Search results for: Piecewise linear inputs

Authors: Hyoup-Sang Yoon

Abstract:

Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.

Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting

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Authors: Eduardo Álvarez, Gerardo Quiroga, Jorge Orozco, Gabriel Chavira

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AmI proposes a new way of thinking about computers, which follows the ideas of the Ubiquitous Computing vision of Mark Weiser. In these, there is what is known as a Disappearing Computer Initiative, with users immersed in intelligent environments. Hence, technologies need to be adapted so that they are capable of replacing the traditional inputs to the system by embedding these in every-day artifacts. In this work, we present an approach, which uses Radiofrequency Identification (RFID) and Near Field Communication (NFC) technologies. In the latter, a new form of interaction appears by contact. We compare both technologies by analyzing their requirements and advantages. In addition, we propose using a combination of RFID and NFC.

Keywords: Touching interaction, ambient intelligence, NFC, RFID.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops for data links operating at 10 Gb/s or faster are low phase noise devices designed to operate with a low jitter reference clock. Characterization of their jitter transfer function is difficult because the intrinsic noise of the device is comparable to the random noise level in the reference clock signal. A linear model is proposed to account for the intrinsic noise of a PLL. The intrinsic noise data of a PLL for 10 Gb/s links is presented. The jitter transfer function of a PLL in a test chip for 12.8 Gb/s data links was determined in experiments using the 400 MHz reference clock as the source of simultaneous excitations over a wide range of frequency. The result shows that the PLL jitter transfer function can be approximated by a second order linear model.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Isti Surjandari, Riara Novita

Abstract:

Maintenance is one of the most important activities in the shipyard industry. However, sometimes it is not supported by adequate services from the shipyard, where inaccuracy in estimating the duration of the ship maintenance is still common. This makes estimation of ship maintenance duration is crucial. This study uses Data Mining approach, i.e., CART (Classification and Regression Tree) to estimate the duration of ship maintenance that is limited to dock works or which is known as dry docking. By using the volume of dock works as an input to estimate the maintenance duration, 4 classes of dry docking duration were obtained with different linear model and job criteria for each class. These linear models can then be used to estimate the duration of dry docking based on job criteria.

Keywords: Classification and regression tree (CART), data mining, dry docking, maintenance duration.

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Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman

Abstract:

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

Abstract:

Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: Covariation reasoning, exponential function, modeling, representations.

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Authors: Yelena Chaiko

Abstract:

This paper presents a developed method for controlling multi-renewable energy generators. The control system depends basically on three sensors (wind anemometer, solar sensor, and voltage sensor). These sensors represent PLC-s analogue inputs. Controlling the output voltage supply can be achieved by an enhanced method of interlocking between the renewable energy generators, depending on those sensors and output contactors.

Keywords: Renewable, energy, control, model, generator.

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Authors: M. Zareiee, A. Dideban

Abstract:

This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Sallem F., Dahhou B., Kamoun A.

Abstract:

In this work, the main problem considered is the  detection and the isolation of the actuator fault. A new formulation of  the linear system is generated to obtain the conditions of the actuator  fault diagnosis. The proposed method is based on the representation  of the actuator as a subsystem connected with the process system in  cascade manner. The designed formulation is generated to obtain the  conditions of the actuator fault detection and isolation. Detectability  conditions are expressed in terms of the invertibility notions. An  example and a comparative analysis with the classic formulation  illustrate the performances of such approach for simple actuator fault  diagnosis by using the linear model of nuclear reactor.

 

Keywords: Actuator fault, Fault detection, left invertibility, nuclear reactor, observability, parameter intervals, system inversion.

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Authors: Long Jye Sheu

Abstract:

This paper presents a linear stability analysis of natural convection in a horizontal layer of a viscoelastic nanofluid. The Oldroyd B model was utilized to describe the rheological behavior of a viscoelastic nanofluid. The model used for the nanofluid incorporated the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was derived analytically. The effects of the Deborah number, retardation parameters, concentration Rayleigh number, Prandtl number, and Lewis number on the stability of the system were investigated. Results indicated that there was competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity which caused oscillatory rather than stationary convection to occur. Oscillatory instability is possible with both bottom- and top-heavy nanoparticle distributions. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

Keywords: instability, viscoelastic, nanofluids, oscillatory, Brownian, thermophoresis

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

Abstract:

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Alexander Kaplunovsky, Vladimir Khailenko, Alexander Bolshoy, Shara Atambayeva, AnatoliyIvashchenko

Abstract:

Eukaryotic protein-coding genes are interrupted by spliceosomal introns, which are removed from the RNA transcripts before translation into a protein. The exon-intron structures of different eukaryotic species are quite different from each other, and the evolution of such structures raises many questions. We try to address some of these questions using statistical analysis of whole genomes. We go through all the protein-coding genes in a genome and study correlations between the net length of all the exons in a gene, the number of the exons, and the average length of an exon. We also take average values of these features for each chromosome and study correlations between those averages on the chromosomal level. Our data show universal features of exon-intron structures common to animals, plants, and protists (specifically, Arabidopsis thaliana, Caenorhabditis elegans, Drosophila melanogaster, Cryptococcus neoformans, Homo sapiens, Mus musculus, Oryza sativa, and Plasmodium falciparum). We have verified linear correlation between the number of exons in a gene and the length of a protein coded by the gene, while the protein length increases in proportion to the number of exons. On the other hand, the average length of an exon always decreases with the number of exons. Finally, chromosome clustering based on average chromosome properties and parameters of linear regression between the number of exons in a gene and the net length of those exons demonstrates that these average chromosome properties are genome-specific features.

Keywords: Comparative genomics, exon-intron structure, eukaryotic clustering, linear regression.

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Authors: Volkan Isbuga, Joman M. Mahmood, Ali Firat Cabalar

Abstract:

This study presents the site response analysis of mica-sand mixtures available in certain parts of the world including Izmir, a highly populated city and located in a seismically active region in western part of Turkey. We performed site response analyses by employing SHAKE, an equivalent linear approach, for the micaceous soil deposits consisting of layers with different amount of mica contents and thicknesses. Dynamic behavior of micaceous sands such as shear modulus reduction and damping ratio curves are input for the ground response analyses. Micaceous sands exhibit a unique dynamic response under a scenario earthquake with a magnitude of Mw=6. Results showed that higher amount of mica caused higher spectral accelerations.

Keywords: Micaceous sands, site response, equivalent linear approach, SHAKE.

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Authors: Baeza S. Roberto

Abstract:

The knitted fabric suffers a deformation in its dimensions due to stretching and tension factors, transverse and longitudinal respectively, during the process in rectilinear knitting machines so it performs a dry relaxation shrinkage procedure and thermal action of prefixed to obtain stable conditions in the knitting. This paper presents a dry relaxation shrinkage prediction of Bordeaux fiber using a feed forward neural network and linear regression models. Six operational alternatives of shrinkage were predicted. A comparison of the results was performed finding neural network models with higher levels of explanation of the variability and prediction. The presence of different reposes is included. The models were obtained through a neural toolbox of Matlab and Minitab software with real data in a knitting company of Southern Guanajuato. The results allow predicting dry relaxation shrinkage of each alternative operation.

Keywords: Neural network, dry relaxation, knitting, linear regression.

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Authors: Jamel Khedri, Mohamed Chaabane, Mansour Souissi, Driss Mehdi

Abstract:

This paper deals with the synthesis of fuzzy controller applied to a permanent magnet synchronous machine (PMSM) with a guaranteed H∞ performance. To design this fuzzy controller, nonlinear model of the PMSM is approximated by Takagi-Sugeno fuzzy model (T-S fuzzy model), then the so-called parallel distributed compensation (PDC) is employed. Next, we derive the property of the H∞ norm. The latter is cast in terms of linear matrix inequalities (LMI-s) while minimizing the H∞ norm of the transfer function between the disturbance and the error ( ) ev T . The experimental and simulations results were conducted on a permanent magnet synchronous machine to illustrate the effects of the fuzzy modelling and the controller design via the PDC.

Keywords: Feedback controller, Takagi-Sugeno fuzzy model, Linear Matrix Inequality (LMI), PMSM, H∞ performance.

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Authors: Badr M. Alshammari, Mohamed A. El-Kady

Abstract:

The paper presents new results of a recent industry supported research and development study in which an efficient framework for evaluating practical and meaningful power system reliability and quality indices was applied. The system-wide integrated performance indices are capable of addressing and revealing areas of deficiencies and bottlenecks as well as redundancies in the composite generation-transmission-demand structure of large-scale power grids. The technique utilizes a linear programming formulation, which simulates practical operating actions and offers a general and comprehensive framework to assess the harmony and compatibility of generation, transmission and demand in a power system. Practical applications to a reduced system model as well as a portion of the Saudi power grid are also presented in the paper for demonstration purposes.

Keywords: Power systems, Linear programming, Quality assessment, Reliability.

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Authors: Pengdi Diao, Zhuo Wang, Zundong Zhang, Hua Cheng

Abstract:

In the urban traffic network, the intersections are the “bottleneck point" of road network capacity. And the arterials are the main body in road network and the key factor which guarantees the normal operation of the city-s social and economic activities. The rapid increase in vehicles leads to seriously traffic jam and cause the increment of vehicles- delay. Most cities of our country are traditional single control system, which cannot meet the need for the city traffic any longer. In this paper, Synchro6.0 as a platform to minimize the intersection delay, optimizesingle signal cycle and split for Zhonghua Street in Handan City. Meanwhile, linear control system uses to optimize the phase for the t arterial road in this system. Comparing before and after use the control, capacities and service levels of this road and the adjacent road have improved significantly.

Keywords: linear control system; delay mode; signal optimization; synchro6.0 simulation

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Authors: Hichem Omrani, Philippe Gerber, Patrick Bousch

Abstract:

The problem of Small Area Estimation (SAE) is complex because of various information sources and insufficient data. In this paper, an approach for SAE is presented for decision-making at national, regional and local level. We propose an Empirical Best Linear Unbiased Predictor (EBLUP) as an estimator in order to combine several information sources to evaluate various indicators. First, we present the urban audit project and its environmental, social and economic indicators. Secondly, we propose an approach for decision making in order to estimate indicators. An application is used to validate the theoretical proposal. Finally, a decision support system is presented based on open-source environment.

Keywords: Small area estimation, statistical method, sampling, empirical best linear unbiased predictor (EBLUP), decision-making.

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Authors: Seksan Chunothaisawat, Pongchanun Luangpaiboon

Abstract:

There are two common types of operational research techniques, optimisation and metaheuristic methods. The latter may be defined as a sequential process that intelligently performs the exploration and exploitation adopted by natural intelligence and strong inspiration to form several iterative searches. An aim is to effectively determine near optimal solutions in a solution space. In this work, a type of metaheuristics called Ant Colonies Optimisation, ACO, inspired by a foraging behaviour of ants was adapted to find optimal solutions of eight non-linear continuous mathematical models. Under a consideration of a solution space in a specified region on each model, sub-solutions may contain global or multiple local optimum. Moreover, the algorithm has several common parameters; number of ants, moves, and iterations, which act as the algorithm-s driver. A series of computational experiments for initialising parameters were conducted through methods of Rigid Simplex, RS, and Modified Simplex, MSM. Experimental results were analysed in terms of the best so far solutions, mean and standard deviation. Finally, they stated a recommendation of proper level settings of ACO parameters for all eight functions. These parameter settings can be applied as a guideline for future uses of ACO. This is to promote an ease of use of ACO in real industrial processes. It was found that the results obtained from MSM were pretty similar to those gained from RS. However, if these results with noise standard deviations of 1 and 3 are compared, MSM will reach optimal solutions more efficiently than RS, in terms of speed of convergence.

Keywords: Ant colony optimisation, metaheuristics, modified simplex, non-linear, rigid simplex.

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Authors: Sagaren Pillay

Abstract:

This study empirically examines the long run equilibrium relationship between South Africa’s exports and imports using quarterly data from 1985 to 2012. The theoretical framework used for the study is based on Johansen’s Maximum Likelihood cointegration technique which tests for both the existence and number of cointegration vectors that exists. The study finds that both the series are integrated of order one and are cointegrated. A statistically significant cointegrating relationship is found to exist between exports and imports. The study models this unique linear and lagged relationship using a Vector Error Correction Model (VECM). The findings of the study confirm the existence of a long run equilibrium relationship between exports and imports.

Keywords: Cointegration lagged, linear, maximum likelihood, vector error correction model.

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Authors: S. Esakkirajan, T. Veerakumar, V. Senthil Murugan, P. Navaneethan

Abstract:

The existing image coding standards generally degrades at low bit-rates because of the underlying block based Discrete Cosine Transform scheme. Over the past decade, the success of wavelets in solving many different problems has contributed to its unprecedented popularity. Due to implementation constraints scalar wavelets do not posses all the properties such as orthogonality, short support, linear phase symmetry, and a high order of approximation through vanishing moments simultaneously, which are very much essential for signal processing. New class of wavelets called 'Multiwavelets' which posses more than one scaling function overcomes this problem. This paper presents a new image coding scheme based on non linear approximation of multiwavelet coefficients along with multistage vector quantization. The performance of the proposed scheme is compared with the results obtained from scalar wavelets.

Keywords: Image compression, Multiwavelets, Multi-stagevector quantization.

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Authors: AL.AL, M. B. I. Reaz, S. M. A. Motakabber, Mohd Alauddin Mohd Ali

Abstract:

Nowadays it is a trend for electronic circuit designers to integrate all system components on a single-chip. This paper proposed the design of a single-chip proportional to absolute temperature (PTAT) sensor including a voltage reference circuit using CEDEC 0.18m CMOS Technology. It is a challenge to design asingle-chip wide range linear response temperature sensor for many applications. The channel widths between the compensation transistor and the reference transistor are critical to design the PTAT temperature sensor circuit. The designed temperature sensor shows excellent linearity between -100°C to 200° and the sensitivity is about 0.05mV/°C. The chip is designed to operate with a single voltage source of 1.6V.

Keywords: PTAT, single-chip circuit, linear temperature sensor, CMOS technology.

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Authors: Ali Nouri Emamzadeh

Abstract:

The experiment was performed to study the relationship between excreta viscosity and Nitrogen-corrected true metabolisable energy quantities of soybean meals using conventional addition method (CAM) in adult cockerels for 7 d: a 3-d preexperiment and a 4-d experiment period. Results indicated that differences between the excreta viscosity values were (P<0.01) significant for SBMs. The excreta viscosity values were less (P<0.01) for SBMs 6, 2, 8, 1 and 3 than other SBMs. The mean TMEn (kcal/kg) values were significant (P<0.01) between SBMs. The most TMEn values were (P<0.01) for SBMs 6, 2, 8 and 1, also the lowest TMEn values were (P<0.01) for SBMs 3, 7, 4, 9 and 5. There was a reverse linear relationship between the values of excreta viscosity and TMEn in SBMs. In conclusion, there was a reverse linear relationship between the values of excreta viscosity and TMEn in SBMs probably due to their various soluble NSPs.

Keywords: soybean meals (SBMs), Nitrogen-corrected true metabolisable energy (TMEn), viscosity

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Authors: Dana M. Ragab, Jasim A Ghaeb

Abstract:

The Voltage Unbalance Factor (VUF) index is recommended to evaluate system performance under unbalanced operation. However, its calculation requires complex algebra which limits its use in the field. Furthermore, one system cycle is required at least to detect unbalance using the VUF. Ideally unbalance mitigation must be performed within 10 ms for 50 Hz systems. In this work, a linear relation for VUF evaluation in three-phase electrical power system using space vector (SV) is derived. It is proposed to determine the voltage unbalance quickly and accurately and to overcome the constraints associated with the traditional methods of VUF evaluation. Aqaba-Qatrana-South Amman (AQSA) power system is considered to study the system performance under unbalanced conditions. The results show that both the complexity of calculations and the time required to evaluate VUF are reduced significantly.

Keywords: Power quality, space vector, unbalance evaluation.

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Authors: Antonio Vitale, Nicola Genito, Giovanni Cuciniello, Ferdinando Montemari

Abstract:

The introduction of tilt-rotor aircraft into the existing civilian air transportation system will provide beneficial effects due to tilt-rotor capability to combine the characteristics of a helicopter and a fixed-wing aircraft into one vehicle. The disposability of reliable tilt-rotor simulation models supports the development of such vehicle. Indeed, simulation models are required to design automatic control systems that increase safety, reduce pilot's workload and stress, and ensure the optimal aircraft configuration with respect to flight envelope limits, especially during the most critical flight phases such as conversion from helicopter to aircraft mode and vice versa. This article presents a process to build a simplified tilt-rotor simulation model, derived from the analysis of flight data. The model aims to reproduce the complex dynamics of tilt-rotor during the in-flight conversion phase. It uses a set of scheduled linear transfer functions to relate the autopilot reference inputs to the most relevant rigid body state variables. The model also computes information about the rotor flapping dynamics, which are useful to evaluate the aircraft control margin in terms of rotor collective and cyclic commands. The rotor flapping model is derived through a mixed theoretical-empirical approach, which includes physical analytical equations (applicable to helicopter configuration) and parametric corrective functions. The latter are introduced to best fit the actual rotor behavior and balance the differences existing between helicopter and tilt-rotor during flight. Time-domain system identification from flight data is exploited to optimize the model structure and to estimate the model parameters. The presented model-building process was applied to simulated flight data of the ERICA Tilt-Rotor, generated by using a high fidelity simulation model implemented in FlightLab environment. The validation of the obtained model was very satisfying, confirming the validity of the proposed approach.

Keywords: Flapping Dynamics, Flight Dynamics, System Identification, Tilt-Rotor Modeling and Simulation.

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Authors: Ε. Giovanis

Abstract:

In this paper we present a Adaptive Neuro-Fuzzy System (ANFIS) with inputs the lagged dependent variable for the prediction of Gross domestic Product growth rate in six countries. We compare the results with those of Autoregressive (AR) model. We conclude that the forecasting performance of neuro-fuzzy-system in the out-of-sample period is much more superior and can be a very useful alternative tool used by the national statistical services and the banking and finance industry.

Keywords: Autoregressive model, Forecasting, Gross DomesticProduct, Neuro-Fuzzy

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Authors: Mohammad Najafi Nobar, Bahareh Pourmehr, Mehdi Hajimirarab

Abstract:

One of the main processes of supply chain management is supplier selection process which its accurate implementation can dramatically increase company competitiveness. In presented article model developed based on the features of second tiers suppliers and four scenarios are predicted in order to help the decision maker (DM) in making up his/her mind. In addition two tiers of suppliers have been considered as a chain of suppliers. Then the proposed approach is solved by a method combined of concepts of fuzzy set theory (FST) and linear programming (LP) which has been nourished by real data extracted from an engineering design and supplying parts company. At the end results reveal the high importance of considering second tier suppliers features as criteria for selecting the best supplier.

Keywords: Supply Chain Management (SCM), SupplierSelection, Second Tier Supplier, Scenario Planning, Green Factor, Linear Programming, Fuzzy Set Theory

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