• Title/Summary/Keyword: least-squares problem

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Design of Partial Discharge Pattern Classifier of Softmax Neural Networks Based on K-means Clustering : Comparative Studies and Analysis of Classifier Architecture (K-means 클러스터링 기반 소프트맥스 신경회로망 부분방전 패턴분류의 설계 : 분류기 구조의 비교연구 및 해석)

  • Jeong, Byeong-Jin;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.1
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    • pp.114-123
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    • 2018
  • This paper concerns a design and learning method of softmax function neural networks based on K-means clustering. The partial discharge data Information is preliminarily processed through simulation using an Epoxy Mica Coupling sensor and an internal Phase Resolved Partial Discharge Analysis algorithm. The obtained information is processed according to the characteristics of the pattern using a Motor Insulation Monitoring System program. At this time, the processed data are total 4 types that void discharge, corona discharge, surface discharge and slot discharge. The partial discharge data with high dimensional input variables are secondarily processed by principal component analysis method and reduced with keeping the characteristics of pattern as low dimensional input variables. And therefore, the pattern classifier processing speed exhibits improved effects. In addition, in the process of extracting the partial discharge data through the MIMS program, the magnitude of amplitude is divided into the maximum value and the average value, and two pattern characteristics are set and compared and analyzed. In the first half of the proposed partial discharge pattern classifier, the input and hidden layers are classified by using the K-means clustering method and the output of the hidden layer is obtained. In the latter part, the cross entropy error function is used for parameter learning between the hidden layer and the output layer. The final output layer is output as a normalized probability value between 0 and 1 using the softmax function. The advantage of using the softmax function is that it allows access and application of multiple class problems and stochastic interpretation. First of all, there is an advantage that one output value affects the remaining output value and its accompanying learning is accelerated. Also, to solve the overfitting problem, L2-normalization is applied. To prove the superiority of the proposed pattern classifier, we compare and analyze the classification rate with conventional radial basis function neural networks.

Development and application of GLS OD matrix estimation with genetic algorithm for Seoul inner-ringroad (유전알고리즘을 이용한 OD 추정모형의 개발과 적용에 관한 연구 (서울시 내부순환도로를 대상으로))

  • 임용택;김현명;백승걸
    • Journal of Korean Society of Transportation
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    • v.18 no.4
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    • pp.117-126
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    • 2000
  • Conventional methods for collecting origin-destination trips have been mainly relied on the surveys of home or roadside interview. However, the methods tend to be costly, labor intensive and time disruptive to the trip makers, thus the methods are not considered suitable for Planning applications such as routing guidance, arterial management and information Provision, as the parts of deployments in Intelligent Transport Systems Motivated by the problems, more economic ways to estimate origin-destination trip tables have been studied since the late 1970s. Some of them, which have been estimating O-D table from link traffic counts are generally Entropy maximizing, Maximum likelihood, Generalized least squares(GLS), and Bayesian inference estimation etc. In the Paper, with user equilibrium constraint we formulate GLS problem for estimating O-D trips and develop a solution a1gorithm by using Genetic Algorithm, which has been known as a g1oba1 searching technique. For the purpose of evaluating the method, we apply it to Seoul inner ringroad and compare it with gradient method proposed by Spiess(1990). From the resu1ts we fond that the method developed in the Paper is superior to other.

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4-D Inversion of Geophysical Data Acquired over Dynamically Changing Subsurface Model (시간에 대해 변화하는 지하구조에서 획득한 물리탐사 자료의 역산)

  • Kim, Jung-Ho;Yi, Myeong-Jong
    • 한국지구물리탐사학회:학술대회논문집
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    • 2006.06a
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    • pp.117-122
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    • 2006
  • In the geophysical monitoring to understand the change of subsurface material properties with time, the time-invariant static subsurface model is commonly adopted to reconstruct a time-lapse image. This assumption of static model, however, can be invalid particularly when fluid migrates very quickly in highly permeable medium in the brine injection experiment. In such case, the resultant subsurface images may be severely distorted. In order to alleviate this problem, we develop a new least-squares inversion algorithm under the assumption that the subsurface model will change continuously in time. Instead of sampling a time-space model into numerous space models with a regular time interval, a few reference models in space domain at different times pre-selected are used to describe the subsurface structure continuously changing in time; the material property at a certain space coordinate are assumed to change linearly in time. Consequently, finding a space-time model can be simplified into obtaining several reference space models. In order to stabilize iterative inversion and to calculate meaningful subsurface images varying with time, the regularization along time axis is introduced assuming that the subsurface model will not change significantly during the data acquisition. The performance of the proposed algorithm is demonstrated by the numerical experiments using the synthetic data of crosshole dc resistivity tomography.

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A Study on Integraion Method for Improvement of Numerical Stability of Meshfree Method (무요소법의 수치적 안정성 개선을 위한 적분기법 연구)

  • Kang, JaeWon;Kang, Da Hoon;Cho, Jin Yeon;Kim, Jeong Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.46 no.3
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    • pp.210-218
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    • 2018
  • In order to generate meshes automatically for finite element analysis of complex structures such as aircraft, a large number of triangular elements are typically created. However, triangular elements are less accurate than rectangular elements, so it is difficult to obtain a reliable solution. This problem can be improved through the meshfree method using the back cell integration. However, this method also causes some problems such as over-use of the integration points and inefficiency of the integral domain. In order to improve these problems, a method of performing integration by setting the integral area based on a node basis has been proposed, but in the case of incompressible material problems, the numerical accuracy deteriorates due to the vibration phenomenon of the solution. Therefore, in this paper, the modified meshfree method is proposed which sets the integral domain as an element domain instead of the nodal domain, and the proposed method improves the numerical instability caused by the conventional meshfree method without decreasing the accuracy regardles of the shape of integral domain. The effectiveness of the modified meshfree method is verified by using 2-D examples.

An Application of loop-loop EM Method for Geotechnical Survey (지반조사를 위한 loop-loop 전자탐사 기법의 적용)

  • You Jin-Sang;Song Yoonho;Seo1 Soon-Jee;Song Young-Soo
    • Geophysics and Geophysical Exploration
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    • v.4 no.2
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    • pp.25-33
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    • 2001
  • Loop-loop electromagnetic (EM) survey in frequency domain has been carried out in order to provide basic solution to geotechnical applications. Source and receiver configuration may be horizontal co-planar (HCP) and/or vertical co-planar (VCP). Three quadrature components of mutual impedance ratio for each configuration are used to construct the subsurface image. For the purpose of obtaining the model response and validating the reasonable performance of the inversion, we obtained each responses of two-layered and three-layered earth models and two-dimensional (2-D) isolated anomalous body. The response of 2-D isolated anomalous body has been calculated using extended Born approximation for the solution of 2.5-D integral equation describing EM scattering problem. As a result of the least-squares inversion with variable Lagrangian multiplier, we could construct more resolvable image from HCP data than VCP data. Furthermore, joint inversion of HCP and VCP data made better stability and resolution of the inversion. Resistivity values, however, did not exactly match the true ones. Loop-loop EM field data was obtained with EM34-3XL system manufactured by Geonics Ltd. (Canada). Electrical resistivity survey was conducted on the same line for the comparison in advance. Since the constructed image from loop-loop EM data by 2-D inversion algorithm showed almost similar resistivity distribution to that from electrical resistivity one, we expect the developed 2.5-D loop-loop EM inversion program can be applied for the reconnaissance site survey.

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Three-dimensional Imaging of Subsurface Structures by Resistivity Tomography (전기비저항 토모그래피에 의한 지하구조의 3차원 영상화)

  • Yi Myeong-Jong;Kim Jung-Ho;Chung Seung-Hwan;Suh Jung Hee
    • Geophysics and Geophysical Exploration
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    • v.5 no.4
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    • pp.236-249
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    • 2002
  • We have extended the three-dimensional (3-D) resistivity imaging algorithm to cover the 3-D resistivity tomography problem, where resistivity data are acquired using electrodes installed in several boreholes as well as at the earth surface. The imaging algorithm consists of the 3-D finite element forward modeling and least-squares inversion scheme, where the ACB (Active Constraint Balancing) is adopted to enhance the resolving power of the inversion. Sensitivity analysis with numerical verifications shows that 3-D resistivity tomography is a very appealing method and can be used to get 3-D attitude of subsurface structures with very high-resolution. Moreover, we could accurately handle the topography effect, which could cause artifacts in the resistivity tomography. In the application of 3-D resistivity tomography to the real field data set acquired at the quarry mine, we could derive a very reasonable and accurate image of the subsurface.

Electrical Impedance Tomography for Material Profile Reconstruction of Concrete Structures (콘크리트 구조의 재료 물성 재구성을 위한 전기 임피던스 단층촬영 기법)

  • Jung, Bong-Gu;Kim, Boyoung;Kang, Jun Won;Hwang, Jin-Ha
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.4
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    • pp.249-256
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    • 2019
  • This paper presents an optimization framework of electrical impedance tomography for characterizing electrical conductivity profiles of concrete structures in two dimensions. The framework utilizes a partial-differential-equation(PDE)-constrained optimization approach that can obtain the spatial distribution of electrical conductivity using measured electrical potentials from several electrodes located on the boundary of the concrete domain. The forward problem is formulated based on a complete electrode model(CEM) for the electrical potential of a medium due to current input. The CEM consists of a Laplace equation for electrical potential and boundary conditions to represent the current inputs to the electrodes on the surface. To validate the forward solution, electrical potential calculated by the finite element method is compared with that obtained using TCAD software. The PDE-constrained optimization approach seeks the optimal values of electrical conductivity on the domain of investigation while minimizing the Lagrangian function. The Lagrangian consists of least-squares objective functional and regularization terms augmented by the weak imposition of the governing equation and boundary conditions via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to the Karush-Kuhn-Tucker condition to obtain an optimal solution for electrical conductivity within the target medium. Numerical inversion results are reported showing the reconstruction of the electrical conductivity profile of a concrete specimen in two dimensions.

Multiple Linear Analysis for Generating Parametric Images of Irreversible Radiotracer (비가역 방사성추적자 파라메터 영상을 위한 다중선형분석법)

  • Kim, Su-Jin;Lee, Jae-Sung;Lee, Won-Woo;Kim, Yu-Kyeong;Jang, Sung-June;Son, Kyu-Ri;Kim, Hyo-Cheol;Chung, Jin-Wook;Lee, Dong-Soo
    • Nuclear Medicine and Molecular Imaging
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    • v.41 no.4
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    • pp.317-325
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    • 2007
  • Purpose: Biological parameters can be quantified using dynamic PET data with compartment modeling and Nonlinear Least Square (NLS) estimation. However, the generation of parametric images using the NLS is not appropriate because of the initial value problem and excessive computation time. In irreversible model, Patlak graphical analysis (PGA) has been commonly used as an alternative to the NLS method. In PGA, however, the start time ($t^*$, time where linear phase starts) has to be determined. In this study, we suggest a new Multiple Linear Analysis for irreversible radiotracer (MLAIR) to estimate fluoride bone influx rate (Ki). Methods: $[^{18}F]Fluoride$ dynamic PET scans was acquired for 60 min in three normal mini-pigs. The plasma input curve was derived using blood sampling from the femoral artery. Tissue time-activity curves were measured by drawing region of interests (ROls) on the femur head, vertebra, and muscle. Parametric images of Ki were generated using MLAIR and PGA methods. Result: In ROI analysis, estimated Ki values using MLAIR and PGA method was slightly higher than those of NLS, but the results of MLAIR and PGA were equivalent. Patlak slopes (Ki) were changed with different $t^*$ in low uptake region. Compared with PGA, the quality of parametric image was considerably improved using new method. Conclusion: The results showed that the MLAIR was efficient and robust method for the generation of Ki parametric image from $[^{18}F]Fluoride$ PET. It will be also a good alternative to PGA for the radiotracers with irreversible three compartment model.

Least-Square Fitting of Intrinsic and Scattering Q Parameters (최소자승법(最小自乘法)에 의(衣)한 고유(固有) Q와 산란(散亂) Q의 측정(測定))

  • Kang, Ik Bum;McMechan, George A.;Min, Kyung Duck
    • Economic and Environmental Geology
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    • v.27 no.6
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    • pp.557-561
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    • 1994
  • Q estimates are made by direct measurements of energy loss per cycle from primary P and S waves, as a function of frequency. Assuming that intrinsic Q is frequency independent and scattering Q is frequency dependent over the frequencies of interest, the relative contributions of each, to a total observed Q, may be estimated. Test examples are produced by computing viscoelastic synthetic seismograms using a pseudo spectral solution with inclusion of relaxation mechanisms (for intrinsic Q) and a fractal distribution of scatterers (for scattering Q). The composite theory implies that when the total Q for S-waves is smaller than that for P-waves (the usual situation), intrinsic Q is dominating; when it is larger, scattering Q is dominating. In the inverse problem, performed by a global least squares search, intrinsic $Q_p$ and $Q_s$ estimates are reliable and unique when their absolute values are sufficiently low that their effects are measurable in the data. Large $Q_p$ and $Q_s$ have no measurable effect and hence are not resolvable. Standard deviation of velocity $({\sigma})$ and scatterer size (A) are less unique as they exhibit a tradeoff as predicted by Blair's equation. For the P-waves, intrinsic and scattering contributions are of approximately the same importance, for S-waves, the intrinsic contributions dominate.

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Determination of methamphetamine, 4-hydroxymethamphetamine, amphetamine and 4-hydroxyamphetamine in urine using dilute-and-shoot liquid chromatography-tandem mass spectrometry (시료 희석 주입 LC-MS/MS를 이용한 소변 중 메스암페타민, 4-하이드록시메스암페타민, 암페타민 및 4-하이드록시암페타민 동시 분석)

  • Heo, Bo-Reum;Kwon, NamHee;Kim, Jin Young
    • Analytical Science and Technology
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    • v.31 no.4
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    • pp.161-170
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    • 2018
  • The epidemic of disorders associated with synthetic stimulants, such as methamphetamine (MA) and amphetamine (AP), is a health, social, legal, and financial problem. Owing to the high potential of their abuse and addiction, reliable analytical methods are required to detect and identify MA, AP, and their metabolites in biological samples. Thus, a dilute-and-shoot liquid chromatography-tandem mass spectrophotometry (LC-MS/MS) was developed for simultaneous determination of MA, 4-hydroxymethamphetamine (4HMA), AP, and 4-hydroxyamphetamine (4HA) in urine. Urine sample ($100{\mu}L$) was mixed with $50{\mu}L$ of mobile phase consisting of 0.4 % formic acid and methanol and $50{\mu}L$ of working internal-standard solution. Aliquots of $8{\mu}L$ diluted urine was injected into the LC-MS/MS system. For all analytes, chromatographic separation was performed using a C18 reversed-phase column with gradient elution and a total run time of 5 min. The identification and quantification were performed by multiple reaction monitoring (MRM). Linear least-squares regression was conducted to generate a calibration curve, with $1/x^2$ as the weighting factor. The linear ranges were 2.0-200, 1.0-800, and 10-2500 ng/mL for 4HA and 4HMA, AP, and MA, respectively. The inter- and intraday precisions were within 6.6 %, whereas the inter- and intraday accuracies ranged from -14.9 to 11.3 %. The low limits of quantification were 2.0 ng/mL (4HA and 4HMA), 1.0 ng/mL (AP), and 10 ng/mL (MA). The proposed method exhibited satisfactory selectivity, dilution integrity, matrix effect, and stability, which are required for validation. Moreover, the purification efficiency of high-speed centrifugation was clearly higher than 6-15 % for QC samples (n=5), which was higher than that of the membrane-filtration method. The applicability of the proposed method was tested by forensic analysis of urine samples from drug abusers.