• Title/Summary/Keyword: Approximating Model

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Behrens-Fisher Problem from a Model Selection Point of View

  • Jeon, Jong-Woo;Lee, Kee-Won
    • Journal of the Korean Statistical Society
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    • v.20 no.2
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    • pp.99-107
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    • 1991
  • Behrens-Fisher problem is viewed from a model selection approach. Normal distribution is regarded as an approximating model, A criterion, called TIC, is derived and is compared with selection criteria such as AIC and a bootstrap estimator. Stochastic approximation is used since no closed form expression is available for the bootstrap estimator.

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On the Model Selection Criteria in Normal Distributions

  • Chung, Han-Yeong;Lee, Kee-Won
    • Journal of the Korean Statistical Society
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    • v.21 no.2
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    • pp.93-110
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    • 1992
  • A model selection approach is used to find out whether the mean and the variance of a unique sample are different from the pre-specified values. Normal distribution is selected as an approximating model. Kullback-Leibler discrepancy comes out as a natural measure of discrepancy between the operating model and the approximating model. Several estimates of selection criterion are computed including AIC, TIC, and a coupleof bootstrap estimator of the selection criterion are considered according to the way of resampling. It is shown that a closed form expression is available for the parametric bootstrap estimated cirterion. A Monte Carlo study is provided to give a formal comparison when the operating family itself is normally distributed.

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Feature Extraction Algorithm from Polygonal Model using Implicit Surface Fitting (음함수 곡면 맞춤을 이용한 다각형 모델로부터 특징 추출 알고리즘)

  • Kim, Soo-Kyun
    • Journal of Korea Multimedia Society
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    • v.12 no.1
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    • pp.50-57
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    • 2009
  • This paper proposes a extraction of feature lines on a polygonal model using local implicit surface fitting technique. To extract feature lines on a polygonal model, the previous technique addressed to compute the curvature and their derivatives at mesh vertices via global implicit surface fitting. It needs a user-specified precision parameter for finding an accurate projection of the mesh vertices onto an approximating implicit surface and requires high-time consumption. But we use a local implicit surface fitting technique to estimate the local differential information near a vertex by means of an approximating surface. Feature vertices are easily detected as zero-crossings, and can then be connected along the direction of principal curvature. Our method, demonstrated on several large polygonal models, produces a good fit which leads to improved visualization.

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THE TRANSPORT OF NUCLEAR CONTAMINATION IN FRACTURED POROUS MEDIA

  • Jim-Douglas, Jr.;Anna M.Spagnuolo
    • Journal of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.723-761
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    • 2001
  • The objects of this paper are to formulated a model for the transport of a chain of radioactive waste products in a fractured porous medium, to devise an effective and efficient numerical method for approximating the solution of the model, and to demonstrated the convergence of the numerical method. The formulation begins from a model in an unfractured (single porosity) medium, passes through a double porosity model in a fractured medium, and ends with a modified single porosity model that takes the relevant time scales of the flow and the nuclear decay.

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Fuzzy Sliding Mode Control for Uncertain Nonlinear Systems Using Fuzzy Models

  • Seo, Sam-Jun;Kim, Dong-Sik
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.1262-1266
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    • 2003
  • Fuzzy sliding mode controller for a class of uncertain nonlinear dynamical systems is proposed and analyzed. The controller's construction and its analysis involve sliding modes. The proposed controller consists of two components. Sliding mode component is employed to eliminate the effects of disturbances, while a fuzzy model component equipped with an adaptation mechanism reduces modeling uncertainties by approximating model uncertainties. To demonstrate its performance, the proposed control algorithm is applied to an inverted pendulum. The results show that both alleviation of chattering and performance are achieved.

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CONTINUOUS DATA ASSIMILATION FOR THE THREE-DIMENSIONAL SIMPLIFIED BARDINA MODEL UTILIZING MEASUREMENTS OF ONLY TWO COMPONENTS OF THE VELOCITY FIELD

  • Anh, Cung The;Bach, Bui Huy
    • Journal of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.1-28
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    • 2021
  • We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.

Estimating the State-of-Charge of Lithium-Ion Batteries Using an H-Infinity Observer with Consideration of the Hysteresis Characteristic

  • Xie, Jiale;Ma, Jiachen;Sun, Yude;Li, Zonglin
    • Journal of Power Electronics
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    • v.16 no.2
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    • pp.643-653
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    • 2016
  • The conventional methods used to evaluate battery state-of-charge (SOC) cannot accommodate the chemistry nonlinearities, measurement inaccuracies and parameter perturbations involved in estimation systems. In this paper, an impedance-based equivalent circuit model has been constructed with respect to a LiFePO4 battery by approximating the electrochemical impedance spectrum (EIS) with RC circuits. The efficiencies of approximating the EIS with RC networks in different series-parallel forms are first discussed. Additionally, the typical hysteresis characteristic is modeled through an empirical approach. Subsequently, a methodology incorporating an H-infinity observer designated for open-circuit voltage (OCV) observation and a hysteresis model developed for OCV-SOC mapping is proposed. Thereafter, evaluation experiments under FUDS and UDDS test cycles are undertaken with varying temperatures and different current-sense bias. Experimental comparisons, in comparison with the EKF based method, indicate that the proposed SOC estimator is more effective and robust. Moreover, test results on a group of Li-ion batteries, from different manufacturers and of different chemistries, show that the proposed method has high generalization capability for all the three types of Li-ion batteries.

Further Approximate Optimum Inspection Intervals

  • Leung, Kit-Nam Francis
    • Industrial Engineering and Management Systems
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    • v.4 no.2
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    • pp.123-128
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    • 2005
  • The author derives a general explicit formula and presents an heuristic algorithm for solving Baker’s model. The examples show that this new approximate solution procedure for determining near optimum inspection intervals is more accurate than the ones suggested by Chung (1993) and Vaurio (1994), and is more efficient computationally than the one suggested by Hariga (1996). The construction and solution of the simplest profit model for an exponential failure distribution were presented in Baker (1990), and approximate analytical results were obtained by Chung (1993) and Vaurio (1994). The author will therefore mainly devote the following discussion to the problem of further approximating optimum inspection intervals.

APPROXIMATION FORMULAS FOR SHORT-MATURITY NEAR-THE-MONEY IMPLIED VOLATILITIES IN THE HESTON AND SABR MODELS

  • HYUNMOOK CHOI;HYUNGBIN PARK;HOSUNG RYU
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.27 no.3
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    • pp.180-193
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    • 2023
  • Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

Error Prediction Considering the Measurement Direction in OMM System (OMM 시스템에서 측정방향을 고려한 가공물의 오차평가)

  • 최진필;이상조;권혁동
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2002.05a
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    • pp.632-635
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    • 2002
  • In this paper, a general procedure to determine machine tool errors from the on-machine measurement (OMM) data is described. First, a parameterized error model of a machine tool is illustrated by approximating error components as linear function of axis positions, and a modified error model is proposed which includes backlash effects. To determine the unknown model coefficient vectors of the forward and backward error model, an artifact with 8 cutes is made and calibrated on CMM. Then, lower-left and upper-right cube corners are measured with a touch-trigger probe mounted on the machine tool spindle. Measured error data are used to determine the coefficient vectors. The positioning errors in the XY plane at the fixed z position are simulated for the forward and backward error model.

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