Search results for: Adaptive Fourier decomposition
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1357

Search results for: Adaptive Fourier decomposition

1327 Energy Efficiency of Adaptive-Rate Medium Access Control Protocols for Sensor Networks

Authors: Rooholah Hasanizadeh, Saadan Zokaei

Abstract:

Energy efficient protocol design is the aim of current researches in the area of sensor networks where limited power resources impose energy conservation considerations. In this paper we care for Medium Access Control (MAC) protocols and after an extensive literature review, two adaptive schemes are discussed. Of them, adaptive-rate MACs which were introduced for throughput enhancement show the potency to save energy, even more than adaptive-power schemes. Then we propose an allocation algorithm for getting accurate and reliable results. Through a simulation study we validated our claim and showed the power saving of adaptive-rate protocols.

Keywords: Adaptive-rate, adaptive-power, MAC protocol, energy efficiency, sensor networks.

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1326 Fault Detection and Diagnosis of Broken Bar Problem in Induction Motors Base Wavelet Analysis and EMD Method: Case Study of Mobarakeh Steel Company in Iran

Authors: M. Ahmadi, M. Kafil, H. Ebrahimi

Abstract:

Nowadays, induction motors have a significant role in industries. Condition monitoring (CM) of this equipment has gained a remarkable importance during recent years due to huge production losses, substantial imposed costs and increases in vulnerability, risk, and uncertainty levels. Motor current signature analysis (MCSA) is one of the most important techniques in CM. This method can be used for rotor broken bars detection. Signal processing methods such as Fast Fourier transformation (FFT), Wavelet transformation and Empirical Mode Decomposition (EMD) are used for analyzing MCSA output data. In this study, these signal processing methods are used for broken bar problem detection of Mobarakeh steel company induction motors. Based on wavelet transformation method, an index for fault detection, CF, is introduced which is the variation of maximum to the mean of wavelet transformation coefficients. We find that, in the broken bar condition, the amount of CF factor is greater than the healthy condition. Based on EMD method, the energy of intrinsic mode functions (IMF) is calculated and finds that when motor bars become broken the energy of IMFs increases.

Keywords: Broken bar, condition monitoring, diagnostics, empirical mode decomposition, Fourier transform, wavelet transform.

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1325 Time-Derivative Estimation of Noisy Movie Data using Adaptive Control Theory

Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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1324 Information Modelling for Adaptive Composition in Collaborative Work Environment

Authors: Sang Keun Rhee, Hyojeong Jin, Jihye Lee, Misoo Kwon, Myon-Woong Park, Sungdo Ha

Abstract:

Extensive information is required within a R&D environment, and a considerable amount of time and efforts are being spent on finding the necessary information. An adaptive information providing system would be beneficial to the environment, and a conceptual model of the resources, people and context is mandatory for developing such applications. In this paper, an information model on various contexts and resources is proposed which provides the possibility of effective applications for use in adaptive information systems within a R&D project and meeting environment.

Keywords: Adaptive Hypermedia, Adaptive System, ContextAwareness, Information Model, Information System, Personalisation.

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1323 Model Reference Adaptive Control and LQR Control for Quadrotor with Parametric Uncertainties

Authors: Alia Abdul Ghaffar, Tom Richardson

Abstract:

A model reference adaptive control and a fixed gain LQR control were implemented in the height controller of a quadrotor that has parametric uncertainties due to the act of picking up an object of unknown dimension and mass. It is shown that an adaptive controller, unlike the fixed gain controller, is capable of ensuring a stable tracking performance under such condition, although adaptive control suffers from several limitations. The combination of both adaptive and fixed gain control in the controller architecture can result in an enhanced tracking performance in the presence parametric uncertainties.

Keywords: UAV, quadrotor, model reference adaptive control, LQR control.

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1322 A Novel Instantaneous Frequency Computation Approach for Empirical Mode Decomposition

Authors: Liming Zhang

Abstract:

This paper introduces a new instantaneous frequency computation approach  -Counting Instantaneous Frequency for a general class of signals called simple waves. The classsimple wave contains a wide range of continuous signals for which the concept instantaneous frequency has a perfect physical sense. The concept of  -Counting Instantaneous Frequency also applies to all the discrete data. For all the simple wave signals and the discrete data, -Counting instantaneous frequency can be computed directly without signal decomposition process. The intrinsic mode functions obtained through empirical mode decomposition belongs to simple wave. So  -Counting instantaneous frequency can be used together with empirical mode decomposition.

Keywords: Instantaneous frequency, empirical mode decomposition, intrinsic mode function.

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1321 Blind Identification and Equalization of CDMA Signals Using the Levenvberg-Marquardt Algorithm

Authors: Mohammed Boutalline, Imad Badi, Belaid Bouikhalene, Said Safi

Abstract:

In this paper we describe the Levenvberg-Marquardt (LM) algorithm for identification and equalization of CDMA signals received by an antenna array in communication channels. The synthesis explains the digital separation and equalization of signals after propagation through multipath generating intersymbol interference (ISI). Exploiting discrete data transmitted and three diversities induced at the reception, the problem can be composed by the Block Component Decomposition (BCD) of a tensor of order 3 which is a new tensor decomposition generalizing the PARAFAC decomposition. We optimize the BCD decomposition by Levenvberg-Marquardt method gives encouraging results compared to classical alternating least squares algorithm (ALS). In the equalization part, we use the Minimum Mean Square Error (MMSE) to perform the presented method. The simulation results using the LM algorithm are important.

Keywords: Identification and equalization, communication channel, Levenvberg-Marquardt, tensor decomposition

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1320 Application of Adaptive Genetic Algorithm in Function Optimization

Authors: Panpan Xu, Shulin Sui

Abstract:

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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1319 Adaptive Kernel Principal Analysis for Online Feature Extraction

Authors: Mingtao Ding, Zheng Tian, Haixia Xu

Abstract:

The batch nature limits the standard kernel principal component analysis (KPCA) methods in numerous applications, especially for dynamic or large-scale data. In this paper, an efficient adaptive approach is presented for online extraction of the kernel principal components (KPC). The contribution of this paper may be divided into two parts. First, kernel covariance matrix is correctly updated to adapt to the changing characteristics of data. Second, KPC are recursively formulated to overcome the batch nature of standard KPCA.This formulation is derived from the recursive eigen-decomposition of kernel covariance matrix and indicates the KPC variation caused by the new data. The proposed method not only alleviates sub-optimality of the KPCA method for non-stationary data, but also maintains constant update speed and memory usage as the data-size increases. Experiments for simulation data and real applications demonstrate that our approach yields improvements in terms of both computational speed and approximation accuracy.

Keywords: adaptive method, kernel principal component analysis, online extraction, recursive algorithm

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1318 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion

Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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1317 Stereotype Student Model for an Adaptive e-Learning System

Authors: Ani Grubišić, Slavomir Stankov, Branko Žitko

Abstract:

This paper describes a concept of stereotype student model in adaptive knowledge acquisition e-learning system. Defined knowledge stereotypes are based on student's proficiency level and on Bloom's knowledge taxonomy. The teacher module is responsible for the whole adaptivity process: the automatic generation of courseware elements, their dynamic selection and sorting, as well as their adaptive presentation using templates for statements and questions. The adaptation of courseware is realized according to student-s knowledge stereotype.

Keywords: Adaptive e-learning systems, adaptive courseware, stereotypes, Bloom's knowledge taxonomy.

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1316 Helicopter Adaptive Control with Parameter Estimation Based on Feedback Linearization

Authors: A. R. Nemati, M. Haddad Zarif, M. M. Fateh

Abstract:

This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback linearization technique and adaptive method. The controller parameters are unknown where an adaptive control law aims to drive them towards their ideal values for providing perfect model matching between the reference model and the closed-loop plant model. The converged parameters of controller would then provide good estimates for the unknown plant parameters.

Keywords: Adaptive control, helicopter, feedback linearization, nonlinear control.

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1315 Performance Comparisons between PID and Adaptive PID Controllers for Travel Angle Control of a Bench-Top Helicopter

Authors: H. Mansor, S. B. Mohd-Noor, T. S. Gunawan, S. Khan, N. I. Othman, N. Tazali, R. B. Islam

Abstract:

This paper provides a comparative study on the performances of standard PID and adaptive PID controllers tested on travel angle of a 3-Degree-of-Freedom (3-DOF) Quanser bench-top helicopter. Quanser, a well-known manufacturer of educational bench-top helicopter has developed Proportional Integration Derivative (PID) controller with Linear Quadratic Regulator (LQR) for all travel, pitch and yaw angle of the bench-top helicopter. The performance of the PID controller is relatively good; however, its performance could also be improved if the controller is combined with adaptive element. The objective of this research is to design adaptive PID controller and then compare the performances of the adaptive PID with the standard PID. The controller design and test is focused on travel angle control only. Adaptive method used in this project is self-tuning controller, which controller’s parameters are updated online. Two adaptive algorithms those are pole-placement and deadbeat have been chosen as the method to achieve optimal controller’s parameters. Performance comparisons have shown that the adaptive (deadbeat) PID controller has produced more desirable performance compared to standard PID and adaptive (poleplacement). The adaptive (deadbeat) PID controller attained very fast settling time (5 seconds) and very small percentage of overshoot (5% to 7.5%) for 10° to 30° step change of travel angle.

Keywords: Adaptive control, bench-top helicopter, deadbeat, pole-placement, self-tuning control.

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1314 A Decomposition Method for the Bipartite Separability of Bell Diagonal States

Authors: Wei-Chih Su, Kuan-Peng Chen, Ming-Chung Tsai, Zheng-Yao Su

Abstract:

A new decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic inequality of the coefficients of a given Bell diagonal states and can be derived via a simple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension.

Keywords: decomposition, bipartite separability, Bell diagonal states.

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1313 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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1312 Laplace Adomian Decomposition Method Applied to a Two-Dimensional Viscous Flow with Shrinking Sheet

Authors: M. A. Koroma, S. Widatalla, A. F. Kamara, C. Zhang

Abstract:

Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet.

Keywords: Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.

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1311 Change Detection and Non Stationary Signals Tracking by Adaptive Filtering

Authors: Mounira RouaÐùnia, Noureddine Doghmane

Abstract:

In this paper we consider the problem of change detection and non stationary signals tracking. Using parametric estimation of signals based on least square lattice adaptive filters we consider for change detection statistical parametric methods using likelihood ratio and hypothesis tests. In order to track signals dynamics, we introduce a compensation procedure in the adaptive estimation. This will improve the adaptive estimation performances and fasten it-s convergence after changes detection.

Keywords: Change detection, Hypothesis test, likelihood ratioleast square lattice adaptive filters.

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1310 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators

Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

Abstract:

Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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1309 ECG Analysis using Nature Inspired Algorithm

Authors: A.Sankara Subramanian, G.Gurusamy, G.Selvakumar, P.Gnanasekar, A.Nagappan

Abstract:

This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the ECG signal and recognition of three types of Ventricular Arrhythmias using neural networks. A set of Discrete Wavelet Transform (DWT) coefficients, which contain the maximum information about the arrhythmias, is selected from the wavelet decomposition. After that a novel clustering algorithm based on nature inspired algorithm (Ant Colony Optimization) is developed for classifying arrhythmia types. The algorithm is applied on the ECG registrations from the MIT-BIH arrhythmia and malignant ventricular arrhythmia databases. We applied Daubechies 4 wavelet in our algorithm. The wavelet decomposition enabled us to perform the task efficiently and produced reliable results.

Keywords: Daubechies 4 Wavelet, ECG, Nature inspired algorithm, Ventricular Arrhythmias, Wavelet Decomposition.

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1308 Border Limited Adaptive Subdivision Based On Triangle Meshes

Authors: Pichayut Peerasathien, Hiroshi Nagahashi

Abstract:

Subdivision is a method to create a smooth surface from a coarse mesh by subdividing the entire mesh. The conventional ways to compute and render surfaces are inconvenient both in terms of memory and computational time as the number of meshes will increase exponentially. An adaptive subdivision is the way to reduce the computational time and memory by subdividing only certain selected areas. In this paper, a new adaptive subdivision method for triangle meshes is introduced. This method defines a new adaptive subdivision rules by considering the properties of each triangle's neighbors and is embedded in a traditional Loop's subdivision. It prevents some undesirable side effects that appear in the conventional adaptive ways. Models that were subdivided by our method are compared with other adaptive subdivision methods

Keywords: Subdivision, loop subdivision, handle cracks, smooth surface.

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1307 Mean-Square Performance of Adaptive Filter Algorithms in Nonstationary Environments

Authors: Mohammad Shams Esfand Abadi, John Hakon Husøy

Abstract:

Employing a recently introduced unified adaptive filter theory, we show how the performance of a large number of important adaptive filter algorithms can be predicted within a general framework in nonstationary environment. This approach is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. This general performance analysis can be used to evaluate the mean square performance of the Least Mean Square (LMS) algorithm, its normalized version (NLMS), the family of Affine Projection Algorithms (APA), the Recursive Least Squares (RLS), the Data-Reusing LMS (DR-LMS), its normalized version (NDR-LMS), the Block Least Mean Squares (BLMS), the Block Normalized LMS (BNLMS), the Transform Domain Adaptive Filters (TDAF) and the Subband Adaptive Filters (SAF) in nonstationary environment. Also, we establish the general expressions for the steady-state excess mean square in this environment for all these adaptive algorithms. Finally, we demonstrate through simulations that these results are useful in predicting the adaptive filter performance.

Keywords: Adaptive filter, general framework, energy conservation, mean-square performance, nonstationary environment.

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1306 MRI Reconstruction Using Discrete Fourier Transform: A tutorial

Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

Abstract:

The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.

Keywords: Discrete Fourier Transform (DFT), K-space Data, Magnetic Resonance (MR), Spin, Windows.

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1305 Cognitive Emotion Regulation in Children Is Attributable to Parenting Style, Not to Family Type and Child’s Gender

Authors: AKM Rezaul Karim, Tania Sharafat, Abu Yusuf Mahmud

Abstract:

The study aimed to investigate whether cognitive emotion regulation in children varies with parenting style, family type and gender. Toward this end, cognitive emotion regulation and perceived parenting style of 206 school children were measured. Standard regression analyses of data revealed that the models were significant and explained 17.3% of the variance in adaptive emotion regulation (Adjusted =0.173; F=9.579, p<.001), and 7.1% of the variance in less adaptive emotion regulation (Adjusted =.071, F=4.135, p=.001). Results showed that children’s cognitive emotion regulation is functionally associated with parenting style, but not with family type and their gender. Amongst three types of parenting, authoritative parenting was the strongest predictor of the overall adaptive emotion regulation while authoritarian parenting was the strongest predictor of the overall less adaptive emotion regulation. Permissive parenting has impact neither on adaptive nor on less adaptive emotion regulation. The findings would have important implications for parents, caregivers, child psychologists, and other professionals working with children or adolescents.

Keywords: Cognitive Emotion Regulation, Adaptive, Less Adaptive, Parenting Style, Family Type.

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1304 Texture Characterization Based on a Chandrasekhar Fast Adaptive Filter

Authors: Mounir Sayadi, Farhat Fnaiech

Abstract:

In the framework of adaptive parametric modelling of images, we propose in this paper a new technique based on the Chandrasekhar fast adaptive filter for texture characterization. An Auto-Regressive (AR) linear model of texture is obtained by scanning the image row by row and modelling this data with an adaptive Chandrasekhar linear filter. The characterization efficiency of the obtained model is compared with the model adapted with the Least Mean Square (LMS) 2-D adaptive algorithm and with the cooccurrence method features. The comparison criteria is based on the computation of a characterization degree using the ratio of "betweenclass" variances with respect to "within-class" variances of the estimated coefficients. Extensive experiments show that the coefficients estimated by the use of Chandrasekhar adaptive filter give better results in texture discrimination than those estimated by other algorithms, even in a noisy context.

Keywords: Texture analysis, statistical features, adaptive filters, Chandrasekhar algorithm.

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1303 Robust Adaptive Vibration Control with Application to a Robot Beam

Authors: J. Fei

Abstract:

This paper presents the adaptive control scheme with sliding mode compensator for vibration control problem in the presence of disturbance. The dynamic model of the flexible cantilever beam using finite element modeling is derived. The adaptive control with sliding mode compensator using output feedback for output tracking is developed to reject the external disturbance, and to improve the tracking performance. Satisfactory simulation results verify that the effectiveness of adaptive control scheme with sliding mode compensator.

Keywords: finite element model, adaptive control, sliding modecontrol, vibration suppression

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1302 Impulsive Noise-Resilient Subband Adaptive Filter

Authors: Young-Seok Choi

Abstract:

We present a new subband adaptive filter (R-SAF) which is robust against impulsive noise in system identification. To address the vulnerability of adaptive filters based on the L2-norm optimization criterion against impulsive noise, the R-SAF comes from the L1-norm optimization criterion with a constraint on the energy of the weight update. Minimizing L1-norm of the a posteriori error in each subband with a constraint on minimum disturbance gives rise to the robustness against the impulsive noise and the capable convergence performance. Experimental results clearly demonstrate that the proposed R-SAF outperforms the classical adaptive filtering algorithms when impulsive noise as well as background noise exist.

Keywords: Subband adaptive filter, L1-norm, system identification, robustness, impulsive interference.

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1301 A Reconfigurable Processing Element Implementation for Matrix Inversion Using Cholesky Decomposition

Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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1300 Adaptive Thermal Comfort Model for Air-Conditioned Lecture Halls in Malaysia

Authors: B. T. Chew, S. N. Kazi, A. Amiri

Abstract:

This paper presents an adaptive thermal comfort model study in the tropical country of Malaysia. A number of researchers have been interested in applying the adaptive thermal comfort model to different climates throughout the world, but so far no study has been performed in Malaysia. For the use as a thermal comfort model, which better applies to hot and humid climates, the adaptive thermal comfort model was developed as part of this research by using the collected results from a large field study in six lecture halls with 178 students. The relationship between the operative temperature and behavioral adaptations was determined. In the developed adaptive model, the acceptable indoor neutral temperatures lay within the range of 23.9-26.0C, with outdoor temperatures ranging between 27.0-34.6C. The most comfortable temperature for students in lecture hall was 25.7C.

Keywords: Hot and humid, Lecture halls, Neutral temperature, Adaptive thermal comfort model.

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1299 Designing Intelligent Adaptive Controller for Nonlinear Pendulum Dynamical System

Authors: R. Ghasemi, M. R. Rahimi Khoygani

Abstract:

This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: Adaptive Neural Controller, Nonlinear Dynamical, Neural Network, RBF, Driven Pendulum, Position Control.

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1298 Design of Adaptive Sliding Mode Controller for Robotic Manipulators Tracking Control

Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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