• Title/Summary/Keyword: Nonlinear least squares

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On the Local Identifiability of Load Model Parameters in Measurement-based Approach

  • Choi, Byoung-Kon;Chiang, Hsiao-Dong
    • Journal of Electrical Engineering and Technology
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    • v.4 no.2
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    • pp.149-158
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    • 2009
  • It is important to derive reliable parameter values in the measurement-based load model development of electric power systems. However parameter estimation tasks, in practice, often face the parameter identifiability issue; whether or not the model parameters can be estimated with a given input-output data set in reliable manner. This paper introduces concepts and practical definitions of the local identifiability of model parameters. A posteriori local identifiability is defined in the sense of nonlinear least squares. As numerical examples, local identifiability of third-order induction motor (IM) model and a Z-induction motor (Z-IM) model is studied. It is shown that parameter ill-conditioning can significantly affect on reliable parameter estimation task. Numerical studies show that local identifiability can be quite sensitive to input data and a given local solution. Finally, several countermeasures are proposed to overcome ill-conditioning problem in measurement-based load modeling.

$^{87}Rb$ NMR Quadrupole Coupling Constants and Asymmetry Parameters in $RbMnCl_3$

  • Woo, Ae-Ja;Park, Young-Sun
    • Journal of the Korean Magnetic Resonance Society
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    • v.3 no.2
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    • pp.84-89
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    • 1999
  • The 87Rb quadrupole coupling constants (e2qQ/h) and the asymmetry parameters (η) in RbMnCl3 were determined from a nonlinear least-squares fit to the 87Rb NMR powder spectra. The spectra were acquired in the temperature range from 260K to 330K. An important feature in this work is the determination of the quadrupole coupling constants and the asymmetry parameters for two physically nonequivalent Rb sites, Rb(I) and Rb(II), as a function of temperature. In addition, a structural phase transition at room temperature was conformed with the changes in the quadrupole coupling constant and the asymmetry parameter of Rb(II) site.

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The Estimation of Theoretical Semivariogram Adapting Genetic Algorithm for Kriging

  • Ryu, Je-Seon;Park, Young-Sun;Cha, Kyung-Joon
    • Communications for Statistical Applications and Methods
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    • v.11 no.2
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    • pp.355-368
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    • 2004
  • In order to use Kriging, one has to estimate three parameters(nugget, sill and range) of semivariogram, which shows the relationship in the given two sites. A visual fit of the semivariogram parameters to a few standard models is widely used. But, it does not give the suitable results and not provide the automated process of Kriging. The gradient based nonlinear least squares is another choices to estimate three parameters, but it has some problems such as initial value problem. In this paper, we suggest the genetic algorithm as a compatible alternative method to solve the above mentioned problem. Finally, we estimate three parameters of semivariogram of rain-fall by adapting the genetic algorithm, compute Kriging estimate and conclude its effectiveness and compatibility.

Precise Edge Detection Method Using Sigmoid Function in Blurry and Noisy Image for TFT-LCD 2D Critical Dimension Measurement

  • Lee, Seung Woo;Lee, Sin Yong;Pahk, Heui Jae
    • Current Optics and Photonics
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    • v.2 no.1
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    • pp.69-78
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    • 2018
  • This paper presents a precise edge detection algorithm for the critical dimension (CD) measurement of a Thin-Film Transistor Liquid-Crystal Display (TFT-LCD) pattern. The sigmoid surface function is proposed to model the blurred step edge. This model can simultaneously find the position and geometry of the edge precisely. The nonlinear least squares fitting method (Levenberg-Marquardt method) is used to model the image intensity distribution into the proposed sigmoid blurred edge model. The suggested algorithm is verified by comparing the CD measurement repeatability from high-magnified blurry and noisy TFT-LCD images with those from the previous Laplacian of Gaussian (LoG) based sub-pixel edge detection algorithm and error function fitting method. The proposed fitting-based edge detection algorithm produces more precise results than the previous method. The suggested algorithm can be applied to in-line precision CD measurement for high-resolution display devices.

Intelligent Parameter Estimation of a Induction Motor Using Immune Algorithm

  • Kim, Dong-Hwa;Cho, Jae-Hoon
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2004.10a
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    • pp.21-25
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    • 2004
  • This paper suggests the techniques in determining the values of the steady-state equivalent circuit parameters of a three-phase squirrel-cage induction machine using immune algorithm. The parameter estimation procedure is based on the steady state phase current versus slip and input power versus slip characteristics. The proposed estimation algorithm is of a nonlinear kind based on clonal selection in immune algorithm. The machine parameters are obtained as the solution of a minimization of least-squares cost function by immune algorithm. Simulation shows better results than the conventional approaches.

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ADAPTIVE CHANDRASEKHAR FILLTER FOR LINEAR DISCRETE-TIME STATIONALY STOCHASTIC SYSTEMS

  • Sugisaka, Masanori
    • 제어로봇시스템학회:학술대회논문집
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    • 1988.10b
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    • pp.1041-1044
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    • 1988
  • This paper considers the design problem of adaptive filters based an the state-space models for linear discrete-time stationary stochastic signal processes. The adaptive state estimator consists of both the predictor and the sequential prediction error estimator. The discrete Chandrasakhar filter developed by author is employed as the predictor and the nonlinear least-squares estimator is used as the sequential prediction error estimator. Two models are presented for calculating the parameter sensitivity functions in the adaptive filter. One is the exact model called the linear innovations model and the other is the simplified model obtained by neglecting the sensitivities of the Chandrasekhar X and Y functions with respect to the unknown parameters in the exact model.

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Mutual Inductance Estimation of IPMSM nonlinear model using the least squares method (최소자승법을 이용한 IPMSM 비선형 모델의 상호인덕턴스 추정 연구)

  • Sim, Jae-Hun;Yang, Doo-young;Mok, Hyung-soo
    • Proceedings of the KIEE Conference
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    • 2015.07a
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    • pp.948-949
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    • 2015
  • 일반적으로 IPMSM의 전압방정식은 d축과 q축이 90도의 위상차를 가지고 있기 때문에 d-q축 간의 상호 인덕턴스를 고려하지 않는다. 하지만 실제로는 d축의 인덕턴스는 q축 전류에 영향을 받으며, 반대로 q축의 인덕턴스도 d축 전류에 영향을 받는다. 따라서 비선형 모델링을 통해 실제 전동기의 형태에 더 가깝게 묘사 하였다. 또한 일반적인 수학식으로 계산하여 Ldq, Lqd를 구해 LPF 필터를 사용하였고 이산적인 최소자승법을 이용한 Gain값을 통해 과도상태에서 더 적합한 LPF와 최소자승법을 비교하는 논문이다.

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Testing for a Unit Root in an ARIMA(p,1,q) Signal Observed with Measurement Error

  • Lee, Jong-Hyup;Shin, Dong-Wan
    • Journal of the Korean Statistical Society
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    • v.24 no.2
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    • pp.481-493
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    • 1995
  • An ARIMA signal observed with measurement error is shown to have another ARIMA representation with nonlinear restrictions on parameters. For this model, the restricted Newton-Raphson estimator(RNRE) of the unit root is shown to have the same limiting distribution as the ordinary least squares estimator of the unit root in an AR(1) model tabulated by Dickey and Fuller (1979). The RNRE of parameters of the ARIMA(p,1,k) process and unit root tests base on the RNRE are developed.

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Modeling and Parameter Estimation of Linear Motor Positioning for Precision Positioning Control (정밀위치 제어를 위한 리니어모터 위치결정기구의 모형화 및 매개변수 추정)

  • Jung, I.K.;Yang, S.S.
    • Proceedings of the KIEE Conference
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    • 1997.07b
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    • pp.409-413
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    • 1997
  • In linear motor positioning systems, nonlinearitys such as friction and cogging exist. These inner system with compliance may cause the steady state error and oscillation. So it is necessary to consider these elements for precision positioning control. In this paper, a nonlinear model of a linear motor positioning system including the friction, cogging and compliance is proposed. The parameters of the proposed model are identified by recursive least-squares method. The validity of the proposed model is confirmed by computer simulation.

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Complex Fuzzy Logic Filter and Learning Algorithm

  • Lee, Ki-Yong;Lee, Joo-Hum
    • The Journal of the Acoustical Society of Korea
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    • v.17 no.1E
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    • pp.36-43
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    • 1998
  • A fuzzy logic filter is constructed from a set of fuzzy IF-THEN rules which change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy logic filter and it's adaptive filtering algorithm to include complex parameters and complex signals. Using the complex Stone-Weierstrass theorem, we prove that linear combinations of the fuzzy basis functions are capable of uniformly approximating and complex continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, a complex orthogonal least-squares (COLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs. Also, we propose an adaptive algorithm based on LMS which adjust simultaneously filter parameters and the parameter of the membership function which characterize the fuzzy concepts in the IF-THEN rules. The modeling of a nonlinear communications channel based on a complex fuzzy is used to demonstrate the effectiveness of these algorithm.

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