• International Journal of Computer Science & Network Security
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• 제24권4호
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• pp.44-50
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• 2024

This paper offers an overview of matrix formation and calculation techniques within the framework of General Linear Models (GLMs). It takes a sequential approach, beginning with a detailed exploration of matrix formation and calculation methods in regression analysis and univariate analysis of variance (ANOVA). Subsequently, it extends the discussion to cover multivariate analysis of variance (MANOVA). The primary objective of this study was to provide a clear and accessible explanation of the underlying matrices that play a crucial role in GLMs. Through linking, essentially different statistical methods, by fundamental principles and algebraic foundations that underpin the GLM estimation. Insights presented here aim to assist researchers, statisticians, and data analysts in enhancing their understanding of GLMs and their practical implementation in diverse research domains. This paper contributes to a better comprehension of the matrix-based techniques that can be extended to GLMs.

• 한국해양공학회지
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• 제6권2호
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• pp.125-132
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• 1992

This paper presents an approach for the derivation of frequency-dependent element matrices for vibration analysis of piping systems containing a moving medium. The dynamic stiffness matrix is deduced from transfer matrix, and, in turn, the frequency-dependent element matrices are derived. Numerical examples show that method gives more accurate results than those obtained using the conventional static shape function based element matrices.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.73-80
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• 2004

Mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory non-conservative force, and Winkler and Pasternak foundation matrix of framed structure in 2-D are calculated for stability analysis of divergence or flutter system. Then, a matrix equation of the motion for the non-conservative system is formulated and numerical results are presented to demonstrate the effect of some parameters with using Newmark method.

• International Journal of Automotive Technology
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• 제8권4호
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• pp.483-491
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• 2007

A closed form solution of a composite mechanics system is performed for the investigation of elastic-plastic behavior in order to predict fiber stresses, fiber/matrix interfacial shear stresses, and matrix yielding behavior in short fiber reinforced metal matrix composites. The model is based on a theoretical development that considers the stress concentration between fiber ends and the propagation of matrix plasticity and is compared with the results of a conventional shear lag model as well as a modified shear lag model. For the region of matrix plasticity, slip mechanisms between the fiber and matrix which normally occur at the interface are taken into account for the derivation. Results of predicted stresses for the small-scale yielding as well as the large-scale yielding in the matrix are compared with other theories. The effects of fiber aspect ratio are also evaluated for the internal elastic-plastic stress field. It is found that the incorporation of strong fibers results in substantial improvements in composite strength relative to the fiber/matrix interfacial shear stresses, but can produce earlier matrix yielding because of intensified stress concentration effects. It is also found that the present model can be applied to investigate the stress transfer mechanism between the elastic fiber and the elastic-plastic matrix, such as in short fiber reinforced metal matrix composites.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권10호
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• pp.3482-3497
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• 2021

Artificial intelligence has emerged as the core of the 4th industrial revolution, and large amounts of data processing, such as big data technology and rapid data analysis, are inevitable. The most fundamental and universal data interpretation technique is an analysis of information through regression, which is also the basis of machine learning. Ridge regression is a technique of regression that decreases sensitivity to unique or outlier information. The time-consuming calculation portion of the matrix computation, however, basically includes the introduction of an inverse matrix. As the size of the matrix expands, the matrix solution method becomes a major challenge. In this paper, a new algorithm is introduced to enhance the speed of ridge regression estimator calculation through series expansion and computation recycle without adopting an inverse matrix in the calculation process or other factorization methods. In addition, the performances of the proposed algorithm and the existing algorithm were compared according to the matrix size. Overall, excellent speed-up of the proposed algorithm with good accuracy was demonstrated.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.655-660
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• 2000

This paper presents the construction of consistent coefficient matrix elements for jointed structures using the reduction of flexibility and mass matrices. The reduced flexibility coefficient matrix hat little structural complexity than Guyan's stiffness matrix reduction since the only element of the original matrix, corresponding to the selected nodal degrees of freedom, contributes. The proposed method was applied to building equivalent coefficient matrices for a clamp jointed structure in finite element modal analysis of a cantilevered beam. The theoretical analysis results were compared with those experimental modal analysis, Comparison of both shows good agreement each other.

• Structural Engineering and Mechanics
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• 제39권5호
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• pp.669-682
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• 2011

A Chebyshev spectral method (CSM) for the dynamic analysis of non-uniform Timoshenko beams under various boundary conditions and concentrated masses at their ends is proposed. The matrix-based Chebyshev spectral approach was used to construct the spectral differentiation matrix of the governing differential operator and its boundary conditions. A matrix condensation approach is crucially presented to impose boundary conditions involving the homogeneous Cauchy conditions and boundary conditions containing eigenvalues. By taking advantage of the standard powerful algorithms for solving matrix eigenvalue and generalized eigenvalue problems that are embodied in the MATLAB commands, chebfun and eigs, the modal parameters of non-uniform Timoshenko beams under various boundary conditions can be obtained from the eigensolutions of the corresponding linear differential operators. Some numerical examples are presented to compare the results herein with those obtained elsewhere, and to illustrate the accuracy and effectiveness of this method.

• 한국콘텐츠학회논문지
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• 제8권1호
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• pp.68-74
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• 2008

데이터베이스로부터 지식을 발견하고 이를 연구기획자, 정책의사결정자들이 활용하는 움직임이 전세계적으로 활발해지고 있다. 이러한 연구분야 중 대표적인 것이 계량정보학이고 이 분야를 지원하기 위해서 주로 선진국을 중심으로 분석시스템이 개발되고 있다. 그러나 외국의 분석시스템은 실제 수요자의 요구를 충분히 반영하지 못하고 있고, 고가이면서 한글이 지원되지 않아 국내 연구기획자가 사용하기에 어려운 점이 있다. 따라서 한국과학기술정보연구원에서는 이러한 단점을 극복하기 위해서 계량정보분석시스템 KnowledgeMatrix를 개발하였다. KnowledgeMatrix는 논문 및 특허의 서지정보를 분석하여 지식을 발견하기 위한 목적으로 설계된 독립형(stand-alone) 시스템이다 KnowledgeMatrix의 주요 구성을 살펴보면 행렬 생성, 클러스터링, 시각화, 데이터 전처리로 요약된다. 본 논문에서 소개하고 있는 KnowledgeMatrix는 외국의 대표적인 정보분석시스템과 비교했을 때 다양한 기능을 제공하고 있고 특히 영문데이터 처리 이외에 한글데이터 처리가 가능하다는 장점을 갖고 있다.

• Earthquakes and Structures
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• 제22권4호
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• pp.387-399
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• 2022

To study the seismic damage of masonry structures and understand the characteristics of the multi-intensity region, according to the Dujiang weir urbanization of China Wenchuan earthquake, the deterioration of 3991 masonry structures was summarized and statistically analysed. First, the seismic damage of multistory masonry structures in this area was investigated. The primary seismic damage of components was as follows: Damage of walls, openings, joints of longitudinal and transverse walls, windows (lower) walls, and tie columns. Many masonry structures with seismic designs were basically intact. Second, according to the main factors of construction, seismic intensity code levels survey, and influence on the seismic capacity, a vulnerability matrix calculation model was proposed to establish a vulnerability prediction matrix, and a comparative analysis was made based on the empirical seismic damage investigation matrix. The vulnerability prediction matrix was established using the proposed vulnerability matrix calculation model. The fitting relationship between the vulnerability prediction matrix and the actual seismic damage investigation matrix was compared and analysed. The relationship curves of the mean damage index for macrointensity and ground motion parameters were drawn through calculation and analysis, respectively. The numerical analysis was performed based on actual ground motion observation records, and fitting models of PGA, PGV, and MSDI were proposed.

• 대한전기학회논문지
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• 제36권11호
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• pp.769-776
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• 1987

This paper deals with the topological observability analysis and the development of an observable island identification algorithm for state estimation in power systems, by using the incidence matrix and bus voltage grouping. An analogy of the DC power flow method to the DC circuit analysis is introduced, and all the relationships between power flows and phase angles are replaced by the corresponding current-voltage relation. As a result, a set of topological measurement equation expressed in the form of the incidince matrix is derived for the topological analysis, and the observability test is carried out by examining the rand of the measuremint matrix. The integer Gauss elimination method is introduced in the determination of matrix rand, so that the proposed observability test yields a precise observability criterion without any nearly-zero pivot problem encountered in the conventional algorithm. Also, an observable island identification algorithm reduced its computational time in comparision with the conventional algorithms. The proposed algorithms have been tested for sample systems, and their practicability has verified.