• Smart Structures and Systems
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• v.16 no.3
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• pp.401-414
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• 2015

A developed hybrid method for crack identification of beams is presented. Based on the Euler-Bernouli beam theory and concepts of fracture mechanics, governing equation of the cracked beams is reformulated. Finite element (FE) method as a powerful numerical tool is used to discritize the equation in space domain. After transferring the equations from time domain to frequency domain, frequencies and mode shapes of the beam are obtained. Efficiency of the governed equation for free vibration analysis of the beams is shown by comparing the results with those available in literature and via ANSYS software. The used equation yields to move the influence of cracks from the stiffness matrix to the mass matrix. For crack identification measured data are produced by applying random error to the calculated frequencies and mode shapes. An objective function is prepared as root mean square error between measured and calculated data. To minimize the function, hybrid genetic algorithms (GAs) and particle swarm optimization (PSO) technique is introduced. Efficiency, Robustness, applicability and usefulness of the mixed optimization numerical tool in conjunction with the finite element method for identification of cracks locations and depths are shown via solving different examples.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.544-547
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• 1997

In this paper, we propose a dynamic localization method using a rotating sonar and a map. The proposed method is implemented by using extended Kalman filter. The state equation is based on the encoder propagation model and the encoder error model, and the measurement equation is a map-based measurement equation using a rotating sonar sensor. By utilizing sonar beam characteristics, map-based measurements are updated while AMR is moving continuously. By modeling and estimating systematic errors of a differential encoder, the position is successfully estimated even the interval of the map-based measurement. Monte-Carlo simulation shows that the proposed global position estimator has the performance of a few millimeter order in position error and of a few tenth degrees in heading error and of compensating systematic errors of the differential encoder well.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.3
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• pp.341-349
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• 1997

The characteristics of defect correction method are discussed in a sample heat conduction problem showing the numerical solution of the error correction equation can predict the error of the numerical solution of the original governing equation. A way of using defect correction method combined with the existing algorithm for the incompressible fluid flow, is proposed and subsequently tested for the driven square cavity problem. The error correction equations for the continuity equation and the momentum equations are considered to estimate the errors of the numerical solutions of the original governing equations. With this new approach, better velocity and pressure fields can be obtained by correcting the original numerical solutions using the estimated errors. These calculated errors also can be used to estimate the orders of magnitude of the errors of the original numerical solutions.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.5 s.170
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• pp.55-62
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• 2005

This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.483-487
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• 1996

We consider the estimation of the position and orientation of 6 DOF motion bed (Stewart platform) from the measured cylinder length. The solution of forward kinematics is not solved yet as a useful realtime application tool because of the complity of the equation with multiple solutiple solutions. Hence we suggest an algorithm for the estimation of forward kinematics solution using Luenberger observer withnonlinear error correction term. The Luenberger observer withlinear model shows that the estimation error does not go to zero in steadystate due to the linearization error of the dynamic model. Hence the linear observer is modified using nonlinear measurement error equation and we prove thd practical stability of the estimation error dynamics of the proposed observer using lyapunov function.

• The Mathematical Education
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• v.53 no.4
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• pp.509-524
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• 2014

This study was to investigate the types of errors and the frequency of errors to understand students' solving process on the descriptive items with the students of an excellent high school which located in a non-leveling local school district of Gyunggi Province. All 11 items were developed in the equation of a circle and 120 students who attended this high school participated in solving them. The result showed a tendency as follows: Logically invalid inference(Type A, 38.83%) of errors, Omission error of the problem solving process(Type B, 25%), Technical error(Type C, 15.67%), Wrong conclusion(Type D, 11.94%), Use of wrong theorem(Type E, 5.97%), and Use of wrong picture(Type F, 2.61%). The logically invalid inference the students showed with a largest tendency was made because of the lack of reflection. This meant that this error could be corrected in a little treatment of carefulness.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.75-83
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• 2016

We propose methodology to analyze the dynamic mechanisms of financial market contagion under market integration using a biological contagion analytical approach. We employ U-statistic to measure market integration, and a dynamic model based on an error correction mechanism (single equation error correction model) and latent factor model to examine market contagion. We also use quantile regression and Wald-Wolfowitz runs test to test market contagion. This methodology is designed to effectively handle heteroscedasticity and correlated errors. Our simulation results show that the single equation error correction model fits well with the linear regression model with a stationary predictor and correlated errors.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.11
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• pp.898-906
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• 2014

This paper presents a reduction method for a straight-line path error of a flexible beam deploying from a rotating rigid hub. Previous studies discussed about only vibration phenomena of flexible beams deploying from rotating hubs; however, this study investigates a vibration reduction of a rotating beam with variable length. The equation of motion and associated boundary conditions are derived for a flexible beam deploying from a rotating rigid hub, and then they are transformed to a variational equation. By applying the Galerkin method, the discretized equations are obtained from the variational equation. Based on the discretized equations, the dynamic responses of a rotating/deploying beam are analyzed when the beam end has a straight line motion. A reduction method for the trajectory error is proposed, using the average length of a rotating/deploying beam. It is shown that the proposed method is able to reduce the residual vibration of a rotating/deploying beam.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Journal of the Korean Society of Safety
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• v.36 no.3
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• pp.60-65
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• 2021

Human error is often in part in the cause of accidents and the result of various factors in an organization. Accidents should be investigated to elucidate all causes. Therefore, to reduce accidents, it is necessary to identify which factors affect human error within the organization. In this study, five groups of influencing factors on human error were selected using previousresearch, and operational definitions were made based on them. In addition, a questionnaire for measuring latent variables by operational definition was developed as an observation variable, and responses were received from employees of chemical companies in Ulsan. Based on SEM (structural equation modeling) analysis, 1) confirmatory factor analysis of variables in the human error model, 2) reliability and validity of latent variables, 3) correlations among latent variables, 4) influencing coefficients among influence factors, and 5) the verification results of the paths that these influencing factors have on human error are introduced in this study.