• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권4호
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• Smart Structures and Systems
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• 제17권3호
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• pp.413-429
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• 2016

The recent research on proper orthogonal decomposition (POD) has revealed the linkage between proper orthogonal modes and linear normal modes. This paper presents an investigation into the modal identifiability of an instrumented cable-stayed bridge using an adapted POD technique with a band-pass filtering scheme. The band-pass POD method is applied to the datasets available for this benchmark study, aiming to identify the vibration modes of the bridge and find out the so-called deficient modes which are unidentifiable under normal excitation conditions. It turns out that the second mode of the bridge cannot be stably identified under weak wind conditions and is therefore regarded as a deficient mode. To judge if the deficient mode is due to its low contribution to the structural response under weak wind conditions, modal coordinates are derived for different modes by the band-pass POD technique and an energy participation factor is defined to evaluate the energy participation of each vibration mode under different wind excitation conditions. From the non-blind datasets, it is found that the vibration modes can be reliably identified only when the energy participation factor exceeds a certain threshold value. With the identified threshold value, modal identifiability in use of the blind datasets from the same structure is examined.

• 한국항공우주학회지
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• 제38권5호
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• pp.414-420
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• 2010

본 연구에서는 천음속 날개/동체 모텔에 대한 축소모델 (Reduced Order Model; ROM)의 정확성을 검증하고, Proper Orthogonal Decomposition(POD)을 이용한 최적설계를 통해 그 효율성을 검토하였다. full order 공력해석을 통한 Snapshot을 추출하기 위해 삼차원 오일러 방정식을 이용하였으며, 이들 Snapshot들을 통해 날개/동체 모델 주위 유동장의 거동을 모사하는 POD의 기저벡터를 계산 하였다. 이러한 과정을 거쳐 구축된 축소모텔은 6개의 Case들로 검증하였으며, 그 결과 ROM을 이용해 관심영역에 대한 유동장의 예측을 할 수 있다는 것을 확인하였다. 그리고 ROM을 통한 날개/동체 모델의 최적설계를 수행 하였으며, 그 결과는 반응면모델 (Response Surface Model; RSM)을 이용한 최적설계 결과와 비교 하였다. 이를 통해 ROM을 바탕으로한 최적설계가 RSM을 이용한 것보다 효율적임을 확인하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2009년도 정기 학술대회
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• pp.205-208
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• 2009

POD(proper orthogonal decomposition)는 가해지는 하중(입력)의 계측없이 출력(응답)만으로 구조물의 동적특성을 파악할 수 있는 기법이다. 하지만 실제의 경우 측정데이터에 노이즈가 포함되어 있으면 분해가 완전하게 일어나지 않아 동적특성(특히 감쇠비)을 완벽히 파악하기 힘들다. 본 연구에서는 이러한 문제점을 보완하기 위해서 POD기법으로 추출된 각 모드의 자유진동파형에 RD(random decrement)법을 적용하여 노이즈에 의한 영향을 제거하는 방법을 제안하였다. 본 논문에서는 먼저 수치모델을 사용하여 계측노이즈가 있을 경우 제안된 방법을 사용하면 노이즈의 영향을 감소시킬 수 있음을 검증한 후 실험실 규모의 구조물모형에서 얻은 자유진동계측치에 제안된 기법을 적용하여 시스템식별을 수행하여 동특성을 파악하였다.

• 한국항공우주학회지
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• 제40권10호
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• pp.833-839
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• 2012

본 논문에서는 후향계단 유동장 모델링 및 복원오차를 분석한다. 유동장의 밀도를 POD(Proper Orthogonal Decomposition) 기법을 통해 공간모드와 시간모드로 추출하여 수학적으로 모델링한다. 모델링 오차를 정립하여 유동에너지와 오차 사이의 관계를 정리한다. 모델링 오차를 시간영역 뿐만 아니라 주파수 영역에서의 분석을 통하여 제어측면에서 오차의 한계를 규정한다.

• Wind and Structures
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• 제10권2호
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• pp.177-208
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• 2007

Few mathematical methods attracted theoretical and applied researches, both in the scientific and humanist fields, as the Proper Orthogonal Decomposition (POD) made throughout the last century. However, most of these fields often developed POD in autonomous ways and with different names, discovering more and more times what other scholars already knew in different sectors. This situation originated a broad band of methods and applications, whose collation requires working out a comprehensive viewpoint on the representation problem for random quantities. Based on these premises, this paper provides and discusses the theoretical foundations of POD in a homogeneous framework, emphasising the link between its general position and formulation and its prevalent use in wind engineering. Referring to this framework, some applications recently developed at the University of Genoa are shown and revised. General remarks and some prospects are finally drawn.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.606-611
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• 2007

Proper orthogonal decomposition (POD) is a method for extracting bases for modal decomposition from the ensemble of dynamic signals. Using the POD method, we analyzed the proper orthogonal modes (POMs) of AFM microcantilevers in dynamic mode operations such as Tapping Mode. The POMs and POVs (proper orthogonal values) were computed through MATLAB simulation for the 5-mode model of the microcantilever. We found that the POV portion of the higher POMs of the tapping microcanilever slightly increased in comparison with no tapping. This implies that the modal energy in the fundamental mode can be transferred to the higher modes during tapping.

• International Journal of Naval Architecture and Ocean Engineering
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• 제7권6호
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• pp.979-994
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• 2015

The mode shapes of a segmented hull model towed in a model basin were predicted using both the Proper Orthogonal Decomposition (POD) and cross random decrement technique. The proper orthogonal decomposition, which is also known as Karhunen-Loeve decomposition, is an emerging technology as a useful signal processing technique in structural dynamics. The technique is based on the fact that the eigenvectors of a spatial coherence matrix become the mode shapes of the system under free and randomly excited forced vibration conditions. Taking advantage of the simplicity of POD, efforts have been made to reveal the mode shapes of vibrating flexible hull under random wave excitation. First, the segmented hull model of a 400 K ore carrier with 3 flexible connections was towed in a model basin under different sea states and the time histories of the vertical bending moment at three different locations were measured. The measured response time histories were processed using the proper orthogonal decomposition, eventually to obtain both the first and second vertical vibration modes of the flexible hull. A comparison of the obtained mode shapes with those obtained using the cross random decrement technique showed excellent correspondence between the two results.

• 한국강구조학회 논문집
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• 제20권6호
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• pp.751-759
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• 2008

본 연구에서는 구조적 기본단면인 사각단면중에서 B/D=2,3,4,5 단면을 대상으로 단면주위 흐름상태가 단면의 공기력 특성에 미치는 영향을 살펴보고, 정지/진동하는 B/D=4 사각실린더 주위의 비정상압력장에 POD해석을 도입함으로써 흐름패턴에 따른 POD해석의 고유벡터를 규정하고 실린더 주위 흐름장 안에 공존하는 서로 다른 흐름패턴의 상호간섭과 물리적 모드분해에 관하여 검토하였다. POD해석의 고유벡터 비교를 통해서 칼만와류는 박리버블에 의해서 거의 영향받지 않지만 칼만와류는 단면후류부에서 박리버블의 발달에 상당히 간섭하고 있음을 확인하 였다. 변장비(B/D=2,34,5) 변화에 따른 ${dC_L/d\alpha}$, ${H_1^{*}}$의 정(+)부(-)의 차이, 즉 갤로핑현상에 대한 안정/불안정성은 박리전단층의 재부착에 깊은 관련이 있는 것으로 판단되며 B/D=3,4에서 시간평균적으로 재부착하던 주위흐름장이 칼만와류의 방출을 제어하면 재부착하지 않는 것으로 생각된다. 즉, 칼만와류의 억제는 후류부에서 박리전단층의 곡률이 작아지도록 간섭하고 단면에 있어서 elongation효과를 나타낸다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집B
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• pp.423-425
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• 2001

The Proper Orthogonal Decomposition (POD) technique was applied to investigate the effects of Reynolds number and the characteristics of the organized motions or coherent structures as a function of downstream position from x/D=2 to 6 in a turbulent axisymmetric shear layer at Reynolds numbers of 78,400, 117,600, and 156,800. Data were collected simultaneously using the 138 hot-wire probe used by Citriniti and George (2000). The POD was then applied to a double Fourier transform in time and azimuthal direction of the double velocity correlation tensor. The lowest azimuthal mode for all POD modes, which dominated the dynamics at x=D = 3 in the previous experiments, dies off rapidly downstream. This is consistent with a trend toward homogeneity in the downstream evolution, and suggests that some residual value may control the growth rate of the far jet. On the other hand, for the higher azimuthal modes, the peak shifts to lower mode numbers and actually increases with downstream distance. These mixing layer data, normalized by similarity variables for the mixing layer, collapse at all downstream positions and are nearly independent of Reynolds numbers.