Search results for: least-squares method

Authors: Michal Polanský, C. Ardil

Abstract:

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

Keywords: H norm, Linear Matrix Inequalities, Observers, Takagi-Sugeno Systems, Parallel Distributed Compensation

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Authors: Nilson Barbieri, Renato Barbieri

Abstract:

–In this paper the damage in clamped-free, clampedclamped and free-free beam are analyzed considering samples without and with structural modifications. The damage location is investigated by the use of the bispectrum and wavelet analysis. The mathematical models are obtained using 2D elasticity theory and the Finite Element Method (FEM). The numerical and experimental data are approximated using the Particle Swarm Optimizer (PSO) method and this way is possible to adjust the localization and the severity of the damage. The experimental data are obtained through accelerometers placed along the sample. The system is excited using impact hammer.

Keywords: Damage, beam, PSO, bispectrum, wavelet transform

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Authors: Aree A. Mohammed

Abstract:

In this work we develop an object extraction method and propose efficient algorithms for object motion characterization. The set of proposed tools serves as a basis for development of objectbased functionalities for manipulation of video content. The estimators by different algorithms are compared in terms of quality and performance and tested on real video sequences. The proposed method will be useful for the latest standards of encoding and description of multimedia content – MPEG4 and MPEG7.

Keywords: Object extraction, Video indexing, Segmentation, Optical flow, Motion estimators.

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Authors: J. Prakash, K. Rajesh

Abstract:

In this paper we present a new method for coin identification. The proposed method adopts a hybrid scheme using Eigenvalues of covariance matrix, Circular Hough Transform (CHT) and Bresenham-s circle algorithm. The statistical and geometrical properties of the small and large Eigenvalues of the covariance matrix of a set of edge pixels over a connected region of support are explored for the purpose of circular object detection. Sparse matrix technique is used to perform CHT. Since sparse matrices squeeze zero elements and contain only a small number of non-zero elements, they provide an advantage of matrix storage space and computational time. Neighborhood suppression scheme is used to find the valid Hough peaks. The accurate position of the circumference pixels is identified using Raster scan algorithm which uses geometrical symmetry property. After finding circular objects, the proposed method uses the texture on the surface of the coins called texton, which are unique properties of coins, refers to the fundamental micro structure in generic natural images. This method has been tested on several real world images including coin and non-coin images. The performance is also evaluated based on the noise withstanding capability.

Keywords: Circular Hough Transform, Coin detection, Covariance matrix, Eigenvalues, Raster scan Algorithm, Texton.

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well known formulas.

Keywords: Conjugate gradient method, conjugate gradient coefficient, global convergence.

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Authors: Ali Sarosh, Dong Yun-Feng, Muhammad Umer

Abstract:

Fully reusable spaceplanes do not exist as yet. This implies that design-qualification for optimized highly-integrated forebody-inlet configuration of booster-stage vehicle cannot be based on archival data of other spaceplanes. Therefore, this paper proposes a novel TIPSO-SVM expert system methodology. A non-trivial problem related to optimization and classification of hypersonic forebody-inlet configuration in conjunction with mass-model of the two-stage-to-orbit (TSTO) vehicle is solved. The hybrid-heuristic machine learning methodology is based on two-step improved particle swarm optimizer (TIPSO) algorithm and two-step support vector machine (SVM) data classification method. The efficacy of method is tested by first evolving an optimal configuration for hypersonic compression system using TIPSO algorithm; thereafter, classifying the results using two-step SVM method. In the first step extensive but non-classified mass-model training data for multiple optimized configurations is segregated and pre-classified for learning of SVM algorithm. In second step the TIPSO optimized mass-model data is classified using the SVM classification. Results showed remarkable improvement in configuration and mass-model along with sizing parameters.

Keywords: TIPSO-SVM expert system, TIPSO algorithm, two-step SVM method, aerothermodynamics, mass-modeling, TSTO vehicle.

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Authors: Yang Zhang, Jian He

Abstract:

Heart disease is one of the leading causes of death in the world, and coronary heart disease (CHD) is one of the major heart diseases. Electrocardiogram (ECG) is widely used in the detection of heart diseases, but the traditional manual method for CHD prediction by analyzing ECG requires lots of professional knowledge for doctors. This paper presents sliding window and continuous wavelet transform (CWT) to transform ECG signals into images, and then ResNet and Bi-LSTM are introduced to build the ECG feature extraction network (namely ECGNet). At last, an auxiliary system for CHD prediction was developed based on modified ResNet18 and Bi-LSTM, and the public ECG dataset of CHD from MIMIC-3 was used to train and test the system. The experimental results show that the accuracy of the method is 83%, and the F1-score is 83%. Compared with the available methods for CHD prediction based on ECG, such as kNN, decision tree, VGGNet, etc., this method not only improves the prediction accuracy but also could avoid the degradation phenomenon of the deep learning network.

Keywords: Bi-LSTM, CHD, coronary heart disease, ECG, electrocardiogram, ResNet, sliding window.

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Authors: Diako Azizi, Hosein Heydari, Ahmad Gholami

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Today with the rapid growth of telecommunications equipment, electronic and developing more and more networks of power, influence of electromagnetic waves on one another has become hot topic discussions. So in this article, this issue and appropriate mechanisms for EMC operations have been presented. First, impact of high voltage lines on the surrounding environment especially on the control room has been investigated, then to reduce electromagnetic radiation, various methods of shielding are provided and shielding effectiveness of them has been compared. It should be expressed that simulations have been done by the finite element method (FEM).

Keywords: Electrical field, EMC, field distribution, finite element method

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Authors: Kyaw Myo Lin, Pyone Lai Swe, Khine Zin Oo

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In this paper, an approach combining analytical method for the distributed generator (DG) sizing and meta-heuristic search for the optimal location of DG has been presented. The optimal size of DG on each bus is estimated by the loss sensitivity factor method while the optimal sites are determined by Particle Swarm Optimization (PSO) based optimal reactive power dispatch for minimizing active power loss. To confirm the proposed approach, it has been tested on IEEE-30 bus test system. The adjustments of operating constraints and voltage profile improvements have also been observed. The obtained results show that the allocation of DGs results in a significant loss reduction with good voltage profiles and the combined approach is competent in keeping the system voltages within the acceptable limits.

Keywords: Analytical approach, distributed generations, optimal size, optimal location, optimal reactive power dispatch, particle swarm optimization algorithm.

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Authors: Kuen-Ming Shu, Jyun-Wei Chen

Abstract:

Encapsulated O-rings are specifically designed to address the problem of sealing the most hostile chemicals and extreme temperature applications. Ultrasonic vibration hot embossing and ultrasonic welding techniques provide a fast and reliable method to fabricate encapsulated O-ring. This paper performs the design and analysis method of the acoustic horns with double extrusion to process tube double side flange simultaneously. The paper deals with study through Finite Element Method (FEM) of ultrasonic stepped horn used to process a capsulated O-ring, the theoretical dimensions of horns, and their natural frequencies and amplitudes are obtained through the simulations of COMOSOL software. Furthermore, real horns were fabricated, tested and verified to proof the practical utility of these horns. 

Keywords: Encapsulated O-rings, ultrasonic vibration hot embossing, flange making, acoustic horn, finite element analysis.

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Authors: Farzin Salmasi

Abstract:

The design of a gravity dam is performed through an interactive process involving a preliminary layout of the structure followed by a stability and stress analysis. This study presents a method to define the optimal top width of gravity dam with genetic algorithm. To solve the optimization task (minimize the cost of the dam), an optimization routine based on genetic algorithms (GAs) was implemented into an Excel spreadsheet. It was found to perform well and GA parameters were optimized in a parametric study. Using the parameters found in the parametric study, the top width of gravity dam optimization was performed and compared to a gradient-based optimization method (classic method). The accuracy of the results was within close proximity. In optimum dam cross section, the ratio of is dam base to dam height is almost equal to 0.85, and ratio of dam top width to dam height is almost equal to 0.13. The computerized methodology may provide the help for computation of the optimal top width for a wide range of height of a gravity dam.

Keywords: Chromosomes, dam, genetic algorithm, globaloptimum, preliminary layout, stress analysis, theoretical profile.

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Authors: M. Z. Alsawalha

Abstract:

The main objective of this study is to investigate basic properties of different natural clays, by two methods. The first method is a gas phase conversion of methylbutynol (MBOH). The second method is the application of Pyrrole-tpd. Based on the product distribution from the first method, the acidic, basic and coordinately unsaturated sites were differentiated. It was shown that both the conversion and the selectivity for basic products did not change with reaction time. Nevertheless, a deviation from the stoichiometric ratio R of formed acetylene to acetone was observed (R=0.8…0.97). The conversion normalized to the surface area was used for establishing the activity sequence: White kaolinite > red kaolinite > bentonite > zeolite > di­ato­mite. In addition, the results were compared with synthetic amorphous alumosilicates and typical basic materials like MgO and ZnO. The basic properties were characterized using the Pyrrole-tpd.  The Pyrrole-tpd results showed the same basicity sequence as the MBOH gas phase reaction.

Keywords: Alumosilicates, basic surface properties, natural clays, normalized conversions with acetylene and acetone, pyrrole-TPD adsorption.

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Authors: Rajesh Kumar, Roopali Dogra, Puneet Aggarwal

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In recent advancements in electric machine and drives, wound rotor motor is extensively used. The merit of using wound rotor induction motor is to control speed/torque characteristics by inserting external resistance. Wound rotor induction motor can be used in the cases such as (a) low inrush current, (b) load requiring high starting torque, (c) lower starting current is required, (d) loads having high inertia, and (e) gradual built up of torque. Examples include conveyers, cranes, pumps, elevators, and compressors. This paper includes speed control of wound induction motor using MATLAB/Simulink for rotor resistance and slip power recovery method. The characteristics of these speed control methods are hence analyzed.

Keywords: Wound rotor induction motor, MATLAB/Simulink, rotor resistance method, slip power recovery method.

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Authors: Srikanth L., Neelima Satyam D.

Abstract:

The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987(Wind Load), IS: 802:1995(Structural steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

Keywords: Response Spectra, Dynamic Analysis, Central Difference Method, Transmission Tower.

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Authors: Isa Ahmadi, Ramin Khamedi

Abstract:

In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C¹ continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: Cyclic Loading, Finite Element Analysis, Prager Kinematic Hardening Model, Torsion of shaft.

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

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In this paper, novel techniques in increasing the accuracy and speed of convergence of a Feed forward Back propagation Artificial Neural Network (FFBPNN) with polynomial activation function reported in literature is presented. These technique was subsequently used to determine the coefficients of Autoregressive Moving Average (ARMA) and Autoregressive (AR) system. The results obtained by introducing sequential and batch method of weight initialization, batch method of weight and coefficient update, adaptive momentum and learning rate technique gives more accurate result and significant reduction in convergence time when compared t the traditional method of back propagation algorithm, thereby making FFBPNN an appropriate technique for online ARMA coefficient determination.

Keywords: Adaptive Learning rate, Adaptive momentum, Autoregressive, Modeling, Neural Network.

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Authors: Chao Qi, Fuyang Peng, Bo Deng, Xiaoyan Su

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In the upgrade process of enterprise information systems, whether new systems will be success and their development will be efficient, depends on how to deal with and utilize those legacy systems. We propose an evaluation system, which comprehensively describes the capacity of legacy information systems in five aspects. Then a practical legacy systems evaluation method is scripted. Base on the evaluation result, we put forward 4 kinds of migration strategy: eliminated, maintenance, modification, encapsulating. The methods and strategies play important roles in practice.

Keywords: Legacy Systems, Evaluation Method, Migration Strategy.

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Authors: J.Yojina, W. Ngamsaad, N. Nuttavut, D.Triampo, Y. Lenbury, W. Triampo, P. Kanthang, S.Sriyab

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The dynamics of Min proteins plays a center role in accurate cell division. Although the nucleoids may presumably play an important role in prokaryotic cell division, there is a lack of models to account for its participation. In this work, we apply the lattice Boltzmann method to investigate protein oscillation based on a mesoscopic model that takes into account the nucleoid-s role. We found that our numerical results are in reasonably good agreement with the previous experimental results On comparing with the other computational models without the presence of nucleoids, the highlight of our finding is that the local densities of MinD and MinE on the cytoplasmic membrane increases, especially along the cell width, when the size of the obstacle increases, leading to a more distinct cap-like structure at the poles. This feature indicated the realistic pattern and reflected the combination of Min protein dynamics and nucleoid-s role.

Keywords: lattice Boltzmann method, cell division, Minproteins oscillation, nucleoid

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Authors: Vahid Zeinoddini-Meimand, Mehdi Ghassemieh, Jalal Kiani

Abstract:

This paper explains the results of an investigation on the analysis of flush end plate steel connections by means of finite element method. Flush end plates are a highly indeterminate type of connection, which have a number of parameters that affect their behavior. Because of this, experimental investigations are complicated and very costly. Today, the finite element method provides an ideal method for analyzing complicated structures. Finite element models of these types of connections under monotonic loading have previously been investigated. A numerical model, which can predict the cyclic behavior of these connections, is of critical importance, as dynamic experiments are more costly. This paper summarizes a study to develop a three-dimensional finite element model that can accurately capture the cyclic behavior of flush end plate connections. Comparisons between FEM results and experimental results obtained from full-scale tests have been carried out, which confirms the accuracy of the finite element model. Consequently, design equations for this connection have been investigated and it is shown that these predictions are not precise in all cases. The effect of end plate thickness and bolt diameter on the overall behavior of this connection is discussed. This research demonstrates that using the appropriate configuration, this connection has the potential to form a plastic hinge in the beam--desirable in seismic behavior.

Keywords: Flush end plate connection, moment-rotation diagram, finite element method, moment frame, cyclic loading.

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Authors: Asghar Shirazpour, Seyed Moein Rassoulinejad Mousavi, Hamid Reza Seyf

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In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

Keywords: Lorentz Force, Porous Media, Homotopy Perturbation method

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Authors: N. Mustamil, M. Quaddus

Abstract:

This research investigates the factors that influence moral judgments when dealing with ethical dilemmas in the organizational context. It also investigates the antecedents of individual ethical ideology (idealism and relativism). A mixed method study, which combines qualitative (field study) and quantitative (survey) approaches, was used in this study. An initial model was developed first, which was then fine-tuned based on field studies. Data were collected from managers in Malaysian large organizations. The results of this study reveal that in-group collectivism culture, power distance culture, parental values, and religiosity were significant as antecedents of ethical ideology. However, direct effects of these variables on moral judgment were not significant. Furthermore, the results of this study confirm the significant effects of ethical ideology on moral judgment. This study provides valuable insight into evaluating the validity of existing theory as proposed in the literature and offers significant practical implications.

Keywords: Antecedents Factors, Ethical Ideology, Mixed Method, Moral Judgment

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Authors: András Barta, István Vajk

Abstract:

In pattern recognition applications the low level segmentation and the high level object recognition are generally considered as two separate steps. The paper presents a method that bridges the gap between the low and the high level object recognition. It is based on a Bayesian network representation and network propagation algorithm. At the low level it uses hierarchical structure of quadratic spline wavelet image bases. The method is demonstrated for a simple circuit diagram component identification problem.

Keywords: Object recognition, Bayesian network, Wavelets, Document processing.

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Authors: Mounira Taileb, Sid Lamrous, Sami Touati

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In order to accelerate the similarity search in highdimensional database, we propose a new hierarchical indexing method. It is composed of offline and online phases. Our contribution concerns both phases. In the offline phase, after gathering the whole of the data in clusters and constructing a hierarchical index, the main originality of our contribution consists to develop a method to construct bounding forms of clusters to avoid overlapping. For the online phase, our idea improves considerably performances of similarity search. However, for this second phase, we have also developed an adapted search algorithm. Our method baptized NOHIS (Non-Overlapping Hierarchical Index Structure) use the Principal Direction Divisive Partitioning (PDDP) as algorithm of clustering. The principle of the PDDP is to divide data recursively into two sub-clusters; division is done by using the hyper-plane orthogonal to the principal direction derived from the covariance matrix and passing through the centroid of the cluster to divide. Data of each two sub-clusters obtained are including by a minimum bounding rectangle (MBR). The two MBRs are directed according to the principal direction. Consequently, the nonoverlapping between the two forms is assured. Experiments use databases containing image descriptors. Results show that the proposed method outperforms sequential scan and SRtree in processing k-nearest neighbors.

Keywords: K-nearest neighbour search, multi-dimensional indexing, multimedia databases, similarity search.

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

Multimodal biometric systems integrate the data presented by multiple biometric sources, hence offering a better performance than the systems based on a single biometric modality. Although the coupling of biometric systems can be done at different levels, the fusion at the scores level is the most common since it has been proven effective than the rest of the fusion levels. However, the scores from different modalities are generally heterogeneous. A step of normalizing the scores is needed to transform these scores into a common domain before combining them. In this paper, we study the performance of several normalization techniques with various fusion methods in a context relating to the merger of three unimodal systems based on the face, the palmprint and the fingerprint. We also propose a new adaptive normalization method that takes into account the distribution of client scores and impostor scores. Experiments conducted on a database of 100 people show that the performances of a multimodal system depend on the choice of the normalization method and the fusion technique. The proposed normalization method has given the best results.

Keywords: Multibiometrics, Fusion, Score level, Score normalization, Adaptive normalization.

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Authors: Jafar Khan Kasi, Ajab Khan Kasi, Muzamil Bokhari

Abstract:

Carbon nanotube is one of the most attractive materials for the potential applications of nanotechnology due to its excellent mechanical, thermal, electrical and optical properties. In this paper we report a supercapacitor made of nickel foil electrodes, coated with multiwall carbon nanotubes (MWCNTs) thin film using electrophoretic deposition (EPD) method. Chemical vapor deposition method was used for the growth of MWCNTs and ethanol was used as a hydrocarbon source. High graphitic multiwall carbon nanotube was found at 750oC analyzing by Raman spectroscopy. We observed the electrochemical performance of supercapacitor by cyclic voltammetry. The electrodes of supercapacitor fabricated from MWCNTs exhibit considerably small equivalent series resistance (ESR), and a high specific power density. Electrophoretic deposition is an easy method in fabricating MWCNT electrodes for high performance supercapacitor.

Keywords: Carbon nanotube, chemical vapor deposition, catalyst, charge, cyclic voltammetry.

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Authors: Guguloth Ramesh, T. K. Sunil Kumar

Abstract:

This paper presents congestion management in deregulated power systems. In a deregulated environment, every buyer wants to buy power from the cheapest generator available, irrespective of relative geographical location of buyer and seller. As a consequence of this, the transmission corridors evacuating the power of cheaper generators would get overloaded if all such transactions are approved. Congestion management is a mechanism to prioritize the transactions and commit to such a schedule which would not overload the network. The congestions in the transmission lines are determined by Optimal Power Flow (OPF) solution, which is carried by primal liner programming method. Congestion in the transmission lines are alleviated by connected Distributed Generation (DG) of micro grid at load bus. A method to determine the optimal location of DG unit has been suggested based on transmission line relief sensitivity based approach. The effectiveness of proposed method has been demonstrated on modified IEEE-14 and 30 bus test systems.

Keywords: Congestion management, Distribution Generation (DG), Transmission Line Relief (TLR) sensitivity index, OPF.

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Authors: Ho Jae Lee, Do Gyeum Kim, Jang Hwa Lee, Myoung Suk Cho

Abstract:

A concrete structure is designed and constructed for its purpose of use, and is expected to maintain its function for the target durable years from when it was planned. Nevertheless, as time elapses the structure gradually deteriorates and then eventually degrades to the point where the structure cannot exert the function for which it was planned. The performance of concrete that is able to maintain the level of the performance required over the designed period of use as it has less deterioration caused by the elapse of time under the designed condition is referred to as Durability. There are a number of causes of durability degradation, but especially chloride damage, carbonation, freeze-thaw, etc are the main causes. In this study, carbonation, one of the main causes of deterioration of the durability of a concrete structure, was investigated via a microstructure analysis technique. The method for the measurement of carbonation was studied using the existing indicator method, and the method of measuring the progress of carbonation in a quantitative manner was simultaneously studied using a FT-IR (Fourier-Transform Infrared) Spectrometer along with the microstructure analysis technique.

Keywords: Concrete, Carbonation, Microsturcture, FT-IR

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Authors: K. Jaroensutasinee

Abstract:

The general global behavior of particle S a non-linear (Q - xy)2 potential cannot be revealed a Poincare surface of section method (PSS) because inost trajectories take practically infinitely long time to integrate numerically before they come back to the surface. In this study as an alternative to PSS, a multiple scale perturbation is applied to analyze global adiabatic, non-adiabatic and chaotic behavior of particles in this potential. It was found that the results can be summarized as a form of a Fermi-like map. Additionally, this method gives a variation of global stochasticity criteria with Q.

Keywords: Multiple Scak Perturbation The Poincare Surface or Section, Fermi Map

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Authors: Sukru Merey, Caglar Sinayuc

Abstract:

Gas hydrate deposits which are found in deep ocean sediments and in permafrost regions are supposed to be a fossil fuel reserve for the future. The Black Sea is also considered rich in terms of gas hydrates. It abundantly contains gas hydrates as methane (CH₄~80 to 99.9%) source. In this study, by using the literature, seismic and other data of the Black Sea such as salinity, porosity of the sediments, common gas type, temperature distribution and pressure gradient, the optimum gas production method for the Black Sea gas hydrates was selected as mainly depressurization method. Numerical simulations were run to analyze gas production from gas hydrate deposited in turbidites in the Black Sea by depressurization.

Keywords: Black Sea hydrates, depressurization, turbidites, HydrateResSim.

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Authors: Hazem M. El-Bakry

Abstract:

In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

Keywords: Boolean Functions, Simplification, KarnoughMap, Implementation of Logic Functions, Modular NeuralNetworks.

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