Search results for: linear parameter varying

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

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: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: M. S. Wickramarachchi, L. S. Nawarathna, C. M. B. Dematawewa

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Hatchery performance is critical for the profitability of poultry breeder operations. Some extrinsic parameters of eggs and breeders cause to increase or decrease the hatchability. This study aims to identify the affecting extrinsic parameters on the commercial hatchability of local chicken's eggs and determine the most efficient classification model with a hatchability rate greater than 90%. In this study, seven extrinsic parameters were considered: egg weight, moisture loss, breeders age, number of fertilised eggs, shell width, shell length, and shell thickness. Multiple linear regression was performed to determine the most influencing variable on hatchability. First, the correlation between each parameter and hatchability were checked. Then a multiple regression model was developed, and the accuracy of the fitted model was evaluated. Linear Discriminant Analysis (LDA), Classification and Regression Trees (CART), k-Nearest Neighbors (kNN), Support Vector Machines (SVM) with a linear kernel, and Random Forest (RF) algorithms were applied to classify the hatchability. This grouping process was conducted using binary classification techniques. Hatchability was negatively correlated with egg weight, breeders' age, shell width, shell length, and positive correlations were identified with moisture loss, number of fertilised eggs, and shell thickness. Multiple linear regression models were more accurate than single linear models regarding the highest coefficient of determination (R²) with 94% and minimum AIC and BIC values. According to the classification results, RF, CART, and kNN had performed the highest accuracy values 0.99, 0.975, and 0.972, respectively, for the commercial hatchery process. Therefore, the RF is the most appropriate machine learning algorithm for classifying the breeder outcomes, which are economically profitable or not, in a commercial hatchery.

Keywords: classification models, egg weight, fertilised eggs, multiple linear regression

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Authors: Ali Albadri

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The logistics equation has never been used or studied in scientific fields outside the field of ecology. It has never been used to understand the behavior of a dynamic system of mechanical machines, like an escalator. We have studied the compatibility of the logistic map against real measurements from an escalator. This study has proven that there is good compatibility between the logistics equation and the experimental measurements. It has discovered the potential of a relationship between the fractal dimension and the non-linearity parameter, R, in the logistics equation. The fractal dimension increases as the R parameter (non-linear parameter) increases. It implies that the fractal dimension increases as the phase of the life span of the machine move from the steady/stable phase to the periodic double phase to a chaotic phase. The fractal dimension and the parameter R can be used as a tool to verify and check the health of machines. We have come up with a theory that there are three areas of behaviors, which they can be classified during the life span of a machine, a steady/stable stage, a periodic double stage, and a chaotic stage. The level of attention to the machine differs depending on the stage that the machine is in. The rate of faults in a machine increases as the machine moves through these three stages. During the double period and the chaotic stages, the number of faults starts to increase and become less predictable. The rate of predictability improves as our monitoring of the changes in the fractal dimension and the parameter R improves. The principles and foundations of our theory in this work have and will have a profound impact on the design of systems, on the way of operation of systems, and on the maintenance schedules of the systems. The systems can be mechanical, electrical, or electronic. The discussed methodology in this paper will give businesses the chance to be more careful at the design stage and planning for maintenance to control costs. The findings in this paper can be implied and used to correlate the three stages of a mechanical system to more in-depth mechanical parameters like wear and fatigue life.

Keywords: logistcs map, bifurcation map, fractal dimension, logistics equation

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Authors: Jatindra Lahkar

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The effect of chemical reaction on laminar mixed convection flow and heat and mass transfer along a vertical unsteady stretching sheet is investigated, in the presence of heat generation/absorption with variable viscosity and viscous dissipation. The governing non-linear partial differential equations are reduced to ordinary differential equations using similarity transformation and solved numerically using the fourth order Runge-Kutta method along with shooting technique. The effects of various flow parameters on the velocity, temperature and concentration distributions are analyzed and presented graphically. Skin-friction coefficient, Nusselt number and Sherwood number are derived at the sheet. It is observed that the influence of chemical reaction, the fluid flow along the sheet accelerate with the increase of chemical reaction parameter, on the other hand, temperature of the fluid increases with increase of chemical reaction parameter but concentration of the fluid reduces with it. The boundary layer decreases on the surface of the sheet for all values of unsteadiness parameter, increasing values of the chemical reaction parameter. The increases in the values of Sc cause the species concentration and its boundary layer thickness to decrease resulting in less induced flow and higher fluid temperatures. This is depicted in the decreases in the velocity and species concentration and increases in the fluid temperature as Sc increases.

Keywords: chemical reaction, heat generation/absorption, magnetic number, unsteadiness, variable viscosity

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Authors: Mehdi Jafari Matehkolaee

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In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Mishu Gupta, Rama Gupta

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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

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

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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

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Authors: Dalvinder Kaur Mangal

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For the past decade, noise corrupted output measurements have been a fundamental research problem to be investigated. On the other hand, the estimation of the parameters for linear dynamic systems when also the input is affected by noise is recognized as more difficult problem which only recently has received increasing attention. Representations where errors or measurement noises/disturbances are present on both the inputs and outputs are usually called errors-in-variables (EIV) models. These disturbances may also have additive effects which are also considered in this paper. Parameter estimation of false EIV problem using equation error, output error and iterative prefiltering identification schemes with and without additive uncertainty, when only the output observation is corrupted by noise has been dealt in this paper. The comparative study of these three schemes has also been carried out.

Keywords: errors-in-variable (EIV), false EIV, equation error, output error, iterative prefiltering, Gaussian noise

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Authors: Liang Zhao, Chong-quan Zhong

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In order to improve the control performance of vector inverter, an improved parameter identification solution for induction motor is proposed in this paper. Dc or AC voltage is applied to the induction motor using the SVPWM through the inverter. Then stator resistance, stator leakage inductance, rotor resistance, rotor leakage inductance and mutual inductance are obtained according to the signal response. The discrete Fourier transform (DFT) is used to deal with the noise and harmonic. The impact on parameter identification caused by delays in the inverter switch tube, tube voltage drop and dead-time is avoided by effective compensation measures. Finally, the parameter identification experiment is conducted based on the vector inverter which using TMS320F2808 DSP as the core processor and results show that the strategy is verified.

Keywords: vector inverter, parameter identification, SVPWM; DFT, dead-time compensation

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Authors: Joon-Hoon Park

Abstract:

In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: Lamia Bourdache, Amar Djema

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The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: Rangoli Goyal, Rama Bhargava

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The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, diffusiophoresis, Brownian motion

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Authors: R. K. Dubey

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Bianchi type cosmological models have been studied on the basis of Lyra’s geometry. Exact solution has been obtained by considering a time dependent displacement field for constant deceleration parameter and varying cosmological term of the universe. The physical behavior of the different models has been examined for different cases.

Keywords: Bianchi type-I cosmological model, variable gravitational coupling, cosmological constant term, Lyra's model

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Authors: G. Nitesh

Abstract:

The shear strength of soils is a crucial parameter instability analysis. Therefore, it is important to determine reliable values for the accuracy of stability analysis. Direct shear tests are mostly performed to determine the shear strength of cohesionless soils. The major limitation of the direct shear test is that the failure takes place through the pre-defined failure plane but the failure is not along pre-defined plane and is along the weakest plane in actual shearing mechanism that goes on in the field. This leads to overestimating the strength parameter; hence, a new apparatus called simple shear is developed and used in this study to determine the shear strength parameter that simulates the field conditions.

Keywords: direct shear, simple shear, angle of shear resistance, cohesionless soils

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Authors: Orkide Donma, Mustafa M. Donma

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Basal metabolic rate (BMR) is widely used and an accepted measure of energy expenditure. Its principal determinant is body mass. However, this parameter is also correlated with a variety of other factors. The objective of this study is to measure BMR and compare it with the values obtained from predictive equations in adults classified according to their body mass index (BMI) values. 276 adults were included into the scope of this study. Their age, height and weight values were recorded. Five groups were designed based on their BMI values. First group (n = 85) was composed of individuals with BMI values varying between 18.5 and 24.9 kg/m². Those with BMI values varying from 25.0 to 29.9 kg/m² constituted Group 2 (n = 90). Individuals with 30.0-34.9 kg/m², 35.0-39.9 kg/m², > 40.0 kg/m² were included in Group 3 (n = 53), 4 (n = 28) and 5 (n = 20), respectively. The most commonly used equations to be compared with the measured BMR values were selected. For this purpose, the values were calculated by the use of four equations to predict BMR values, by name, introduced by Food and Agriculture Organization (FAO)/World Health Organization (WHO)/United Nations University (UNU), Harris and Benedict, Owen and Mifflin. Descriptive statistics, ANOVA, post-Hoc Tukey and Pearson’s correlation tests were performed by a statistical program designed for Windows (SPSS, version 16.0). p values smaller than 0.05 were accepted as statistically significant. Mean ± SD of groups 1, 2, 3, 4 and 5 for measured BMR in kcal were 1440.3 ± 210.0, 1618.8 ± 268.6, 1741.1 ± 345.2, 1853.1 ± 351.2 and 2028.0 ± 412.1, respectively. Upon evaluation of the comparison of means among groups, differences were highly significant between Group 1 and each of the remaining four groups. The values were increasing from Group 2 to Group 5. However, differences between Group 2 and Group 3, Group 3 and Group 4, Group 4 and Group 5 were not statistically significant. These insignificances were lost in predictive equations proposed by Harris and Benedict, FAO/WHO/UNU and Owen. For Mifflin, the insignificance was limited only to Group 4 and Group 5. Upon evaluation of the correlations of measured BMR and the estimated values computed from prediction equations, the lowest correlations between measured BMR and estimated BMR values were observed among the individuals within normal BMI range. The highest correlations were detected in individuals with BMI values varying between 30.0 and 34.9 kg/m². Correlations between measured BMR values and BMR values calculated by FAO/WHO/UNU as well as Owen were the same and the highest. In all groups, the highest correlations were observed between BMR values calculated from Mifflin and Harris and Benedict equations using age as an additional parameter. In conclusion, the unique resemblance of the FAO/WHO/UNU and Owen equations were pointed out. However, mean values obtained from FAO/WHO/UNU were much closer to the measured BMR values. Besides, the highest correlations were found between BMR calculated from FAO/WHO/UNU and measured BMR. These findings suggested that FAO/WHO/UNU was the most reliable equation, which may be used in conditions when the measured BMR values are not available.

Keywords: adult, basal metabolic rate, fao/who/unu, obesity, prediction equations

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: M. Berrehail, F. Benamira

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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

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Authors: Kang-Gyu Park, Sun-Jong Park, Hong Jae Yim, Hyo-Gyung Kwak

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This paper attempts to evaluate the effect of fire damage on concrete by using nonlinear resonance vibration method, one of the nonlinear nondestructive method. Concrete exhibits not only nonlinear stress-strain relation but also hysteresis and discrete memory effect which are contained in consolidated materials. Hysteretic materials typically show the linear resonance frequency shift. Also, the shift of resonance frequency is changed according to the degree of micro damage. The degree of the shift can be obtained through nonlinear resonance vibration method. Five exposure scenarios were considered in order to make different internal micro damage. Also, the effect of post-fire-curing on fire-damaged concrete was taken into account to conform the change in internal damage. Hysteretic non linearity parameter was obtained by amplitude-dependent resonance frequency shift after specific curing periods. In addition, splitting tensile strength was measured on each sample to characterize the variation of residual strength. Then, a correlation between the hysteretic non linearity parameter and residual strength was proposed from each test result.

Keywords: nonlinear resonance vibration method, non linearity parameter, splitting tensile strength, micro damage, post-fire-curing, fire damaged concrete

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Authors: Pouya Molana, Zeinab Alimohammadi

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Determining wind wave characteristics is essential for implementing projects related to Coastal and Marine engineering such as designing coastal and marine structures, estimating sediment transport rates and coastal erosion rates in order to predict significant wave height (H_s), this study applies the third generation spectral wave model, Mike 21 SW, along with CEM model. For SW model calibration and verification, two data sets of meteorology and wave spectroscopy are used. The model was exposed to time-varying wind power and the results showed that difference ratio mean, standard deviation of difference ratio and correlation coefficient in SW model for H_s parameter are 1.102, 0.279 and 0.983, respectively. Whereas, the difference ratio mean, standard deviation and correlation coefficient in The Choice Experiment Method (CEM) for the same parameter are 0.869, 1.317 and 0.8359, respectively. Comparing these expected results it is revealed that the Choice Experiment Method CEM has more errors in comparison to MIKE 21 SW third generation spectral wave model and higher correlation coefficient does not necessarily mean higher accuracy.

Keywords: MIKE 21 SW, CEM method, significant wave height, difference ratio

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Authors: Farmesk Abubaker, Francesco Tortorici, Marco Capogni, Concetta Sutera, Vincenzo Bellini

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This project concerns with the detection efficiency of the portable triple-to-double coincidence ratio (TDCR) at the National Institute of Metrology of Ionizing Radiation (INMRI-ENEA) which allows direct activity measurement and radionuclide standardization for pure-beta emitter or pure electron capture radionuclides. The dependency of the simulated detection efficiency of the TDCR, by using Monte Carlo simulation Geant4 code, on the Birks factor (kB) and defocusing parameter has been examined especially for low energy beta-emitter radionuclides such as 3H and 14C, for which this dependency is relevant. The results achieved in this analysis can be used for selecting the best kB factor and the defocusing parameter for computing theoretical TDCR parameter value. The theoretical results were compared with the available ones, measured by the ENEA TDCR portable detector, for some pure-beta emitter radionuclides. This analysis allowed to improve the knowledge of the characteristics of the ENEA TDCR detector that can be used as a traveling instrument for in-situ measurements with particular benefits in many applications in the field of nuclear medicine and in the nuclear energy industry.

Keywords: Birks constant, defocusing parameter, GEANT4 code, TDCR parameter

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Tulin Coskun

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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

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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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

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Authors: C. J. Coetzee, E. Horn

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One of the main challenges in using the Discrete Element Method (DEM) is to specify the correct input parameter values. In general, the models are sensitive to the input parameter values and accurate results can only be achieved if the correct values are specified. For the linear contact model, micro-parameters such as the particle density, stiffness, coefficient of friction, as well as the particle size and shape distributions are required. There is a need for a procedure to accurately calibrate these parameters before any attempt can be made to accurately model a complete bulk materials handling system. Since DEM is often used to model applications in the mining and quarrying industries, a calibration procedure was developed for materials that consist of relatively large (up to 40 mm in size) particles. A coarse crushed aggregate was used as the test material. Using a specially designed large shear box with a diameter of 590 mm, the confined Young’s modulus (bulk stiffness) and internal friction angle of the material were measured by means of the confined compression test and the direct shear test respectively. DEM models of the experimental setup were developed and the input parameter values were varied iteratively until a close correlation between the experimental and numerical results was achieved. The calibration process was validated by modelling the pull-out of an anchor from a bed of material. The model results compared well with experimental measurement.

Keywords: Discrete Element Method (DEM), calibration, shear box, anchor pull-out

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Authors: Jae-Jeong Kim, Ki-Ro Kim, Hyoung-Kyu Song

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In this paper, we propose an efficient signal detector that switches M parameter of QRD-M detection scheme is proposed for MIMO-OFDM system. The proposed detection scheme calculates the threshold by 1-norm condition number and then switches M parameter of QRD-M detection scheme according to channel information. If channel condition is bad, the parameter M is set to high value to increase the accuracy of detection. If channel condition is good, the parameter M is set to low value to reduce complexity of detection. Therefore, the proposed detection scheme has better trade off between BER performance and complexity than the conventional detection scheme. The simulation result shows that the complexity of proposed detection scheme is lower than QRD-M detection scheme with similar BER performance.

Keywords: MIMO-OFDM, QRD-M, channel condition, BER

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Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

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The present analysis considers the steady stagnation point flow and heat transfer towards a permeable sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow, and a local heat generation within the boundary layer with a heat generation rate proportional to (T-T_inf)^p. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the shrinking/stretching parameter lambda, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value lambda_c whose value depends on the value of M, K, and s. In the presence of internal heat absorbtion (Q<0), the surface heat transfer rate decreases with increasing p but increases with parameter Q and s, when the sheet is either stretched or shrunk.

Keywords: magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet

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