Search results for: modelling and analysis

Authors: Ahmad Izani M. Ismail, Md. Fazlul Karim, Mai Duc Thanh

Abstract:

A well balanced numerical scheme based on stationary waves for shallow water flows with arbitrary topography has been introduced by Thanh et al. [18]. The scheme was constructed so that it maintains equilibrium states and tests indicate that it is stable and fast. Applying the well-balanced scheme for the one-dimensional shallow water equations, we study the early shock waves propagation towards the Phuket coast in Southern Thailand during a hypothetical tsunami. The initial tsunami wave is generated in the deep ocean with the strength that of Indonesian tsunami of 2004.

Keywords: Tsunami study, shallow water, conservation law, well-balanced scheme, topography. Subject classification: 86 A 05, 86 A 17.

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Authors: Indunil Jayatilake, Warna Karunasena

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Fiber Reinforced Polymer (FRP) composites enjoy an array of applications ranging from aerospace, marine and military to automobile, recreational and civil industry due to their outstanding properties. A structural glass fiber reinforced polymer (GFRP) composite sandwich panel made from E-glass fiber skin and a modified phenolic core has been manufactured in Australia for civil engineering applications. One of the major mechanisms of damage in FRP composites is skin-core debonding. The presence of debonding is of great concern not only because it severely affects the strength but also it modifies the dynamic characteristics of the structure, including natural frequency and vibration modes. This paper deals with the investigation of the dynamic characteristics of a GFRP beam with single and multiple debonding by finite element based numerical simulations and analyses using the STRAND7 finite element (FE) software package. Three-dimensional computer models have been developed and numerical simulations were done to assess the dynamic behavior. The FE model developed has been validated with published experimental, analytical and numerical results for fully bonded as well as debonded beams. A comparative analysis is carried out based on a comprehensive parametric investigation. It is observed that the reduction in natural frequency is more affected by single debonding than the equally sized multiple debonding regions located symmetrically to the single debonding position. Thus it is revealed that a large single debonding area leads to more damage in terms of natural frequency reduction than isolated small debonding zones of equivalent area, appearing in the GFRP beam. Furthermore, the extents of natural frequency shifts seem mode-dependent and do not seem to have a monotonous trend of increasing with the mode numbers.

Keywords: Debonding, dynamic response, finite element modelling, FRP beams.

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Authors: Kaltima Phichai, Pornchanoke Pragrobpondee, Thaweesak Khumpart, Samorn Hirunpraditkoon

Abstract:

The paper provides biomasses characteristics by proximate analysis (volatile matter, fixed carbon and ash) and ultimate analysis (carbon, hydrogen, nitrogen and oxygen) for the prediction of the heating value equations. The heating value estimation of various biomasses can be used as an energy evaluation. Thirteen types of biomass were studied. Proximate analysis was investigated by mass loss method and infrared moisture analyzer. Ultimate analysis was analyzed by CHNO analyzer. The heating values varied from 15 to 22.4MJ kg-1. Correlations of the calculated heating value with proximate and ultimate analyses were undertaken using multiple regression analysis and summarized into three and two equations, respectively. Correlations based on proximate analysis illustrated that deviation of calculated heating values from experimental heating values was higher than the correlations based on ultimate analysis.

Keywords: Heating value equation, Proximate analysis, Ultimate analysis.

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Authors: Muhammad E. Rahman, Trevor Orr

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This paper presents the use of three-dimensional finite elements coupled with infinite elements to investigate the ground vibrations at the surface in terms of the peak particle velocity (PPV) due to construction of the first bore of the Dublin Port Tunnel. This situation is analysed using a commercially available general-purpose finite element package ABAQUS. A series of parametric studies is carried out to examine the sensitivity of the predicted vibrations to variations in the various input parameters required by finite element method, including the stiffness and the damping of ground. The results of this study show that stiffness has a more significant effect on the PPV rather than the damping of the ground.

Keywords: Finite Elements, PPV, Tunnelling, Vibration

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Authors: Laurent Pitteloud, Jörg Meier

Abstract:

Piled raft foundations represent an efficient and reliable technique for transferring high vertical and horizontal loads to the subsoil. Piled raft foundations were success­fully implemented for several high-rise buildings world­wide over the last decades. For the structural design of this foundation type the stiffnesses of both the piles and the raft have to be deter­mined for the static (e.g. dead load, live load) and the dynamic load cases (e.g. earthquake). In this context the question often arises, to which proportion wind loads are to be considered as dynamic loads. Usually a piled raft foundation has to be monitored in order to verify the design hypotheses. As an additional benefit, the analysis of this monitoring data may lead to a better under­standing of the behaviour of this foundation type for future projects in similar subsoil conditions. In case the measurement frequency is high enough, one may also draw conclusions on the effect of wind loading on the piled raft foundation. For a 41-storey office building in Basel, Switzerland, the preliminary design showed that a piled raft foundation was the best solution to satisfy both design requirements, as well as economic aspects. A high-frequency monitoring of the foundation including pile loads, vertical stresses under the raft, as well as pore water pressures was performed over 5 years. In windy situations the analysis of the measure­ments shows that the pile load increment due to wind consists of a static and a cyclic load term. As piles and raft react with different stiffnesses under static and dynamic loading, these measure­ments are useful for the correct definition of stiffnesses of future piled raft foundations. This paper outlines the design strategy and the numerical modelling of the aforementioned piled raft foundation. The measurement results are presented and analysed. Based on the findings, comments and conclusions on the definition of pile and raft stiffnesses for vertical and wind loading are proposed.

Keywords: Dynamic loading, high-frequency monitoring, piled raft foundations, wind loading.

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Authors: Jindřiška Šedová, Miloš Šeda

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This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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Authors: Ridha Ghayoula, Mbarek Traii, Ali Gharsallah

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In this paper, we intend to study the synthesis of the multibeam arrays. The synthesis implementation-s method for this type of arrays permits to approach the appropriated radiance-s diagram. The used approach is based on neural network that are capable to model the multibeam arrays, consider predetermined general criteria-s, and finally it permits to predict the appropriated diagram from the neural model. Our main contribution in this paper is the extension of a synthesis model of these multibeam arrays.

Keywords: Multibeam, modelling, neural networks, synthesis, antennas.

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Authors: Smajo Bisanovic, Mensur Hajro, Muris Dlakic

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This paper presents one comprehensive modelling approach for maintenance scheduling problem of thermal power units in competitive market. This problem is formulated as a 0/1 mixedinteger linear programming model. Model incorporates long-term bilateral contracts with defined profiles of power and price, and weekly forecasted market prices for market auction. The effectiveness of the proposed model is demonstrated through case study with detailed discussion.

Keywords: Maintenance scheduling, bilateral contracts, market prices, profit.

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Authors: YongXian, JIN

Abstract:

Introducing survivability into embedded real-time system (ERTS) can improve the survivability power of the system. This paper mainly discusses about the survivability of ERTS. The first is the survivability origin of ERTS. The second is survivability analysis. According to the definition of survivability based on survivability specification and division of the entire survivability analysis process for ERTS, a survivability analysis profile is presented. The quantitative analysis model of this profile is emphasized and illuminated in detail, the quantifying analysis of system was showed helpful to evaluate system survivability more accurate. The third is platform design of survivability analysis. In terms of the profile, the analysis process is encapsulated and assembled into one platform, on which quantification, standardization and simplification of survivability analysis are all achieved. The fourth is survivability design. According to character of ERTS, strengthened design method is selected to realize system survivability design. Through the analysis of embedded mobile video-on-demand system, intrusion tolerant technology is introduced in whole survivability design.

Keywords: ERTS (embedded real-time system), survivability, quantitative analysis, survivability specification, intrusion tolerant

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Authors: Sannikumar Patel, Brian Nolan, Markus Hofmann, Philip Owende, Kunjan Patel

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Sentiment analysis and opinion mining have become emerging topics of research in recent years but most of the work is focused on data in the English language. A comprehensive research and analysis are essential which considers multiple languages, machine translation techniques, and different classifiers. This paper presents, a comparative analysis of different approaches for multilingual sentiment analysis. These approaches are divided into two parts: one using classification of text without language translation and second using the translation of testing data to a target language, such as English, before classification. The presented research and results are useful for understanding whether machine translation should be used for multilingual sentiment analysis or building language specific sentiment classification systems is a better approach. The effects of language translation techniques, features, and accuracy of various classifiers for multilingual sentiment analysis is also discussed in this study.

Keywords: Cross-language analysis, machine learning, machine translation, sentiment analysis.

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Authors: E. Farshidi

Abstract:

This paper presents a new general technique for analysis of noise in static log-domain translinear circuits. It is demonstrated that employing this technique, leads to a general, simple and routine method of the noise analysis. The circuit has been simulated by HSPICE. The simulation results are seen to conform to the theoretical analysis and shows benefits of the proposed circuit.

Keywords: Noise analysis, log-domain, static, dynamic, translinear loop, companding.

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Authors: Rahul Bansal, Sudipta Majumdar

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This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: G. A. Khalid, M. D. Jones, R. Prabhu, A. Mason-Jones, W. Whittington, H. Bakhtiarydavijani, P. S. Theobald

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Head injury in childhood is a common cause of death or permanent disability from injury. However, despite its frequency and significance, there is little understanding of how a child’s head responds during injurious loading. Whilst Infant Post Mortem Human Subject (PMHS) experimentation is a logical approach to understand injury biomechanics, it is the authors’ opinion that a lack of subject availability is hindering potential progress. Computer modelling adds great value when considering adult populations; however, its potential remains largely untapped for infant surrogates. The complexities of child growth and development, which result in age dependent changes in anatomy, geometry and physical response characteristics, present new challenges for computational simulation. Further geometric challenges are presented by the intricate infant cranial bones, which are separated by sutures and fontanelles and demonstrate a visible fibre orientation. This study presents an FE model of a newborn infant’s head, developed from high-resolution computer tomography scans, informed by published tissue material properties. To mimic the fibre orientation of immature cranial bone, anisotropic properties were applied to the FE cranial bone model, with elastic moduli representing the bone response both parallel and perpendicular to the fibre orientation. Biofiedility of the computational model was confirmed by global validation against published PMHS data, by replicating experimental impact tests with a series of computational simulations, in terms of head kinematic responses. Numerical results confirm that the FE head model’s mechanical response is in favourable agreement with the PMHS drop test results.

Keywords: Finite element analysis, impact simulation, infant head trauma, material properties, post mortem human subjects.

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Authors: Ju Peng Poh, Jun Yu Charles Lee, Jonathan Chew Hoe Khoo

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The emergence of digital twin technology, a digital replica of physical world, has improved the real-time access to data from sensors about the performance of buildings. This digital transformation has opened up many opportunities to improve the management of the building by using the data collected to help monitor consumption patterns and energy leakages. One example is the integration of predictive models for anomaly detection. In this paper, we use the GAM (Generalised Additive Model) for the anomaly detection of Air Handling Units (AHU) power consumption pattern. There is ample research work on the use of GAM for the prediction of power consumption at the office building and nation-wide level. However, there is limited illustration of its anomaly detection capabilities, prescriptive analytics case study, and its integration with the latest development of digital twin technology. In this paper, we applied the general GAM modelling framework on the historical data of the AHU power consumption and cooling load of the building between Jan 2018 to Aug 2019 from an education campus in Singapore to train prediction models that, in turn, yield predicted values and ranges. The historical data are seamlessly extracted from the digital twin for modelling purposes. We enhanced the utility of the GAM model by using it to power a real-time anomaly detection system based on the forward predicted ranges. The magnitude of deviation from the upper and lower bounds of the uncertainty intervals is used to inform and identify anomalous data points, all based on historical data, without explicit intervention from domain experts. Notwithstanding, the domain expert fits in through an optional feedback loop through which iterative data cleansing is performed. After an anomalously high or low level of power consumption detected, a set of rule-based conditions are evaluated in real-time to help determine the next course of action for the facilities manager. The performance of GAM is then compared with other approaches to evaluate its effectiveness. Lastly, we discuss the successfully deployment of this approach for the detection of anomalous power consumption pattern and illustrated with real-world use cases.

Keywords: Anomaly detection, digital twin, Generalised Additive Model, Power Consumption Model.

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Authors: E. Kaygan, A. Gatto

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An investigation of adaptable winglets for morphing aircraft control and performance is described in this paper. The concepts investigated consist of various winglet configurations fundamentally centred on a baseline swept wing. The impetus for the work was to identify and optimize winglets to enhance controllability and the aerodynamic efficiency of a small unmanned aerial vehicle. All computations were performed with Athena Vortex Lattice modelling with varying degrees of twist, swept, and dihedral angle considered. The results from this work indicate that if adaptable winglets were employed on small scale UAV’s improvements in both aircraft control and performance could be achieved.

Keywords: Aircraft, rolling, wing, winglet.

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Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

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Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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Authors: Weerachi Sarakorn, I-Ming Tang

Abstract:

A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.

Keywords: SARS, mathematical modelling, differential evolution algorithm.

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Authors: W. Swiderski

Abstract:

In the paper introduced the diagnostic technique making possible the research of internal structures in composite materials reinforced fibres using in different applications. The main reason of damages in structures of these materials is the changing distribution of load in constructions in the lifetime. Appearing defect is largely complicated because of the appearance of disturbing of continuity of reinforced fibres, binder cracks and loss of fibres adhesiveness from binders. Defect in composite materials is usually more complicated than in metals. At present, infrared thermography is the most effective method in non-destructive testing composite. One of IR thermography methods used in non-destructive evaluation is vibrothermography. The vibrothermography is not a new non-destructive method, but the new solution in this test is use ultrasonic waves to thermal stimulation of materials. In this paper, both modelling and experimental results which illustrate the advantages and limitations of ultrasonic IR thermography in inspecting composite materials will be presented. The ThermoSon computer program for computing 3D dynamic temperature distribuions in anisotropic layered solids with subsurface defects subject to ulrasonic stimulation was used to optimise heating parameters in the detection of subsurface defects in composite materials. The program allows for the analysis of transient heat conduction and ultrasonic wave propagation phenomena in solids. The experiments at MIAT were fulfilled by means of FLIR SC 7600 IR camera. Ultrasonic stimulation was performed with the frequency from 15 kHz to 30 kHz with maximum power up to 2 kW.

Keywords: Composite material, ultrasonic, infrared thermography, non-destructive testing.

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Authors: Halim Djerroud, Arab Ali Cherif

Abstract:

We assume that conscious functions are implemented automatically. In other words that consciousness as well as the non-consciousness aspect of human thought, planning and perception, are produced by biologically adaptive algorithms. We propose that the mechanisms of consciousness can be produced using similar adaptive algorithms to those executed by the mechanism. In this paper, we present a computational model of consciousness, the ”Global Abstraction Workspace” which is an internal environmental modelling perceived as a multi-agent system. This system is able to evolve and generate new data and processes as well as actions in the environment.

Keywords: Artificial consciousness, cognitive architecture, global abstraction workspace, mutli-agents system.

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Authors: Anton Golubkov, Gleb Ermachkov, Aleksandr Smerdin, Oleg Sidorov, Victor Philippov

Abstract:

Current collection quality is one of the limiting factors when increasing trains movement speed in the rail sector. With the movement speed growth, the impact forces on the current collector from the rolling stock and the aerodynamic influence increase, which leads to the spread in the contact pressure values, separation of the current collector head from the contact wire, contact arcing and excessive wear of the contact elements. The upcoming trend in resolving this issue is the use of the automatic control systems providing stabilization of the contact pressure value. The present paper considers the features of the contemporary automatic control systems of the current collector’s pressure; their major disadvantages have been stated. A scheme of current collector pressure automatic control has been proposed, distinguished by a proactive influence on undesirable effects. A mathematical model of contact strips wearing has been presented, obtained in accordance with the provisions of the central composition rotatable design program. The analysis of the obtained dependencies has been carried out. The procedures for determining the optimal current collector pressure on the contact wire and the pressure control principle in the pneumatic drive have been described.

Keywords: High-speed running, current collector, contact strip, mathematical model, contact pressure, program control, wear, life cycle.

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Authors: Jagannath Aryal, Don Kulasiri, Garth A. Carnaby

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This paper provides an overview of auction theory literature. We present a general review on literature of various auctions and focus ourselves specifically on an English auction. We are interested in modelling bidder-s behavior in an English auction environment. And hence, we present an overview of the New Zealand wool auction followed by a model that would describe a bidder-s decision making behavior from the New Zealand wool auction. The mathematical assumptions in an English auction environment are demonstrated from the perspective of the New Zealand wool auction.

Keywords: Bidder, English auction, New Zealand, Wool

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Authors: Mohd Aftar Abu Bakar, Noratiqah Mohd Ariff, Abdul Aziz Jemain

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Storm Event Analysis (SEA) provides a method to define rainfalls events as storms where each storm has its own amount and duration. By modelling daily probability of different types of storms, the onset, offset and cycle of rainfall seasons can be determined and investigated. Furthermore, researchers from the field of meteorology will be able to study the dynamical characteristics of rainfalls and make predictions for future reference. In this study, four categories of storms; short, intermediate, long and very long storms; are introduced based on the length of storm duration. Daily probability models of storms are built for these four categories of storms in Peninsular Malaysia. The models are constructed by using Bernoulli distribution and by applying linear regression on the first Fourier harmonic equation. From the models obtained, it is found that daily probability of storms at the Eastern part of Peninsular Malaysia shows a unimodal pattern with high probability of rain beginning at the end of the year and lasting until early the next year. This is very likely due to the Northeast monsoon season which occurs from November to March every year. Meanwhile, short and intermediate storms at other regions of Peninsular Malaysia experience a bimodal cycle due to the two inter-monsoon seasons. Overall, these models indicate that Peninsular Malaysia can be divided into four distinct regions based on the daily pattern for the probability of various storm events.

Keywords: Daily probability model, monsoon seasons, regions, storm events.

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Authors: Gilbert Ndjatou

Abstract:

We propose a formal framework for the specification of the behavior of a system of agents, as well as those of the constituting agents. This framework allows us to model each agent-s effectoric capability including its interactions with the other agents. We also provide an algorithm based on Milner-s "observation equivalence" to derive an agent-s perception of its task domain situations from its effectoric capability, and use "system computations" to model the coordinated efforts of the agents in the system . Formal definitions of the concept of "behavior equivalence" of two agents and that of system computations equivalence for an agent are also provided.

Keywords: Multiagent system, object system, observation equivalence, reactive systems.

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Authors: E. H. N. Gashti, M. Zarrini, M. Irannezhad, J. R. Langroudi

Abstract:

Using ETABS software, this study analyzed 23 buildings to evaluate effects of mistakes during construction phase on buildings structural behavior. For modelling, two different loadings were assumed: 1) design loading and 2) loading due to the effects of mistakes in construction phase. Research results determined that considering traditional construction methods for buildings resulted in a significant increase in dead loads and consequently intensified the displacements and base-shears of buildings under seismic loads.

Keywords: Reinforced-concrete buildings, Construction mistakes, Base-shear, displacements, Failure.

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Authors: Carlo Bianchini, Lorenzo Catena

Abstract:

The appearance of 3D scanners and then, more recently, of image-based systems that generate point clouds directly from common digital images have deeply affected the survey process in terms of both capturing and 2D/3D modelling. In this context, low cost and mobile systems are increasingly playing a key role and actually paving the way to the democratization of what in the past was the realm of few specialized technicians and expensive equipment. The application of Google Tango on the ancient church of Santa Maria delle Vigne in Pratica di Mare – Rome presented in this paper is one of these examples.

Keywords: Architectural survey, augmented/mixed/virtual reality, Google Tango project, image-based 3D capturing.

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Authors: Anthony Spiteri Staines

Abstract:

This paper examines the modeling and analysis of a cruise control system using a Petri net based approach, task graphs, invariant analysis and behavioral properties. It shows how the structures used can be verified and optimized.

Keywords: Software Engineering, Real Time Analysis andDesign, Petri Nets, Task Graphs, Parallelism.

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Authors: Ibrahim A. Aref, Tarek A. El-Mihoub

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This paper shows how we can integrate communication modeling into the design modeling at early stages of the design flow. We consider effect of incorporating noise such as impulsive noise on system stability. We show that with change of the system model and investigate the system performance under the different communication effects. We modeled a unmanned aerial vehicle (UAV) as a demonstration using SystemC methodology. Moreover the system is modeled by joining the capabilities of UML and SystemC to operate at system level.

Keywords: Modelling, SoC, SystemC, UAV, Simulation, SoC.

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Authors: A. Naamane, M. Hasnaoui

Abstract:

Numerical modeling of fluid flows, whether compressible or incompressible, laminar or turbulent presents a considerable contribution in the scientific and industrial fields. However, the development of an approximate model of a supersonic flow requires the introduction of specific and more precise techniques and methods. For this purpose, the object of this paper is modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtained a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness that characterizes a perturbation parameter. This result has been dealt with by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The comparison of the different Mach number downstream results of our model with those of the existing theoretical data (relative margin between 0.07% and 4%) and with experimental results (concordance for a deflection angle between 1° and 11°) support the validation of our model with accuracy.

Keywords: Asymptotic modelling, dihedral airfoil, supersonic flow, supersonic wind tunnel.

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Authors: Luciana Abednego, Cecilia Nugraheni

Abstract:

There are many approaches proposed for solving Sudoku puzzles. One of them is by modelling the puzzles as block world problems. There have been three model for Sudoku solvers based on this approach. Each model expresses Sudoku solver as a parameterized multi agent systems. In this work, we propose a new model which is an improvement over the existing models. This paper presents the development of a Sudoku solver that implements all the proposed models. Some experiments have been conducted to determine the performance of each model.

Keywords: Sudoku puzzle, Sudoku solver, block world problem, parameterized multi agent systems.

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Authors: E. Menga, S. Hernandez

Abstract:

Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: Frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber.

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