• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.1
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• pp.1-9
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• 1980

In this paper several basic techniques for signal processing and analysis are surveyed. Firstly by the intervention of the uncertainty principle, an equality sign may have different degree of precision if non commutable operators are applied. Seconds y maximum entropy estimate and randam process based viewpoint must be enhanced to get rid of the well established and reigning deterministic image of science. Thirdly techniques for the analysis of a signal namely detection. ess]motion and modulation are explained as well as the positive definiteness of a covariance function, Karhunen-Loeve expansion and SVD of an image.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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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.

• Tunnel and Underground Space
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• v.17 no.4
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• pp.285-294
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• 2007

Material properties of geomaterials are usually heterogeneous. And the limitted number of investigation for the subsurface material properties in terms of boreholes are not sufficient enough for identifying the heterogeneity. In most civil engineering work, pre-investigation results can be different from those by in-situ inspection during the construction work. With these points of view, a new analysis concept aiming to evaluate the uncertainty resulted from the heterogeneity of the geomaterial properties as well as to enhance a construction workability and design qualify by a prompt feedback of in-situ conditions was proposed. It was accomplished by linking the Element Free analysis and pre-developed stochastic methods represented by Karhunen-Loeve expansion. Simple ID problem was solved by the developed method, and its validity as well as the characteristic results by different stochastic methods were clarified.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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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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• v.24 no.2
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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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• v.28 no.2
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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.

• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.3
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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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• v.35 no.3
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• pp.188-195
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• 2022

This paper proposes a multiscale process-structural analysis methodology and applies to a battery housing part made of the short fiber-reinforced and fabric-reinforced composite layers. In particular, uncertainties of the material properties within the microscale representative volume element (RVE) were considered. The random spatial distribution of matrix properties in the microscale RVE was realized by the Karhunen-Loeve Expansion (KLE) method. Then, effective properties of the RVE reflecting on spatially varying matrix properties were obtained by the computational homogenization and mapped to a macroscale FE (finite element) model. Morever, through the hybrid process simulation, a FE (finite element) model mapping residual stress and fiber orientation from compression molding simulation is combined with one mapping fiber orientation from the draping process simulation. The proposed method is expected to rigorously evaluate the design requirements of the battery housing part and composite materials having various material configurations.

• International Journal of Aerospace System Engineering
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• v.6 no.2
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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.