Search results for: finite element method

Authors: Yelena Chaiko

Abstract:

This paper presents a developed method for controlling multi-renewable energy generators. The control system depends basically on three sensors (wind anemometer, solar sensor, and voltage sensor). These sensors represent PLC-s analogue inputs. Controlling the output voltage supply can be achieved by an enhanced method of interlocking between the renewable energy generators, depending on those sensors and output contactors.

Keywords: Renewable, energy, control, model, generator.

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Authors: H. Shayeghi, B. Mohamadi

Abstract:

This paper presents a possibilistic (fuzzy) model in optimal siting and sizing of Distributed Generation (DG) for loss reduction and improve voltage profile in power distribution system. Multi-objective problem is developed in two phases. In the first one, the set of non-dominated planning solutions is obtained (with respect to the objective functions of fuzzy economic cost, and exposure) using genetic algorithm. In the second phase, one solution of the set of non-dominated solutions is selected as optimal solution, using a suitable max-min approach. This method can be determined operation-mode (PV or PQ) of DG. Because of considering load uncertainty in this paper, it can be obtained realistic results. The whole process of this method has been implemented in the MATLAB7 environment with technical and economic consideration for loss reduction and voltage profile improvement. Through numerical example the validity of the proposed method is verified.

Keywords: Fuzzy Power Flow, DG siting and sizing, LoadUncertainty, Multi-objective Possibilistic Model.

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Authors: S. Kahvecioglu, A. Karamancioglu, A. Yazici

Abstract:

In this paper, a nonlinear model predictive swing-up and stabilizing sliding controller is proposed for an inverted pendulum-cart system. In the swing up phase, the nonlinear model predictive control is formulated as a nonlinear programming problem with energy based objective function. By solving this problem at each sampling instant, a sequence of control inputs that optimize the nonlinear objective function subject to various constraints over a finite horizon are obtained. Then, this control drives the pendulum to a predefined neighborhood of the upper equilibrium point, at where sliding mode based model predictive control is used to stabilize the systems with the specified constraints. It is shown by the simulations that, due to the way of formulating the problem, short horizon lengths are sufficient for attaining the swing up goal.

Keywords: Inverted pendulum, model predictive control, swingup, stabilization.

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Authors: A. Denker, U. Akıncıoğlu

Abstract:

In this paper a neural adaptive control method has been developed and applied to robot control. Simulation results are presented to verify the effectiveness of the controller. These results show that the performance by using this controller is better than those which just use either direct inverse control or predictive control. In addition, they show that the resulting is a useful method which combines the advantages of both direct inverse control and predictive control.

Keywords: Neural networks, robotics, direct inverse control, predictive control.

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Authors: Samrand Rashahmadi, Morteza Abbaszadeh, Sana Hoseyni, Raziyeh Alizadeh

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Design of a constant chord propeller is presented in this paper in order to reduce propeller-s design procedure-s costs. The design process was based on Lock and Goldstein-s techniques of propeller design and analysis. In order to calculate optimum chord of propeller, chord of a referential element is generalized as whole blades chord. The design outcome which named CS-X-1 is modeled & analyzed by CFD methods using K-ε: R.N.G turbulence model. Convergence of results of two codes proved that outcome results of design process are reliable. Design result is a two-blade propeller with a total diameter of 1.1 meter, radial velocity of 3000 R.P.M, efficiency above .75 and power coefficient near 1.05.

Keywords: Single rotating propeller, Design, C.F.D. test, constant chord

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Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: R. S. Chandan, M. Vasudevan, Deecaraman, B. M. Gurupadayya

Abstract:

In Pharmaceutical industries, it is very important to remove drug residues from the equipment and areas used. The cleaning procedure must be validated, so special attention must be devoted to the methods used for analysis of trace amounts of drugs. A rapid, sensitive and specific reverse phase ultra performance liquid chromatographic (UPLC) method was developed for the quantitative determination of Albendazole in cleaning validation swab samples. The method was validated using an ACQUITY HSS C₁₈, 50 x 2.1mm, 1.8μ column with a isocratic mobile phase containing a mixture of 1.36g of Potassium dihydrogenphosphate in 1000mL MilliQ water, 2mL of triethylamine and pH adjusted to 2.3 ± 0.05 with ortho-phosphoric acid, Acetonitrile and Methanol (50:40:10 v/v). The flow rate of the mobile phase was 0.5 mL min^-1 with a column temperature of 35⁰C and detection wavelength at 254nm using PDA detector. The injection volume was 2µl. Cotton swabs, moisten with acetonitrile were used to remove any residue of drug from stainless steel, teflon, rubber and silicon plates which mimic the production equipment surface and the mean extraction-recovery was found to be 91.8. The selected chromatographic condition was found to effectively elute Albendazole with retention time of 0.67min. The proposed method was found to be linear over the range of 0.2 to 150µg/mL and correlation coefficient obtained is 0.9992. The proposed method was found to be accurate, precise, reproducible and specific and it can also be used for routine quality control analysis of these drugs in biological samples either alone or in combined pharmaceutical dosage forms.

Keywords: Cleaning validation, Albendazole, residues, swab analysis, UPLC.

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Authors: Mohamed Saladin Abdul Rasool, Arifin Md Salleh, Mohd Fauzi Mohd Harun

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Islamic institutions in Malaysia play a variety of socioeconomic roles such as poverty alleviation. To perform this role, these institutions face a major task in identifying the poverty group. Most of these institutions measure and operationalize poverty from the monetary perspective using variables such as income, expenditure or consumption. In practice, most Islamic institutions in Malaysia use the monetary approach in measuring poverty through the conventional Poverty Line Income (PLI) method and recently, the had al kifayah (HAK) method using total necessities of a household from an Islamic perspective. The objective of this paper is to present the PLI and also the HAK method. This micro-data study would highlight the similarities and differences of both the methods.A survey aided by a structured questionnaire was carried out on 260 selected head of households in the state of Selangor. The paper highlights several demographic factors that are associated with the three monetary indicators in the study, namely income, PLI and HAK. In addition, the study found that these monetary variables are significantly related with each other.

Keywords: Poverty line, multidimensional, necessities, monetary

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Authors: A. H. Fatah, A. H. Ahmed

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Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Keywords: Gamma-Ray, Spectrum analysis, Non-linear leastsquare fitting.

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter N_rc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.

Keywords: Convective boundary, radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate.

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Authors: M. Rominu, C. Sinescu, A.G. Podoleanu

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The purpose of this study is to present a non invasive method for the marginal adaptation evaluation in class V composite restorations. Standardized class V cavities, prepared in human extracted teeth, were filled with Premise (Kerr) composite. The specimens were thermo cycled. The interfaces were examined by Optical Coherence Tomography method (OCT) combined with the confocal microscopy and fluorescence. The optical configuration uses two single mode directional couplers with a superluminiscent diode as the source at 1300 nm. The scanning procedure is similar to that used in any confocal microscope, where the fast scanning is enface (line rate) and the depth scanning is much slower (at the frame rate). Gaps at the interfaces as well as inside the composite resin materials were identified. OCT has numerous advantages which justify its use in vivo as well as in vitro in comparison with conventional techniques.

Keywords: Class V Cavities, Marginal Adaptation, Optical Coherence Tomography Fluorescence, Confocal Microscopy

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Authors: Robert Niese, Ayoub Al-Hamadi, Bernd Michaelis

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In modern human computer interaction systems (HCI), emotion recognition is becoming an imperative characteristic. The quest for effective and reliable emotion recognition in HCI has resulted in a need for better face detection, feature extraction and classification. In this paper we present results of feature space analysis after briefly explaining our fully automatic vision based emotion recognition method. We demonstrate the compactness of the feature space and show how the 2d/3d based method achieves superior features for the purpose of emotion classification. Also it is exposed that through feature normalization a widely person independent feature space is created. As a consequence, the classifier architecture has only a minor influence on the classification result. This is particularly elucidated with the help of confusion matrices. For this purpose advanced classification algorithms, such as Support Vector Machines and Artificial Neural Networks are employed, as well as the simple k- Nearest Neighbor classifier.

Keywords: Facial expression analysis, Feature extraction, Image processing, Pattern Recognition, Application.

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Authors: Sorina Adriana Mitrea, Silvia Maria Hodorogea, Anca Duta, Luminita Isac, Elena Purghel, Mihaela Voinea

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Solar energy is the most “available", ecological and clean energy. This energy can be used in active or passive mode. The active mode implies the transformation of solar energy into a useful energy. The solar energy can be transformed into thermal energy, using solar collectors. In these collectors, the active and the most important element is the absorber, material which performs the absorption of solar radiation and, in at the same time, limits its reflection. The paper presents some aspects regarding the IR absorbing material – a type of cermets, used as absorber in the solar collectors, by X Ray Diffraction Technique (XRD) characterization.

Keywords: Alumina films, solar energy, X-ray diffraction.

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Authors: A. Lawanna, J. Daengdej

Abstract:

Case-Based Reasoning (CBR) is one of machine learning algorithms for problem solving and learning that caught a lot of attention over the last few years. In general, CBR is composed of four main phases: retrieve the most similar case or cases, reuse the case to solve the problem, revise or adapt the proposed solution, and retain the learned cases before returning them to the case base for learning purpose. Unfortunately, in many cases, this retain process causes the uncontrolled case base growth. The problem affects competence and performance of CBR systems. This paper proposes competence-based maintenance method based on deletion policy strategy for CBR. There are three main steps in this method. Step 1, formulate problems. Step 2, determine coverage and reachability set based on coverage value. Step 3, reduce case base size. The results obtained show that this proposed method performs better than the existing methods currently discussed in literature.

Keywords: Case-Based Reasoning, Case Base Maintenance, Coverage, Reachability.

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Authors: Arnaud Nougues

Abstract:

This paper describes a two-stage methodology derived from IMC (Internal Model Control) for tuning a PID (Proportional-Integral-Derivative) controller for levels or other integrating processes in an industrial environment. Focus is ease of use and implementation speed which are critical for an industrial application. Tuning can be done with minimum effort and without the need of time-consuming open-loop step tests on the plant. The first stage of the method applies to levels only: the vessel residence time is calculated from equipment dimensions and used to derive a set of preliminary PI (Proportional-Integral) settings with IMC. The second stage, re-tuning in closed-loop, applies to levels as well as other integrating processes: a tuning correction mechanism has been developed based on a series of closed-loop simulations with model errors. The tuning correction is done from a simple closed-loop step test and application of a generic correlation between observed overshoot and integral time correction. A spin-off of the method is that an estimate of the vessel residence time (levels) or open-loop process gain (other integrating process) is obtained from the closed-loop data.

Keywords: closed-loop model identification, IMC-PID tuning method, integrating process control, on-line PID tuning adaptation

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Authors: Dibyendu Ghoshal, Shimal Das

Abstract:

Image compression based on fractal coding is a lossy compression method and normally used for gray level images range and domain blocks in rectangular shape. Fractal based digital image compression technique provide a large compression ratio and in this paper, it is proposed using YUV colour space and the fractal theory which is based on iterated transformation. Fractal geometry is mainly applied in the current study towards colour image compression coding. These colour images possesses correlations among the colour components and hence high compression ratio can be achieved by exploiting all these redundancies. The proposed method utilises the self-similarity in the colour image as well as the cross-correlations between them. Experimental results show that the greater compression ratio can be achieved with large domain blocks but more trade off in image quality is good to acceptable at less than 1 bit per pixel.

Keywords: Fractal coding, Iterated Function System (IFS), Image compression, YUV colour space.

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Authors: Gioacchino Lavanco, Elisabetta Di Giovanni, Floriana Romano

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The aim of this paper is to study in depth some methodological aspects of social interventation, focusing on desirable passage from social maternage method to peer advocacy method. For this purpose, we intend analyze social and organizative components, that affect operator's professional action and that are part of his psychological environment, besides the physical and social one. In fact, operator's interventation should not be limited to a pure supply of techniques, nor to take shape as improvised action, but “full of good purposes".

Keywords: Advocacy, education, relationship, social mandate.

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Authors: Kjersti Engan, Karl Skretting, Jostein Herredsvela, Thor Ole Gulsrud

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Texture classification is an important image processing task with a broad application range. Many different techniques for texture classification have been explored. Using sparse approximation as a feature extraction method for texture classification is a relatively new approach, and Skretting et al. recently presented the Frame Texture Classification Method (FTCM), showing very good results on classical texture images. As an extension of that work the FTCM is here tested on a real world application as detection of abnormalities in mammograms. Some extensions to the original FTCM that are useful in some applications are implemented; two different smoothing techniques and a vector augmentation technique. Both detection of microcalcifications (as a primary detection technique and as a last stage of a detection scheme), and soft tissue lesions in mammograms are explored. All the results are interesting, and especially the results using FTCM on regions of interest as the last stage in a detection scheme for microcalcifications are promising.

Keywords: detection, mammogram, texture classification, dictionary learning, FTCM

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Authors: S. Mahmoodzadeh, J. Shahrabi, M. A. Torkamani, J. Sabaghzadeh Ghomi

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Recognizing behavioral patterns of financial markets is essential for traders. Japanese candlestick chart is a common tool to visualize and analyze such patterns in an economic time series. Since the world was introduced to Japanese candlestick charting, traders saw how combining this tool with intelligent technical approaches creates a powerful formula for the savvy investors. This paper propose a generalization to box counting method of Grassberger-Procaccia, which is based on computing the correlation dimension of Japanese candlesticks instead commonly used 'close' points. The results of this method applied on several foreign exchange rates vs. IRR (Iranian Rial). Satisfactorily show lower chaotic dimension of Japanese candlesticks series than regular Grassberger-Procaccia method applied merely on close points of these same candles. This means there is some valuable information inside candlesticks.

Keywords: Chaos, Japanese candlestick, generalized box counting, strange attractor.

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Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari

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The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: Optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization.

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Authors: Ashish Thakur, Radhey Shyam Anand

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This paper presents the region based segmentation method for ultrasound images using local statistics. In this segmentation approach the homogeneous regions depends on the image granularity features, where the interested structures with dimensions comparable to the speckle size are to be extracted. This method uses a look up table comprising of the local statistics of every pixel, which are consisting of the homogeneity and similarity bounds according to the kernel size. The shape and size of the growing regions depend on this look up table entries. The algorithms are implemented by using connected seeded region growing procedure where each pixel is taken as seed point. The region merging after the region growing also suppresses the high frequency artifacts. The updated merged regions produce the output in formed of segmented image. This algorithm produces the results that are less sensitive to the pixel location and it also allows a segmentation of the accurate homogeneous regions.

Keywords: Local statistics, region growing, segmentation, ultrasound images.

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Authors: Kenji Suyama, Masahiro Oshida, Noboru Owada

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In this paper, an estimation accuracy of multiple moving talker tracking using a microphone array is improved. The tracking can be achieved by the adaptive method in which two algorithms are integrated, namely, the PAST (Projection Approximation Subspace Tracking) algorithm and the IPLS (Interior Point Least Square) algorithm. When either talker begins to speak again after a silent period, an appropriate feasible region for an evaluation function of the IPLS algorithm might not be set. Then, the tracking fails due to the incorrect updating. Therefore, if an increment of the number of active talkers is detected, the feasible region must be reset. Then, a low cost realization is required for the high speed tracking and a high accuracy realization is desired for the precise tracking. In this paper, the directions roughly estimated using the delayed-sum-array method are used for the resetting. Several results of experiments performed in an actual room environment show the effectiveness of the proposed method.

Keywords: moving talkers tracking, microphone array, signal subspace

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this paper, conventional laser Keratoplasty surgeries in the human eye are studied. For this purpose, a validated 3D finite volume model of the human eye is introduced. In this model the fluid flow has also been considered. The discretized domain of the human eye incorporates a bio-heat transfer equation coupled with a Boussinesq equation. Both continuous and pulsed lasers have been modeled and the results are compared. Moreover, two different conventional surgical positions that are upright and recumbent are compared for these laser therapies. The simulation results show that in these conventional surgeries, the temperature rises above the critical values at the laser insertion areas. However, due to the short duration and the localized nature, the potential damages are restricted to very small regions and can be ignored. The conclusion is that the present day lasers are acceptably safe to the human eye.

Keywords: Eye, heat-transfer, keratoplasty laser, surgery.

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Authors: Reza Hossseynie, Amir Jafari

Abstract:

This paper presents a method for steering velocity bounded mobile robots in environments with partially known stationary obstacles. The exact location of obstacles is unknown and only a probability distribution associated with the location of the obstacles is known. Kinematic model of a 2-wheeled differential drive robot is used as the model of mobile robot. The presented control strategy uses the Artificial Potential Field (APF) method for devising a desired direction of movement for the robot at each instant of time while the Constrained Directions Control (CDC) uses the generated direction to produce the control signals required for steering the robot. The location of each obstacle is considered to be the mean value of the 2D probability distribution and similarly, the magnitude of the electric charge in the APF is set as the trace of covariance matrix of the location probability distribution. The method not only captures the challenges of planning the path (i.e. probabilistic nature of the location of unknown obstacles), but it also addresses the output saturation which is considered to be an important issue from the control perspective. Moreover, velocity of the robot can be controlled during the steering. For example, the velocity of robot can be reduced in close vicinity of obstacles and target to ensure safety. Finally, the control strategy is simulated for different scenarios to show how the method can be put into practice.

Keywords: Steering, obstacle avoidance, mobile robots, constrained directions control, artificial potential field.

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Authors: Ling-fei Xu, Qi Zhao, Yan-ru Chen, Mu-chun Zhou, Meng Zhang, Shi-xue Xu

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SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we found that there exist some regular in the characteristic curve of the flame from the mouse of pudding. And we can use SVM to predict end point of the BOF, just single spectrum intensity should be required as the input parameter. Moreover, its compatibility for the input space is better than the BP network.

Keywords: SVM, predict, BOF, single spectrum intensity.

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Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

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This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab

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In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.

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Authors: Sadaoui Djaouida

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In the paper, the predictive control method is proposed to control the synchronization of two perturbed satellites attitude motion. Based on delayed feedback control of continuous-time systems combines with the prediction-based method of discrete-time systems, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation.

Keywords: Predictive control, Synchronization, Satellite attitude.

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Authors: Yaser Mohammad Taheri, Alireza Zolghadr–asli, Mehran Yazdi

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Video watermarking is usually considered as watermarking of a set of still images. In frame-by-frame watermarking approach, each video frame is seen as a single watermarked image, so collusion attack is more critical in video watermarking. If the same or redundant watermark is used for embedding in every frame of video, the watermark can be estimated and then removed by watermark estimate remodolulation (WER) attack. Also if uncorrelated watermarks are used for every frame, these watermarks can be washed out with frame temporal filtering (FTF). Switching watermark system or so-called SS-N system has better performance against WER and FTF attacks. In this system, for each frame, the watermark is randomly picked up from a finite pool of watermark patterns. At first SS-N system will be surveyed and then a new collusion attack for SS-N system will be proposed using a new algorithm for separating video frame based on watermark pattern. So N sets will be built in which every set contains frames carrying the same watermark. After that, using WER attack in every set, N different watermark patterns will be estimated and removed later.

Keywords: Watermark estimation remodulation (WER), Frame Temporal Averaging (FTF), switching watermark system.

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Authors: O. Poleshchuk, E. Komarov

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The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtained rating points are used in decision making based on fuzzy expert opinions.

Keywords: complete orthogonal semantic space, qualitativecharacteristic, rating points.

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