Search results for: simulation model.

Authors: C. Shih, J. R. Wang, H. C. Chang, S. W. Chen, S. C. Chiang, T. Y. Yu

Abstract:

After the measurement uncertainty recapture (MUR) power uprates, Kuosheng nuclear power plant (NPP) was uprated the power from 2894 MWt to 2943 MWt. For power upgrade, several codes (e.g., TRACE, RELAP5, etc.) were applied to assess the safety of Kuosheng NPP. Hence, the main work of this research is to establish a RELAP5/MOD3.3 model of Kuosheng NPP with SNAP interface. The establishment of RELAP5/SNAP model was referred to the FSAR, training documents, and TRACE model which has been developed and verified before. After completing the model establishment, the startup test scenarios would be applied to the RELAP5/SNAP model. With comparing the startup test data and TRACE analysis results, the applicability of RELAP5/SNAP model would be assessed.

Keywords: RELAP5, TRACE, SNAP, BWR.

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Authors: Jolanta Tamošaitienė

Abstract:

The article focuses on a developed comprehensive model to be used in an agile environment for the risk assessment and selection based on multi-attribute methods. The model is based on a multi-attribute evaluation of risk in construction, and the determination of their optimality criterion values are calculated using complex Multiple Criteria Decision-Making methods. The model may be further applied to risk assessment in an agile construction environment. The attributes of risk in a construction project are selected by applying the risk assessment condition to the construction sector, and the construction process efficiency in the construction industry accounts for the agile environment. The paper presents the comprehensive risk assessment model in an agile construction environment. It provides a background and a description of the proposed model and the developed analysis of the comprehensive risk assessment model in an agile construction environment with the criteria.

Keywords: Assessment, environment, agile, model, risk.

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Authors: V. T. S. Dao, T. G. Etoh, C. Vo Le, H. D. Nguyen, K. Takehara, T. Akino, K. Nishi

Abstract:

We present an explicit expression to estimate driving voltage attenuation through RC networks representation of an ultrahigh- speed image sensor. Elmore delay metric for a fundamental RC chain is employed as the first-order approximation. By application of dimensional analysis to SPICE simulation data, we found a simple expression that significantly improves the accuracy of the approximation. Estimation error of the resultant expression for uniform RC networks is less than 2%. Similarly, another simple closed-form model to estimate 50 % delay through fundamental RC networks is also derived with sufficient accuracy. The framework of this analysis can be extended to address delay or attenuation issues of other VLSI structures.

Keywords: Dimensional Analysis, Elmore model, RC network, Signal Attenuation, Ultra-High-Speed Image Sensor.

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Authors: Tamara Nestorović, Jean Lefèvre, Stefan Ringwelski, Ulrich Gabbert

Abstract:

Two approaches for model development of a smart acoustic box are suggested in this paper: the finite element (FE) approach and the subspace identification. Both approaches result in a state-space model, which can be used for obtaining the frequency responses and for the controller design. In order to validate the developed FE model and to perform the subspace identification, an experimental set-up with the acoustic box and dSPACE system was used. Experimentally obtained frequency responses show good agreement with the frequency responses obtained from the FE model and from the identified model.

Keywords: Acoustic box, experimental verification, finite element model, subspace identification.

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Authors: Gilberto Gonzalez-A, Octavio Barriga

Abstract:

A bond graph model of a hydroelectric plant is proposed. In order to analyze the system some structural properties of a bond graph are used. The structural controllability of the hydroelctric plant is described. Also, the steady state of the state variables applying the bond graph in a derivative causality assignment is obtained. Finally, simulation results of the system are shown.

Keywords: Bond graph, hydraulic plant, steady state.

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Authors: M. Tahar Bouzaher

Abstract:

This study involves a numerical simulation of the flow around a NACA2415 airfoil, with a 15°angle of attack, and flow separation control using a rod, It reposes inputting a cylindrical rod upstream of the leading edge in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The viscous, non-stationary flow is simulated using ANSYS FLUENT 13. Our results showed a substantial modification in the flow behavior and a maximum drag reduction of 51%.

Keywords: CFD, Flow separation, Active control, Boundary layer, rod, NACA 2415.

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Authors: Wararat Rungworawut, Twittie Senivongse

Abstract:

Business process model describes process flow of a business and can be seen as the requirement for developing a software application. This paper discusses a BPM2CD guideline which complements the Model Driven Architecture concept by suggesting how to create a platform-independent software model in the form of a UML class diagram from a business process model. An important step is the identification of UML classes from the business process model. A technique for object-oriented analysis called domain analysis is borrowed and key concepts in the business process model will be discovered and proposed as candidate classes for the class diagram. The paper enhances this step by using ontology search to help identify important classes for the business domain. As ontology is a source of knowledge for a particular domain which itself can link to ontologies of related domains, the search can give a refined set of candidate classes for the resulting class diagram.

Keywords: Business Process Model, Model DrivenArchitecture, Ontology, UML Class Diagram.

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Authors: Saeid Khajehmandali, Fattah Mollakarimi, Zohreh Seyf

Abstract:

There was a high rate of corrosion in Pyrolysis Gasoline Hydrogenation (PGH) unit of Arak Petrochemical Company (ARPC), and it caused some operational problem in this plant. A commercial chemical had been used as anti-corrosion in the depentanizer column overhead in order to control the corrosion rate. Injection of commercial corrosion inhibitor caused some operational problems such as fouling in some heat exchangers. It was proposed to replace this commercial material with another more effective trouble free, and well-known additive by R&D and operation specialists. At first, the system was simulated by commercial simulation software in electrolytic system to specify low pH points inside the plant. After a very comprehensive study of the situation and technical investigations ,ammonia / monoethanol amine solution was proposed as neutralizer or corrosion inhibitor to be injected in a suitable point of the plant. For this purpose, the depentanizer column and its accessories system was simulated again in case of this solution injection. According to the simulation results, injection of new anticorrosion substance has no any side effect on C5 cut product and operating conditions of the column. The corrosion rate will be cotrolled, if the pH remains at the range of 6.5 to 8 . Aactual plant test run was also carried out by injection of ammonia / monoethanol amine solution at the rate of 0.6 Kg/hr and the results of iron content of water samples and corrosion test coupons confirmed the simulation results. Now, ammonia / monoethanol amine solution is injected to a suitable pint inside the plant and corrosion rate has decreased significantly.

Keywords: Corrosion, Pyrolysis Gasoline, Simulation, Corrosion test copoun.

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Authors: Yongsuk Jang Kim, Sun-Tae Chung, Boogyun Kim, Seongwon Cho

Abstract:

Realistic 3D face model is more precise in representing pose, illumination, and expression of face than 2D face model so that it can be utilized usefully in various applications such as face recognition, games, avatars, animations, and etc. In this paper, we propose a 3D face modeling method based on 3D dense morphable shape model. The proposed 3D modeling method first constructs a 3D dense morphable shape model from 3D face scan data obtained using a 3D scanner. Next, the proposed method extracts and matches facial landmarks from 2D image sequence containing a face to be modeled, and then reconstructs 3D vertices coordinates of the landmarks using a factorization-based SfM technique. Then, the proposed method obtains a 3D dense shape model of the face to be modeled by fitting the constructed 3D dense morphable shape model into the reconstructed 3D vertices. Also, the proposed method makes a cylindrical texture map using 2D face image sequence. Finally, the proposed method generates a 3D face model by rendering the 3D dense face shape model using the cylindrical texture map. Through building processes of 3D face model by the proposed method, it is shown that the proposed method is relatively easy, fast and precise.

Keywords: 3D Face Modeling, 3D Morphable Shape Model, 3DReconstruction, 3D Correspondence.

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Authors: İres İskender, Ahmet Karaarslan

Abstract:

In this study, the performance of a high-frequency arc welding machine including a two-switch inverter is analyzed. The control of the system is achieved using two different control techniques i- fuzzy logic control (FLC) ii- state space averaging based sliding control. Fuzzy logic control does not need accurate mathematical model of a plant and can be used in nonlinear applications. The second method needs the mathematical model of the system. In this method the state space equations of the system are derived for two different “on" and “off" states of the switches. The derived state equations are combined with the sliding control rule considering the duty-cycle of the converter. The performance of the system is analyzed by simulating the system using SIMULINK tool box of MATLAB. The simulation results show that fuzzy logic controller is more robust and less sensitive to parameter variations.

Keywords: Fuzzy logic, arc welding, sliding state space control, PWM, current control.

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Authors: Nagulapati Kiran, V. Rangavalli, B. Vanajakshi

Abstract:

This paper designs the four-phase Boost Converter which overcomes the problem of high input ripple current and output ripple voltage. Digital control is more convenient for such a topology on basis of synchronization, phase shift operation, etc. Simulation results are presented for open-loop and closed-loop for four phase boost converter. This control scheme is applicable for PFC rectifiers as well. Thus a comparative analysis based on the obtained results is performed.

Keywords: Boost Converter, Bode plot, PI Controller, Four phase.

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Authors: John Kabuba, Antoine Mulaba-Bafubiandi, Kim Battle

Abstract:

This paper presents a critical study about the application of Neural Networks to ion-exchange process. Ionexchange is a complex non-linear process involving many factors influencing the ions uptake mechanisms from the pregnant solution. The following step includes the elution. Published data presents empirical isotherm equations with definite shortcomings resulting in unreliable predictions. Although Neural Network simulation technique encounters a number of disadvantages including its “black box", and a limited ability to explicitly identify possible causal relationships, it has the advantage to implicitly handle complex nonlinear relationships between dependent and independent variables. In the present paper, the Neural Network model based on the back-propagation algorithm Levenberg-Marquardt was developed using a three layer approach with a tangent sigmoid transfer function (tansig) at hidden layer with 11 neurons and linear transfer function (purelin) at out layer. The above mentioned approach has been used to test the effectiveness in simulating ion exchange processes. The modeling results showed that there is an excellent agreement between the experimental data and the predicted values of copper ions removed from aqueous solutions.

Keywords: Copper, ion-exchange process, neural networks, simulation

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Authors: Hashim Isam Jameel Al-Safi, P. Ranjan Sarukkalige

Abstract:

Climate change is likely to impact the Australian continent by changing the trends of rainfall, increasing temperature, and affecting the accessibility of water quantity and quality. This study investigates the possible impacts of future climate change on the hydrological system of the Harvey River catchment in Western Australia by using the conceptual modelling approach (HBV mode). Daily observations of rainfall and temperature and the long-term monthly mean potential evapotranspiration, from six weather stations, were available for the period (1961-2015). The observed streamflow data at Clifton Park gauging station for 33 years (1983-2015) in line with the observed climate variables were used to run, calibrate and validate the HBV-model prior to the simulation process. The calibrated model was then forced with the downscaled future climate signals from a multi-model ensemble of fifteen GCMs of the CMIP3 model under three emission scenarios (A2, A1B and B1) to simulate the future runoff at the catchment outlet. Two periods were selected to represent the future climate conditions including the mid (2046-2065) and late (2080-2099) of the 21^st century. A control run, with the reference climate period (1981-2000), was used to represent the current climate status. The modelling outcomes show an evident reduction in the mean annual streamflow during the mid of this century particularly for the A1B scenario relative to the control run. Toward the end of the century, all scenarios show a relatively high reduction trends in the mean annual streamflow, especially the A1B scenario, compared to the control run. The decline in the mean annual streamflow ranged between 4-15% during the mid of the current century and 9-42% by the end of the century.

Keywords: Climate change impact, Harvey catchment, HBV model, hydrological modelling, GCMs, LARS-WG, Australia.

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Authors: M. H. Kazemi, D. Salac

Abstract:

A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: Coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method.

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Authors: Mu-Yen Chen, Min-Hsuan Fan, Chia-Chen Chen, Siang-Yu Jhong

Abstract:

In recent years, real estate prediction or valuation has been a topic of discussion in many developed countries. Improper hype created by investors leads to fluctuating prices of real estate, affecting many consumers to purchase their own homes. Therefore, scholars from various countries have conducted research in real estate valuation and prediction. With the back-propagation neural network that has been popular in recent years and the orthogonal array in the Taguchi method, this study aimed to find the optimal parameter combination at different levels of orthogonal array after the system presented different parameter combinations, so that the artificial neural network obtained the most accurate results. The experimental results also demonstrated that the method presented in the study had a better result than traditional machine learning. Finally, it also showed that the model proposed in this study had the optimal predictive effect, and could significantly reduce the cost of time in simulation operation. The best predictive results could be found with a fewer number of experiments more efficiently. Thus users could predict a real estate transaction price that is not far from the current actual prices.

Keywords: Artificial Neural Network, Taguchi Method, Real Estate Valuation Model.

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Authors: Ahmad F. Subahi, Anthony J. H. Simons

Abstract:

This Paper presents an on-going research in the area of Model-Driven Engineering (MDE). The premise is that UML is too unwieldy to serve as the basis for model-driven engineering. We need a smaller, simpler notation with a cleaner semantics. We propose some ideas for a simpler notation with a clean semantics. The result is known as μML, or the Micro-Modelling Language.

Keywords: Model-driven engineering, model transformations, domain-specific languages, end-user development.

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Authors: Xun Liang

Abstract:

In this paper, we probe into the traffic assignment problem by the chromosome-learning-based path finding method in simulation, which is to model the driver' behavior in the with-in-a-day process. By simply making a combination and a change of the traffic route chromosomes, the driver at the intersection chooses his next route. The various crossover and mutation rules are proposed with extensive examples.

Keywords: Chromosome learning, crossover, mutation, traffic path finding.

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Authors: T. Benyetho, L. El Abdellaoui, J. Terhzaz, H. Bennis, N. Ababssi, A. Tajmouati, A. Tribak, M. Latrach

Abstract:

This work presents a new planar multiband antenna based on fractal geometry. This structure is optimized and validated into simulation by using CST-MW Studio. To feed this antenna we have used a CPW line which makes it easy to be incorporated with integrated circuits. The simulation results presents a good matching input impedance and radiation pattern in the GSM band at 900 MHz and ISM band at 2.4 GHz. The final structure is a dual band fractal antenna with 70 x 70 mm² as a total area by using an FR4 substrate.

Keywords: Antenna, CPW, Fractal, GSM, Multiband.

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Authors: Hyojin Lim, Cuong Nguyen Khac, Ho-Youl Jung

Abstract:

In this paper, we propose moving object detection method which is helpful for driver to safely take his/her car out of parking lot. When moving objects such as motorbikes, pedestrians, the other cars and some obstacles are detected at the rear-side of host vehicle, the proposed algorithm can provide to driver warning. We assume that the host vehicle is just before departure. Gaussian Mixture Model (GMM) based background subtraction is basically applied. Pre-processing such as smoothing and post-processing as morphological filtering are added. We examine “which color space has better performance for detection of moving objects?” Three color spaces including RGB, YCbCr, and Y are applied and compared, in terms of detection rate. Through simulation, we prove that RGB space is more suitable for moving object detection based on background subtraction.

Keywords: Gaussian mixture model, background subtraction, Moving object detection, color space, morphological filtering.

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Authors: Young-Jin Baikand, Minsung Kim

Abstract:

In order to compare the performance of the carbon dioxide and HFC-125 heat pumps for medium-and high-temperature heating, both heat pump cycles were optimized using a simulation method. To fairly compare the performance of the cycles by using different working fluids, each cycle was optimized from the viewpoint of heating COP by two design parameters. The first is the gas cooler exit temperature and the other is the ratio of the overall heat conductance of the gas cooler to the combined overall heat conductance of the gas cooler and the evaporator. The inlet and outlet temperatures of secondary fluid of the gas cooler were fixed at 40/90°C and 40/150°C.The results shows that the HFC-125 heat pump has 6% higher heating COP than carbon dioxide heat pump when the heat sink exit temperature is fixed at 90ºC, while the latter outperforms the former when the heat sink exit temperature is fixed at 150ºC under the simulation conditions considered in the present study.

Keywords: Carbon dioxide, HFC-125, trans critical, heat pump.

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Authors: J. Menčík, B. Culek, Jr., L. Beran, J. Mareš

Abstract:

Large metal and concrete structures suffer by various kinds of deterioration, and accurate prediction of the remaining life is important. This paper informs about two methods for its assessment. One method, suitable for steel bridges and other constructions exposed to fatigue, monitors the loads and damage accumulation using information systems for the operation and the finite element model of the construction. In addition to the operation load, the dead weight of the construction and thermal stresses can be included into the model. The second method is suitable for concrete bridges and other structures, which suffer by carbonatation and other degradation processes, driven by diffusion. The diffusion constant, important for the prediction of future development, can be determined from the depth-profile of pH, obtained by pH measurement at various depths. Comparison with measurements on real objects illustrates the suitability of both methods.

Keywords: Bridges, carbonatation, concrete, diagnostics, fatigue, life prediction, monitoring, railway, simulation, structures.

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Authors: M. Boulakroune, M. Challal, H. Louazene, S. Fentiz

Abstract:

This paper presents two types of microstrip bandpass filter (BPF) at microwave frequencies. The first one is a tunable BPF using planar patch resonators based on a varactor diode. The filter is formed by a triple mode circular patch resonator with two pairs of slots, in which the varactor diodes are connected. Indeed, this filter is initially centered at 2.4 GHz; the center frequency of the tunable patch filter could be tuned up to 1.8 GHz simultaneously with the bandwidth, reaching high tuning ranges. Lossless simulations were compared to those considering the substrate dielectric, conductor losses and the equivalent electrical circuit model of the tuning element in order to assess their effects. Within these variations, simulation results showed insertion loss better than 2 dB and return loss better than 10 dB over the passband. The second structure is a BPF for ultra-wideband (UWB) applications based on multiple-mode resonator (MMR) and rectangular-shaped defected ground structure (DGS). This filter, which is compact size of 25.2 x 3.8 mm2, provides in the pass band an insertion loss of 0.57 dB and a return loss greater than 12 dB. The proposed filters presents good performances and the simulation results are in satisfactory agreement with the experimentation ones reported elsewhere.

Keywords: Defected ground structure, varactor diode, microstrip bandpass filter, multiple-mode resonator.

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Authors: Mohammad Hadi Bordbar, Timo Hyppänen

Abstract:

The radiative exchange method is introduced as a numerical method for the simulation of radiative heat transfer in an absorbing, emitting and isotropically scattering media. In this method, the integro-differential radiative balance equation is solved by using a new introduced concept for the exchange factor. Even though the radiative source term is calculated in a mesh structure that is coarser than the structure used in computational fluid dynamics, calculating the exchange factor between different coarse elements by using differential integration elements makes the result of the method close to that of integro-differential radiative equation. A set of equations for calculating exchange factors in two and threedimensional Cartesian coordinate system is presented, and the method is used in the simulation of radiative heat transfer in twodimensional rectangular case and a three-dimensional simple cube. The result of using this method in simulating different cases is verified by comparing them with those of using other numerical radiative models.

Keywords: Exchange factor, Numerical simulation, Thermal radiation.

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Authors: B. Nasri, M. Bensaada

Abstract:

We present a simulation and realization of a battery charge regulator (BCR) in microsatellite earth observation. The tests were performed on battery pack 12volt, capacity 24Ah and the solar array open circuit voltage of 100 volt and optimum power of about 250 watt. The battery charge is made by solar module. The principle is to adapt the output voltage of the solar module to the battery by using the technique of pulse width modulation (PWM). Among the different techniques of charge battery, we opted for the technique of the controller ON/OFF is a standard technique and simple, it-s easy to be board executed validation will be made by simulation "Proteus Isis Professional software ". The circuit and the program of this prototype are based on the PIC16F877 microcontroller, a serial interface connecting a PC is also realized, to view and save data and graphics in real time, for visualization of data and graphs we develop an interface tool “visual basic.net (VB)--.

Keywords: Battery Charge Regulator, Batteries, Buck converter, Power System, Power Conditioning, Power Distribution, Solar arrays.

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Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: Catherine Maware, Olufemi Adetunji

Abstract:

The paper is aimed at developing a model to measure the impact of Lean manufacturing deployment on organizational performance. The model will help industry practitioners to assess the impact of implementing Lean constructs on organizational performance. It will also harmonize the measurement models of Lean performance with the house of Lean that seems to have become the industry standard. The sheer number of measurement models for impact assessment of Lean implementation makes it difficult for new adopters to select an appropriate assessment model or deployment methodology. A literature review is conducted to classify the Lean performance model. Pareto analysis is used to select the Lean constructs for the development of the model. The model is further formalized through the use of Structural Equation Modeling (SEM) in defining the underlying latent structure of a Lean system. An impact assessment measurement model developed can be used to measure Lean performance and can be adopted by different industries.

Keywords: Impact measurement model, lean bundles, lean manufacturing, organizational performance.

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Authors: Y. Boutiche, N. Ramou, M. Ben Gharsallah

Abstract:

This paper is devoted to present and discuss a model that allows a local segmentation by using statistical information of a given image. It is based on Chan-Vese model, curve evolution, partial differential equations and binary level sets method. The proposed model uses the piecewise constant approximation of Chan-Vese model to compute Signed Pressure Force (SPF) function, this one attracts the curve to the true object(s)-s boundaries. The implemented model is used to extract weld defects from weld radiographic images in the aim to calculate the perimeter and surfaces of those weld defects; encouraged resultants are obtained on synthetic and real radiographic images.

Keywords: Active contour, Chan-Vese Model, local segmentation, weld radiographic images.

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Authors: Igor Astrov, Andrus Pedai, Boris Gordon

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for tactical unmanned aerial vehicle (TUAV). With the SA strategy, we proposed a two stage flight control procedure using two autonomous control subsystems to address the dynamics variation and performance requirement difference in initial and final stages of flight trajectory for an unmanned helicopter model with coaxial rotor and ducted fan configuration. This control strategy for chosen model of TUAV has been verified by simulation of hovering maneuvers using software package Simulink and demonstrated good performance for fast stabilization of engines in hovering, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Coaxial rotors, ducted fan, NARMA-L2 neurocontroller, situational awareness, tactical unmanned aerial vehicle.

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Authors: Pham Van Nha, Le Cam Binh

Abstract:

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

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Authors: Jixiang Zhang, Guocheng Wang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, Discrete dynamical system, Heterogeneous expectations, Nash equilibrium.

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