Search results for: four-dimensional analysis method

Authors: Nan Li, Ying Wang

Abstract:

Using entropy weight and TOPSIS method, a comprehensive evaluation is done on the development level of Chinese regional service industry in this paper. Firstly, based on existing research results, an evaluation index system is constructed from the scale of development, the industrial structure and the economic benefits. An evaluation model is then built up based on entropy weight and TOPSIS, and an empirical analysis is conducted on the development level of service industries in 31 Chinese provinces during 2006 and 2009 from the two dimensions or time series and cross section, which provides new idea for assessing regional service industry. Furthermore, the 31 provinces are classified into four categories based on the evaluation results, and deep analysis is carried out on the evaluation results.

Keywords: Chinese regional service industry, Development level, Entropy weight, TOPSIS Evaluation Method

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Authors: Zongyan Li, Matt Best

Abstract:

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: Correlation analysis, F-ratio, Levenberg-Marquardt, MSE, NARX, neural network, optimisation.

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Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, element-free Galerkin, moving least squares, meshless methods.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Muniyasamy Kalanchiam, Baskar Mannai

Abstract:

Topology Optimization is a defined as the method of determining optimal distribution of material for the assumed design space with functionality, loads and boundary conditions [1]. Topology optimization can be used to optimize shape for the purposes of weight reduction, minimizing material requirements or selecting cost effective materials [2]. Topology optimization has been implemented through the use of finite element methods for the analysis, and optimization techniques based on the method of moving asymptotes, genetic algorithms, optimality criteria method, level sets and topological derivatives. Case study of Typical “Fuselage design" is considered for this paper to explain the benefits of Topology Optimization in the design cycle. A cylindrical shell is assumed as the design space and aerospace standard pay loads were applied on the fuselage with wing attachments as constraints. Then topological optimization is done using Finite Element (FE) based software. This optimization results in the structural concept design which satisfies all the design constraints using minimum material.

Keywords: Fuselage, Topology optimization, payloads, designoptimization, Finite Element Analysis.

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Authors: Nitin Kumar Jain

Abstract:

The distributions of stresses and deflection in rectangular isotropic and orthotropic plates with central circular hole under transverse static loading have been studied using finite element method. The aim of author is to analyze the effect of D/A ratio (where D is hole diameter and A is plate width) upon stress concentration factor (SCF) and deflection in isotropic and orthotropic plates under transverse static loading. The D/A ratio is varied from 0.01 to 0.9. The analysis is done for plates of isotropic and two different orthotropic materials. The results are obtained for three different boundary conditions. The variations of SCF and deflection with respect to D/A ratio are presented in graphical form and discussed. The finite element formulation is carried out in the analysis section of the ANSYS package.

Keywords: Finite Element Method, SCF, Deflection, Plate, Boundary conditions

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Authors: Wei Yee Teoh, Chee Wei Tan

Abstract:

The issue of unintentional islanding in PV grid interconnection still remains as a challenge in grid-connected photovoltaic (PV) systems. This paper discusses the overview of popularly used anti-islanding detection methods, practically applied in PV grid-connected systems. Anti-islanding methods generally can be classified into four major groups, which include passive methods, active methods, hybrid methods and communication base methods. Active methods have been the preferred detection technique over the years due to very small non-detected zone (NDZ) in small scale distribution generation. Passive method is comparatively simpler than active method in terms of circuitry and operations. However, it suffers from large NDZ that significantly reduces its performance. Communication base methods inherit the advantages of active and passive methods with reduced drawbacks. Hybrid method which evolved from the combination of both active and passive methods has been proven to achieve accurate anti-islanding detection by many researchers. For each of the studied anti-islanding methods, the operation analysis is described while the advantages and disadvantages are compared and discussed. It is difficult to pinpoint a generic method for a specific application, because most of the methods discussed are governed by the nature of application and system dependent elements. This study concludes that the setup and operation cost is the vital factor for anti-islanding method selection in order to achieve minimal compromising between cost and system quality.

Keywords: Active method, hybrid method, islanding detection, passive method, photovoltaic (PV), utility method

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

Abstract:

Real-time hand tracking is a challenging task in many computer vision applications such as gesture recognition. This paper proposes a robust method for hand tracking in a complex environment using Mean-shift analysis and Kalman filter in conjunction with 3D depth map. The depth information solve the overlapping problem between hands and face, which is obtained by passive stereo measuring based on cross correlation and the known calibration data of the cameras. Mean-shift analysis uses the gradient of Bhattacharyya coefficient as a similarity function to derive the candidate of the hand that is most similar to a given hand target model. And then, Kalman filter is used to estimate the position of the hand target. The results of hand tracking, tested on various video sequences, are robust to changes in shape as well as partial occlusion.

Keywords: Computer Vision and Image Analysis, Object Tracking, Gesture Recognition.

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Authors: Thirasak Panyaphirawat, Pairoj Sapsmarnwong, Teeratas Pornyungyuen

Abstract:

This paper presents the findings of an experimental investigation of important machining parameters for the horizontal boring tool modified to mouth with a horizontal lathe machine to bore an overlength workpiece. In order to verify a usability of a modified tool, design of experiment based on Taguchi method is performed. The parameters investigated are spindle speed, feed rate, depth of cut and length of workpiece. Taguchi L9 orthogonal array is selected for four factors three level parameters in order to minimize surface roughness (Ra and Rz) of S45C steel tubes. Signal to noise ratio analysis and analysis of variance (ANOVA) is performed to study an effect of said parameters and to optimize the machine setting for best surface finish. The controlled factors with most effect are depth of cut, spindle speed, length of workpiece, and feed rate in order. The confirmation test is performed to test the optimal setting obtained from Taguchi method and the result is satisfactory.

Keywords: Design of Experiment, Taguchi Design, Optimization, Analysis of Variance, Machining Parameters, Horizontal Boring Tool.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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Authors: S. Sarumathi, N. Shanthi, S. Vidhya, M. Sharmila

Abstract:

An extensive amount of work has been done in data clustering research under the unsupervised learning technique in Data Mining during the past two decades. Moreover, several approaches and methods have been emerged focusing on clustering diverse data types, features of cluster models and similarity rates of clusters. However, none of the single clustering algorithm exemplifies its best nature in extracting efficient clusters. Consequently, in order to rectify this issue, a new challenging technique called Cluster Ensemble method was bloomed. This new approach tends to be the alternative method for the cluster analysis problem. The main objective of the Cluster Ensemble is to aggregate the diverse clustering solutions in such a way to attain accuracy and also to improve the eminence the individual clustering algorithms. Due to the massive and rapid development of new methods in the globe of data mining, it is highly mandatory to scrutinize a vital analysis of existing techniques and the future novelty. This paper shows the comparative analysis of different cluster ensemble methods along with their methodologies and salient features. Henceforth this unambiguous analysis will be very useful for the society of clustering experts and also helps in deciding the most appropriate one to resolve the problem in hand.

Keywords: Clustering, Cluster Ensemble Methods, Coassociation matrix, Consensus Function, Median Partition.

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Authors: Tang Wei, Yang Xiaofeng, Gui Yewei, Du Yanxia

Abstract:

Complex lifting entry was selected for precise landing performance during the Mars Science Laboratory entry. This study aims to develop the three-dimensional numerical method for precise computation and the surface panel method for rapid engineering prediction. Detailed flow field analysis for Mars exploration mission was performed by carrying on a series of fully three-dimensional Navier-Stokes computations. The static aerodynamic performance was then discussed, including the surface pressure, lift and drag coefficient, lift-to-drag ratio with the numerical and engineering method. Computation results shown that the shock layer is thin because of lower effective specific heat ratio, and that calculated results from both methods agree well with each other, and is consistent with the reference data. Aerodynamic performance analysis shows that CG location determines trim characteristics and pitch stability, and certain radially and axially shift of the CG location can alter the capsule lifting entry performance, which is of vital significance for the aerodynamic configuration design and inner instrument layout of the Mars entry capsule.

Keywords: Mars entry capsule, static aerodynamics, computational fluid dynamics, hypersonic.

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Authors: Wookyung Baik, Seungchan Lee, Choongmin Jeong, Siwoo Kim, Myungwon Suh

Abstract:

Development of motor car safety devices has reduced fatality rates in car accidents. Yet despite this increase in car safety, neck injuries resulting from rear impact collisions, particularly at low speed, remain a primary concern. In this study, FEA(Finite Element Analysis) of seat was performed to evaluate neck injuries in rear impact. And the FEA result was verified by comparison with the actual test results. The dummy used in FE model and actual test is BioRID II which is regarded suitable for rear impact collision analysis. A threshold of the BioRID II neck injury indicators was also proposed to upgrade seat performance in order to reduce whiplash injury. To optimize the seat for a low-speed rear impact collision, a method was proposed, which is multi-objective optimization idea using DOE (Design of Experiments) results.

Keywords: Whiplash injury, Dynamic assessment, Finite element method, Optimization, DOE (Design of Experiments), WSM (Weighed Sum Method).

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Authors: Saleem Z. Ramadan

Abstract:

In this paper, a model is proposed to determine the life distribution parameters of the useful life region for the PV system utilizing a combination of non-parametric and linear regression analysis for the failure data of these systems. Results showed that this method is dependable for analyzing failure time data for such reliable systems when the data is scarce.

Keywords: Masking, Bathtub model, reliability, non-parametric analysis, useful life.

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Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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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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Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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Authors: Hossein Mohammadpour, Rahman Dashti

Abstract:

Power transformers are among the most important and expensive equipments in the electric power systems. Consequently the transformer protection is an essential part of the system protection. This paper presents a new method for locating transformer winding faults such as turn-to-turn, turn-to-core, turn-totransformer body, turn-to-earth, and high voltage winding to low voltage winding. In this study the current and voltage signals of input and output terminals of the transformer are measured, which the Fourier transform of measured signals and harmonic analysis determine the fault's location.

Keywords: turn-to-turn faults, short circuit, Fourier transform, harmonic analysis.

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Authors: Emrah Bulut, Okan Duru, Shigeru Yoshida

Abstract:

In this study, a fuzzy integrated logical forecasting method (FILF) is extended for multi-variate systems by using a vector autoregressive model. Fuzzy time series forecasting (FTSF) method was recently introduced by Song and Chissom [1]-[2] after that Chen improved the FTSF method. Rather than the existing literature, the proposed model is not only compared with the previous FTS models, but also with the conventional time series methods such as the classical vector autoregressive model. The cluster optimization is based on the C-means clustering method. An empirical study is performed for the prediction of the chartering rates of a group of dry bulk cargo ships. The root mean squared error (RMSE) metric is used for the comparing of results of methods and the proposed method has superiority than both traditional FTS methods and also the classical time series methods.

Keywords: C-means clustering, Fuzzy time series, Multi-variate design

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Authors: T. Yamaguchi, Y. Fujii, A. Takita, T. Kanai

Abstract:

To compute dynamic characteristics of nonlinear viscoelastic springs with elastic structures having huge degree-of-freedom, Yamaguchi proposed a new fast numerical method using finite element method [1]-[2]. In this method, restoring forces of the springs are expressed using power series of their elongation. In the expression, nonlinear hysteresis damping is introduced. In this expression, nonlinear complex spring constants are introduced. Finite element for the nonlinear spring having complex coefficients is expressed and is connected to the elastic structures modeled by linear solid finite element. Further, to save computational time, the discrete equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. In this report, the proposed method is applied to simulation for impact responses of a viscoelastic shock absorber with an elastic structure (an S-shaped structure) by colliding with a concentrated mass. The concentrated mass has initial velocities and collides with the shock absorber. Accelerations of the elastic structure and the concentrated mass are measured using Levitation Mass Method proposed by Fujii [3]. The calculated accelerations from the proposed FEM, corresponds to the experimental ones. Moreover, using this method, we also investigate dynamic errors of the S-shaped force transducer due to elastic mode in the S-shaped structure.

Keywords: Transient response, Finite Element analysis, Numerical analysis, Viscoelastic shock absorber, Force transducer.

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Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.

Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.

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Authors: Diako Azizi, Ahmad Gholami, Vahid Abbasi

Abstract:

High voltage generators are being subject to higher voltage rating and are being designed to operate in harsh conditions. Stator windings are the main component of generators in which Electrical, magnetically and thermal stresses remain major failures for insulation degradation accelerated aging. A large number of generators failed due to stator winding problems, mainly insulation deterioration. Insulation degradation assessment plays vital role in the asset life management. Mostly the stator failure is catastrophic causing significant damage to the plant. Other than generation loss, stator failure involves heavy repair or replacement cost. Electro thermal analysis is the main characteristic for improvement design of stator slot-s insulation. Dielectric parameters such as insulation thickness, spacing, material types, geometry of winding and slot are major design consideration. A very powerful method available to analyze electro thermal performance is Finite Element Method (FEM) which is used in this paper. The analysis of various stator coil and slot configurations are used to design the better dielectric system to reduce electrical and thermal stresses in order to increase the power of generator in the same volume of core. This paper describes the process used to perform classical design and improvement analysis of stator slot-s insulation.

Keywords: Electromagnetic field, field distribution, insulation, winding, finite element method

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Authors: Jeong Yup Han, Su Kyung Lee, Hong Bae Park

Abstract:

In this paper, we propose a method to reduce the various kinds of noise while gathering and recording the electrocardiogram (ECG) signal. Because of the defects of former method in the noise elimination of ECG signal, we use translation invariant (TI) multiwavelet denoising method to the noise elimination. The advantage of the proposed method is that it may not only remain the geometrical characteristics of the original ECG signal and keep the amplitudes of various ECG waveforms efficiently, but also suppress impulsive noise to some extent. The simulation results indicate that the proposed method are better than former removing noise method in aspects of remaining geometrical characteristics of ECG signal and the signal-to-noise ratio (SNR).

Keywords: ECG, TI multiwavelet, denoise.

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Authors: Azeemsha Thacham Poyil, Nasimudeen KM

Abstract:

This research paper presents some methods to assess the performance of Wigner Ville Distribution for Time-Frequency representation of non-stationary signals, in comparison with the other representations like STFT, Spectrogram etc. The simultaneous timefrequency resolution of WVD is one of the important properties which makes it preferable for analysis and detection of linear FM and transient signals. There are two algorithms proposed here to assess the resolution and to compare the performance of signal detection. First method is based on the measurement of area under timefrequency plot; in case of a linear FM signal analysis. A second method is based on the instantaneous power calculation and is used in case of transient, non-stationary signals. The implementation is explained briefly for both methods with suitable diagrams. The accuracy of the measurements is validated to show the better performance of WVD representation in comparison with STFT and Spectrograms.

Keywords: WVD: Wigner Ville Distribution, STFT: Short Time Fourier Transform, FT: Fourier Transform, TFR: Time-Frequency Representation, FM: Frequency Modulation, LFM Signal: Linear FM Signal, JTFA: Joint time frequency analysis.

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Authors: A. Farshidianfar, P. Oliazadeh, M. H. Farshidianfar

Abstract:

In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.

Keywords: Circular Cylindrical Shell, Free Vibration, Natural Frequency.

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Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

Abstract:

In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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Authors: Diako Azizi, Ahmad Gholami, Vahid Abbasi

Abstract:

High voltage generators are being subject to higher voltage rating and are being designed to operate in harsh conditions. Stator windings are the main component of generators in which Electrical, magnetical and thermal stresses remain major failures for insulation degradation accelerated aging. A large number of generators failed due to stator winding problems, mainly insulation deterioration. Insulation degradation assessment plays vital role in the asset life management. Mostly the stator failure is catastrophic causing significant damage to the plant. Other than generation loss, stator failure involves heavy repair or replacement cost. Electro thermal analysis is the main characteristic for improvement design of stator slot-s insulation. Dielectric parameters such as insulation thickness, spacing, material types, geometry of winding and slot are major design consideration. A very powerful method available to analyze electro thermal performance is Finite Element Method (FEM) which is used in this paper. The analysis of various stator coil and slot configurations are used to design the better dielectric system to reduce electrical and thermal stresses in order to increase the power of generator in the same volume of core. This paper describes the process used to perform classical design and improvement analysis of stator slot-s insulation.

Keywords: Electrical field, field distribution, insulation, winding, finite element method, electro thermal

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Authors: José Peralta, Gabriela Peretti, Eduardo Romero, Carlos Marqués

Abstract:

This paper proposes a new performance characterization for the test strategy intended for second order filters denominated Transient Analysis Method (TRAM). We evaluate the ability of the addressed test strategy for detecting deviation faults under simultaneous statistical fluctuation of the non-faulty parameters. For this purpose, we use Monte Carlo simulations and a fault model that considers as faulty only one component of the filter under test while the others components adopt random values (within their tolerance band) obtained from their statistical distributions. The new data reported here show (for the filters under study) the presence of hard-to-test components and relatively low fault coverage values for small deviation faults. These results suggest that the fault coverage value obtained using only nominal values for the non-faulty components (the traditional evaluation of TRAM) seem to be a poor predictor of the test performance.

Keywords: testing, fault analysis, analog filter test, parametric faults detection.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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