Search results for: The linear quantum hydrodynamic model

Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

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In this paper, application of Sliding Mode Control (SMC) technique for an Active Magnetic Bearing (AMB) system with varying rotor speed is considered. The gyroscopic effect and mass imbalance inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Transformation of the AMB dynamic model into regular system shows that these gyroscopic effect and imbalance lie in the mismatched part of the system. A H2-based sliding surface is designed which bound the mismatched parts. The solution of the surface parameter is obtained using Linear Matrix Inequality (LMI). The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active magnetic bearing, sliding mode control, linear matrix inequality, mismatched uncertainty and imbalance.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

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Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: Sara Barati, Karim Ivaz

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In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

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In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: A. A. Purohit, A. Basu, K. A. Chavan, M. D. Kudale

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Many estuarine harbours in the world are facing the problem of siltation in docks, channel entrances, etc. The harbours in India are not an exception and require maintenance dredging to achieve navigable depths for keeping them operable. Hence, dredging is inevitable and is a costly affair. The heavy siltation in docks in well mixed tide dominated estuaries is mainly due to settlement of cohesive sediments in suspension. As such there is a need to have a permanent solution for minimising the siltation in such docks to alter the hydrodynamic flow field responsible for siltation by constructing structures outside the dock. One of such docks on the west coast of India, wherein siltation of about 2.5-3 m/annum prevails, was considered to understand the hydrodynamic flow field responsible for siltation. The dock is situated in such a region where macro type of semi-diurnal tide (range of about 5m) prevails. In order to change the flow field responsible for siltation inside the dock, suitability of Current Deflecting Wall (CDW) outside the dock was studied, which will minimise the sediment exchange rate and siltation in the dock. The well calibrated physical tidal model was used to understand the flow field during various phases of tide for the existing dock in Mumbai harbour. At the harbour entrance where the tidal flux exchanges in/out of the dock, measurements on water level and current were made to estimate the sediment transport capacity. The distorted scaled model (1:400 (H) & 1:80 (V)) of Mumbai area was used to study the tidal flow phenomenon, wherein tides are generated by automatic tide generator. Hydraulic model studies carried out under the existing condition (without CDW) reveal that, during initial hours of flood tide, flow hugs the docks breakwater and part of flow which enters the dock forms number of eddies of varying sizes inside the basin, while remaining part of flow bypasses the entrance of dock. During ebb, flow direction reverses, and part of the flow re-enters the dock from outside and creates eddies at its entrance. These eddies do not allow water/sediment-mass to come out and result in settlement of sediments in dock both due to eddies and more retention of sediment. At latter hours, current strength outside the dock entrance reduces and allows the water-mass of dock to come out. In order to improve flow field inside the dockyard, two CDWs of length 300 m and 40 m were proposed outside the dock breakwater and inline to Pier-wall at dock entrance. Model studies reveal that, during flood, major flow gets deflected away from the entrance and no eddies are formed inside the dock, while during ebb flow does not re-enter the dock, and sediment flux immediately starts emptying it during initial hours of ebb. This reduces not only the entry of sediment in dock by about 40% but also the deposition by about 42% due to less retention. Thus, CDW is a promising solution to significantly reduce siltation in dock.

Keywords: Current deflecting wall, eddies, hydraulic model, macro tide, siltation.

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Authors: Zeinab Galavani, Reza Rezaei-Nasirabad, Rasoul Sadighi-Bonabi

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Using a force balanced translational-radial dynamics, phase space of the moving single bubble sonoluminescence (m- SBSL) in 85% wt sulfuric acid has been numerically calculated. This phase space is compared with that of single bubble sonoluminescence (SBSL) in pure water which has been calculated by using the mere radial dynamics. It is shown that in 85% wt sulfuric acid, in a general agreement with experiment, the bubble-s positional instability threshold lays under the shape instability threshold. At the onset of spatial instability of moving sonoluminescing (SL) bubble in 85% wt sulfuric acid, temporal effects of the hydrodynamic force on the bubble translational-radial dynamics have been investigated. The appearance of non-zero history force on the moving SL bubble is because of proper condition which was produced by high viscosity of acid. Around the moving bubble collapse due to the rapid contraction of the bubble wall, the inertial based added mass force overcomes the viscous based history force and induces acceleration on the bubble translational motion.

Keywords: Bjerknes force, History force, Reynolds number, Sonoluminescence.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

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This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: Yusoff Y. S., Streftaris, G., Waters, H. R

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Death within 30 days is an important factor to be looked into, as there is a significant risk of deaths immediately following or soon after, myocardial infarction (MI) or stroke. In this paper, we will model the deaths within 30 days following a myocardial infarction (MI) or stroke in the UK. We will see how the probabilities of sudden deaths from MI or stroke have changed over the period 1981-2000. We will model the sudden deaths using a generalized linear model (GLM), fitted using the R statistical package, under a Binomial distribution for the number of sudden deaths. We parameterize our model using the extensive and detailed data from the Framingham Heart Study, adjusted to match UK rates. The results show that there is a reduction for the sudden deaths following a MI over time but no significant improvement for sudden deaths following a stroke.

Keywords: Sudden deaths, myocardial infarction, stroke, ischemic heart disease.

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

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Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: Rotating shaft, flexible blades, centrifugal stiffening, stability.

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Authors: Ramaswamy Palaniappan

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In this paper, a second order autoregressive (AR) model is proposed to discriminate alcoholics using single trial gamma band Visual Evoked Potential (VEP) signals using 3 different classifiers: Simplified Fuzzy ARTMAP (SFA) neural network (NN), Multilayer-perceptron-backpropagation (MLP-BP) NN and Linear Discriminant (LD). Electroencephalogram (EEG) signals were recorded from alcoholic and control subjects during the presentation of visuals from Snodgrass and Vanderwart picture set. Single trial VEP signals were extracted from EEG signals using Elliptic filtering in the gamma band spectral range. A second order AR model was used as gamma band VEP exhibits pseudo-periodic behaviour and second order AR is optimal to represent this behaviour. This circumvents the requirement of having to use some criteria to choose the correct order. The averaged discrimination errors of 2.6%, 2.8% and 11.9% were given by LD, MLP-BP and SFA classifiers. The high LD discrimination results show the validity of the proposed method to discriminate between alcoholic subjects.

Keywords: Linear Discriminant, Neural Network, VisualEvoked Potential.

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Authors: Kejun Zhuang, Hailong Zhu

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The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.

Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop

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Authors: Yung-Yuan Hsu

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The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: Guangbin Wang, Fuping Tan

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In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

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Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear identification, NNARX.

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Authors: Srinivasan Chandrasekaran, Shihas A. Khader

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Motion response of floating structures is of great concern in marine engineering. Nonlinearity is an inherent property of any floating bodies subjected to irregular waves. These floating structures are continuously subjected to environmental loadings from wave, current, wind etc. This can result in undesirable motions of the vessel which may challenge the operability. For a floating body to remain in its position, it should be able to induce a restoring force when displaced. Mooring is provided to enable this restoring force. This paper discusses the hydrodynamic performance and motion characteristics of an 8 point spread mooring system applied to a pipe laying barge operating in the West African sea. The modelling of the barge is done using a computer aided-design (CAD) software RHINOCEROS. Irregular waves are generated using a suitable wave spectrum. Both frequency domain and time domain analysis is done. Numerical simulations based on potential theory are carried out to find the responses and hydrodynamic performance of the barge in both free floating as well as moored conditions. Initially, potential flow frequency domain analysis is done to obtain the Response Amplitude Operator (RAO) which gives an idea about the structural motion in free floating state. RAOs for different wave headings are analyzed. In the following step, a time domain analysis is carried out to obtain the responses of the structure in the moored condition. In this study, wave induced motions are only taken into consideration. Wind and current loads are ruled out and shall be included in further studies. For the current study, 2000 seconds simulation is taken. The results represent wave induced motion responses, mooring line tensions and identify critical mooring lines.

Keywords: Irregular wave, moored barge, time domain analysis, numerical simulation.

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Authors: Zunaira Asif, Zhi Chen

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The sustainable measures on air quality management are recognized as one of the most serious environmental concerns in the mining region. The mining operations emit various types of pollutants which have significant impacts on the environment. This study presents a stochastic control strategy by developing the air pollution control model to achieve a cost-effective solution. The optimization method is formulated to predict the cost of treatment using linear programming with an objective function and multi-constraints. The constraints mainly focus on two factors which are: production of metal should not exceed the available resources, and air quality should meet the standard criteria of the pollutant. The applicability of this model is explored through a case study of an open pit metal mine, Utah, USA. This method simultaneously uses meteorological data as a dispersion transfer function to support the practical local conditions. The probabilistic analysis and the uncertainties in the meteorological conditions are accomplished by Monte Carlo simulation. Reasonable results have been obtained to select the optimized treatment technology for PM_2.5, PM₁₀, NO_x, and SO₂. Additional comparison analysis shows that baghouse is the least cost option as compared to electrostatic precipitator and wet scrubbers for particulate matter, whereas non-selective catalytical reduction and dry-flue gas desulfurization are suitable for NO_x and SO₂ reduction respectively. Thus, this model can aid planners to reduce these pollutants at a marginal cost by suggesting control pollution devices, while accounting for dynamic meteorological conditions and mining activities.

Keywords: Air pollution, linear programming, mining, optimization, treatment technologies.

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Authors: Smajo Bisanovic, Mensur Hajro, Muris Dlakic

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

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

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Authors: M. Palanivel, R. Uthayakumar

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In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous Weibull distribution deteriorating items with power demand pattern is presented. In this model, the holding cost per unit of the item per unit time is assumed to be an increasing linear function of time spent in storage. Here the retailer is allowed a trade-credit offer by the supplier to buy more items. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimizing the total inventory cost by finding the optimal time interval and finding the optimal order quantity. The optimal solution of the model is illustrated with the help of numerical examples. Finally sensitivity analysis and graphical representations are given to demonstrate the model.

Keywords: Power demand pattern, Partial backlogging, Time dependent holding cost, Trade credit, Weibull deterioration.

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Authors: Tooraj Hakim Elahi, Abdolamir Nekoubin

Abstract:

In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. in this paper an optimal controller based on discontinuous mathematical model of the system for an electromagnetic suspension system which is applied in magnetic trains has been designed . Simulations show that the new controller can adapt well to the variance of suspension mass and gap, and keep its dynamic performance, thus it is superior to the classic controller.

Keywords: Magnetic Levitation, optimal controller, mass and gap

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

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This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: Md. M. Biswas, Md. M. Hossain, Shaikh Nuruddin

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This paper reports on the theoretical performance analysis of the 1.3 μm In0.42Ga0.58As /In0.26Ga0.74As multiple quantum well (MQW) vertical cavity surface emitting laser (VCSEL) on the ternary In0.31Ga0.69As substrate. The output power of 2.2 mW has been obtained at room temperature for 7.5 mA injection current. The material gain has been estimated to be ~3156 cm-1 at room temperature with the injection carrier concentration of 2×1017 cm-3. The modulation bandwidth of this laser is measured to be 9.34 GHz at room temperature for the biasing current of 2 mA above the threshold value. The outcomes reveal that the proposed InGaAsbased MQW laser is the promising one for optical communication system.

Keywords: Quantum well, VCSEL, output power, materialgain, modulation bandwidth.

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Authors: Adam Czornik, Aleksander Nawrat

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This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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Authors: Yong Zhang, Ruimin Hu

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This paper presents a vocoder to obtain high quality synthetic speech at 600 bps. To reduce the bit rate, the algorithm is based on a sinusoidally excited linear prediction model which extracts few coding parameters, and three consecutive frames are grouped into a superframe and jointly vector quantization is used to obtain high coding efficiency. The inter-frame redundancy is exploited with distinct quantization schemes for different unvoiced/voiced frame combinations in the superframe. Experimental results show that the quality of the proposed coder is better than that of 2.4kbps LPC10e and achieves approximately the same as that of 2.4kbps MELP and with high robustness.

Keywords: Speech coding, Vector quantization, linear predicition, Mixed sinusoidal excitation

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

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A model based fault detection and diagnosis technique for DC motor is proposed in this paper. Fault detection using Kalman filter and its different variants are compared. Only incipient faults are considered for the study. The Kalman Filter iterations and all the related computations required for fault detection and fault confirmation are presented. A second order linear state space model of DC motor is used for this work. A comparative assessment of the estimates computed from four different observers and their relative performance is evaluated.

Keywords: DC motor model, Fault detection and diagnosis Kalman Filter, Unscented Kalman Filter

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Authors: Eduardo F. Arias, William Cooke III, Zhaofei Fan, William Kingery

Abstract:

During the last decade Panicum virgatum, known as Switchgrass, has been broadly studied because of its remarkable attributes as a substitute pasture and as a functional biofuel source. The objective of this investigation was to establish soil suitability for Switchgrass in the State of Mississippi. A linear weighted additive model was developed to forecast soil suitability. Multicriteria analysis and Sensitivity analysis were utilized to adjust and optimize the model. The model was fit using seven years of field data associated with soils characteristics collected from Natural Resources Conservation System - United States Department of Agriculture (NRCS-USDA). The best model was selected by correlating calculated biomass yield with each model's soils-based output for Switchgrass suitability. Coefficient of determination (r2) was the decisive factor used to establish the 'best' soil suitability model. Coefficients associated with the 'best' model were implemented within a Geographic Information System (GIS) to create a map of relative soil suitability for Switchgrass in Mississippi. A Geodatabase associated with soil parameters was built and is available for future Geographic Information System use.

Keywords: Aptness, GIS, sensitivity analysis, switchgrass, soil.

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Authors: Phruksaphanrat B.

Abstract:

This research proposes a Preemptive Possibilistic Linear Programming (PPLP) approach for solving multiobjective Aggregate Production Planning (APP) problem with interval demand and imprecise unit price and related operating costs. The proposed approach attempts to maximize profit and minimize changes of workforce. It transforms the total profit objective that has imprecise information to three crisp objective functions, which are maximizing the most possible value of profit, minimizing the risk of obtaining the lower profit and maximizing the opportunity of obtaining the higher profit. The change of workforce level objective is also converted. Then, the problem is solved according to objective priorities. It is easier than simultaneously solve the multiobjective problem as performed in existing approach. Possible range of interval demand is also used to increase flexibility of obtaining the better production plan. A practical application of an electronic company is illustrated to show the effectiveness of the proposed model.

Keywords: Aggregate production planning, Fuzzy sets theory, Possibilistic linear programming, Preemptive priority

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Authors: M. Satya Sai Ram, P. Siddaiah, M. Madhavi Latha

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This paper investigates the performance of a speech recognizer in an interactive voice response system for various coded speech signals, coded by using a vector quantization technique namely Multi Switched Split Vector Quantization Technique. The process of recognizing the coded output can be used in Voice banking application. The recognition technique used for the recognition of the coded speech signals is the Hidden Markov Model technique. The spectral distortion performance, computational complexity, and memory requirements of Multi Switched Split Vector Quantization Technique and the performance of the speech recognizer at various bit rates have been computed. From results it is found that the speech recognizer is showing better performance at 24 bits/frame and it is found that the percentage of recognition is being varied from 100% to 93.33% for various bit rates.

Keywords: Linear predictive coding, Speech Recognition, Voice banking, Multi Switched Split Vector Quantization, Hidden Markov Model, Linear Predictive Coefficients.

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Authors: M.V Rajesh, Archana R, A Unnikrishnan, R Gopikakumari, Jeevamma Jacob

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The System Identification problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a performance function based on error between the given process output and identified process output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems. The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5]. The work reported here is an attempt to implement few of the well known algorithms in the context of modeling of nonlinear systems, and to make a performance comparison to establish the relative merits and demerits.

Keywords: Multilayer neural networks, Radial Basis Functions, Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.

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Authors: Sang-Lae Lee, Ji-Hwan Kim

Abstract:

In this study, it is investigated the stability boundary of Functionally Graded (FG) panel under the heats and supersonic airflows. Material properties are assumed to be temperature dependent, and a simple power law distribution is taken. First-order shear deformation theory (FSDT) of plate is applied to model the panel, and the von-Karman strain- displacement relations are adopted to consider the geometric nonlinearity due to large deformation. Further, the first-order piston theory is used to model the supersonic aerodynamic load acting on a panel and Rayleigh damping coefficient is used to present the structural damping. In order to find a critical value of the speed, linear flutter analysis of FG panels is performed. Numerical results are compared with the previous works, and present results for the temperature dependent material are discussed in detail for stability boundary of the panel with various volume fractions, and aerodynamic pressures.

Keywords: Functionally graded panels, Linear flutter analysis, Supersonic airflows, Temperature dependent material property.

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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