Search results for: Optimization method

Authors: Seul-Kee Kim, Chi-Seung Lee, Myung-Hyun Kim, Jae-Myung Lee

Abstract:

In this study, the hydrogen transport phenomenon was numerically evaluated by using hydrogen-enhanced localized plasticity (HELP) mechanisms. Two dominant governing equations, namely, the hydrogen transport model and the elasto-plastic model, were introduced. In addition, the implicitly formulated equations of the governing equations were implemented into ABAQUS UMAT user-defined subroutines. The simulation results were compared to published results to validate the proposed method.

Keywords: Hydrogen-enhanced localized plasticity (HELP), Hydrogen embrittlement, Hydrogen transport analysis, ABAQUS UMAT, Finite element method (FEM).

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Authors: Hamed Qazanfari, Hamid Hassanpour, Kazem Qazanfari

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In this paper, a method is provided for content-based image retrieval. Content-based image retrieval system searches query an image based on its visual content in an image database to retrieve similar images. In this paper, with the aim of simulating the human visual system sensitivity to image's edges and color features, the concept of color difference histogram (CDH) is used. CDH includes the perceptually color difference between two neighboring pixels with regard to colors and edge orientations. Since the HSV color space is close to the human visual system, the CDH is calculated in this color space. In addition, to improve the color features, the color histogram in HSV color space is also used as a feature. Among the extracted features, efficient features are selected using entropy and correlation criteria. The final features extract the content of images most efficiently. The proposed method has been evaluated on three standard databases Corel 5k, Corel 10k and UKBench. Experimental results show that the accuracy of the proposed image retrieval method is significantly improved compared to the recently developed methods.

Keywords: Content-based image retrieval, color difference histogram, efficient features selection, entropy, correlation.

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Authors: M.V.R.K Sarma, Krishna Saharan, Lalit Kumar, Ashwani Gautam, Avhijeet Kapoor, Nishant Srivastava, Vikram Sahai, V.S Bisaria

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The fluorescent pseudomonad strain R81 is a root colonizing rhizobacteria which promotes the growth of many plants by various mechanisms. Its broth containing siderophore (ironchelating compound) and 2,4- diacetyl phloroglucinol (DAPG) is used for preparing bioinoculant formulations for agronomical applications. Glycerol was found to be the best carbon source for improved biomass production. Splitting of nitrogen source to NH4Cl and urea had a stabilizing effect on pH during batch cultivation. Ltryptophan at 0.5 % in the medium increased the siderophore production to 850 mg/l. During batch cultivation of the strain in a bioreactor, a maximum of 4 g/l of dry cell mass, 1.8 g/l of siderophore and 20 mg/l of DAPG was achieved when glycerol was 15 g/l and C/N ratio was maintained at 12.5. In case of intermittent feeding of fresh medium during fed-batch cultivation, the dry cell mass was increased to 25 g/l with improved production of DAPG to 70 mg/l.

Keywords: Batch cultivation, Fed-batch cultivation, fluorescent pseudomonad, Metabolites

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Authors: G. Bhushan, S. Dhingra, K. K. Dubey

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This paper presents the evaluation of performance (BSFC and BTE), combustion (P_max) and emission (CO, NO_x, HC and smoke opacity) parameters of karanja biodiesel in a single cylinder, four stroke, direct injection diesel engine by considering significant engine input parameters (blending ratio, compression ratio and load torque). Multi-objective optimization of performance, combustion and emission parameters is also carried out in a karanja biodiesel engine using hybrid RSM-NSGA-II technique. The pareto optimum solutions are predicted by running the hybrid RSM-NSGA-II technique. Each pareto optimal solution is having its own importance. Confirmation tests are also conducted at randomly selected few pareto solutions to check the authenticity of the results.

Keywords: Karanja biodiesel, single cylinder direct injection diesel engine, response surface methodology, central composite rotatable design, genetic algorithm.

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Authors: Nhon Do, Tuyen Trong Tran, Phan Hoai Truong

Abstract:

Nowadays e-Learning is more popular, in Vietnam especially. In e-learning, materials for studying are very important. It is necessary to design the knowledge base systems and expert systems which support for searching, querying, solving of problems. The ontology, which was called Computational Object Knowledge Base Ontology (COB-ONT), is a useful tool for designing knowledge base systems in practice. In this paper, a design method for knowledge base systems in education using COKB-ONT will be presented. We also present the design of a knowledge base system that supports studying knowledge and solving problems in higher mathematics.

Keywords: artificial intelligence, knowledge base systems, ontology, educational software.

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Authors: Semeh Ben Salem, Sami Naouali, Moetez Sallami

Abstract:

Clustering is a well known data mining technique used in pattern recognition and information retrieval. The initial dataset to be clustered can either contain categorical or numeric data. Each type of data has its own specific clustering algorithm. In this context, two algorithms are proposed: the k-means for clustering numeric datasets and the k-modes for categorical datasets. The main encountered problem in data mining applications is clustering categorical dataset so relevant in the datasets. One main issue to achieve the clustering process on categorical values is to transform the categorical attributes into numeric measures and directly apply the k-means algorithm instead the k-modes. In this paper, it is proposed to experiment an approach based on the previous issue by transforming the categorical values into numeric ones using the relative frequency of each modality in the attributes. The proposed approach is compared with a previously method based on transforming the categorical datasets into binary values. The scalability and accuracy of the two methods are experimented. The obtained results show that our proposed method outperforms the binary method in all cases.

Keywords: Clustering, k-means, categorical datasets, pattern recognition, unsupervised learning, knowledge discovery.

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Authors: E. N. Mathioudakis, E. P. Papadopoulou

Abstract:

The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.

Keywords: Collocation, Preconditioned Bi-CGSTAB, MPI, Grid and DSM Systems.

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Authors: Yunyong Guo, Sudhakar Ganti, Bryan Guo

Abstract:

The rapid growth of telehealth Internet of Things (IoT) devices has raised concerns about energy consumption and efficient data processing. This paper presents an energy-efficient model that integrates telehealth IoT devices with a fog and cloud computing-based platform, offering a sustainable and robust solution to overcome these challenges. Our model employs fog computing as a localized data processing layer while leveraging cloud computing for resource-intensive tasks, significantly reducing energy consumption. We incorporate adaptive energy-saving strategies. Simulation analysis validates our approach's effectiveness in enhancing energy efficiency for telehealth IoT systems integrated with localized fog nodes and both private and public cloud infrastructures. Future research will focus on further optimization of the energy-saving model, exploring additional functional enhancements, and assessing its broader applicability in other healthcare and industry sectors.

Keywords: Energy-efficient, fog computing, IoT, telehealth.

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Authors: S. Boukais, A. Nekmouche, N. Khelil, A. Kezmane

Abstract:

The first intent of this study is to develop a finite element model that can predict correctly the behavior of the reinforced concrete column. Second aim is to use the finite element model to investigate and evaluate the effect of the strengthening method by jacketing of the reinforced concrete column, by considering different interface contact between the old and the new concrete. Four models were evaluated, one by considering perfect contact, the other three models by using friction coefficient of 0.1, 0.3 and 0.5. The simulation was carried out by using Abaqus software. The obtained results show that the jacketing reinforcement led to significant increase of the global performance of the behavior of the simulated reinforced concrete column.

Keywords: Strengthening, jacketing, reinforced concrete column, 3D simulation, Abaqus.

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Authors: S. Sowmyayani, P. Arockia Jansi Rani

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This paper integrates Octagon and Square Search pattern (OCTSS) motion estimation algorithm into H.264/AVC (Advanced Video Coding) video codec in Adaptive Group of Pictures (AGOP) mode. AGOP structure is computed based on scene change in the video sequence. Octagon and square search pattern block-based motion estimation method is implemented in inter-prediction process of H.264/AVC. Both these methods reduce bit rate and computational complexity while maintaining the quality of the video sequence respectively. Experiments are conducted for different types of video sequence. The results substantially proved that the bit rate, computation time and PSNR gain achieved by the proposed method is better than the existing H.264/AVC with fixed GOP and AGOP. With a marginal gain in quality of 0.28dB and average gain in bitrate of 132.87kbps, the proposed method reduces the average computation time by 27.31 minutes when compared to the existing state-of-art H.264/AVC video codec.

Keywords: Block Distortion Measure, Block Matching Algorithms, H.264/AVC, Motion estimation, Search patterns, Shot cut detection.

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Authors: Ramlan Zailani, Halim Ghafar, Mohamad Sofian So'aib

Abstract:

Air infiltration in mass scale industrial applications of bio char production is inevitable. The presence of oxygen during the carbonization process is detrimental to the production of biochar yield and properties. The experiment was carried out on several wood species in a fixed-bed pyrolyser under various fractions of oxygen ranging from 0% to 11% by varying nitrogen and oxygen composition in the pyrolysing gas mixtures at desired compositions. The bed temperature and holding time were also varied. Process optimization was carried out by Response Surface Methodology (RSM) by employing Central Composite Design (CCD) using Design Expert 6.0 Software. The effect of oxygen ratio and holding time on biochar yield within the range studied were statistically significant. From the analysis result, optimum condition of 15.2% biochar yield of mangrove wood was predicted at pyrolysis temperature of 403 oC, oxygen percentage of 2.3% and holding time of two hours. This prediction agreed well with the experiment finding of 15.1% biochar yield.

Keywords: Mangrove wood, slow pyrolysis, oxygen infiltration.

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Authors: Hadi Veisi, Mansour Jamzad

Abstract:

In this paper we present an adaptive method for image compression that is based on complexity level of the image. The basic compressor/de-compressor structure of this method is a multilayer perceptron artificial neural network. In adaptive approach different Back-Propagation artificial neural networks are used as compressor and de-compressor and this is done by dividing the image into blocks, computing the complexity of each block and then selecting one network for each block according to its complexity value. Three complexity measure methods, called Entropy, Activity and Pattern-based are used to determine the level of complexity in image blocks and their ability in complexity estimation are evaluated and compared. In training and evaluation, each image block is assigned to a network based on its complexity value. Best-SNR is another alternative in selecting compressor network for image blocks in evolution phase which chooses one of the trained networks such that results best SNR in compressing the input image block. In our evaluations, best results are obtained when overlapping the blocks is allowed and choosing the networks in compressor is based on the Best-SNR. In this case, the results demonstrate superiority of this method comparing with previous similar works and JPEG standard coding.

Keywords: Adaptive image compression, Image complexity, Multi-layer perceptron neural network, JPEG Standard, PSNR.

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Authors: Boontita Suchyukorn, Raweewan Auepanwiriyakul

Abstract:

A Data Warehouses is a repository of information integrated from source data. Information stored in data warehouse is the form of materialized in order to provide the better performance for answering the queries. Deciding which appropriated views to be materialized is one of important problem. In order to achieve this requirement, the constructing search space close to optimal is a necessary task. It will provide effective result for selecting view to be materialized. In this paper we have proposed an approach to reoptimize Multiple View Processing Plan (MVPP) by using global common subexpressions. The merged queries which have query processing cost not close to optimal would be rewritten. The experiment shows that our approach can help to improve the total query processing cost of MVPP and sum of query processing cost and materialized view maintenance cost is reduced as well after views are selected to be materialized.

Keywords: Data Warehouse, materialized views, query rewriting, common subexpressions.

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Authors: Hiba Hasan, Khalid Raza

Abstract:

Reverse engineering of genetic regulatory network involves the modeling of the given gene expression data into a form of the network. Computationally it is possible to have the relationships between genes, so called gene regulatory networks (GRNs), that can help to find the genomics and proteomics based diagnostic approach for any disease. In this paper, clustering based method has been used to reconstruct genetic regulatory network from time series gene expression data. Supercoiled data set from Escherichia coli has been taken to demonstrate the proposed method.

Keywords: Gene expression, gene regulatory networks (GRNs), clustering, data preprocessing, network visualization.

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Authors: Tae-Hyub Hong, Choeng-Ryul Choi, Chang-Nyung Kim

Abstract:

Human heart valves diseased by congenital heart defects, rheumatic fever, bacterial infection, cancer may cause stenosis or insufficiency in the valves. Treatment may be with medication but often involves valve repair or replacement (insertion of an artificial heart valve). Bileaflet mechanical heart valves (BMHVs) are widely implanted to replace the diseased heart valves, but still suffer from complications such as hemolysis, platelet activation, tissue overgrowth and device failure. These complications are closely related to both flow characteristics through the valves and leaflet dynamics. In this study, the physiological flow interacting with the moving leaflets in a bileaflet mechanical heart valve (BMHV) is simulated with a strongly coupled implicit fluid-structure interaction (FSI) method which is newly organized based on the Arbitrary-Lagrangian-Eulerian (ALE) approach and the dynamic mesh method (remeshing) of FLUENT. The simulated results are in good agreement with previous experimental studies. This study shows the applicability of the present FSI model to the complicated physics interacting between fluid flow and moving boundary.

Keywords: Bileaflet Mechanical Heart Valve, Fluid- Structure Interaction.

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Authors: Magdi M. Nabi, Ding-Li Yu

Abstract:

This paper presents a neural network based model predictive control (MPC) strategy to control a strongly exothermic reaction with complicated nonlinear kinetics given by Chylla-Haase polymerization reactor that requires a very precise temperature control to maintain product uniformity. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. Such a process usually controlled by conventional cascade control, it provides a robust operation, but often lacks accuracy concerning the required strict temperature tolerances. The predictive control strategy based on the RBF neural model is applied to solve this problem to achieve set-point tracking of the reactor temperature against disturbances. The result shows that the RBF based model predictive control gives reliable result in the presence of some disturbances and keeps the reactor temperature within a tight tolerance range around the desired reaction temperature.

Keywords: Chylla-Haase reactor, RBF neural network modelling, model predictive control.

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Authors: Sheikh Muhammad Azam, Masood-ur-Rehman, Adnan Khalid Bhatti, Nadeem Daudpota

Abstract:

Very Large and/or computationally complex optimization problems sometimes require parallel or highperformance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is “Traveling Salesman Problem". In this paper we have introduced a Branch & Bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the “symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.

Keywords: Parallel execution, symmetric traveling salesman problem, branch and bound algorithm, logarithmic sampling.

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Authors: T. Mahalakshmi, Aswathi B. L., Achuthsankar S. Nair

Abstract:

Transcription factors are a group of proteins that helps for interpreting the genetic information in DNA. Protein-protein interactions play a major role in the execution of key biological functions of a cell. These interactions are represented in the form of a graph with nodes and edges. Studies have showed that some nodes have high degree of connectivity and such nodes, known as hub nodes, are the inevitable parts of the network. In the present paper a method is proposed to identify hub transcription factor proteins using sequence information. On a complete data set of transcription factor proteins available from the APID database, the proposed method showed an accuracy of 77%, sensitivity of 79% and specificity of 76%.

Keywords: Transcription Factor Proteins, Hub Proteins, Shannon Index, Transfer Free Energy to Surface (TFES).

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Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: Jürgen Roßmann, Gerrit Alves

Abstract:

In today-s world, the efficient utilization of wood resources comes more and more to the mind of forest owners. It is a very complex challenge to ensure an efficient harvest of the wood resources. This is one of the scopes the project “Virtual Forest II" addresses. Its core is a database with data about forests containing approximately 260 million trees located in North Rhine-Westphalia (NRW). Based on this data, tree growth simulations and wood mobilization simulations can be conducted. This paper focuses on the latter. It describes a discrete-event-simulation with an attached 3-D real time visualization which simulates timber harvest using trees from the database with different crop resources. This simulation can be displayed in 3-D to show the progress of the wood crop. All the data gathered during the simulation is presented as a detailed summary afterwards. This summary includes cost-benefit calculations and can be compared to those of previous runs to optimize the financial outcome of the timber harvest by exchanging crop resources or modifying their parameters.

Keywords: Timber harvest, simulation, 3-D, optimization.

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Authors: Hadjira Bentoumi, Pascal Gautron, Kadi Bouatouch

Abstract:

We present a method for fast volume rendering using graphics hardware (GPU). To our knowledge, it is the first implementation on the GPU. Based on the Shear-Warp algorithm, our GPU-based method provides real-time frame rates and outperforms the CPU-based implementation. When the number of slices is not sufficient, we add in-between slices computed by interpolation. This improves then the quality of the rendered images. We have also implemented the ray marching algorithm on the GPU. The results generated by the three algorithms (CPU-based and GPU-based Shear- Warp, GPU-based Ray Marching) for two test models has proved that the ray marching algorithm outperforms the shear-warp methods in terms of speed up and image quality.

Keywords: Volume rendering, graphics processors

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Authors: K. Amudha, C. Nelson Kennedy Babu, S. Balu

Abstract:

The security of the medical images and its related data is the major research area which is to be concentrated in today’s era. Security in the medical image indicates that the physician may hide patients’ related data in the medical image and transfer it safely to a defined location using reversible watermarking. Many reversible watermarking methods had proposed over the decade. This paper enhances the security level in brain tumor images to hide the patient’s detail, which has to be conferred with other physician’s suggestions. The details or the information will be hidden in Non-ROI area of the image by using the block cipher algorithm. The block cipher uses different keys to extract the details that are difficult for the intruder to detect all the keys and to spot the details, which are the key advantage of this method. The ROI is the tumor area and Non-ROI is the area rest of ROI. The Non-ROI should not be spoiled in any cause and the details in the Non-ROI should be extracted correctly. The reversible watermarking method proposed in this paper performs well when compared to existing methods in the process of extraction of an original image and providing information security.

Keywords: Brain tumor images, Block Cipher, Reversible watermarking, ROI.

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Authors: Hongjoong Sin, Jangsoo Lee, Sungju Lee, Seunghwan Yoo, Sanghyuck Lee, Jaesik Lee, Yongjun Lee, Sungchun Kim

Abstract:

Wireless sensor networks are consisted of hundreds or thousands of small sensors that have limited resources. Energy-efficient techniques are the main issue of wireless sensor networks. This paper proposes an energy efficient agent-based framework in wireless sensor networks. We adopt biologically inspired approaches for wireless sensor networks. Agent operates automatically with their behavior policies as a gene. Agent aggregates other agents to reduce communication and gives high priority to nodes that have enough energy to communicate. Agent behavior policies are optimized by genetic operation at the base station. Simulation results show that our proposed framework increases the lifetime of each node. Each agent selects a next-hop node with neighbor information and behavior policies. Our proposed framework provides self-healing, self-configuration, self-optimization properties to sensor nodes.

Keywords: Agent, Energy Efficiency, Genetic algorithm, Wireless Sensor Networks.

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Authors: Bala Dhandayuthapani Veerasamy

Abstract:

Rapid steps made in the field of Information and Communication Technology (ICT) has facilitated the development of teaching and learning methods and prepared them to serve the needs of an assorted educational institution. In other words, the information age has redefined the fundamentals and transformed the institutions and method of services delivery forever. The vision is the articulation of a desire to transform the method of teaching and learning could proceed through e-learning. E-learning is commonly deliberated to use of networked information and communications technology in teaching and learning practice. This paper deals the general aspects of the e-leaning with its issues, developments, opportunities and challenges, which can the higher institutions own.

Keywords: 2D & 3D Animations, challenges, E-learning, Flash, HTML, issues, Multimedia, opportunities, VRML

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Authors: M. Tarafdar Haque, A. Taheri

Abstract:

Application of neural networks in execution of programmed pulse width modulation (PPWM) of a voltage source inverter (VSI) is studied in this paper. Using the proposed method it is possible to cancel out the desired harmonics in output of VSI in addition to control the magnitude of fundamental harmonic, contineously. By checking the non-trained values and a performance index, the most appropriate neural network is proposed. It is shown that neural networks may solve the custom difficulties of practical utilization of PPWM such as large size of memory, complex digital circuits and controlling the magnitude of output voltage in a discrete manner.

Keywords: Neural Network, Inverter, PPWM.

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Authors: P. Kumsawat, K. Pasitwilitham, K. Attakitmongcol, A. Srikaew

Abstract:

In this paper, an artificial intelligent technique for robust digital image watermarking in multiwavelet domain is proposed. The embedding technique is based on the quantization index modulation technique and the watermark extraction process does not require the original image. We have developed an optimization technique using the genetic algorithms to search for optimal quantization steps to improve the quality of watermarked image and robustness of the watermark. In addition, we construct a prediction model based on image moments and back propagation neural network to correct an attacked image geometrically before the watermark extraction process begins. The experimental results show that the proposed watermarking algorithm yields watermarked image with good imperceptibility and very robust watermark against various image processing attacks.

Keywords: Watermarking, Multiwavelet, Quantization index modulation, Genetic algorithms, Neural networks.

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Authors: Benalia Nadia, Bensiali Nadia, Mekki Mounira

Abstract:

In this paper, we propose an easily computable proximity index for predicting voltage collapse of a load bus using only measured values of the bus voltage and power; Using these measurements a polynomial of fourth order is obtained by using LES estimation algorithms. The sum of the absolute values of the polynomial coefficient gives an idea of the critical bus. We demonstrate the applicability of our proposed method on 6 bus test system. The results obtained verify its applicability, as well as its accuracy and the simplicity. From this indicator, it is allowed to predict the voltage instability or the proximity of a collapse. Results obtained by the PV curve are compared with corresponding values by QV curves and are observed to be in close agreement.

Keywords: least square method, Voltage Collapse, Voltage Stability, PV curve

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Authors: Yi-Pin Hsu, Shin-Yu Lin

Abstract:

An efficient parallel form in digital signal processor can improve the algorithm performance. The butterfly structure is an important role in fast Fourier transform (FFT), because its symmetry form is suitable for hardware implementation. Although it can perform a symmetric structure, the performance will be reduced under the data-dependent flow characteristic. Even though recent research which call as novel memory reference reduction methods (NMRRM) for FFT focus on reduce memory reference in twiddle factor, the data-dependent property still exists. In this paper, we propose a parallel-computing approach for FFT implementation on digital signal processor (DSP) which is based on data-independent property and still hold the property of low-memory reference. The proposed method combines final two steps in NMRRM FFT to perform a novel data-independent structure, besides it is very suitable for multi-operation-unit digital signal processor and dual-core system. We have applied the proposed method of radix-2 FFT algorithm in low memory reference on TI TMSC320C64x DSP. Experimental results show the method can reduce 33.8% clock cycles comparing with the NMRRM FFT implementation and keep the low-memory reference property.

Keywords: Parallel-computing, FFT, low-memory reference, TIDSP.

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Authors: Kyong-min Lee, Moon Soo Chang, PooGyeon Park

Abstract:

In this paper, we propose a geometric modeling of illumination on the patterned image containing etching transistor. This image is captured by a commercial camera during the inspection of a TFT-LCD panel. Inspection of defect is an important process in the production of LCD panel, but the regional difference in brightness, which has a negative effect on the inspection, is due to the uneven illumination environment. In order to solve this problem, we present a geometric modeling of illumination consisting of an interpolation using the least squares method and 3D modeling using bezier surface. Our computational time, by using the sampling method, is shorter than the previous methods. Moreover, it can be further used to correct brightness in every patterned image.

Keywords: Bezier, defect, geometric modeling, illumination, inspection, LCD, panel.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: Monomial form, rectangular surfaces, CAGD curves, monomial matrix applications.

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