• 대한전자공학회논문지
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• 제17권1호
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• pp.1-9
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• 1980

신호처리와 analysis를 위한 여러 기초적인 기술이 소개되었다. 이들은 먼저 불확정성순리의 개입에 의하여 특히 교환불가능한 operator 들이 작용한 결과의 등호는 tolerance가 있을 수 있음과 random process 처리방법과 manmum entropy estimate적인 ,사고방식을 통하여 재래식 확정론적 사고방식으로부터의 이탈을 길잡았다. 마지막으로 검출, 추정 및 함수추정의 여러 기법과 covariance functron의 posltive semi-definite-ness 그리고 Karhunen-Loeve 전개, 한 화상의 SVD 등이 설명됐다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2010년도 정기 학술대회
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• pp.171-174
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• 2010

적절한 근사화 과정을 통하여 구축된 축소 시스템은 전체 시스템의 거동을 적은 수의 정보를 통하여 효과적으로 표현할 수 있다. 효과적인 시스템 축소를 위하여 본 연구에서는 주파수 영역 Karhunen-Loeve (Frequency-domain Karhunen-Loeve, FDKL) 기법과 시스템 등가 확장 축소 과정(System equivalent expansion reduction process, SEREP)을 연동한 축소 기법을 제안한다. 적합직교분해(Proper orthogonal decomposition)의 한 방법인 FDKL기법을 통하여 최적모드(Optimal mode)를 구하고 이에 SEREP을 적용하여 자유도 변환 행렬을 구한다. 이때 주자유도 선정은 2단계 축소기법을 적용한다. 최종적으로 제안된 기법은 수치예제를 통하여 검증한다.

• 대한기계학회논문집
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• 제19권3호
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• pp.751-762
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• 1995

The snapshot method is introduced to approximate the coherent structures of planar jet flow. The numerical simulation of instantaneous flow field is analyzed by SIMPLE algorithm. An ensemble of realizations is collected using a sampling condition that corresponds to the passage of a large scale vortex at positions 4 and 6 diameters downstream from the nozzle. With snapshot mothod we could treat the data efficiently and approximate coherent structures inhered in the planar jet flow successfully 94% of total turbulent kinetic energy with 10 terms of Karhunen-Loeve expansions. Finally, In accordance with the recent trend to try to explain and model turbulence phenomena with the existence of coherent structures, in the present study, we express the underlying coherent structures of planar jet flow in the minimum number of modes by calculating Karhunen-Loeve expansions in order to improve to understanding of jet flow and to make the information storage and management in computers easier.

• 터널과지하공간
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• 제17권4호
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• pp.285-294
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• 2007

일반적으로 지반재료의 물성은 불균질할 뿐만 아니라 제한된 수량의 시추공을 이용한 지반재료의 물성조사는 그 불균질성을 파악하기에 충분하지 못한 경우가 대부분이다. 또한, 지반 굴착 등의 토목공사에 있어서 굴착 결과로 얻어지는 현장조건은 사전 지반조사와 상이한 경우가 많으며 이를 반영한 해석조건의 수정과정은 유한요소해석으로 대표되는 기존해석의 경우 상당한 비용과 시간을 요구한다. 이러한 관점에서 본 연구에서는 무요소해석법과 연속확률변수의 급수전개법의 하나인 Karhunen-Loeve 전개법을 결합함으로써, 지반재료물성의 불균질성에 기인한 불확실성의 정량적 평가가 가능하고 현장조건의 신속한 반영이 상대적으로 수월한 해석툴의 개발을 위한 기초연구를 수행하였다. 이를 위해 개발된 해석법을 1차원 문제에 적용하여 타당성을 검증하고 서로 다른 해석결과의 특징을 비교분석 하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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• pp.11-18
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• 2004

In this paper, an efficient model reduction scheme is presented for large scale dynamic systems. The method is founded on a modal analysis in which optimal eigenvalue is extracted from time samples of the given system response. The techniques we discuss are based on classical theory such as the Karhunen-Loeve expansion. Only recently has it been applied to structural dynamics problems. It consists in obtaining a set of orthogonal eigenfunctions where the dynamics is to be projected. Practically, one constructs a spatial autocorrelation tensor and then performs its spectral decomposition. The resulting eigenfunctions will provide the required proper orthogonal modes(POMs) or empirical eigenmodes and the correspondent empirical eigenvalues (or proper orthogonal values, POVs) represent the mean energy contained in that projection. The purpose of this paper is to compare the reduced order model using Karhunen-Loeve expansion with the full model analysis. A cantilever beam and a simply supported plate subjected to sinusoidal force demonstrated the validity and efficiency of the reduced order technique by K-L method.

• Geomechanics and Engineering
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• 제24권2호
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• pp.167-178
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• 2021

Spatial variability is an inherent uncertainty of soil properties. Current reliability analyses generally incorporate random field theory and Monte Carlo simulation (MCS) when dealing with spatial variability, in which the computational efficiency is a significant challenge. This paper proposes a KL-FORM algorithm to improve the computational efficiency. In the proposed KL-FORM, Karhunen-Loeve (KL) expansion is used for discretizing random fields, and first-order reliability method (FORM) is employed for reliability analysis. The KL expansion and FORM can be used in conjunction, through adopting independent standard normal variables in the discretization of KL expansion as the basic variables in the FORM. To illustrate the effectiveness of this KL-FORM, it is applied to a case study of a strip footing in spatially variable unsaturated soil under rainfall, in which the bearing capacity of the footing is computed by numerical simulation. This case study shows that the KL-FORM is accurate and efficient. The parametric analyses suggest that ignoring the spatial variability of the soil may lead to an underestimation of the reliability index of the footing.

• Structural Engineering and Mechanics
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• 제28권2호
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• 한국농공학회논문집
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• 제54권3호
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• pp.55-63
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• 2012

Soil properties are not random values which is represented by mean and standard deviation but show spatial correlation. Especially, soils are highly variable in their properties and rarely homogeneous. Thus, the accuracy and reliability of probabilistic analysis results is decreased when using only one random variable as design parameter. In this paper, to consider spatial variability of soil property, one-dimensional random fields of coefficient of consolidation ($C_v$) were generated based on a Karhunen-Loeve expansion. A Latin hypercube Monte Calro simulation coupled with finite difference method for Terzaghi's one dimensional consolidation theory was then used to probabilistic analysis. The results show that the failure probability is smaller when consider spatial variability of $C_v$ than not considered and the failure probability increased when the autocorrelation distance increased. Thus, the uncertainty of soil can be overestimated when spatial variability of soil property is not considered, and therefore, to perform a more accurate probabilistic analysis, spatial variability of soil property needed to be considered.

• Composites Research
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• 제35권3호
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• pp.188-195
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• 2022

본 논문은 멀티스케일 공정-구조 해석의 방법론을 제안하고 단섬유층과 직물층으로 이루어진 배터리 하우징 파트에 적용한다. 특별히 마이크로스케일 대표체적요소(RVE: Representative Volume Element)안 기지의 불확정성을 고려하였다. 마이크로스케일의 RVE내 기지 물성의 랜덤한 공간내 분포는 KLE(Karhunen-Loeve Expansion)을 통해 구현하였다. 공간상 랜덤분포된 기지 물성을 갖는 RVE의 유효 물성을 전산균질화를 통해 얻어 매크로스케일 유한요소 모델에 매핑하였다. 또한 하이브리드 공정해석을 통해 압축 성형 해석으로부터 얻은 잔류응력과 섬유배향을 매핑한 유한요소 모델과 드레이핑 공정 해석결과로부터 얻어진 섬유배향을 매핑한 모델을 결합하였다. 본 연구에 제안된 방법은 배터리 하우징 뿐만 아니라 다양한 재료 구성을 갖는 복합재료의 공정-구조해석을 통해 설계요구도를 엄밀하게 평가할 수 있을 것이라 기대된다.

• International Journal of Aerospace System Engineering
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• 제6권2호
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• pp.1-10
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• 2019

In this paper, the probabilistic free vibration analysis of a geometrically coupled cantilever wing with uncertain material properties is carried out using stochastic finite element (SFEM) based on first order perturbation technique. Here, both stiffness and damping of the system are considered as random parameters. The bending and torsional rigidities are assumed as spatially varying second order Gaussian random fields and represented by Karhunen Loeve (K-L) expansion. Here, the expected value, standard deviation, and probability distribution of random natural frequencies and damping ratios are computed. The results obtained from the present approach are also compared with Monte Carlo simulations (MCS). The results show that the uncertain bending rigidity has more influence on the damping ratio and frequency of modes 1 and 3 while uncertain torsional rigidity has more influence on the damping ratio and frequency of modes 2 and 3.