• Wind and Structures
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• v.38 no.1
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• pp.1-13
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• 2024

In order to effectively simulate nonstationary stochastic turbulent wind fields, four separation hybrid (SEP-H) models are proposed in the present study. Based on the assumption that the lateral turbulence component at one single-point is uncorrelated with the longitudinal and vertical turbulence components, the fluctuating wind is separated into 2nV-1D and nV1D nonstationary stochastic vector processes. The first process can be expressed as double proper orthogonal decomposition (DPOD) or proper orthogonal decomposition and spectral representation method (POD-SRM), and the second process can be expressed as POD or SRM. On this basis, four SEP-H models of nonstationary stochastic turbulent wind fields are developed. In addition, the orthogonal random variables in the SEP-H models are presented as random orthogonal functions of elementary random variables. Meanwhile, the number theoretical method (NTM) is conveniently adopted to select representative points set of the elementary random variables. The POD-FFT (Fast Fourier transform) technique is introduced in frequency to give full play to the computational efficiency of the SEP-H models. Finally, taking a long-span bridge as the engineering background, the SEP-H models are compared with the dimension-reduction DPOD (DR-DPOD) model to verify the effectiveness and superiority of the proposed models.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.7
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• pp.535-540
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• 2019

The coupling between different models for MDO (Multi-disciplinary Optimization) greatly increases the complexity of the computational framework, while at the same time increasing CPU time and memory usage. To overcome these difficulties, POD (Proper Orthogonal Decomposition) and RBF (Radial Basis Function) are used to solve the optimization problem of determining the thickness of composites and sandwich cores when composite sandwich structures are used as aircraft wing skin materials. POD and RBF are used to construct surrogate models for the wing shape and the load data. Optimization is performed using the objective function and constraint function values which are obtained from the surrogate models.

• IEIE Transactions on Smart Processing and Computing
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• v.6 no.2
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• pp.117-123
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• 2017

N-continuous orthogonal frequency division multiplexing (OFDM) is a precoding method for sidelobe suppression of OFDM signals and seamlessly connects OFDM symbols up to the high-order derivative for sidelobe suppression, which is suitable for suppressing out-of-band radiation. However, it severely degrades the error rate as it increases the continuous derivative order. Two schemes for orthogonal precoding of N-continuous OFDM have been proposed to achieve an ideal error rate while maintaining sidelobe suppression performance; however, the large size of the precoder matrices in both schemes causes very high computational complexity for precoding and decoding. This paper proposes matrix decomposition of precoder matrices with a large size in the orthogonal precoding schemes in order to reduce computational complexity. Numerical experiments show that the proposed method can drastically reduce computational complexity without any performance degradation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.10
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• pp.833-839
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• 2012

In this paper, we analyze the reconstruction error in the modeling of flow field on BFS(Backward Facing Step). In order for the mathematical modelling of a density on the field, the spatial and temporal modes are extracted by POD(Proper Orthogonal Decomposition) method. After formulating the modeling error, we summarize the relationship between the energy strength and the reconstruction errors. Moreover the allowable modeling error limits in the flow control point of view are confined by analysing in the frequency domain as well as time domain of the reconstructed data.

• Wind and Structures
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• v.3 no.2
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• pp.97-115
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• 2000

The technique of proper orthogonal decomposition is potentially useful in specifying the fluctuating surface pressure field around structures. However there has been a degree of controversy over whether or not the calculated modes have physical meanings. This paper addresses this issue through consideration of the results of full scale experiments, and through an analytical investigation. It is concluded that the lower, most energetic modes are likely to reflect different fluctuating flow mechanisms, although no mode is likely to be associated with just one flow mechanism or vice versa. The higher, less energetic modes are likely to represent interactions between different flow mechanisms, and to be significantly affected by the number of measurement points and measurement errors. The paper concludes with a brief description of the application of POD to the problem of building ventilation, and the calculation of cladding pressures.

• 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.

• Wind and Structures
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• v.3 no.4
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• pp.221-241
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• 2000

Structural dynamics usually applies modal transformation rules aimed at de-coupling and/or minimizing the equations of motion. Proper orthogonal decomposition provides mathematical and conceptual tools to define suitable transformed spaces where a multi-variate and/or multi-dimensional random process is represented as a linear combination of one-variate and one-dimensional uncorrelated processes. Double modal transformation is the joint application of modal analysis and proper orthogonal decomposition applied to the loading process. By adopting this method the structural response is expressed as a double series expansion in which structural and loading mode contributions are superimposed. The simultaneous use of the structural modal truncation, the loading modal truncation and the cross-modal orthogonality property leads to efficient solutions that take into account only a few structural and loading modes. In addition the physical mechanisms of the dynamic response are clarified and interpreted.