• Title/Summary/Keyword: Nonlinear Fitting Method

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Nonlinear Regression Analysis of Acid-Base Titration System (산-염기 적정 시스템의 비선형 회귀분석에 관한 고찰)

  • Park, Chung-Oh;Hong, Jae-Jin
    • Korean Journal of Clinical Laboratory Science
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    • v.40 no.1
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    • pp.18-25
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    • 2008
  • In classical titrimetric analyses, the major concern is the concentration of titrant, usually the aqueous solution of hydrochloric acid or sodium hydroxide, that could be changed as time goes by and it is accompanied with the inaccuracy of the resulting data. And the statistical approach, the nonlinear regression analysis, which is a well-known statistical method, was introduced to determine the accurate concentration of the titrant and the exact value of parameters, $K_a$, r, $C_a$, $C_b$, for 0.01 M aqueous solutions of analytes, sodium pyruvate, sodium acetate, sodium bicarbonate, ammonium hydroxide, ammonium chloride and acetic acid at $25^{\circ}C$. We used Gauss-Newton method for the linearlization of the nonlinear titration system and the two-parameter fitting showed appreciable convergent data for the parameters of the analytes set with the various range of $K_a$ value.

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Stabilization of optical fiber sensor array using a semiconductor optical amplifier source (SOA를 광원으로 사용하는 광섬유 센서 어레이의 출력 안정화)

  • Park, Hyoung-Jun;Kim, Hyun-Jin;Song, Min-Ho
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • 2008.05a
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    • pp.383-386
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    • 2008
  • We developed a fiber-optic Bragg grating sensor system using a SOA fiber laser for over heat detection in power systems. To compensate the nonlinear wavelength tuning of the fiber laser, we used fixed passband wavelengths from Fabry-Perot ITU filter as reference wavelengths. Gaussian line-fitting algorithm was also used to reduce the FBG peak detection error. Compared with a highest-peak-detection and a polynomial-fitting method, the proposed Gaussian fitting algorithm could drastically reduce the measurement errors. Also the SOA fiber laser made it possible to enhance the signal-to-noise-ratio even with several kilometers of lead fiber.

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Z-Domain Frequency Dependent AC System Equivalent for Electromagnetic Transient Studies (전자기 과도현상 해석을 위한 Z 영역에서의 주파수 의존 교류시스템 등가)

  • Wang, Yong-Pil;Jeong, Hyeong-Hwan
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.51 no.6
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    • pp.296-301
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    • 2002
  • Modern power systems are very complex and to model them completely is impractical for electromagnetic transient studies. Therefore areas outside the immediate area of interest must be represented by some form of Frequency Dependent Network Equivalent (FDNE). In this paper a method for developing Frequency Dependent AC system Equivalent (FDACSE) using Z-domain rational Function Fitting is presented and demonstrated. The FDACSE is generated by Linearized Least Squares Fitting(LSF) of the frequency response of a Z-domain formulation. This 1 & 2 port FDACSE have been applied to the New Zealand South Island AC power system. The electromagnetic transient package PSCAD/EMTDC is used to assess the transient response of the 1 & 2 port FDACSE developed under different condition (linear load, fault and nonlinear loading). The study results have indicated the robustness and accuracy of 1 & 2 port FDACSE for electromagnetic transient studies.

Inductance Calculation in a Switched Reluctance Motor using Permeance Method (퍼미언스 방법을 이용한 스위치드 릴럭턴스 전동기의 인덕턴스 산정)

  • Lee, Cheewoo
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.12
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    • pp.1836-1842
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    • 2012
  • Torque is proportional to the rate of change of inductance in a switched reluctance motor (SRM), and hence, phase inductance is an important parameter in determining the behavior of an SRM. Therefore, the accurate prediction of inductance with respect to rotor position makes a significant contribution to designing an SRM and its analytical approach is not straightforward due to nonlinear flux distribution. Although several different approaches using a finite element analysis (FEA) or curve-fitting tool have been employed to compute phase inductance [2-5], they are not suitable for a simple design procedure because the FEA necessitates a large amount of time in both modeling and solving with complexity for every motor design, and the curve-fitting requires the data of flux linkage from either an experimental test or an FEA simulation. In this paper, phase inductance is predicted by means of a permeance method, and the proposed approach is analytically verified in terms of the accuracy of estimated inductance compared to inductance obtained by FEA.

Analytical Estimation of Inductance at Aligned and Unaligned Rotor Positions in a Switched Reluctance Motor (스위치드 릴럭턴스 전동기의 회전자 정렬과 비정렬 위치에서의 인덕턴스 예측)

  • Lee, Chee-Woo
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.1
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    • pp.34-40
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    • 2012
  • Flux linkage of phase windings or phase inductance is an important parameter in determining the behavior of a switched reluctance motor (SRM) [1-8]. Therefore, the accurate prediction of inductance at aligned and unaligned rotor positions makes a significant contribution to the design of an SRM and its analytical approach is not straightforward due to nonlinear flux distribution. Although several different approaches using a finite element analysis (FEA) or curve-fitting tool have been employed to compute phase inductance [2-5], they are not suitable for a simple design procedure because the FEA necessitates a large amount of time in both modeling and solving with complexity for every motor design, and the curve-fitting requires the data of flux linkage from either an experimental test or an FEA simulation. In this paper, phase inductance at aligned and unaligned rotor positions is estimated by means of numerical method and magnetic equivalent circuit as well, and the proposed approach is analytically verified in terms of the accuracy of estimated inductance compared to inductance computed by an FEA simulation.

Method of Deciding Elastic Modulus of Left and Right Ventricle Reconstructed by Echocardiography Using Finite Element Method and Stress Analysis

  • Han, Geun-Jo;Kim, Sang-Hyun
    • Journal of Biomedical Engineering Research
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    • v.15 no.2
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    • pp.217-224
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    • 1994
  • In order to study the shape and dimensions of heart, a procedure to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images was studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and by optimization techniques which compared the computer predicted 3D deformation with the experimentally determined deformation. Elastic modulus ranged from 3.5g/$cm^2$ at early diastole to l53g/$cm^2$ at around end diastole showing slightly nonlinear relationship between the modulus and the pressure. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed. The maximum and minimum of ${\sigma}_1$ (max. principal stress) occurred at nodes on the second level intersection points of x-axis with endocardium and with epicardium, respectively. And the tendency of the interventricular septum to be flattened was observed from the compressive ${\sigma}_1$ on the anterior, posterior nodes of left ventricle and from the most significant change of dimension in $D_{RL}$ (septal-lateral dimension of right ventricle).

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Long-term Creep Strain-Time Curve Modeling of Alloy 617 for a VHTR Intermediate Heat Exchanger (초고온가스로 중간 열교환기용 Alloy 617의 장시간 크리프 변형률-시간 곡선 모델링)

  • Kim, Woo-Gon;Yin, Song-Nam;Kim, Yong-Wan
    • Korean Journal of Metals and Materials
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    • v.47 no.10
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    • pp.613-620
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    • 2009
  • The Kachanov-Rabotnov (K-R) creep model was proposed to accurately model the long-term creep curves above $10^5$ hours of Alloy 617. To this end, a series of creep data was obtained from creep tests conducted under different stress levels at $950^{\circ}C$. Using these data, the creep constants used in the K-R model and the modified K-R model were determined by a nonlinear least square fitting (NLSF) method, respectively. The K-R model yielded poor correspondence with the experimental curves, but the modified K-R model provided good agreement with the curves. Log-log plots of ${\varepsilon}^{\ast}$-stress and ${\varepsilon}^{\ast}$-time to rupture showed good linear relationships. Constants in the modified K-R model were obtained as ${\lambda}$=2.78, and $k=1.24$, and they showed behavior close to stress independency. Using these constants, long-term creep curves above $10^5$ hours obtained from short-term creep data can be modeled by implementing the modified K-R model.

Dynamic increase factor for progressive collapse analysis of semi-rigid steel frames

  • Zhu, Yan Fei;Chen, Chang Hong;Yao, Yao;Keer, Leon M.;Huang, Ying
    • Steel and Composite Structures
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    • v.28 no.2
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    • pp.209-221
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    • 2018
  • An empirical and efficient method is presented for calculating the dynamic increase factor to amplify the applied loads on the affected bays of a steel frame structure with semi-rigid connections. The nonlinear static alternate path analysis is used to evaluate the dynamic responses. First, the polynomial models of the extended end plate and the top and seat connection are modified, and the proposed polynomial model of the flush end plate connection shows good agreement as compared with experimental results. Next, a beam model with nonlinear spring elements and plastic hinges is utilized to incorporate the combined effect of connection flexibility and material nonlinearity. A new step-by-step analysis procedure is established to obtain quickly the dynamic increase factor based on a combination of the pushdown analysis and nonlinear dynamic analysis. Finally, the modified dynamic increase factor equation, defined as a function of the maximum ratio value of energy demand to energy capacity of an affected beam, is derived by curve fitting data points generated by the different analysis cases with different column removal scenarios and five types of semi-rigid connections.

Estimation of Ultimate Pullout Resistance of Soil-Nailing Using Nonlinear (비선형회귀분석을 이용한 가압식 쏘일네일링의 극한인발저항력 판정)

  • Park, Hyun-Gue;Lee, Kang-Il
    • Journal of the Korean Geosynthetics Society
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    • v.15 no.2
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    • pp.65-75
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    • 2016
  • In this study, we constructed a database by collecting field pullout test data of the soil nailing using pressurized grouting, and suggested a method to estimate the ultimate pullout resistance using nonlinear regression analysis to overcome the problems of ultimate pullout resistance estimation using graphical methods. The load-displacement curve estimated by nonlinear regression showed a very high correlation with the field pullout test data. Estimated ultimate pullout load by nonlinear regression method was average 29% higher than estimated ultimate pullout load using previous graphical method. A sigmoidal growth model was found to be the best-fitting nonlinear regression model against rapid pullout failure. Further, an asymptotic regression model was found to be the best fit against progressive nail pullout. The unit ultimate skin friction suggested in this research reflected in the domestic geotechnical characteristics and the specifications of the pressurized grouting method. This research is expected to contribute towards establishing an independent design standard for the soil nailing by providing solutions to the problems that occur when using design charts based on foreign research.

Stress analysis of ventricular myocarda according to heart pressure in diastole using finite element method (유한요소법을 이용하여 확장기때 압력에 따른 심실심근의 응력 해석)

  • Han, Geun-Jo;Kim, Sang-Hyun;Shin, Jung-Woog
    • Proceedings of the KOSOMBE Conference
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    • v.1994 no.05
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    • pp.131-135
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    • 1994
  • In order to study the shape and dimensions of heart, the procedures to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images is studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and optimization techniques which compare the computer predicted 3D deformation with the experimentally determined deformation. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed.

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