Search results for: pseudo arclength method.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8190

Search results for: pseudo arclength method.

7500 Finite Volume Method for Flow Prediction Using Unstructured Meshes

Authors: Juhee Lee, Yongjun Lee

Abstract:

In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.

Keywords: Finite volume method, fluid flow, laminar flow, unstructured grid.

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7499 Aircraft Selection Problem Using Decision Uncertainty Distance in Fuzzy Multiple Criteria Decision Making Analysis

Authors: C. Ardil

Abstract:

Aircraft have different capabilities and specifications according to the required strategic goals and objectives in operations. With various types on the market with different aircraft characteristics, it becomes difficult to select a suitable aircraft for certain operations and requirements. The entropy weighting method (EWM) is a useful, highly consistent, and reliable method for obtaining the weights of the criteria and is worth integrating with the decision uncertainty distance (DUD) method, which is more applicable and requires less computation than other methods. An illustrative example is presented to demonstrate the validity and usability of the proposed methodology. Comparing the ranking results matches the distance-based approach, which is the technique for order preference by similarity to ideal solution (TOPSIS) method, which shows the robustness of the entropy DUD hybrid method. Validity analysis shows that the proposed hybrid multiple criteria decision-making analysis (MCDMA) methodology is quantitatively stable and reliable.

Keywords: aircraft selection, decision uncertainty distance (DUD), multiple criteria decision making analysis, MCDMA, TOPSIS

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7498 Key Frames Extraction for Sign Language Video Analysis and Recognition

Authors: Jaroslav Polec, Petra Heribanová, Tomáš Hirner

Abstract:

In this paper we proposed a method for finding video frames representing one sign in the finger alphabet. The method is based on determining hands location, segmentation and the use of standard video quality evaluation metrics. Metric calculation is performed only in regions of interest. Sliding mechanism for finding local extrema and adaptive threshold based on local averaging is used for key frames selection. The success rate is evaluated by recall, precision and F1 measure. The method effectiveness is compared with metrics applied to all frames. Proposed method is fast, effective and relatively easy to realize by simple input video preprocessing and subsequent use of tools designed for video quality measuring.

Keywords: Key frame, video, quality, metric, MSE, MSAD, SSIM, VQM, sign language, finger alphabet.

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7497 Analytical Based Truncation Principle of Higher-Order Solution for a x1/3 Force Nonlinear Oscillator

Authors: Md. Alal Hosen

Abstract:

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x1/3 force nonlinear oscillator but it is also useful for many other nonlinear problems.

Keywords: Approximate solutions, Harmonic balance method, Nonlinear oscillator, Perturbation.

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7496 Slip Suppression of Electric Vehicles using Model Predictive PID Controller

Authors: Tohru Kawabe

Abstract:

In this paper, a new model predictive PID controller design method for the slip suppression control of EVs (electric vehicles) is proposed. The proposed method aims to improve the maneuverability and the stability of EVs by controlling the wheel slip ratio. The optimal control gains of PID framework are derived by the model predictive control (MPC) algorithm. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Model Predictive Control, PID controller, Electric Vehicle, Slip suppression

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7495 Model Order Reduction for Frequency Response and Effect of Order of Method for Matching Condition

Authors: Aref Ghafouri, Mohammad Javad Mollakazemi, Farhad Asadi

Abstract:

In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further.

Keywords: Frequency response, Order of model reduction, frequency matching condition.

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7494 Heuristic Method for Judging the Computational Stability of the Difference Schemes of the Biharmonic Equation

Authors: Guang Zeng, Jin Huang, Zicai Li

Abstract:

In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

Keywords: Finite-difference equation, computational stability, hirt method.

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7493 Application of KL Divergence for Estimation of Each Metabolic Pathway Genes

Authors: Shohei Maruyama, Yasuo Matsuyama, Sachiyo Aburatani

Abstract:

Development of a method to estimate gene functions is an important task in bioinformatics. One of the approaches for the annotation is the identification of the metabolic pathway that genes are involved in. Since gene expression data reflect various intracellular phenomena, those data are considered to be related with genes’ functions. However, it has been difficult to estimate the gene function with high accuracy. It is considered that the low accuracy of the estimation is caused by the difficulty of accurately measuring a gene expression. Even though they are measured under the same condition, the gene expressions will vary usually. In this study, we proposed a feature extraction method focusing on the variability of gene expressions to estimate the genes' metabolic pathway accurately. First, we estimated the distribution of each gene expression from replicate data. Next, we calculated the similarity between all gene pairs by KL divergence, which is a method for calculating the similarity between distributions. Finally, we utilized the similarity vectors as feature vectors and trained the multiclass SVM for identifying the genes' metabolic pathway. To evaluate our developed method, we applied the method to budding yeast and trained the multiclass SVM for identifying the seven metabolic pathways. As a result, the accuracy that calculated by our developed method was higher than the one that calculated from the raw gene expression data. Thus, our developed method combined with KL divergence is useful for identifying the genes' metabolic pathway.

Keywords: Metabolic pathways, gene expression data, microarray, Kullback–Leibler divergence, KL divergence, support vector machines, SVM, machine learning.

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7492 Design of Speed and Power Control System for Wind Turbine with Reference Tracking Method

Authors: H. Ghanbari, H. Nikbakht, A. Zahedi, M. Ghanbari

Abstract:

This paper is focusing on designing a control system for wind turbine which can control the speed and output power according to arbitrary algorithm. Reference Tracking Method is used to control the turbine spinning speed in order to increase its output energy.

Keywords: Wind Turbine, Simulink, Reference Tracking Method.

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7491 On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm

Authors: Tomohiro Hachino, Kengo Nagatomo, Hitoshi Takata

Abstract:

This paper deals with an on-line identification method of continuous-time Hammerstein systems by using the radial basis function (RBF) networks and immune algorithm (IA). An unknown nonlinear static part to be estimated is approximately represented by the RBF network. The IA is efficiently combined with the recursive least-squares (RLS) method. The objective function for the identification is regarded as the antigen. The candidates of the RBF parameters such as the centers and widths are coded into binary bit strings as the antibodies and searched by the IA. On the other hand, the candidates of both the weighting parameters of the RBF network and the system parameters of the linear dynamic part are updated by the RLS method. Simulation results are shown to illustrate the proposed method.

Keywords: Continuous-time System, Hammerstein System, OnlineIdentification, Immune Algorithm, RBF network.

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7490 Vendor Selection and Supply Quotas Determination by using Revised Weighting Method and Multi-Objective Programming Methods

Authors: Tunjo Perić, Marin Fatović

Abstract:

In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology has been tested on the example of flour purchase for a bakery with two decision makers.

Keywords: Cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection.

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7489 Geometric Operators in Decision Making with Minimization of Regret

Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We study different types of aggregation operators and the decision making process with minimization of regret. We analyze the original work developed by Savage and the recent work developed by Yager that generalizes the MMR method creating a parameterized family of minimal regret methods by using the ordered weighted averaging (OWA) operator. We suggest a new method that uses different types of geometric operators such as the weighted geometric mean or the ordered weighted geometric operator (OWG) to generalize the MMR method obtaining a new parameterized family of minimal regret methods. The main result obtained in this method is that it allows to aggregate negative numbers in the OWG operator. Finally, we give an illustrative example.

Keywords: Decision making, Regret, Aggregation operators, OWA operator, OWG operator.

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7488 Laser-Ultrasonic Method for Measuring the Local Elastic Moduli of Porous Isotropic Composite Materials

Authors: Alexander A. Karabutov, Natalia B. Podymova, Elena B. Cherepetskaya, Vladimir A. Makarov, Yulia G. Sokolovskaya

Abstract:

The laser-ultrasonic method is realized for quantifying the influence of porosity on the local Young’s modulus of isotropic composite materials. The method is based on a laser thermooptical method of ultrasound generation combined with measurement of the phase velocity of longitudinal and shear acoustic waves in samples. The main advantage of this method compared with traditional ultrasonic research methods is the efficient generation of short and powerful probing acoustic pulses required for reliable testing of ultrasound absorbing and scattering heterogeneous materials. Using as an example samples of a metal matrix composite with reinforcing microparticles of silicon carbide in various concentrations, it is shown that to provide an effective increase in Young’s modulus with increasing concentration of microparticles, the porosity of the final sample should not exceed 2%.

Keywords: Laser ultrasonic, longitudinal and shear ultrasonic waves, porosity, composite, local elastic moduli.

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7487 Objective Evaluation of Mathematical Morphology Edge Detection on Computed Tomography (CT) Images

Authors: Emhimed Saffor, Abdelkader Salama

Abstract:

In this paper problem of edge detection in digital images is considered. Edge detection based on morphological operators was applied on two sets (brain & chest) ct images. Three methods of edge detection by applying line morphological filters with multi structures in different directions have been used. 3x3 filter for first method, 5x5 filter for second method, and 7x7 filter for third method. We had applied this algorithm on (13 images) under MATLAB program environment. In order to evaluate the performance of the above mentioned edge detection algorithms, standard deviation (SD) and peak signal to noise ratio (PSNR) were used for justification for all different ct images. The objective method and the comparison of different methods of edge detection,  shows that high values of both standard deviation and PSNR values of edge detection images were obtained. 

Keywords: Medical images, Matlab, Edge detection.

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7486 Non–Geometric Sensitivities Using the Adjoint Method

Authors: Marcelo Hayashi, João Lima, Bruno Chieregatti, Ernani Volpe

Abstract:

The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation.

Keywords: Adjoint method, optimisation, non–geometric sensitivities, boundary conditions.

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7485 Some Results on New Preconditioned Generalized Mixed-Type Splitting Iterative Methods

Authors: Guangbin Wang, Fuping Tan, Deyu Sun

Abstract:

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.

Keywords: Preconditioned, GMTS method, linear system, convergence, comparison.

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7484 High Performance Electrocardiogram Steganography Based on Fast Discrete Cosine Transform

Authors: Liang-Ta Cheng, Ching-Yu Yang

Abstract:

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

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

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7483 Building a Trend Based Segmentation Method with SVR Model for Stock Turning Detection

Authors: Jheng-Long Wu, Pei-Chann Chang, Yi-Fang Pan

Abstract:

This research focus on developing a new segmentation method for improving forecasting model which is call trend based segmentation method (TBSM). Generally, the piece-wise linear representation (PLR) can finds some of pair of trading points is well for time series data, but in the complicated stock environment it is not well for stock forecasting because of the stock has more trends of trading. If we consider the trends of trading in stock price for the trading signal which it will improve the precision of forecasting model. Therefore, a TBSM with SVR model used to detect the trading points for various stocks of Taiwanese and America under different trend tendencies. The experimental results show our trading system is more profitable and can be implemented in real time of stock market

Keywords: Trend based segmentation method, support vector machine, turning detection, stock forecasting.

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7482 Modified Hankel Matrix Approach for Model Order Reduction in Time Domain

Authors: C. B. Vishwakarma

Abstract:

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

Keywords: Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error.

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7481 3D High-Precision Tunnel Gravity Exploration Method for Concealed High-Density Ore-Bodies: A Case Study on the Zhaotong Maoping Carbonate-Hosted Zn-Pb-(Ag-Ge) Deposit in Northeastern Yunnan, China

Authors: Han Run-Sheng, Li Wen-Yao, Wang Feng, Liu Fei, Qiu Wen-Long, Lei Li

Abstract:

Accurately positioning detection of concealed deposits or ore-bodies is one of the difficult problems in mineral exploration field. Theory calculation and exploration practices for tunnel gravity indicate that 3D high-precision Tunnel Gravity Exploration Method (TGEM) can find concealed high-density three-dimensional ore-bodies in the depth. The ore-finding breakthroughs at the depth of the Zhaotong Maoping carbonate-hosted Zn–Pb–(Ag–Ge) deposit in Northeastern Yunnan have proved that the exploration method in combination with MEAHFZ method is effective to detect concealed high-density ore-bodies. TGEM may overcome anomalous ambiguity of other geophysical methods for 3D positioning of concealed ore-bodies.

Keywords: 3D tunnel gravity exploration method, concealed high-density ore-bodies, Zn–Pb–(Ag–Ge) deposit, Zaotong Maoping, Northeastern Yunnan.

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7480 The Projection Methods for Computing the Pseudospectra of Large Scale Matrices

Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du

Abstract:

The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.

Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)

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7479 Dynamics of a Vapour Bubble inside a Vertical Rigid Cylinder in the Absence of Buoyancy Forces

Authors: S. Mehran, S. Rouhi, F.Rouzbahani, E. Haghgoo

Abstract:

In this paper, growth and collapse of a vapour bubble generated due to a local energy input inside a rigid cylinder and in the absence of buoyancy forces is investigated using Boundary Integral Equation Method and Finite Difference Method .The fluid is treated as potential flow and Boundary Integral Equation Method is used to solve Laplace-s equation for velocity potential. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.

Keywords: Vapour bubble, Vertical rigid cylinder, Boundaryelement method, Finite difference method, Buoyancy forces.

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7478 Transient Heat Transfer of a Spiral Fin

Authors: Sen-Yung Lee, Li-Kuo Chou, Chao-Kuang Chen

Abstract:

In this study, the problem of temperature transient response of a spiral fin, with its end insulated, is analyzed with base end subjected to a variation of fluid temperature. The hybrid method of Laplace transforms/Adomian decomposed method-Padé, is applied to the temperature transient response of the fin, the result of the temperature distribution and the heat flux at the base of the spiral fin are obtained, show a good agreement in the physical phenomenon.

Keywords: Laplace transforms/Adomian decomposed method- Padé, transient response, heat transfer.

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7477 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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7476 Non-Convex Multi Objective Economic Dispatch Using Ramp Rate Biogeography Based Optimization

Authors: Susanta Kumar Gachhayat, S. K. Dash

Abstract:

Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances.

Keywords: Economic load dispatch, Biogeography based optimization, Ramp rate biogeography based optimization, Valve Point loading, Moderate random particle swarm optimization method, Weight improved particle swarm optimization method

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7475 Black Box Model and Evolutionary Fuzzy Control Methods of Coupled-Tank System

Authors: S. Yaman, S. Rostami

Abstract:

In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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7474 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

Authors: Minghui Wang

Abstract:

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

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7473 The Analysis of Own Signals of PM Electrical Machines – Example of Eccentricity

Authors: M. Barański

Abstract:

This article presents a vibration diagnostic method designed for Permanent Magnets (PM) electrical machines–traction motors and generators. Those machines are commonly used in traction drives of electrical vehicles and small wind or water systems. The described method is very innovative and unique. Specific structural properties of machines excited by permanent magnets are used in this method - electromotive force (EMF) generated due to vibrations. There was analyzed number of publications, which describe vibration diagnostic methods, and tests of electrical machines and there was no method found to determine the technical condition of such machine basing on their own signals. This work presents field-circuit model, results of static tests, results of calculations and simulations.

Keywords: Electrical vehicle, permanent magnet, traction drive, vibrations, electrical machine, eccentricity, diagnostics, data acquisition, data analysis.

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7472 A System Functions Set-Up through Near Field Communication of a Smartphone

Authors: Jaemyoung Lee

Abstract:

We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: System set-up, near field communication, smartphone, Android.

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7471 Robust Stabilization of Rotational Motion of Underwater Robots against Parameter Uncertainties

Authors: Riku Hayashida, Tomoaki Hashimoto

Abstract:

This paper provides a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. Underwater robots are expected to be used for various work assignments. The large variety of applications of underwater robots motivates researchers to develop control systems and technologies for underwater robots. Several control methods have been proposed so far for the stabilization of nominal system model of underwater robots with no parameter uncertainty. Parameter uncertainties are considered to be obstacles in implementation of the such nominal control methods for underwater robots. The objective of this study is to establish a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: Robust control, stabilization method, underwater robot, parameter uncertainty.

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