Search results for: error floors.

Authors: R. Sabre, W. Horrigue, J. C. Simon

Abstract:

This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: Jun Sung Go, Jong Kang Park, Jong Tae Kim

Abstract:

As semi-conductor manufacturing technology evolves; the single event transient problem becomes more significant issue. Single event transient has a critical impact on both combinational and sequential logic circuits, so it is important to evaluate the soft error tolerance of the circuits at the design stage. In this paper, we present a soft error detecting simulation using scan chain. The simulation model generates a single event transient randomly in the circuit, and detects the soft error during the execution of the test patterns. We verified this model by inserting a scan chain in an 8051 microprocessor using 65 nm CMOS technology. While the test patterns generated by ATPG program are passing through the scan chain, we insert a single event transient and detect the number of soft errors per sub-module. The experiments show that the soft error rates per cell area of the SFR module is 277% larger than other modules.

Keywords: Scan chain, single event transient, soft error, 8051 processor.

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Authors: Chaiwat Tantarangsee

Abstract:

The purposes of this study are 1) to study the frequent English writing errors of students registering the course: Reading and Writing English for Academic Purposes II, and 2) to find out the results of writing error correction by using coded indirect corrective feedback and writing error treatments. Samples include 28 2nd year English Major students, Faculty of Education, Suan Sunandha Rajabhat University. Tool for experimental study includes the lesson plan of the course; Reading and Writing English for Academic Purposes II, and tool for data collection includes 4 writing tests of short texts. The research findings disclose that frequent English writing errors found in this course comprise 7 types of grammatical errors, namely Fragment sentence, Subject-verb agreement, Wrong form of verb tense, Singular or plural noun endings, Run-ons sentence, Wrong form of verb pattern and Lack of parallel structure. Moreover, it is found that the results of writing error correction by using coded indirect corrective feedback and error treatment reveal the overall reduction of the frequent English writing errors and the increase of students’ achievement in the writing of short texts with the significance at .05.

Keywords: Coded indirect corrective feedback, error correction, error treatment, frequent English writing errors.

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Authors: Johann Barbier, Guillaume Sicot, Sebastien Houcke

Abstract:

In this paper we present a generic approach for the problem of the blind estimation of the parameters of linear and convolutional error correcting codes. In a non-cooperative context, an adversary has only access to the noised transmission he has intercepted. The intercepter has no knowledge about the parameters used by the legal users. So, before having acess to the information he has first to blindly estimate the parameters of the error correcting code of the communication. The presented approach has the main advantage that the problem of reconstruction of such codes can be expressed in a very simple way. This allows us to evaluate theorical bounds on the complexity of the reconstruction process but also bounds on the estimation rate. We show that some classical reconstruction techniques are optimal and also explain why some of them have theorical complexities greater than these experimentally observed.

Keywords: Blind estimation parameters, error correcting codes, non-cooperative context, reconstruction algorithm

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Authors: A. Shayeghi, H. Shayeghi, H. Eimani Kalasar

Abstract:

In recent years, tuned mass damper (TMD) control systems for civil engineering structures have attracted considerable attention. This paper emphasizes on the application of particle swarm application (PSO) to design and optimize the parameters of the TMD control scheme for achieving the best results in the reduction of the building response under earthquake excitations. The Integral of the Time multiplied Absolute value of the Error (ITAE) based on relative displacement of all floors in the building is taken as a performance index of the optimization criterion. The problem of robustly TMD controller design is formatted as an optimization problem based on the ITAE performance index to be solved using the PSO technique which has a story ability to find the most optimistic results. An 11- story realistic building, located in the city of Rasht, Iran is considered as a test system to demonstrate effectiveness of the proposed method. The results analysis through the time-domain simulation and some performance indices reveals that the designed PSO based TMD controller has an excellent capability in reduction of the seismically excited example building.

Keywords: TMD, Particle Swarm Optimization, Tall Buildings, Structural Dynamics.

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Authors: Chaiwat Tantarangsee

Abstract:

The purposes of this study are 1) to study the frequent English writing errors of students registering the course: Reading and Writing English for Academic Purposes II, and 2) to find out the results of writing error correction by using coded indirect corrective feedback and writing error treatments. Samples include 28 2nd year English Major students, Faculty of Education, Suan Sunandha Rajabhat University. Tool for experimental study includes the lesson plan of the course; Reading and Writing English for Academic Purposes II, and tool for data collection includes 4 writing tests of short texts. The research findings disclose that frequent English writing errors found in this course comprise 7 types of grammatical errors, namely Fragment sentence, Subject-verb agreement, Wrong form of verb tense, Singular or plural noun endings, Run-ons sentence, Wrong form of verb pattern and Lack of parallel structure. Moreover, it is found that the results of writing error correction by using coded indirect corrective feedback and error treatment reveal the overall reduction of the frequent English writing errors and the increase of students’ achievement in the writing of short texts with the significance at .05.

Keywords: Coded indirect corrective feedback, error correction, and error treatment.

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Authors: Matthias Kirmse, Uwe Petersohn, Elief Paffrath

Abstract:

As in today's semiconductor industries test costs can make up to 50 percent of the total production costs, an efficient test error detection becomes more and more important. In this paper, we present a new machine learning approach to test error detection that should provide a faster recognition of test system faults as well as an improved test error recall. The key idea is to learn a classifier ensemble, detecting typical test error patterns in wafer test results immediately after finishing these tests. Since test error detection has not yet been discussed in the machine learning community, we define central problem-relevant terms and provide an analysis of important domain properties. Finally, we present comparative studies reflecting the failure detection performance of three individual classifiers and three ensemble methods based upon them. As base classifiers we chose a decision tree learner, a support vector machine and a Bayesian network, while the compared ensemble methods were simple and weighted majority vote as well as stacking. For the evaluation, we used cross validation and a specially designed practical simulation. By implementing our approach in a semiconductor test department for the observation of two products, we proofed its practical applicability.

Keywords: Ensemble methods, fault detection, machine learning, semiconductor test.

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Authors: A. Shayeghi, H. Eimani Kalasar, H. Shayeghi

Abstract:

This paper emphasizes on the application of genetic algorithm (GA) to optimize the parameters of the TMD for achieving the best results in the reduction of the building response under earthquake excitations. The Integral of the Time multiplied Absolute value of the Error (ITAE) based on relative displacement of all floors in the building is taken as a performance index of the optimization criterion. The problem of robustly TMD controller design is formatted as an optimization problem based on the ITAE performance index to be solved using GA that has a story ability to find the most optimistic results. An 11–story realistic building, located in the city of Rasht, Iran is considered as a test system to demonstrate effectiveness of the proposed GA based TMD (GATMD) controller without specifying which mode should be controlled. The results of the proposed GATMD controller are compared with the uncontrolled structure through timedomain simulation and some performance indices. The results analysis reveals that the designed GA based TMD controller has an excellent capability in reduction of the seismically excited example building and the ITAE performance, that is so for remains as unknown, can be introduced a new criteria - method for structural dynamic design.

Keywords: Tuned Mass Damper, Genetic Algorithm, TallBuildings, Structural Dynamics.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: Zasiah Tafheem, Mahadee Hasan Shourav, Zahidul Islam, Saima Islam Tumpa

Abstract:

The paper aims at investigating the effect of number of story on different structural components of reinforced concrete building due to gravity and lateral loading. For the study, three building models having same building plan of three, six and nine stories are analyzed and designed using software package. All the buildings are residential and are located in Dhaka city of Bangladesh. Lateral load including wind and earthquake loading are applied to the building along both longitudinal and transverse direction as per Bangladesh National Building Code (BNBC, 2006). Equivalent static force method is followed for the applied seismic loading. The present study investigates as well as compares mainly total steel requirement in different structural components for those buildings. It has been found that total longitudinal steel requirement for beams at each floor is 48.57% for three storied building, 61.36% for six storied building when the total percentage is taken as 100% in case of nine storied building. For an exterior column, the steel ratio is 2.1%, 3.06%, 4.55% for three, six and nine storied building respectively for the first three floors. In addition, it has been noted that total weight of longitudinal reinforcement of an interior column is 14.02 % for threestoried building and 43.12% for six storied building when the total reinforcement is considered 100% for nine storied building for the first three floors.

Keywords: Equivalent Static Force Method, longitudinal reinforcement, seismic loading, steel ratio.

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Authors: Sandra Ondrušová, Jaroslav Polec

Abstract:

Arbitrarily shaped video objects are an important concept in modern video coding methods. The techniques presently used are not based on image elements but rather video objects having an arbitrary shape. In this paper, spatial shape error concealment techniques to be used for object-based image in error-prone environments are proposed. We consider a geometric shape representation consisting of the object boundary, which can be extracted from the α-plane. Three different approaches are used to replace a missing boundary segment: Bézier interpolation, Bézier approximation and NURBS approximation. Experimental results on object shape with different concealment difficulty demonstrate the performance of the proposed methods. Comparisons with proposed methods are also presented.

Keywords: error concealment, shape coding, object-based image, NURBS, Bézier curves.

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Authors: Hyun-Gwang Cho, Wan-Seok Yang, Su-Jin Kim, Jeong-Seok Oh, Chun-Hong Park

Abstract:

Machine tools are improved capacity remarkably during the 20th century. Improving the precision of machine tools are related with precision of products and accurate processing is always associated with the subject of interest. There are a lot of the elements that determine the precision of the machine, as guides, motors, structure, control, etc. In this paper we focused on the phenomenon that vertical movement system has worse precision than horizontal movement system even they were made up with same components. The vertical movement system needs to be studied differently from the horizontal movement system to develop its precision. The vertical movement system has load on its transfer direction and it makes the movement system weak in precision than the horizontal one. Some machines have mechanical counter balance, hydraulic or pneumatic counter balance to compensate the weight of the machine head. And there is several type of compensating the weight. It can push the machine head and also can use chain or wire lope to transfer the compensating force from counter balance to machine head. According to the type of compensating, there could be error from friction, pressure error of hydraulic or pressure control error. Also according to what to use for transferring the compensating force, transfer error of compensating force could be occur.

Keywords: Chain chordal action, counter balance, setup error, vertical positioning system.

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Authors: Kalyan Chatterjee

Abstract:

The optimal design of PI controller for Automatic Generation Control in two area is presented in this paper. The concept of Dual mode control is applied in the PI controller, such that the proportional mode is made active when the rate of change of the error is sufficiently larger than a specified limit otherwise switched to the integral mode. A digital simulation is used in conjunction with the Hooke-Jeeve’s optimization technique to determine the optimum parameters (individual gain of proportional and integral controller) of the PI controller. Integrated Square of the Error (ISE), Integrated Time multiplied by Absolute Error(ITAE) , and Integrated Absolute Error(IAE) performance indices are considered to measure the appropriateness of the designed controller.  The proposed controller are tested for a two area single nonreheat thermal system considering the practical aspect of the problem such as Deadband and Generation Rate Constraint(GRC). Simulation results show that  dual mode with optimized values of the gains improved the control performance than the commonly used Variable Structure .

Keywords: Load Frequency Control, Area Control Error(ACE), Dual Mode PI Controller, Performance Index

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Authors: Insung Jung, lockjo Koo, Gi-Nam Wang

Abstract:

The objective of this paper is to design a model of human vital sign prediction for decreasing prediction error by using two states mapping based time series neural network BP (back-propagation) model. Normally, lot of industries has been applying the neural network model by training them in a supervised manner with the error back-propagation algorithm for time series prediction systems. However, it still has a residual error between real value and prediction output. Therefore, we designed two states of neural network model for compensation of residual error which is possible to use in the prevention of sudden death and metabolic syndrome disease such as hypertension disease and obesity. We found that most of simulations cases were satisfied by the two states mapping based time series prediction model compared to normal BP. In particular, small sample size of times series were more accurate than the standard MLP model. We expect that this algorithm can be available to sudden death prevention and monitoring AGENT system in a ubiquitous homecare environment.

Keywords: Neural network, U-healthcare, prediction, timeseries, computer aided prediction.

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Authors: Mehmet Ozcan

Abstract:

This study is designed to investigate errors emerged in written texts produced by 30 Turkish EFL learners with an explanatory, and thus, qualitative perspective. Erroneous language elements were identified by the researcher first and then their grammaticality and intelligibility were checked by five native speakers of English. The analysis of the data showed that it is difficult to claim that an error stems from only one single factor since different features of an error are triggered by different factors. Our findings revealed two different types of errors: those which stem from the interference of L1 with L2 and those which are developmental ones. The former type contains more global errors whereas the errors in latter type are more intelligible.

Keywords: Contrastive analysis, Error analysis, Language acquisition, Language transfer, Turkish

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Authors: Davod Khojasteh Salkuyeh

Abstract:

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

Keywords: Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.

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Authors: Michal Martinovič, Jaroslav Polec, Kvetoslava Kotuliaková

Abstract:

In this paper we proposed multistage adaptive ARQ/HARQ/HARQ scheme. This method combines pure ARQ (Automatic Repeat reQuest) mode in low channel bit error rate and hybrid ARQ method using two different Reed-Solomon codes in middle and high error rate conditions. It follows, that our scheme has three stages. The main goal is to increase number of states in adaptive HARQ methods and be able to achieve maximum throughput for every channel bit error rate. We will prove the proposal by calculation and then with simulations in land mobile satellite channel environment. Optimization of scheme system parameters is described in order to maximize the throughput in the whole defined Signal-to- Noise Ratio (SNR) range in selected channel environment.

Keywords: Signal-to-noise ratio, throughput, forward error correction (FEC), pure and hybrid automatic repeat request (ARQ).

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Authors: D. Vidhyaprakash, A. Elango

Abstract:

In real-time applications, wheeled mobile robots are increasingly used and operated in extreme and diverse conditions traversing challenging surfaces such as a pitted, uneven terrain, natural flat, smooth terrain, as well as wet and dry surfaces. In order to accomplish such tasks, it is critical that the motion control functions without wheel slip and odometry error during the navigation of the two-wheeled mobile robot (WMR). Wheel slip and odometry error are disrupting factors on overall WMR performance in the form of deviation from desired trajectory, navigation, travel time and budgeted energy consumption. The wheeled mobile robot’s ability to operate at peak performance on various work surfaces without wheel slippage and odometry error is directly connected to four main parameters, which are the range of payload distribution, speed, wheel diameter, and wheel width. This paper analyses the effects of those parameters on overall performance and is concerned with determining the ideal range of parameters for optimum performance.

Keywords: Wheeled mobile robot (WMR), terrain, wheel slippage, odometry error, navigation.

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Authors: Man Li, Wanting Zhou, Lei Li

Abstract:

Communication stability is the primary concern of communication satellites. Communication satellites are easily affected by particle radiation to generate single event effects (SEE), which leads to soft errors (SE) of combinational logic circuit. The existing research on soft error rates (SER) of combined logic circuit is mostly based on the assumption that the logic gates being bombarded have the same pulse width. However, in the actual radiation environment, the pulse widths of the logic gates being bombarded are different due to different linear energy transfers (LET). In order to improve the accuracy of SER evaluation model, this paper proposes a soft error rates evaluation method based on LET. In this paper, we analyze the influence of LET on the pulse width of combinational logic and establish the pulse width model based on LET. Based on this model, the error rate of test circuit ISCAS’85 is calculated. Experimental results show that this model can be used for SER evaluation.

Keywords: Communication satellite, pulse width, soft error rates, linear energy transfer, LET.

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Authors: Insah Bhurtah, P. Clarel Catherine, K. M. Sunjiv Soyjaudah

Abstract:

The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the error-correcting performance keeps increasing with increasing number of iterations.

Keywords: Error-correcting codes, information theory, low-density parity-check codes, sum-product algorithm.

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Authors: M. Siosemarde, F. Kave, E. Pazira, H. Sedghi, S. J. Ghaderi

Abstract:

Salinity is a measure of the amount of salts in the water. Total Dissolved Solids (TDS) as salinity parameter are often determined using laborious and time consuming laboratory tests, but it may be more appropriate and economical to develop a method which uses a more simple soil salinity index. Because dissolved ions increase salinity as well as conductivity, the two measures are related. The aim of this research was determine of constant coefficients for predicting of Total Dissolved Solids (TDS) based on Electrical Conductivity (EC) with Statistics of Correlation coefficient, Root mean square error, Maximum error, Mean Bias error, Mean absolute error, Relative error and Coefficient of residual mass. For this purpose, two experimental areas (S1, S2) of Khuzestan province-IRAN were selected and four treatments with three replications by series of double rings were applied. The treatments were included 25cm, 50cm, 75cm and 100cm water application. The results showed the values 16.3 & 12.4 were the best constant coefficients for predicting of Total Dissolved Solids (TDS) based on EC in Pilot S1 and S2 with correlation coefficient 0.977 & 0.997 and 191.1 & 106.1 Root mean square errors (RMSE) respectively.

Keywords: constant coefficients, electrical conductivity, Khuzestan plain and total dissolved solids.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.

Keywords: bit error rate, block codes, code correlation matrix, eigenstructure, soft-decision decoding, weight vector.

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Authors: T Panigrahi, G Panda, Mulgrew

Abstract:

This paper introduces a new approach for the performance analysis of adaptive filter with error saturation nonlinearity in the presence of impulsive noise. The performance analysis of adaptive filters includes both transient analysis which shows that how fast a filter learns and the steady-state analysis gives how well a filter learns. The recursive expressions for mean-square deviation(MSD) and excess mean-square error(EMSE) are derived based on weighted energy conservation arguments which provide the transient behavior of the adaptive algorithm. The steady-state analysis for co-related input regressor data is analyzed, so this approach leads to a new performance results without restricting the input regression data to be white.

Keywords: Error saturation nonlinearity, transient analysis, impulsive noise.

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Authors: Khaled M. EL-Naggar, Khaled A. AL-Rumaih

Abstract:

This paper presents performance comparison of three estimation techniques used for peak load forecasting in power systems. The three optimum estimation techniques are, genetic algorithms (GA), least error squares (LS) and, least absolute value filtering (LAVF). The problem is formulated as an estimation problem. Different forecasting models are considered. Actual recorded data is used to perform the study. The performance of the above three optimal estimation techniques is examined. Advantages of each algorithms are reported and discussed.

Keywords: Forecasting, Least error squares, Least absolute Value, Genetic algorithms

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Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

Abstract:

In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

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Authors: Y. Bentoutou

Abstract:

Memory Errors Detection and Correction aim to secure the transaction of data between the central processing unit of a satellite onboard computer and its local memory. In this paper, the application of a double-bit error detection and correction method is described and implemented in Field Programmable Gate Array (FPGA) technology. The performance of the proposed EDAC method is measured and compared with two different EDAC devices, using the same FPGA technology. Statistical analysis of single-event upset (SEU) and multiple-bit upset (MBU) activity in commercial memories onboard the first Algerian microsatellite Alsat-1 is given.

Keywords: Error Detection and Correction, On-board computer, small satellite missions.

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Authors: R. Ebrahimpour, M. Abbasnezhad Arabi, H. Babamiri Moghaddam

Abstract:

Combining classifiers is a useful method for solving complex problems in machine learning. The ECOC (Error Correcting Output Codes) method has been widely used for designing combining classifiers with an emphasis on the diversity of classifiers. In this paper, in contrast to the standard ECOC approach in which individual classifiers are chosen homogeneously, classifiers are selected according to the complexity of the corresponding binary problem. We use SATIMAGE database (containing 6 classes) for our experiments. The recognition error rate in our proposed method is %10.37 which indicates a considerable improvement in comparison with the conventional ECOC and stack generalization methods.

Keywords: Error correcting output code, combining classifiers, neural networks.

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Authors: Parit Kanjanavirojkul, Kiatwarakorn Keeratishananond, Prapun Suksompong

Abstract:

We study the performance of compressed beamforming weights feedback technique in generalized triangular decomposition (GTD) based MIMO system. GTD is a beamforming technique that enjoys QoS flexibility. The technique, however, will perform at its optimum only when the full knowledge of channel state information (CSI) is available at the transmitter. This would be impossible in the real system, where there are channel estimation error and limited feedback. We suggest a way to implement the quantized beamforming weights feedback, which can significantly reduce the feedback data, on GTD-based MIMO system and investigate the performance of the system. Interestingly, we found that compressed beamforming weights feedback does not degrade the BER performance of the system at low input power, while the channel estimation error and quantization do. For comparison, GTD is more sensitive to compression and quantization, while SVD is more sensitive to the channel estimation error. We also explore the performance of GTDbased MU-MIMO system, and find that the BER performance starts to degrade largely at around -20 dB channel estimation error.

Keywords: MIMO, MU-MIMO, GTD, Imperfect CSI.

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Authors: Zainab Almukhtar, Adel Merabet

Abstract:

In this paper, a method for maximum power point tracking of a photovoltaic energy conversion system is presented. This method is based on using the difference between the power from the solar panel and an estimated power value to control the DC-DC converter of the photovoltaic system. The difference is continuously compared with a preset error permitted value. If the power difference is more than the error, the estimated power is multiplied by a factor and the operation is repeated until the difference is less or equal to the threshold error. The difference in power will be used to trigger a DC-DC boost converter in order to raise the voltage to where the maximum power point is achieved. The proposed method was experimentally verified through a PV energy conversion system driven by the OPAL-RT real time controller. The method was tested on varying radiation conditions and load requirements, and the Photovoltaic Panel was operated at its maximum power in different conditions of irradiation.

Keywords: Control system, power error, solar panel, MPPT.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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