sara M. Kamel

Abstract:

Software Development Risks Identification (SDRI), using Fault Tree Analysis (FTA), is a proposed technique to identify not only the risk factors but also the causes of the appearance of the risk factors in software development life cycle. The method is based on analyzing the probable causes of software development failures before they become problems and adversely affect a project. It uses Fault tree analysis (FTA) to determine the probability of a particular system level failures that are defined by A Taxonomy for Sources of Software Development Risk to deduce failure analysis in which an undesired state of a system by using Boolean logic to combine a series of lower-level events. The major purpose of this paper is to use the probabilistic calculations of Fault Tree Analysis approach to determine all possible causes that lead to software development risk occurrence

Keywords: Software Development Risks Identification (SDRI), Fault Tree Analysis (FTA), Taxonomy for Software Development Risks (TSDR), Probabilistic Risk Assessment (PRA).

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Authors: Kemal Comakli, Meryem Terhan

Abstract:

In this study, the potential of heat recovery from waste flue gas was examined in 60 MW district heating system of a university, and fuel saving was aimed by using the recovered heat in the system as a source again. Various scenarios are intended to make use of waste heat. For this purpose, actual operation data of the system were taken. Besides, the heat recovery units that consist of heat exchangers such as flue gas condensers, economizers or air pre-heaters were designed theoretically for each scenario. Energy analysis of natural gas-fired boiler’s exhaust flue gas in the system, and economic analysis of heat recovery units to predict payback periods were done. According to calculation results, the waste heat loss ratio from boiler flue gas in the system was obtained as average 16%. Thanks to the heat recovery units, thermal efficiency of the system can be increased, and fuel saving can be provided. At the same time, a huge amount of green gas emission can be decreased by installing the heat recovery units.

Keywords: Heat recovery from flue gas, energy analysis of flue gas, economical analysis, payback period.

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Authors: Sarah O. Alhumoud, Mawaheb I. Altuwaijri, Tarfa M. Albuhairi, Wejdan M. Alohaideb

Abstract:

Large-scale data stream analysis has become one of the important business and research priorities lately. Social networks like Twitter and other micro-blogging platforms hold an enormous amount of data that is large in volume, velocity and variety. Extracting valuable information and trends out of these data would aid in a better understanding and decision-making. Multiple analysis techniques are deployed for English content. Moreover, one of the languages that produce a large amount of data over social networks and is least analyzed is the Arabic language. The proposed paper is a survey on the research efforts to analyze the Arabic content in Twitter focusing on the tools and methods used to extract the sentiments for the Arabic content on Twitter.

Keywords: Big Data, Social Networks, Sentiment Analysis.

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Authors: Michelle Zeyuan Ma, Hermann Heilmeier

Abstract:

Recently, meat production ecosystem impacts initiated many hot discussions and researchers, and it is a difficult implementation to reduce such impacts due to the demand of meat products. It calls for better management and control of ecosystem impacts from every aspects of meat production. This article analyzes the ecosystem impacts of meat production based on meat products life cycle. The analysis shows that considerable ecosystem impacts are caused by different meat production steps: initial establishment phase, animal raising, slaughterhouse processing, meat consumption, and wastes management. Based on this analysis, the impacts are summarized as: leading factor for biodiversity loss; water waste, land use waste and land degradation; greenhouse gases emissions; pollution to air, water, and soil; related major diseases. The article also provides a discussion on a solution-sustainable food system, which could help in reducing ecosystem impacts. The analysis method is based on the life cycle level, it provides a concept of the whole meat industry ecosystem impacts, and the analysis result could be useful to manage or control meat production ecosystem impacts from investor, producer and consumer sides.

Keywords: Eutrophication, life cycle based analysis, sustainable food, waste management.

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Authors: Sepulveda Juan

Abstract:

This article explains the elements and considerations taken into account when implementing and applying patent evaluation and scientometric study in the identifications of technology trends, and the tools that led to the implementation of a software application for patent revision. Univariate analysis helped recognize the technological leaders in the field of energy, and steered the way for a multivariate analysis of this sample, which allowed for a graphical description of the techniques of mature technologies, as well as the detection of emerging technologies. This article ends with a validation of the methodology as applied to the case of fuel cells.

Keywords: Energy, technology mapping, patents.

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Authors: Sunil Patel, Pallab Maji

Abstract:

To study the effect of adversarial attack environment must be controlled. Autonomous driving includes mainly 5 phases sense, perceive, map, plan, and drive. Autonomous vehicles sense their surrounding with the help of different sensors like cameras, radars, and lidars. Deep learning techniques are considered Blackbox and found to be vulnerable to adversarial attacks. In this research, we study the effect of the various known adversarial attacks with the help of the Unreal Engine-based, high-fidelity, real-time raytraced simulated environment. The goal of this experiment is to find out if adversarial attacks work in moving vehicles and if an unknown network may be targeted. We discovered that the existing Blackbox and Whitebox attacks have varying effects on different traffic signs. We observed that attacks that impair detection in static scenarios do not have the same effect on moving vehicles. It was found that some adversarial attacks with hardly noticeable perturbations entirely blocked the recognition of certain traffic signs. We observed that the daylight condition has a substantial impact on the model's performance by simulating the interplay of light on traffic signs. Our findings have been found to closely resemble outcomes encountered in the real world.

Keywords: Adversarial attack simulation, computer simulation, ray-traced environment, realistic simulation, unreal engine.

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Authors: C. Ardil

Abstract:

In this paper, a neutrosophic multiple criteria decision analysis method is proposed to select stealth fighter aircraft. Neutrosophic multiple criteria decision analysis methods are used to analyze the neutrosophic environment and give results under uncertainty and incompleteness. Neutrosophic numbers are used to evaluate alternatives over a set of evaluation criteria in decision making problems. Finally, the proposed model is applied to a practical decision problem for selecting stealth fighter aircraft.

Keywords: neutrosophic sets, multiple criteria decision making analysis, stealth fighter aircraft, aircraft selection, MCDMA, SVNNs

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Authors: Omid A. Zargar

Abstract:

Vibration analysis is the most important factor in preventive maintenance. Gas turbine vibration analysis is also one of the most challenging categories in most critical equipment monitoring systems. Utilities are heart of the process in big industrial plants like petrochemical zones. Vibration analysis methods and condition monitoring systems of this kind of equipment developed too much in recent years. On the other hand, too much operation condition consideration in this kind of equipment should be adjusted properly like inlet and outlet pressure and temperature for both turbine and compressor. In this paper the most important tools and hypothesis used for analyzing of gas turbine power plants discussed in details through a real case history related to an Alstom Typhoon gas turbine power plant in Iran oil industries. In addition, the basic principal of vibration behavior caused by mechanical unbalance in gas turbine rotor discussed in details.

Keywords: Vibration analysis, gas turbine, time wave form (TWF), fast Fourier transform (FFT), phase angle.

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Authors: Ehsan Bashiri

Abstract:

A 7-step method (with 25 sub-steps) to assess risk of air pollutants is introduced. These steps are: pre-considerations, sampling, statistical analysis, exposure matrix and likelihood, doseresponse matrix and likelihood, total risk evaluation, and discussion of findings. All mentioned words and expressions are wellunderstood; however, almost all steps have been modified, improved, and coupled in such a way that a comprehensive method has been prepared. Accordingly, the SADRA (Statistical Analysis-Driven Risk Assessment) emphasizes extensive and ongoing application of analytical statistics in traditional risk assessment models. A Sulfur Dioxide case study validates the claim and provides a good illustration for this method.

Keywords: Criteria air pollutants, Matrix of risk, Riskassessment, Statistical analysis.

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Authors: C. Ardil

Abstract:

This paper proposes entropic programming for the freighter aircraft selection problem using the multiple criteria decision analysis method. The study aims to propose a systematic and comprehensive framework by focusing on the perspective of freighter aircraft selection. In order to achieve this goal, an integrated entropic programming approach was proposed to evaluate and rank alternatives. The decision criteria and aircraft alternatives were identified from the research data analysis. The objective criteria weights were determined by the mean weight method and the standard deviation method. The proposed entropic programming model was applied to a practical decision problem for evaluating and selecting freighter aircraft. The proposed entropic programming technique gives robust, reliable, and efficient results in modeling decision making analysis problems. As a result of entropic programming analysis, Boeing B747-8F, a freighter aircraft alternative ( a3), was chosen as the most suitable freighter aircraft candidate.   

Keywords: entropic programming, additive weighted model, multiple criteria decision making analysis, MCDMA, TOPSIS, aircraft selection, freighter aircraft, Boeing B747-8F, Boeing B777F, Airbus A350F

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Authors: Jagadish H. Pujar, S. F. Kodad

Abstract:

Recent developments in Soft computing techniques, power electronic switches and low-cost computational hardware have made it possible to design and implement sophisticated control strategies for sensorless speed control of AC motor drives. Such an attempt has been made in this work, for Sensorless Speed Control of Induction Motor (IM) by means of Direct Torque Fuzzy Control (DTFC), PI-type fuzzy speed regulator and MRAS speed estimator strategy, which is absolutely nonlinear in its nature. Direct torque control is known to produce quick and robust response in AC drive system. However, during steady state, torque, flux and current ripple occurs. So, the performance of conventional DTC with PI speed regulator can be improved by implementing fuzzy logic techniques. Certain important issues in design including the space vector modulated (SVM) 3-Ф voltage source inverter, DTFC design, generation of reference torque using PI-type fuzzy speed regulator and sensor less speed estimator have been resolved. The proposed scheme is validated through extensive numerical simulations on MATLAB. The simulated results indicate the sensor less speed control of IM with DTFC and PI-type fuzzy speed regulator provides satisfactory high dynamic and static performance compare to conventional DTC with PI speed regulator.

Keywords: Sensor-less Speed Estimator, Fuzzy Logic Control(FLC), SVM, DTC, DTFC, IM, fuzzy speed regulator.

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Authors: Dong-Joong Kim, Sangho Choi, Woong Lim

Abstract:

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

Keywords: Commognitive framework, discourse analysis, mathematical discourse, mathematics education.

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