• Title/Summary/Keyword: The Least Squares Method

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Partitioning likelihood method in the analysis of non-monotone missing data

  • Kim Jae-Kwang
    • Proceedings of the Korean Statistical Society Conference
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    • 2004.11a
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    • pp.1-8
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    • 2004
  • We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Robin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is also presented to illustrate the method.

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Milling tool wear forecast based on the partial least-squares regression analysis

  • Xu, Chuangwen;Chen, Hualing
    • Structural Engineering and Mechanics
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    • v.31 no.1
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    • pp.57-74
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    • 2009
  • Power signals resulting from spindle and feed motor, present a rich content of physical information, the appropriate analysis of which can lead to the clear identification of the nature of the tool wear. The partial least-squares regression (PLSR) method has been established as the tool wear analysis method for this purpose. Firstly, the results of the application of widely used techniques are given and their limitations of prior methods are delineated. Secondly, the application of PLSR is proposed. The singular value theory is used to noise reduction. According to grey relational degree analysis, sample variable is filtered as part sample variable and all sample variables as independent variables for modelling, and the tool wear is taken as dependent variable, thus PLSR model is built up through adapting to several experimental data of tool wear in different milling process. Finally, the prediction value of tool wear is compare with actual value, in order to test whether the model of the tool wear can adopt to new measuring data on the independent variable. In the new different cutting process, milling tool wear was predicted by the methods of PLSR and MLR (Multivariate Linear Regression) as well as BPNN (BP Neural Network) at the same time. Experimental results show that the methods can meet the needs of the engineering and PLSR is more suitable for monitoring tool wear.

Least Squares Based PID Control of an Electromagnetic Suspension System

  • Park, Yon-Mook;Tahk, Min-Jea;Nam, Myeong-Ryong;Seo, In-Ho;Lee, Sang-Hyun;Lim, Jong-Tae
    • International Journal of Aeronautical and Space Sciences
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    • v.4 no.2
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    • pp.69-78
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    • 2003
  • In this paper, we develop the so-called functional test model for magnetic bearing wheels. The functional test model developed in this paper is a kind of electromagnetic suspension systems and has three degree of freedom, which consists of one axial suspension from gravity and the other two axes gimbaling capability to small angle, and does not include the motor. For the control of the functional test model, we derive the optimal electromagnetic forces based on the least squares method, and use the proportional-integral derivative controller. Then, we develop a hardware setup, which mainly consists of the digital signal processor and the 12-bit analog-to-digital and digital-to-analog converters, and show the experimental results.

Least Squares Based PID Control of an Electromagnetic Suspension System

  • Park, Yon-Mook;Nam, Myeong-Ryong;Seo, In-Ho;Lee, Sang-Hyun;Lim, Jong-Tae;Tahk, Min-Jea
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.2252-2257
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    • 2003
  • In this paper, we develop the so-called functional test model for magnetic bearing reaction wheels. The functional test model has three degree of freedom, which consists of one axial suspension from gravity and the other two axes gimbaling capability to small angle, and does not include the motor. For the control of the functional test model, we derive the optimal electromagnetic forces based on the least squares method, and use the proportional-integral-derivative controller. Then, we develop a hardware setup, which mainly consists of the digital signal processor and the 12-bit analog-to-digital and digital-to-analog converters, and show the experimental results.

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Development of a Method for Health Monitoring of Rotating Object for Mobility based on Multiple RLS Algorithm (다중 재귀 최소 자승 추정 알고리즘 기반 모빌리티의 회전체 건전성 모니터링 방법 개발)

  • Hanbyeol La;Jiung Lee;Kwangseok Oh
    • Journal of Auto-vehicle Safety Association
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    • v.16 no.2
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    • pp.51-59
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    • 2024
  • This study presents a method for health monitoring of rotating objects for mobility based on multiple recursive least squares(RLS) algorithms. The performance degradation of the rotating objects causes low handing / low driving performances and even fatal accidents. Therefore, health monitoring algorithm of rotating objects is one of the important technologies for mobility fail-safe and maintenance areas. In order for health monitoring of rotating objects, four recursive least squares algorithms with forgetting factor were designed in this study. The health monitoring algorithm proposed in this study consists of two steps such as uncertainty estimation and parameter changes estimation. In order to improve estimation accuracy, time delay function was applied to the estimated signals based on the first order differential equation and forgetting factors used for the RLS were reasonably tuned. The health monitoring algorithm was constructed in Matlab/Simulink environment and simulation-based performance evaluation was conducted using DC motor model. The evaluation results showed that the proposed algorithm estimates the actual parameter differences reasonably using velocity and current information.

Block Adjustment and Orthorectification for Multi-Orbit Satellite Images

  • Chen, Liang-Chien;Liu, Chien-Liang;Teo, Tee-Ann
    • Proceedings of the KSRS Conference
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    • 2003.11a
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    • pp.888-890
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    • 2003
  • The objective of this investigation is to establish a simple yet effective block adjustment procedure for the orthorectification of multi-orbit satellite images. The major works of the proposed scheme are: (1) adjustment of satellite‘s orbit accurately, (2) calculation of the error vectors for each tie point using digital terrain model and ray tracing technique, (3) refining the orbit using the Least Squares Filtering technique and (4) generation of the orthophotos. In the process of least squares filtering, we use the residual vectors on ground control points and tie points to collocate the orbit. In orthorectification, we use the indirect method to generate the orthoimage. Test areas cover northern Taiwan. Test images are from SPOT 5 satellite. Experimental results indicate that proposed method improves the relative accuracy significantly.

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Design and Implementation of the Combline Bandpass Filter for the Satellite Transponder using Least-squares Curve-fitting Method (Least-squares Curve-fitting 방법을 이용한 위성중계기용 Combline 대역통과여파기의 설계 및 제작)

  • 정근욱;이재현;박광량;김재명
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.19 no.8
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    • pp.1485-1492
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    • 1994
  • In this paper, we design and implement the Combline Bandpass Filters for the satellite transponder by using the least-squares curve-fitting method. The Combline Bandpass Filters are located front of the mixer and behind of it, which is the component of down converter. Comparing with the filters which have $\lambda$/4 resonance length. Combline Filter has wide range of stop-band by using $\lambda$/8. So, it is useful to the satellite transponder owing to its low mass and small size. The filters described are realized as coupled rectangular coaxial transmission lines. The choice of this type is due to the ease of machining and wide variations in coupling coefficients rather than the use of the round rod resonators. We determine 800 MHz bandwidths for the combline bandpass filters. By using Chebyshev filter function, we design and implement 4-pole combline filters.

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Automatic Selection of Optimal Parameter for Baseline Correction using Asymmetrically Reweighted Penalized Least Squares (Asymmetrically Reweighted Penalized Least Squares을 이용한 기준선 보정에서 최적 매개변수 자동 선택 방법)

  • Park, Aaron;Baek, Sung-June;Park, Jun-Qyu;Seo, Yu-Gyung;Won, Yonggwan
    • Journal of the Institute of Electronics and Information Engineers
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    • v.53 no.3
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    • pp.124-131
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    • 2016
  • Baseline correction is very important due to influence on performance of spectral analysis in application of spectroscopy. Baseline is often estimated by parameter selection using visual inspection on analyte spectrum. It is a highly subjective procedure and can be tedious work especially with a large number of data. For these reasons, it is an objective and automatic procedure is necessary to select optimal parameter value for baseline correction. Asymmetrically reweighted penalized least squares (arPLS) based on penalized least squares was proposed for baseline correction in our previous study. The method uses a new weighting scheme based on the generalized logistic function. In this study, we present an automatic selection of optimal parameter for baseline correction using arPLS. The method computes fitness and smoothness values of fitted baseline within available range of parameters and then selects optimal parameter when the sum of normalized fitness and smoothness gets minimum. According to the experimental results using simulated data with varying baselines, sloping, curved and doubly curved baseline, and real Raman spectra, we confirmed that the proposed method can be effectively applied to optimal parameter selection for baseline correction using arPLS.

A STUDY OF SPECTRAL ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS WITH NONSMOOTH SOLUTIONS IN ℝ2

  • KUMAR, N. KISHORE;BISWAS, PANKAJ;REDDY, B. SESHADRI
    • Journal of applied mathematics & informatics
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    • v.38 no.3_4
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    • pp.311-334
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    • 2020
  • The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

Gene Selection and Classification by Partial Least Squares and Principal component analysis (부분최소자승법과 주성분분석을 이용한 유전자 선택과 분류)

  • Park, Hoseok;Kim, Hey-Jin;Park, Seugj in;Bang, Sung-Yang
    • Proceedings of the Korean Information Science Society Conference
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    • 2001.10a
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    • pp.598-600
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    • 2001
  • DNA chip technology enables us to monitor thousands of gene expressions per sample simultaneously. Typically, DNA microarray data has at least several thousands of variables (genes) wish relatively smal1 number of samples. Thus feature (gene) selection by dimensionality reduction is necessary for efficient data analysis. In this paper we employ the partial least squares (PLS) method for gene selection and the principal component analysis (PCA) method for classification. The useful behavior of the PLS is verified by computer simulations.

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