Search results for: Reduced order model

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

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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: M. A. Omoloye, M. I. Yusuff, O. K. S. Emiola

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The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.

Keywords: Differential Transform Method, Existence and uniqueness, Lassa fever, Runge-Kutta Method.

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Authors: Li Yu, Chenlu Jiao, Hongrun Xin, Yan Wang, Kaiyang Wang

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In order to study the impact of various factors on the housing price, we propose to build different prediction models based on deep learning to determine the existing data of the real estate in order to more accurately predict the housing price or its changing trend in the future. Considering that the factors which affect the housing price vary widely, the proposed prediction models include two categories. The first one is based on multiple characteristic factors of the real estate. We built Convolution Neural Network (CNN) prediction model and Long Short-Term Memory (LSTM) neural network prediction model based on deep learning, and logical regression model was implemented to make a comparison between these three models. Another prediction model is time series model. Based on deep learning, we proposed an LSTM-1 model purely regard to time series, then implementing and comparing the LSTM model and the Auto-Regressive and Moving Average (ARMA) model. In this paper, comprehensive study of the second-hand housing price in Beijing has been conducted from three aspects: crawling and analyzing, housing price predicting, and the result comparing. Ultimately the best model program was produced, which is of great significance to evaluation and prediction of the housing price in the real estate industry.

Keywords: Deep learning, convolutional neural network, LSTM, housing prediction.

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Authors: Ashwani K. Rana, Narottam Chand, Vinod Kapoor

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This paper presents a new compact analytical model of the gate leakage current in high-k based nano scale MOSFET by assuming a two-step inelastic trap-assisted tunneling (ITAT) process as the conduction mechanism. This model is based on an inelastic trap-assisted tunneling (ITAT) mechanism combined with a semiempirical gate leakage current formulation in the BSIM 4 model. The gate tunneling currents have been calculated as a function of gate voltage for different gate dielectrics structures such as HfO2, Al2O3 and Si3N4 with EOT (equivalent oxide thickness) of 1.0 nm. The proposed model is compared and contrasted with santaurus simulation results to verify the accuracy of the model and excellent agreement is found between the analytical and simulated data. It is observed that proposed analytical model is suitable for different highk gate dielectrics simply by adjusting two fitting parameters. It was also shown that gate leakages reduced with the introduction of high-k gate dielectric in place of SiO2.

Keywords: Analytical model, High-k gate dielectrics, inelastic trap assisted tunneling, metal–oxide–semiconductor (MOS) devices.

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Authors: M. Abouelatta, A. Shaker, M. El-Banna, G. T. Sayah, C. Gontrand, A. Zekry

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In this paper, a methodology for physically modeling the intrinsic MOS part and the drift region of the n-channel Laterally Double-diffused MOSFET (LDMOS) is presented. The basic physical effects like velocity saturation, mobility reduction, and nonuniform impurity concentration in the channel are taken into consideration. The analytical model is implemented using MATLAB. A comparison of the simulations from technology computer aided design (TCAD) and that from the proposed analytical model, at room temperature, shows a satisfactory accuracy which is less than 5% for the whole voltage domain.

Keywords: LDMOS, MATLAB, RESURF, modeling, TCAD.

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Authors: Makram Ben Jeddou

Abstract:

ABC classification is widely used by managers for inventory control. The classical ABC classification is based on Pareto principle and according to the criterion of the annual use value only. Single criterion classification is often insufficient for a closely inventory control. Multi-criteria inventory classification models have been proposed by researchers in order to consider other important criteria. From these models, we will consider a specific model in order to make a sensitive analysis on the composite score calculated for each item. In fact, this score, based on a normalized average between a good and a bad optimized index, can affect the ABC-item classification. We will focus on items differently assigned to classes and then propose a classification compromise.

Keywords: ABC classification, Multi criteria inventory classification models, ZF-model.

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Authors: Eric Jiang

Abstract:

As a popular rank-reduced vector space approach, Latent Semantic Indexing (LSI) has been used in information retrieval and other applications. In this paper, an LSI-based content vector model for text classification is presented, which constructs multiple augmented category LSI spaces and classifies text by their content. The model integrates the class discriminative information from the training data and is equipped with several pertinent feature selection and text classification algorithms. The proposed classifier has been applied to email classification and its experiments on a benchmark spam testing corpus (PU1) have shown that the approach represents a competitive alternative to other email classifiers based on the well-known SVM and naïve Bayes algorithms.

Keywords: Feature Selection, Latent Semantic Indexing, Text Classification, Vector Space Model.

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Fractional calculus, fractional–order proportional integral controller, cascade control system, internal model control approach.

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Authors: Worachat Wannawong, Usa W. Humphries, Prungchan Wongwises, Suphat Vongvisessomjai

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The three steps of the standard one-way nested grid for a regional scale of the third generation WAve Model Cycle 4 (WAMC4) is scrutinized. The model application is enabled to solve the energy balance equation on a coarse resolution grid in order to produce boundary conditions for a smaller area by the nested grid technique. In the present study, the model takes a full advantage of the fine resolution of wind fields in space and time produced by the available U.S. Navy Global Atmospheric Prediction System (NOGAPS) model with 1 degree resolution. The nested grid application of the model is developed in order to gradually increase the resolution from the open ocean towards the South China Sea (SCS) and the Gulf of Thailand (GoT) respectively. The model results were compared with buoy observations at Ko Chang, Rayong and Huahin locations which were obtained from the Seawatch project. In addition, the results were also compared with Satun based weather station which was provided from Department of Meteorology, Thailand. The data collected from this station presented the significant wave height (Hs) reached 12.85 m. The results indicated that the tendency of the Hs from the model in the spherical coordinate propagation with deep water condition in the fine grid domain agreed well with the Hs from the observations.

Keywords: energy balance equation, Gulf of Thailand, nested gridapplication, South China Sea, wave model.

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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Authors: L. Torchane

Abstract:

The study is devoted to define the optimal conditions for the nitriding of pure iron at atmospheric pressure by using NH3- Ar-C3H8 gas mixtures. After studying the mechanisms of phase formation and mass transfer at the gas-solid interface, a mathematical model is developed in order to predict the nitrogen transfer rate in the solid, the ε-carbonitride layer growth rate and the nitrogen and carbon concentration profiles. In order to validate the model and to show its possibilities, it is compared with thermogravimetric experiments, analyses and metallurgical observations (X-ray diffraction, optical microscopy and electron microprobe analysis). Results obtained allow us to demonstrate the sound correlation between the experimental results and the theoretical predictions.

Keywords: Gaseous Nitrocarburizing, Kinetic Model, Diffusion, Layer Growth Kinetic.

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Authors: Aung Myo Thu, Sang Eon Jeon, Yung Hwan Byun, Soo Hyung Park

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The unsteady flow field around oscillating OA-209 airfoil at a Reynolds number of 3.5×105 were investigated. Three different reduced frequencies were tested in order to see how it affects the hysteresis loop of an airfoil. At a reduced frequency of 0.05 the deep dynamic stall phenomenon was observed. Lift overshooting was observed as a result of dynamic stall vortex (DSV) shedding. Further investigation was carried out to find out the cause of DSV formation and shedding over airfoil. Particle image velocimetry (PIV) and CFD tools were used and it was found out that dynamic stall separation (DSS), which is separated from leading edge separation (LES) and trailing edge separation (TES), triggered the dynamic stall vortex (DSV).

Keywords: Airfoil Flow, CFD, PIV, Dynamic Stall, Flow Separation.

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Authors: J.C. Umavathi

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The linear stability of nanofluid convection in a horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. The model used for the nanofluid incorporates the effects of Brownian motion and thermopherosis, while the Darcy model is used for the porous medium. The analysis revels that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles. The contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be found reduced or decreased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution, phase angle and frequency of modulation.

Keywords: Brownian motion and thermophoresis, Porous medium, Nanofluid, Natural convection, Thermal modulation.

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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: Huan Xiong, Ming Chen

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In order to research Internet quantificationally and better model the performance of network, this paper proposes a novel AS level network performance model (MNPM), it takes autonomous system (AS) as basic modeling unit, measures E2E performance between any two outdegrees of an AS and organizes measurement results into matrix form which called performance matrix (PM). Inter-AS performance calculation is defined according to performance information stored in PM. Simulation has been implemented to verify the correctness of MNPM and a practical application of MNPM (network congestion detection) is given.

Keywords: AS, network performance, model, metric, congestion.

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Authors: Joonas Pääkkönen

Abstract:

In sports, individuals and teams are typically interested in final rankings. Final results, such as times or distances, dictate these rankings, also known as places. Places can be further associated with ordered random variables, commonly referred to as order statistics. In this work, we introduce a simple, yet accurate order statistical ordinal regression function that predicts relay race places with changeover-times. We call this function the Fenton-Wilkinson Order Statistics model. This model is built on the following educated assumption: individual leg-times follow log-normal distributions. Moreover, our key idea is to utilize Fenton-Wilkinson approximations of changeover-times alongside an estimator for the total number of teams as in the notorious German tank problem. This original place regression function is sigmoidal and thus correctly predicts the existence of a small number of elite teams that significantly outperform the rest of the teams. Our model also describes how place increases linearly with changeover-time at the inflection point of the log-normal distribution function. With real-world data from Jukola 2019, a massive orienteering relay race, the model is shown to be highly accurate even when the size of the training set is only 5% of the whole data set. Numerical results also show that our model exhibits smaller place prediction root-mean-square-errors than linear regression, mord regression and Gaussian process regression.

Keywords: Fenton-Wilkinson approximation, German tank problem, log-normal distribution, order statistics, ordinal regression, orienteering, sports analytics, sports modeling.

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Authors: Mohammadreza Razzazi, Maryam Bayat

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Selection of the best possible set of suppliers has a significant impact on the overall profitability and success of any business. For this reason, it is usually necessary to optimize all business processes and to make use of cost-effective alternatives for additional savings. This paper proposes a new efficient context-aware supplier selection model that takes into account possible changes of the environment while significantly reducing selection costs. The proposed model is based on data clustering techniques while inspiring certain principles of online algorithms for an optimally selection of suppliers. Unlike common selection models which re-run the selection algorithm from the scratch-line for any decision-making sub-period on the whole environment, our model considers the changes only and superimposes it to the previously defined best set of suppliers to obtain a new best set of suppliers. Therefore, any recomputation of unchanged elements of the environment is avoided and selection costs are consequently reduced significantly. A numerical evaluation confirms applicability of this model and proves that it is a more optimal solution compared with common static selection models in this field.

Keywords: Supplier Selection, Context-Awareness, OnlineAlgorithms, Data Clustering.

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Authors: N. Jinesh, K. Shankar

Abstract:

This article presents a method of using the one dimensional piezo-electric patch on beam model for structural identification. A hybrid element constituted of one dimensional beam element and a PZT sensor is used with reduced material properties. This model is convenient and simple for identification of beams. Accuracy of this element is first verified against a corresponding 3D finite element model (FEM). The structural identification is carried out as an inverse problem whereby parameters are identified by minimizing the deviation between the predicted and measured voltage response of the patch, when subjected to excitation. A non-classical optimization algorithm Particle Swarm Optimization is used to minimize this objective function. The signals are polluted with 5% Gaussian noise to simulate experimental noise. The proposed method is applied on beam structure and identified parameters are stiffness and damping. The model is also validated experimentally.

Keywords: Structural identification, PZT patches, inverse problem, particle swarm optimization.

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Authors: Yi Huang, Clemens Guehmann

Abstract:

In order to monitor the thermal behavior of an asynchronous machine with squirrel cage rotor, a 9th-order extended Kalman filter (EKF) algorithm is implemented to estimate the temperatures of the stator windings, the rotor cage and the stator core. The state-space equations of EKF are established based on the electrical, mechanical and the simplified thermal models of an asynchronous machine. The asynchronous machine with simplified thermal model in Dymola is compiled as DymolaBlock, a physical model in MATLAB/Simulink. The coolant air temperature, three-phase voltages and currents are exported from the physical model and are processed by EKF estimator as inputs. Compared to the temperatures exported from the physical model of the machine, three parts of temperatures can be estimated quite accurately by the EKF estimator. The online EKF estimator is independent from the machine control algorithm and can work under any speed and load condition if the stator current is nonzero current system.

Keywords: Asynchronous machine, extended Kalman filter, resistance, simulation, temperature estimation, thermal model.

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Authors: S. Benzarti, H. Mhiri, H. Bournot

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In the current work, a numerical parametric study was performed in order to model the fluid mechanics in the riser of a bubbling fluidized bed (BFB). The gas-solid flow was simulated by mean of a multi-fluid Eulerian model incorporating the kinetic theory for solid particles. The bubbling fluidized bed was simulated two dimensionally by mean of a Computational Fluid Dynamic (CFD) commercial software package, Fluent. The effects of using different inter-phase drag function (the drag model of Gidaspow, Syamlal and O-Brien and the EMMS drag model) on the model predictions were evaluated and compared. The results showed that the drag models of Gidaspow and Syamlal and O-Brien overestimated the drag force for the FCC particles and predicted a greater bed expansion in comparison to the EMMS drag model.

Keywords: Bubbling fluidized bed, CFD, drag model, EMMS

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Authors: I. V. Pinto, M. R. Sooriyarachchi

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It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.

Keywords: Goodness-of-fit test, marginal quasi-likelihood, multilevel modelling, type-I error, penalized quasi-likelihood, power, quasi-likelihood.

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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Authors: H. Kiani, S. Moradi, B. Soltani Soulgani, S. Mousavian

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Desalting/dehydration plants (DDP) are often installed in crude oil production units in order to remove water-soluble salts from an oil stream. In order to optimize this process, desalting unit should be modeled. In this research, artificial neural network is used to model efficiency of desalting unit as a function of input parameter. The result of this research shows that the mentioned model has good agreement with experimental data.

Keywords: Desalting unit, Crude oil, Neural Networks, Simulation, Recovery, Separation.

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Authors: Asok Adak, Debabrata Mazumder, Pratip Bandyopadhyay

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Anaerobic Digestion has become a promising technology for biological transformation of organic fraction of the municipal solid wastes (MSW). In order to represent the kinetic behavior of such biological process and thereby to design a reactor system, development of a mathematical model is essential. Addressing this issue, a simplistic mathematical model has been developed for anaerobic digestion of MSW in a continuous flow reactor unit under homogeneous steady state condition. Upon simulated hydrolysis, the kinetics of biomass growth and substrate utilization rate are assumed to follow first order reaction kinetics. Simulation of this model has been conducted by studying sensitivity of various process variables. The model was simulated using typical kinetic data of anaerobic digestion MSW and typical MSW characteristics of Kolkata. The hydraulic retention time (HRT) and solid retention time (SRT) time were mainly estimated by varying different model parameters like efficiency of reactor, influent substrate concentration and biomass concentration. Consequently, design table and charts have also been prepared for ready use in the actual plant operation.

Keywords: Anaerobic digestion, municipal solid waste (MSW), process design model, simulation study, hydraulic retention time(HRT), solid retention time (SRT).

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: Bahareh Amirjabbari, Nadia Bhuiyan

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In recent decades, the lean methodology, and the development of its principles and concepts have widely been applied in supply chain management. One of the most important strategies of being lean is having efficient inventory within the chain. On the other hand, managing inventory efficiently requires appropriate management of safety stock in order to protect against increasing stretch in the breaking points of the supply chain, which in turn can result in possible reduction of inventory. This paper applies a safety stock cost minimization model in a manufacturing company. The model results in optimum levels and locations of safety stock within the company-s supply chain in order to minimize total logistics costs.

Keywords: Cost, efficient inventory, optimization, safety stock, supply chain

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Authors: T. M. Al Muhareb, J. Graham-Jones

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The service quality is a significant element in aviation industry especially in the international airports. Through this paper, the researchers built a model based on Lean six sigma methodologies and applied it in the departure area at KKIA (King Khalid International Airport) in order to assess it. This model characterized with many special features that can become over the cultural differences in aviation industry since it is considered the most critical circumstance in this field. Applying the model of this study is depending on following the DMAIC procedure systemized in lean thinking aspects. This model of Lean-six-sigma as a managerial procedure is mostly focused on the change management culture that requires high level of planning, organizing, modifying, and controlling in order to benefit from strengths as well as revoke weaknesses.

Keywords: Lean-six-sigma, Service quality, Aviation industry, KKIA (King Khalid International Airport), SERVQUAL.

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Authors: M. A. Tayfun

Abstract:

Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.

Keywords: Large waves, non-linear effects, simulation, spectra, spurious crests, Stokes waves, wave breaking, wave statistics.

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Authors: Ε. Giovanis

Abstract:

In this paper we present an autoregressive model with neural networks modeling and standard error backpropagation algorithm training optimization in order to predict the gross domestic product (GDP) growth rate of four countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final optimum weights from input-hidden layer after the training process. The forecasts are compared with those of the ordinary autoregressive model and we conclude that the proposed regression-s forecasting results outperform significant those of autoregressive model in the out-of-sample period. The idea behind this approach is to propose a parametric regression with weighted variables in order to test for the statistical significance and the magnitude of the estimated autoregressive coefficients and simultaneously to estimate the forecasts.

Keywords: Autoregressive model, Error back-propagation Feed-Forward neural networks, , Gross Domestic Product

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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