Search results for: Integral transform

Authors: Fei Long Wei, Hua Yang, Hai Tao Zhang, Zhou Ping Yin

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment.

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: H. Kelkoul, Y. Zaz

Abstract:

Nowadays, the vigorous popularity of video processing techniques has resulted in an explosive growth of multimedia data illegal use. So, watermarking security has received much more attention. The purpose of this paper is to explore some watermarking techniques in order to observe their specificities and select the finest methods to apply in digital cinema domain against movie piracy by creating an invisible watermark that includes the date, time and the place where the hacking was done. We have studied three principal watermarking techniques in the frequency domain: Spread spectrum, Wavelet transform domain and finally the digital cinema watermarking transform domain. In this paper, a detailed technique is presented where embedding is performed using direct sequence spread spectrum technique in DWT transform domain. Experiment results shows that the algorithm provides high robustness and good imperceptibility.

Keywords: Digital cinema, watermarking, wavelet, spread spectrum, JPEG2000.

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a  priori information of the uncertainties is not available. For such  systems, we assume that the upper bound of the uncertainties is  represented as a Fredholm integral equation of the first kind and we  propose an adaptation law that is capable of estimating the upper  bound and design a continuous robust control which renders nonlinear  uncertain systems ultimately bounded.

 

Keywords: Adaptive Control, Estimation, Fredholm Integral, Uncertain System.

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Authors: Chun-Yao Lee, Yao-chen Lee

Abstract:

This paper describes a method of signal process applied on an end effects of Hilbert-Huang transform (HHT) to provide an improvement in the reality of spectrum. The method is based on back-propagation network (BPN). To improve the effect, the end extension of the original signal is obtained by back-propagation network. A full waveform including origin and its extension is decomposed by using empirical mode decomposition (EMD) to obtain intrinsic mode functions (IMFs) of the waveform. Then, the Hilbert transform (HT) is applied to the IMFs to obtain the Hilbert spectrum of the waveform. As a result, the method is superiority of the processing of end effect of HHT to obtain the real frequency spectrum of signals.

Keywords: Neural network, back-propagation network, Hilbert-Huang transform

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Authors: Rafiullah Chamlawi, Asifullah Khan, Adnan Idris, Zahid Munir

Abstract:

Authentication of multimedia contents has gained much attention in recent times. In this paper, we propose a secure semi-fragile watermarking, with a choice of two watermarks to be embedded. This technique operates in integer wavelet domain and makes use of semi fragile watermarks for achieving better robustness. A self-recovering algorithm is employed, that hides the image digest into some Wavelet subbands to detect possible malevolent object manipulation undergone by the image (object replacing and/or deletion). The Semi-fragility makes the scheme tolerant for JPEG lossy compression as low as quality of 70%, and locate the tempered area accurately. In addition, the system ensures more security because the embedded watermarks are protected with private keys. The computational complexity is reduced using parameterized integer wavelet transform. Experimental results show that the proposed scheme guarantees the safety of watermark, image recovery and location of the tempered area accurately.

Keywords: Integer Wavelet Transform (IWT), Discrete Cosine Transform (DCT), JPEG Compression, Authentication and Self- Recovery.

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Authors: P. S. Gomathi, B. Kalaavathi

Abstract:

The process in which the complementary information from multiple images is integrated to provide composite image that contains more information than the original input images is called image fusion. Medical image fusion provides useful information from multimodality medical images that provides additional information to the doctor for diagnosis of diseases in a better way. This paper represents the wavelet based medical image fusion algorithm on different multimodality medical images. In order to fuse the medical images, images are decomposed using Redundant Wavelet Transform (RWT). The high frequency coefficients are convolved with morphological operator followed by the maximum-selection (MS) rule. The low frequency coefficients are processed by MS rule. The reconstructed image is obtained by inverse RWT. The quantitative measures which includes Mean, Standard Deviation, Average Gradient, Spatial frequency, Edge based Similarity Measures are considered for evaluating the fused images. The performance of this proposed method is compared with Pixel averaging, PCA, and DWT fusion methods. When compared with conventional methods, the proposed framework provides better performance for analysis of multimodality medical images.

Keywords: Discrete Wavelet Transform (DWT), Image Fusion, Morphological Processing, Redundant Wavelet Transform (RWT).

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Authors: Oğuzhan Urhan

Abstract:

In this paper, an improved motion estimation (ME) approach based on weighted constrained one-bit transform is proposed for block-based ME employed in video encoders. Binary ME approaches utilize low bit-depth representation of the original image frames with a Boolean exclusive-OR based hardware efficient matching criterion to decrease computational burden of the ME stage. Weighted constrained one-bit transform (WC‑1BT) based approach improves the performance of conventional C-1BT based ME employing 2-bit depth constraint mask instead of a 1-bit depth mask. In this work, the range of constraint mask is further extended to increase ME performance of WC-1BT approach. Experiments reveal that the proposed method provides better ME accuracy compared existing similar ME methods in the literature.

Keywords: Fast motion estimation, low-complexity motion estimation, video coding.

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Authors: Liang-Ta Cheng, Ching-Yu Yang

Abstract:

Based on fast discrete cosine transform (FDCT), the authors present a high capacity and high perceived quality method for electrocardiogram (ECG) signal. By using a simple adjusting policy to the 1-dimentional (1-D) DCT coefficients, a large volume of secret message can be effectively embedded in an ECG host signal and be successfully extracted at the intended receiver. Simulations confirmed that the resulting perceived quality is good, while the hiding capability of the proposed method significantly outperforms that of existing techniques. In addition, our proposed method has a certain degree of robustness. Since the computational complexity is low, it is feasible for our method being employed in real-time applications.

Keywords: Data hiding, ECG steganography, fast discrete cosine transform, 1-D DCT bundle, real-time applications.

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Authors: Shang-Lin Hsieh, Lung-Yao Hsu, I-Ju Tsai

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This paper proposes a copyright protection scheme for color images using secret sharing and wavelet transform. The scheme contains two phases: the share image generation phase and the watermark retrieval phase. In the generation phase, the proposed scheme first converts the image into the YCbCr color space and creates a special sampling plane from the color space. Next, the scheme extracts the features from the sampling plane using the discrete wavelet transform. Then, the scheme employs the features and the watermark to generate a principal share image. In the retrieval phase, an expanded watermark is first reconstructed using the features of the suspect image and the principal share image. Next, the scheme reduces the additional noise to obtain the recovered watermark, which is then verified against the original watermark to examine the copyright. The experimental results show that the proposed scheme can resist several attacks such as JPEG compression, blurring, sharpening, noise addition, and cropping. The accuracy rates are all higher than 97%.

Keywords: Color image, copyright protection, discrete wavelet transform, secret sharing, watermarking.

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Authors: Sunil Dehipawala, Aregama Sirisumana, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden T. Cheung

Abstract:

The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, Fourier Transform, metalloproteins, XANES.

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Authors: Liu Dan, Wang Xue, Wang Guiqin, Qian Zhihong

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The burst noise is a kind of noises that are destructive and frequently found in semiconductor devices and ICs, yet detecting and removing the noise has proved challenging for IC designers or users. According to the properties of burst noise, a methodological approach is presented (proposed) in the paper, by which the burst noise can be analysed and detected in time domain. In this paper, principles and properties of burst noise are expounded first, Afterwards, feasibility (viable) of burst noise detection by means of wavelet transform in the time domain is corroborated in the paper, and the multi-resolution characters of Gaussian noise, burst noise and blurred burst noise are discussed in details by computer emulation. Furthermore, the practical method to decide parameters of wavelet transform is acquired through a great deal of experiment and data statistics. The methodology may yield an expectation in a wide variety of applications.

Keywords: Burst noise, detection, wavelet transform

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

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This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: M.Ghazvini, S. A. Monadjemi, N. Movahhedinia, K. Jamshidi

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In this article, a method has been offered to classify normal and defective tiles using wavelet transform and artificial neural networks. The proposed algorithm calculates max and min medians as well as the standard deviation and average of detail images obtained from wavelet filters, then comes by feature vectors and attempts to classify the given tile using a Perceptron neural network with a single hidden layer. In this study along with the proposal of using median of optimum points as the basic feature and its comparison with the rest of the statistical features in the wavelet field, the relational advantages of Haar wavelet is investigated. This method has been experimented on a number of various tile designs and in average, it has been valid for over 90% of the cases. Amongst the other advantages, high speed and low calculating load are prominent.

Keywords: Defect detection, tile and ceramic quality inspection, wavelet transform, classification, neural networks, statistical features.

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Authors: Yu Bin, Zhang Yan

Abstract:

The prediction of transmembrane helical segments (TMHs) in membrane proteins is an important field in the bioinformatics research. In this paper, a new method based on discrete wavelet transform (DWT) has been developed to predict the number and location of TMHs in membrane proteins. PDB coded as 1KQG was chosen as an example to describe the prediction of the number and location of TMHs in membrane proteins by using this method. To access the effect of the method, 80 proteins with known 3D-structure from Mptopo database are chosen at random as the test objects (including 325 TMHs), 308 of which can be predicted accurately, the average predicted accuracy is 96.3%. In addition, the above 80 membrane proteins are divided into 13 groups according to their function and type. In particular, the results of the prediction of TMHs of the 13 groups are satisfying.

Keywords: discrete wavelet transform, hydrophobicity, membrane protein, transmembrane helical segments

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Ali Essam El Shazly

Abstract:

The social logic of 'Sequina' slum area in Alexandria details the integral measure of space syntax at the room-level of twenty-building samples. The essence of spatial structure integrates the central 'visitor' domain with the 'living' frontage of the 'children' zone against the segregated privacy of the opposite 'parent' depth. Meanwhile, the multifunctioning of shallow rooms optimizes the integral 'visitor' structure through graph and visibility dimensions in contrast to the 'inhabitant' structure of graph-tails out of sight. Common theme of the layout integrity increases in compensation to the decrease of room visibility. Despite the 'pheno-type' of collective integration, the individual layouts observe 'geno-type' structure of spatial diversity per room adjoins. In this regard, the layout integrity alternates the cross-correlation of the 'kitchen & living' rooms with the 'inhabitant & visitor' domains of 'motherhood' dynamic structure. Moreover, the added 'grandparent' restructures the integral measure to become the deepest space, but opens to the 'living' of 'household' integrity. Some isomorphic layouts change the integral structure just through the 'balcony' extension of access, visual or ignored 'ringiness' of space syntax. However, the most integrated or segregated layouts invert the 'geno-type' into a shallow 'inhabitant' centrality versus the remote 'visitor' structure. Overview of the multivariate social logic of spatial integrity could never clarify without the micro-data analysis.

Keywords: Alexandria, Sequina slum, spatial integration, space syntax.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

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This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: S. Sabbour, H. Lasi, P. von Tessin

Abstract:

The purpose of this study is two-fold. First, it attempts to explore potential opportunities for utilizing visual interactive simulations along with Business Intelligence (BI) as a decision support tool for strategic decision making. Second, it tries to figure out the essential top-level managerial requirements that would transform strategic decision simulation into an integral component of BI systems. The domain of particular interest was the application of visual interactive simulation capabilities in the field of supply chains. A qualitative exploratory method was applied, through the use of interviews with two leading companies. The collected data was then analysed to demonstrate the difference between the literature perspective and the practical managerial perspective on the issue. The results of the study suggest that although the use of simulation particularly in managing supply chains is very evident in literature, yet, in practice such utilization is still in its infancy, particularly regarding strategic decisions. Based on the insights a prototype of a simulation based BI-solution-extension was developed and evaluated.

Keywords: Business Intelligence, decision support, strategic decisions, simulation, SCM.

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Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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Authors: C. Sinescu, M. Negrutiu, M. Romînu, C. Haiduc, E. Petrescu, M. Leretter, A.G. Podoleanu

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Optical Coherence Tomography (OCT) combined with the Confocal Microscopy, as a noninvasive method, permits the determinations of materials defects in the ceramic layers depth. For this study 256 anterior and posterior metal and integral ceramic fixed partial dentures were used, made with Empress (Ivoclar), Wollceram and CAD/CAM (Wieland) technology. For each investigate area 350 slices were obtain and a 3D reconstruction was perform from each stuck. The Optical Coherent Tomography, as a noninvasive method, can be used as a control technique in integral ceramic technology, before placing those fixed partial dentures in the oral cavity. The purpose of this study is to evaluate the capability of En face Optical Coherence Tomography (OCT) combined with a fluorescent method in detection and analysis of possible material defects in metalceramic and integral ceramic fixed partial dentures. As a conclusion, it is important to have a non invasive method to investigate fixed partial prostheses before their insertion in the oral cavity in order to satisfy the high stress requirements and the esthetic function.

Keywords: Ceramic Fixed Partial Dentures, Material Defects, En face Optical Coherence Tomography, Fluorescence.

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Authors: Yang Zhong, Mei-jie Xu

Abstract:

To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. So the dynamic change of parameter in asphalt mixture should be taken into consideration when theoretical analysis is taken out.

Keywords: Asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress.

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Authors: Juyoung Kim, Taegeun Park

Abstract:

In this paper, we propose a fully-utilized, block-based 2D DWT (discrete wavelet transform) architecture, which consists of four 1D DWT filters with two-channel QMF lattice structure. The proposed architecture requires about 2MN-3N registers to save the intermediate results for higher level decomposition, where M and N stand for the filter length and the row width of the image respectively. Furthermore, the proposed 2D DWT processes in horizontal and vertical directions simultaneously without an idle period, so that it computes the DWT for an N×N image in a period of N2(1-2-2J)/3. Compared to the existing approaches, the proposed architecture shows 100% of hardware utilization and high throughput rates. To mitigate the long critical path delay due to the cascaded lattices, we can apply the pipeline technique with four stages, while retaining 100% of hardware utilization. The proposed architecture can be applied in real-time video signal processing.

Keywords: discrete wavelet transform, VLSI architecture, QMF lattice filter, pipelining.

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Authors: K. Sakthivel, R. Nallusamy, C. Kavitha

Abstract:

The system is designed to show images which are related to the query image. Extracting color, texture, and shape features from an image plays a vital role in content-based image retrieval (CBIR). Initially RGB image is converted into HSV color space due to its perceptual uniformity. From the HSV image, Color features are extracted using block color histogram, texture features using Haar transform and shape feature using Fuzzy C-means Algorithm. Then, the characteristics of the global and local color histogram, texture features through co-occurrence matrix and Haar wavelet transform and shape are compared and analyzed for CBIR. Finally, the best method of each feature is fused during similarity measure to improve image retrieval effectiveness and accuracy.

Keywords: Color Histogram, Haar Wavelet Transform, Fuzzy C-means, Co-occurrence matrix; Similarity measure.

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

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This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: Object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation.

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Authors: G. Van Dijck, M. M. Van Hulle, M. Wevers

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A genetic algorithm (GA) based feature subset selection algorithm is proposed in which the correlation structure of the features is exploited. The subset of features is validated according to the classification performance. Features derived from the continuous wavelet transform are potentially strongly correlated. GA-s that do not take the correlation structure of features into account are inefficient. The proposed algorithm forms clusters of correlated features and searches for a good candidate set of clusters. Secondly a search within the clusters is performed. Different simulations of the algorithm on a real-case data set with strong correlations between features show the increased classification performance. Comparison is performed with a standard GA without use of the correlation structure.

Keywords: Classification, genetic algorithm, hierarchicalagglomerative clustering, wavelet transform.

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Authors: Bahi brahim, El hassane Ibn Elhaj, Driss Aboutajdine

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In this paper we propose a Multiple Description Image Coding(MDIC) scheme to generate two compressed and balanced rates descriptions in the wavelet domain (Daubechies biorthogonal (9, 7) wavelet) using pairwise correlating transform optimal and application method for Generalized Multiple Description Coding (GMDC) to image coding in the wavelet domain. The GMDC produces statistically correlated streams such that lost streams can be estimated from the received data. Our performance test shown that the proposed method gives more improvement and good quality of the reconstructed image when the wavelet coefficients are normalized by Gaussian Scale Mixture (GSM) model then the Gaussian one ,.

Keywords: Multiple description coding (MDC), gaussian scale mixture (GSM) model, joint source-channel coding, pairwise correlating transform, GMDCT.

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper represents performance of particle swarm optimisation (PSO) algorithm based integral (I) controller and proportional-integral controller (PI) for interconnected hydro-thermal automatic generation control (AGC) with generation rate constraint (GRC) and Thyristor controlled phase shifter (TCPS) in series with tie line. The control strategy of TCPS provides active control of system frequency. Conventional objective function integral square error (ISE) and another objective function considering square of derivative of change in frequencies of both areas and change in tie line power are considered. The aim of designing the objective function is to suppress oscillation in frequency deviations and change in tie line power oscillation. The controller parameters are searched by PSO algorithm by minimising the objective functions. The dynamic performance of the controllers I and PI, for both the objective functions, are compared with conventionally optimized I controller.

Keywords: Automatic generation control (AGC), Generation rate constraint (GRC), Thyristor control phase shifter (TCPS), Particle swarm optimization (PSO).

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai

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One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

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