• Title/Summary/Keyword: Method of Least Squares

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Approximate Optimization Using Moving Least Squares Response Surface Methods: Application to FPSO Riser Support Design

  • Song, Chang-Yong;Lee, Jong-Soo;Choung, Joon-Mo
    • Journal of Ocean Engineering and Technology
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    • v.24 no.1
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    • pp.20-33
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    • 2010
  • The paper deals with strength design of a riser support installed on floating production storage and offloading (FPSO) vessel under various loading conditions - operation, extreme, damaged, one line failure case (OLFC) and installation. The design problem is formulated such that thickness sizing variables are determined by minimizing the weight of a riser support structure subject to stresses constraints. The initial design model is generated based on an actual FPSO riser support specification. The finite element analysis (FEA) is conducted using MSC/NASTRAN, and optimal solutions are obtained via moving least squares method (MLSM) in the context of response surface based approximate optimization. For the meta-modeling of inequality constraint functions of stresses, a constraint-feasible moving least squares method (CF-MLSM) is used in the present study. The method of CF-MLSM, compared to a conventional MLSM, has been shown to ensure the constraint feasibility in a case where the approximate optimization process is employed. The optimization results present improved design performances under various riser operating conditions.

Robust Total Least Squares Method and its Applications to System Identifications (견인한 완전최소자승법과 시스템 식별에의 적용)

  • Kim, Jin-Young;Choi, Seung-Ho
    • The Journal of the Acoustical Society of Korea
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    • v.15 no.4
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    • pp.93-97
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    • 1996
  • The Total Least Squares(TLS) method is an unbiased estimator for solving overdetermined sets of linear equations Ax${\simeq}$b when errors occur in all data. However, as well as Least Squares(LS) method it doesn't show robustness while the errors have a heavy tailed probability density function. In this paper we proposed a robust method of TLS (Robust TLS, ROTLS) based on the characteristics of TLS solution. And the ROTLS is verified by applying it to system identification problems.

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Missing Values Estimation for Time Course Gene Expression Data Using the Sequential Partial Least Squares Regression Fitting (순차적 부분최소제곱 회귀적합에 의한 시간경로 유전자 발현 자료의 결측치 추정)

  • Kim, Kyung-Sook;Oh, Mi-Ra;Baek, Jang-Sun;Son, Young-Sook
    • The Korean Journal of Applied Statistics
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    • v.21 no.2
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    • pp.275-290
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    • 2008
  • The size of microarray gene expression data is very big and its observation process is also very complex. Thus missing values are frequently occurred. In this paper we propose the sequential partial least squares(SPLS) regression fitting method to estimate missing values for time course gene expression data that has correlations among observations over time points. The SPLS method is to combine the sequential technique with the partial least squares(PLS) regression fitting method. The usefulness of method proposed is evaluated through some simulation study for three yeast time course data.

Preference Map using Weighted Regression

  • S.Y. Hwang;Jung, Su-Jin;Kim, Young-Won
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.651-659
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    • 2001
  • Preference map is a widely used graphical method for the preference data set which is frequently encountered in the field of marketing research. This provides joint configuration usually in two dimensional space between "products" and their "attributes". Whereas the classical preference map adopts the ordinary least squares method in deriving map, the present article suggests the weighted least squares approach providing the better graphical display and interpretation compared to the classical one. Internet search engine data in Korea are analysed for illustration.

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A study on robust recursive total least squares algorithm based on iterative Wiener filter method (반복형 위너 필터 방법에 기반한 재귀적 완전 최소 자승 알고리즘의 견실화 연구)

  • Lim, Jun Seok
    • The Journal of the Acoustical Society of Korea
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    • v.40 no.3
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    • pp.213-218
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    • 2021
  • It is known that total least-squares method shows better estimation performance than least-squares method when noise is present at the input and output at the same time. When total least squares method is applied to data with time series characteristics, Recursive Total Least Squares (RTS) algorithm has been proposed to improve the real-time performance. However, RTLS has numerical instability in calculating the inverse matrix. In this paper, we propose an algorithm for reducing numerical instability as well as having similar convergence to RTLS. For this algorithm, we propose a new RTLS using Iterative Wiener Filter (IWF). Through the simulation, it is shown that the convergence of the proposed algorithm is similar to that of the RTLS, and the numerical robustness is superior to the RTLS.

Comparative Analysis of Learning Methods of Fuzzy Clustering-based Neural Network Pattern Classifier (퍼지 클러스터링기반 신경회로망 패턴 분류기의 학습 방법 비교 분석)

  • Kim, Eun-Hu;Oh, Sung-Kwun;Kim, Hyun-Ki
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.9
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    • pp.1541-1550
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    • 2016
  • In this paper, we introduce a novel learning methodology of fuzzy clustering-based neural network pattern classifier. Fuzzy clustering-based neural network pattern classifier depicts the patterns of given classes using fuzzy rules and categorizes the patterns on unseen data through fuzzy rules. Least squares estimator(LSE) or weighted least squares estimator(WLSE) is typically used in order to estimate the coefficients of polynomial function, but this study proposes a novel coefficient estimate method which includes advantages of the existing methods. The premise part of fuzzy rule depicts input space as "If" clause of fuzzy rule through fuzzy c-means(FCM) clustering, while the consequent part of fuzzy rule denotes output space through polynomial function such as linear, quadratic and their coefficients are estimated by the proposed local least squares estimator(LLSE)-based learning. In order to evaluate the performance of the proposed pattern classifier, the variety of machine learning data sets are exploited in experiments and through the comparative analysis of performance, it provides that the proposed LLSE-based learning method is preferable when compared with the other learning methods conventionally used in previous literature.

A modified partial least squares regression for the analysis of gene expression data with survival information

  • Lee, So-Yoon;Huh, Myung-Hoe;Park, Mira
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.5
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    • pp.1151-1160
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    • 2014
  • In DNA microarray studies, the number of genes far exceeds the number of samples and the gene expression measures are highly correlated. Partial least squares regression (PLSR) is one of the popular methods for dimensional reduction and known to be useful for the classifications of microarray data by several studies. In this study, we suggest a modified version of the partial least squares regression to analyze gene expression data with survival information. The method is designed as a new gene selection method using PLSR with an iterative procedure of imputing censored survival time. Mean square error of prediction criterion is used to determine the dimension of the model. To visualize the data, plot for variables superimposed with samples are used. The method is applied to two microarray data sets, both containing survival time. The results show that the proposed method works well for interpreting gene expression microarray data.

The Geolocation Based on Total Least Squares Algorithm Using Satellites (위성을 이용한 Total Least Squares 기반 신호원 측위 알고리즘)

  • 박영미;조상우;전주환
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.2C
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    • pp.255-261
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    • 2004
  • The problem of geolocation using multiple satellites is to determine the position of a transmitter located on the Earth by processing received signals. The specific problem addressed in this paper is that of estimating the position of a stationary transmitter located on or above the Earth's surface from measured time difference of arrivals (TDOA) by a geostationary orbiting (GSO) satellite and a low earth orbiting (LEO) satellite. The proposed geolocation method is based on the total least squares (TLS) algorithm. Under erroneous positions of the satellites together with noisy TDOA measurements, the TLS algorithm provides a better solution. By running Monte-Carlo simulations, the proposed method is compared with the ordinary least squares (LS) approach.

Estimation of the Separate Primary and Secondary Leakage Inductances of a Y-Δ Transformer Using Least Squares Method

  • Kang, Yong-Cheol;Lee, Byung-Eun;Hwang, Tae-Keun
    • Journal of Electrical Engineering and Technology
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    • v.5 no.4
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    • pp.538-544
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    • 2010
  • This paper proposes an estimation algorithm for the separate primary and secondary leakage inductances of a three phase $Y-\Delta$ transformer using least squares method. The voltage equations from the primary and secondary windings are combined into a differential equation to estimate the separate primary and secondary leakage inductances in order to use the line current of the delta winding. Separate primary and secondary leakage inductances are obtained by applying least squares method to the differential equation. The performance of the proposed algorithm is validated under transient states, such as magnetic inrush and overexcitation, as well as in the steady state with various cut-off frequencies of low-pass filter. The proposed technique can accurately generate separate leakage inductances both in the steady and transient states.