Search results for: equivalent linear approach

Authors: Mishu Gupta, Rama Gupta

Abstract:

It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

Procedia PDF Downloads 155

Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

Abstract:

In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

Procedia PDF Downloads 595

Authors: Qasim M. Kriri

Abstract:

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: parameter linear programming, objective function, sensitivity analysis, optimize profit

Procedia PDF Downloads 205

Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

Abstract:

Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

Procedia PDF Downloads 330

Authors: Muskaan Sethi, Arnab Banerjee, Bappaditya Manna

Abstract:

The present paper aims to investigate a suitable contact between a wheel rolling over a flexible beam. A Linear Complementary (LCP) based approach has been adopted to simulate the contact dynamics for a rigid wheel traversing over a flexible Euler Bernoulli simply supported beam. The adopted methodology is suitable to incorporate the effect of frictional force acting at the wheel-beam interface. Moreover, the possibility of the generation of a gap between the two bodies has also been considered. The present method is based on a unilateral contact assumption which assumes that no penetration would occur when the two bodies come in contact. This assumption helps to predict the contact between wheels and beams in a more practical sense. The proposed methodology is validated with the previously published results and is found to be in good agreement. Further, this method is applied to simulate the contact between wheels and beams for various railway configurations. Moreover, different parametric studies are conducted to study the contact dynamics between the wheel and beam more thoroughly.

Keywords: contact dynamics, linear complementary problem, railway dynamics, unilateral contact

Procedia PDF Downloads 101

Authors: Saeed Javaherzadeh, Babak Dindar Safa

Abstract:

Structure, given its ductility, can depreciate significant amount of seismic energy in the form of hysteresis behavior; the amount of energy depreciation depends on the structure ductility rate. So in seismic guidelines such as ASCE7-10 code, to reduce the number of design forces and using the seismic energy dissipation capacity of structure, when entering non-linear behavior range of the materials, the response modification factor is used. Various parameters such as ductility modification factor, overstrength factor and reliability factor, are effective in determining the value of this factor. Also, gradually, energy dissipation systems, especially added dampers, have become an inseparable part of the seismic design. In this paper, in addition to reviewing of previous studies, using the response modification factor caused by using more added viscoelastic dampers, a new design method has introduced for steel moment-frame with added dampers installed. To do this, in addition to using bilinear behavior models and quick ways such as using the equivalent lateral force method and capacity spectrum method for the proposed design methodology, the results has been controlled with non-linear time history analysis for a number of structural. The analysis is done by Opensees Software.

Keywords: added viscoelastic damper, design base shear, response modification factor, non-linear time history

Procedia PDF Downloads 441

Authors: Gupta. Ashok, V. talakokula, S. bhalla

Abstract:

Rebar corrosion is one of the main causes of damage and premature failure of the reinforced concrete (RC) structures worldwide, causing enormous costs for inspection, maintenance, restoration and replacement. Therefore, early detection of corrosion and timely remedial action on the affected portion can facilitate an optimum utilization of the structure, imparting longevity to it. The recent advent of the electro-mechanical impedance (EMI) technique using piezo sensors (PZT) for structural health monitoring (SHM) has provided a new paradigm to the maintenance engineers to diagnose the onset of the damage at the incipient stage itself. This paper presents a model based approach for corrosion assessment based on the equivalent parameters extracted from the impedance spectrum of concrete-rebar system using the EMI technique via the PZT sensors.

Keywords: impedance, electro-mechanical, stiffness, mass, damping, equivalent parameters

Procedia PDF Downloads 543

Authors: Erindi Allaj

Abstract:

This paper studies arbitrage pricing theory in financial markets with transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Transaction costs are composed of two terms, one is able to capture the implicit transaction costs and the other the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies which have left and right limit and finite quadratic variation. That is, predictable trading strategies of infinite variation and of finite quadratic variation are allowed in our setting. Within this framework, the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also proved that, when this probability measure is unique, any contingent claim in the market is hedgeable in an L2-sense. The price of any contingent claim is equal to the risk-neutral price. To better understand how to apply the theory proposed we provide an example with linear transaction costs.

Keywords: arbitrage pricing theory,
transaction costs, fundamental theorems of arbitrage, financial markets

Procedia PDF Downloads 360

Authors: Alex Contarino

Abstract:

Professional sports leagues often have a “free agency” period, during which teams may sign players with expiring contracts.To promote parity, many leagues operate under a salary cap that limits the amount teams can spend on player’s salaries in a given year. Similarly, in fantasy sports leagues, salary cap drafts are a popular method for selecting players. In order to sign a free agent in either setting, teams must bid against one another to buy the player’s services while ensuring the sum of their player’s salaries is below the salary cap. This paper models the bidding process for a free agent as a constrained optimization problem that can be solved using linear programming. The objective is to determine the largest bid that a team should offer the player subject to the constraint that the value of signing the player must exceed the value of using the salary cap elsewhere. Iteratively solving this optimization problem for each available free agent provides teams with an effective framework for maximizing the talent on their rosters. The utility of this approach is demonstrated for team sport roster construction and fantasy sport drafts, using recent data sets from both settings.

Keywords: linear programming, optimization, roster management, salary cap

Procedia PDF Downloads 111

Authors: Hasan Vural

Abstract:

The purpose of this study was to determine energy equivalents of inputs and output in tomato production in Bursa province. The data in this study were collected from tomato farms in Bursa province, Karacabey and Mustafakemalpasa district. Questionnaires were administered through face-to-face interview in 2011-2012. The results of the study show that diesel have the highest rate of energy equivalency of all the inputs used in tomato production at 60,07%. The energy equivalent rate of electricity is 4,26% and the energy equivalent rate of water is 0,87%. The energy equivalent rates for human power, machinery, chemicals and water for irrigation were determined to be low in tomato production. According to the output/input ratio calculated, the energy ratio is 1,50 in tomato production in the research area. This ratio implies that the inputs used in tomato production have not been used effectively. Ineffective use of these resources also causes environmental problems.

Keywords: Tomato production, energy ratio, energy input, Turkey

Procedia PDF Downloads 231

Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif

Abstract:

This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

Procedia PDF Downloads 394

Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, dynamics, Lagrange, parallel platform

Procedia PDF Downloads 345

Authors: Ming-Chu Yin, Ping-An Du

Abstract:

The shielding ability of a shielding cavity is affected greatly by its resonances, which include resonance modes and frequencies. The equivalent circuit method and numerical method of transmission line matrix (TLM) are used to analyze the effect of aperture-cavity coupling on electromagnetic resonances of a cavity with an aperture in this paper. Both theoretical and numerical results show that the resonance modes of a shielding cavity with an aperture can be considered as the combination of cavity and aperture inherent resonance modes with resonance frequencies shifting, and the reason of this shift is aperture-cavity coupling. Because aperture sizes are important parameters to aperture-cavity coupling, variation rules of electromagnetic resonances of a shielding cavity with its aperture sizes are given, which will be useful for the design of shielding cavities.

Keywords: aperture-cavity coupling, equivalent circuit method, resonances, shielding equipment

Procedia PDF Downloads 444

Authors: P. Michael Preetam Raj, Souri Banerjee, Souvik Kundu

Abstract:

Oxide based memristors were fabricated in order to establish its potential applications in analog/digital electronics. BaTiO₃-BiFeO₃ (BT-BFO) was employed as an active material, whereas platinum (Pt) and Nb-doped SrTiO₃ (Nb:STO) were served as a top and bottom electrodes, respectively. Piezoelectric force microscopy (PFM) was utilized to present the ferroelectricity and repeatable polarization inversion in the BT-BFO, demonstrating its effectiveness for resistive switching. The fabricated memristors exhibited excellent electrical characteristics, such as hysteresis current-voltage (I-V), high on/off ratio, high retention time, cyclic endurance, and low operating voltages. The band-alignment between the active material BT-BFO and the substrate Nb:STO was experimentally investigated using X-Ray photoelectron spectroscopy, and it attributed to staggered heterojunction alignment. An energy band diagram was proposed in order to understand the electrical transport in BT-BFO/Nb:STO heterojunction. It was identified that the I-V curves of these memristors have several discontinuities. Curve fitting technique was utilized to analyse the I-V characteristic, and the obtained I-V equations were found to be parabolic. Utilizing this analysis, a non-linear BT-BFO memristors equivalent circuit model was developed. Interestingly, the obtained equivalent circuit of the BT-BFO memristors mimics the identical electrical performance, those obtained in the fabricated devices. Based on the developed equivalent circuit, a finite state machine (FSM) design was proposed. Efforts were devoted to fabricate the same FSM, and the results were well matched with those in the simulated FSM devices. Its multilevel noise filtering and immunity to external noise characteristics were also studied. Further, the feature of variable negative resistance was established by controlling the current through the memristor.

Keywords: band alignment, finite state machine, polarization inversion, resistive switching

Procedia PDF Downloads 133

Authors: Suparman

Abstract:

Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

Procedia PDF Downloads 521

Authors: Sergey Kuznetsov, Yuri Urman

Abstract:

We present an approach to investigate non-linear dynamical effects occurring in the noncontact superconducting and diamagnetic suspensions, when levitated body has finite size. This approach is based on the calculation of interaction energy between spherical finite size superconducting or diamagnetic body with external magnetic field. Effects of small deviations from spherical shape may be also taken into account by introducing small corrections to the energy. This model allows investigating dynamical effects important for practical applications, such as nonlinear resonances, change of vibration plane, coupling of rotational and translational motions etc. We also show how the geometry of suspension affects various dynamical effects and how an inverse problem may be formulated to enforce or diminish various dynamical effects.

Keywords: levitation, non-linear dynamics, superconducting, diamagnetic stability

Procedia PDF Downloads 410

Authors: Ridha Salhi, Mondher Labidi, Fethi Choubani

Abstract:

Metamaterials have attracted much attention in recent years because of their electromagnetic exquisite proprieties. We will present, in this paper, the modeling of three metamaterial structures by equivalent circuit model. We begin by modeling the SRR (Split Ring Resonator), then we model the HIS (High Impedance Surfaces), and finally, we present the model of the CPW (Coplanar Wave Guide). In order to validate models, we compare the results obtained by an equivalent circuit models with numerical simulation.

Keywords: metamaterials, SRR, HIS, CPW, IDC

Procedia PDF Downloads 429

Authors: Hyon I. Paek, Sang Rim Kim, Hyon A. Ryu

Abstract:

In functional linear regression, one typical problem is to reduce dimension. Compared with multivariate linear regression, functional linear regression is regarded as an infinite-dimensional case, and the main task is to reduce dimensions of functional response and functional predictors. One common approach is to adapt functional principal component analysis (FPCA) on functional predictors and then use a few leading functional principal components (FPC) to predict the functional model. The leading FPCs estimated by the typical FPCA explain a major variation of the functional predictor, but these leading FPCs may not be mostly correlated with the functional response, so they may not be significant in the prediction for response. In this paper, we propose a supervised functional principal component analysis method for a functional response model with FPCs obtained by considering the correlation of the functional response. Our method would have a better prediction accuracy than the typical FPCA method.

Keywords: supervised, functional principal component analysis, functional response, functional linear regression

Procedia PDF Downloads 75

Authors: Elias K. Maragos, Petros E. Maravelakis

Abstract:

In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.

Keywords: Dynamic Data Envelopment Analysis, DDEA, piecewise linear inputs, piecewise linear outputs

Procedia PDF Downloads 160

Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: autonomous vehicles, convoy, non-linear control, non-linear observer, sliding mode

Procedia PDF Downloads 140

Authors: M. Berrehail, F. Benamira

Abstract:

We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

Procedia PDF Downloads 492

Authors: Shivani Sharma, Prashant Saxena, Inamul Hasan Madar

Abstract:

Since the time of Darwin, it has been considered that genetic change is the direct indicator of variation in phenotype. But a few studies in system biology in the past years have proposed that epigenetic developmental processes also affect the phenotype thus shifting the focus from a linear genotype-phenotype map to a non-linear G-P map. In this paper, we attempt at explaining the evolution of colour vision in mammals by taking LWS/ Long-wave sensitive gene under consideration.

Keywords: evolution, phenotypes, epigenetics, LWS gene, G-P map

Procedia PDF Downloads 521

Authors: Birinderjit Singh Kalyan, Inderpreet Kaur, Balwinder Singh Sohi

Abstract:

In this paper, an equivalent model for floating gate transistor has been proposed. Using the floating gate voltage value, capacitive coupling coefficients has been found at different bias conditions. The amount of charge present on the gate has been then calculated using the transient models of hot electron programming and Fowler-Nordheim Tunnelling. The proposed model can be extended to the transient conditions as well. The SPICE equivalent model is designed and current-voltage characteristics and Transfer characteristics are comparatively analysed. The dc current-voltage characteristics, as well as dc transfer characteristics, have been plotted for an FGMOS with W/L=0.25μm/0.375μm, the inter-poly capacitance of 0.8fF for both programmed and erased states. The Comparative analysis has been made between the present model and capacitive coefficient coupling methods which were already available.

Keywords: FGMOS, floating gate transistor, capacitive coupling coefficient, SPICE model

Procedia PDF Downloads 545

Authors: Yi-Fei Yang, Nai-Bao He, Shao-Bang Xing

Abstract:

This study investigates the permanent magnet synchronous linear motor (PMSLM) chaotic motion under the specific physical parameters, the stability and the security of motor-driven system will be unavoidably influenced. Therefore, it is really necessary to investigate the methods of controlling or suppressing chaos in PMSLM. Firstly, we derive a chaotic model of PMSLM in the closed-loop system. Secondly, in order to realize the local asymptotic stabilization of the mechanical subsystem and the global stabilization of the motor-driven system including electrical subsystem, we propose an improved uniting control lyapunov functions by introducing backstepping approach. Finally, an illustrated example is also given to show the electiveness of the obtained results.

Keywords: linear motor, lyapunov functions, chao control, hybrid controller

Procedia PDF Downloads 337

Authors: Tulin Coskun

Abstract:

We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

Procedia PDF Downloads 338

Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

Abstract:

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

Procedia PDF Downloads 395

Authors: Chivon Choeung, Heng Tang, Panha Soth, Vichet Huy

Abstract:

This paper presents a robust control strategy for a single-phase DC-AC inverter with an output LC-filter. An all-pass filter is utilized to create an artificial β-signal so that the proposed controller can be simply used in dq-synchronous frame. The proposed robust controller utilizes a state feedback control with integral action in the dq-synchronous frame. A linear matrix inequality-based optimization scheme is used to determine stabilizing gains of the controllers to maximize the convergence rate to steady state in the presence of uncertainties. The uncertainties of the system are described as the potential variation range of the inductance and resistance in the LC-filter.

Keywords: single-phase inverter, linear matrix inequality, robust control, all-pass filter

Procedia PDF Downloads 140

Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

Abstract:

The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

Procedia PDF Downloads 148

Authors: Adilah Abdul Ghapor, Yong Zulina Zubairi, Rahmatullah Imon

Abstract:

Missing value problem is common in statistics and has been of interest for years. This article considers two modern techniques in handling missing data for linear functional relationship model (LFRM) namely the Expectation-Maximization (EM) algorithm and Expectation-Maximization with Bootstrapping (EMB) algorithm using three performance indicators; namely the mean absolute error (MAE), root mean square error (RMSE) and estimated biased (EB). In this study, we applied the methods of imputing missing values in the LFRM. Results of the simulation study suggest that EMB algorithm performs much better than EM algorithm in both models. We also illustrate the applicability of the approach in a real data set.

Keywords: expectation-maximization, expectation-maximization with bootstrapping, linear functional relationship model, performance indicators

Procedia PDF Downloads 399

Authors: Ebrahim Asadi-Gangraj

Abstract:

Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems.

Keywords: hybrid flow shop, mixed integer linear programming, Benders decomposition, makespan

Procedia PDF Downloads 188