• Title/Summary/Keyword: Taylor approximation

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Residual-based Robust CUSUM Control Charts for Autocorrelated Processes (자기상관 공정 적용을 위한 잔차 기반 강건 누적합 관리도)

  • Lee, Hyun-Cheol
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.35 no.3
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    • pp.52-61
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    • 2012
  • The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.

Moveout Velocities and Effective Anellipticity of the Crust in the Korean Peninsula (한반도 지각의 무브아웃 속도 및 유효비타원율 시험적 산출)

  • Kim, Ki Young;Park, Iseul;Byun, Joongmoo;Lee, Jung Mo
    • Geophysics and Geophysical Exploration
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    • v.20 no.2
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    • pp.96-99
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    • 2017
  • Virtual source data were produced by applying the seismic interferometry to the 2002 experimental seismic refraction data. Using the data, moveout velocities and effective anellipticity were experimentally computed for the crust at eight sites in the Korean peninsula. The moveout velocities of reflection events at approximate Moho depths were yielded to be $6.30{\pm}0.25km/s$ using near-offset traveltimes. Expanding the Taylor approximation to the $3^{rd}$ term for far-offset traveltimes, the effective anellipticity parameters were computed to be $0.18{\pm}0.07$ for the crust material.

Lagrangian Chaos and Dispersion of Passive Particles on the Ripple Bed (해저 파문에서의 입자의 라그란지적 혼돈 및 확산)

  • 김현민;서용권
    • Journal of Ocean Engineering and Technology
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    • v.7 no.1
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    • pp.13-24
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    • 1993
  • The dispersion in the oscillatory flow generated by gravitational waves above the spatially periodic repples is studied. The steady parts of equations describing the orbit of the passive particle in a two dimensional field are assumed to be simply trigonometric functions. From the view point of nonlinear dynamics, the motion of the particle is chaotic under externally time-periodic perturbations which come from the wave motion. Two cases considered here are; (i) shallow water, and (ii) deep water approximation.

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Study on the Solution of Reinitialization Equation for Level Set Method in the Simulation of Incompressible Two-Phase Flows (비압축성 2 상유동의 모사를 위한 Level Set 방법의 Reinitialization 방정식의 해법에 관한 연구)

  • Cho, Myung-Hwan;Choi, Hyoung-Gwon;Yoo, Jung-Yul
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.32 no.10
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    • pp.754-760
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    • 2008
  • Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function $\phi$ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving there-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.

New Target Transfer Functions with No Overshoot

  • Yang, Dae--Jeong;Kim, Young-Chol
    • Journal of KIEE
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    • v.11 no.1
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    • pp.14-20
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    • 2001
  • To design a controller based on the pole placement method, it is necessary to obtain either a target transfer function or a desired characteristic equation which results in the closed-loop response. Specially, a step response in which no overshoot occurs in highly desirable in many applications. In this paper, we present two new present two new prototypes of Type I target transfer functions whose step responses have an overshoot of less than 0.1%. One prototype is obtained by Taylor's approximation of a Gaussian function. It is, however, observed that the response delays increase with increasing order, while the rise times are nearly constant. The other prototype is a modification of the first prototype, so that their transfer function coefficients have particular values in terms of specific parameters ${\gamma}$i and $\tau$ (see section 2). The second prototype gives very useful properties in which step responses are almost the same shape, irrespective of the order. It, also, has no overshoot. Some other properties of the prototypes and an application example are given.

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A Efficient Calculation for log and exponent with A Dual Phase Instruction Architecture (효율적인 로그와 지수 연산을 위한 듀얼 페이즈 명령어 구조)

  • Kim, Jun-Seo;Lee, Kwang-Yeob;Kwak, Jae-Chang
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2010.05a
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    • pp.320-323
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    • 2010
  • This paper proposes efficient log and exponent calculation methods using a dual phase instruction set without additional ALU unit for a mobile enviroment. Using the Dual Phase Instruction set, it extracts exponent and mantissa from expression of floating point and calculates 24bit single precision floating point of log approximation using the Taylor series expansion algorithm. And with dual phase instruction set, it reduces instruction excution cycles. The proposed Dual Phase architecture reduces the performance degradation and maintain smaller size.

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Maximum Power Point Tracking of Photovoltaic System using Approximation Method (근사기법을 이용한 태양광 발전의 MPPT 제어)

  • Park, Ki-Tae;Choi, Jung-Sik;Ko, Jae-Sub;Park, Byung-Sang;Chung, Dong-Hwa
    • Proceedings of the KIEE Conference
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    • 2007.07a
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    • pp.1215-1217
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    • 2007
  • This paper is proposed a novel method to approximate the maximum power for a photovoltaic inverter system. It is designed for power systems application and utilities. The proposed Maximum Power Point Tracking(MPPT) control has the advantage to provide a new simple way to approximate the optimal or rated voltage, the optimal or rated current and maximum power rating produced by a solar panel and the photovoltaic inverter. And this straightforward method will be named linear reoriented coordinates method(LRCM) with the advantage that Pmax and $V_{op}$ can be approximated using the same variable as the dynamic model without using complicate approximations or Taylor series. This paper is proposed MPPT using LRMC method using weather condition of domestic moderate program technique. This paper is proposed the experimental results to verify the effectiveness of the new methods.

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Capabilities of 1D CUF-based models to analyse metallic/composite rotors

  • Filippi, Matteo;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • v.3 no.1
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    • pp.1-14
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    • 2016
  • The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of "fundamental nuclei", whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

Scattering analysis of curved FSS using Floquet harmonics and asymptotic waveform evaluation technique

  • Jeong, Yi-Ru;Hong, Ic-Pyo;Chun, Heoung-Jae;Park, Yong Bae;Kim, Youn-Jae;Yook, Jong-Gwan
    • Steel and Composite Structures
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    • v.17 no.5
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    • pp.561-572
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    • 2014
  • In this paper, we present the scattering characteristics of infinite and finite array using method of moment (MoM) with Floquet harmonics and asymptotic waveform evaluation (AWE) technique. First, infinite cylindrical dipole array is analyzed using the MoM with entire domain basis function and cylindrical Floquet harmonics. To provide the validity of results, we fabricated the cylindrical dipole array and measured the transmission characteristics. The results show good agreements. Second, we analyzed the scattering characteristics of finite array. A large simulation time is needed to obtain the scattering characteristics of finite array over wide frequency range because Floquet harmonics can't be applied. So, we used the MoM with AWE technique using Taylor series and Pade approximation to overcome the shortcomings of conventional MoM. We calculated the radar cross section (RCS) as scattering characteristics using the proposed method in this paper and the conventional MoM for finite planar slot array, finite spherical slot array, and finite cylindrical dipole array, respectively. The compared results agree well and show that the proposed method in this paper is good for electromagnetic analysis of finite FSS.

Implementing Linear Models in Genetic Programming to Utilize Accumulated Data in Shipbuilding (조선분야의 축적된 데이터 활용을 위한 유전적프로그래밍에서의 선형(Linear) 모델 개발)

  • Lee, Kyung-Ho;Yeun, Yun-Seog;Yang, Young-Soon
    • Journal of the Society of Naval Architects of Korea
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    • v.42 no.5 s.143
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    • pp.534-541
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    • 2005
  • Until now, Korean shipyards have accumulated a great amount of data. But they do not have appropriate tools to utilize the data in practical works. Engineering data contains experts' experience and know-how in its own. It is very useful to extract knowledge or information from the accumulated existing data by using data mining technique This paper treats an evolutionary computation based on genetic programming (GP), which can be one of the components to realize data mining. The paper deals with linear models of GP for the regression or approximation problem when given learning samples are not sufficient. The linear model, which is a function of unknown parameters, is built through extracting all possible base functions from the standard GP tree by utilizing the symbolic processing algorithm. In addition to a standard linear model consisting of mathematic functions, one variant form of a linear model, which can be built using low order Taylor series and can be converted into the standard form of a polynomial, is considered in this paper. The suggested model can be utilized as a designing tool to predict design parameters with small accumulated data.