• Structural Engineering and Mechanics
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• v.76 no.5
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• pp.643-651
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• 2020

Generally, it is necessary to perform transient structural analysis in order to verify and improve the seismic performance of high-rise buildings and bridges against earthquake loads. In this paper, we propose the model order reduction (MOR) method using the Krylov vectors to perform seismic analysis for linear and elastic systems in an efficient way. We then compared the proposed method with the mode superposition method (MSM) by using the limited numbers of modal vectors (or eigenvectors) calculated from the modal analysis. In the calculation, the data of the El Centro earthquake in 1940 were adopted for the seismic loading in the transient analysis. The numerical accuracy and efficiency of the two methods were compared in detail in the case of a simplified high-rise building.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.8
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• pp.333-340
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• 1986

This paper presents an approach for determining the discrete reduced-order models for largescale system by using matrix sign function. We define projection operators based on the matrix sign function and develop the algorithm for model-reduction by using them. Simulation studies show that the proposed altgorithm is very useful.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.6
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• pp.465-470
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• 2001

This paper considers a new weighed model reduction method using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of the reduced order system is guaranteed and an a priori error bound is proposed. to achieve this after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical examples.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.411-428
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• 2022

This paper presents the Campbell diagram analysis of the rotordynamic system using the full order model (FOM) and the reduced order model (ROM) techniques to determine the critical speeds, identify the stability and reduce the computational time. Due to the spin-speed-dependent matrices (e.g., centrifugal stiffening matrix), several model order reduction (MOR) techniques may be considered, such as the modal superposition (MS) method and the Krylov subspace-based MOR techniques (e.g., Ritz vector (RV), quasi-static Ritz vector (QSRV), multifrequency quasi-static Ritz vector (MQSRV), multifrequency/ multi-spin-speed quasi-static Ritz vector (MMQSRV) and the combined Ritz vector & modal superposition (RV+MS) methods). The proposed MMQSRV method in this study is extended from the MQSRV method by incorporating the rotational-speed-dependent stiffness matrices into the Krylov subspace during the MOR process. Thus, the objective of this note is to respond to the question of whether to use the MS method or the Krylov subspace-based MOR technique in establishing the Campbell diagram of the shaft-disc-blade assembly systems in three-dimensional (3D) finite element analysis (FEA). The Campbell diagrams produced by the FOM and various MOR methods are presented and discussed thoroughly by computing the norm of relative errors (ER). It is found that the RV and the MS methods are dominant at low and high rotating speeds, respectively. More precisely, as the spinning velocity becomes large, the calculated ER produced by the RV method is significantly increased; in contrast, the ER produced by the MS method is smaller and more consistent. From a computational point of view, the MORs have substantially reduced the time computing considerably compared to the FOM. Additionally, the verification of the 3D FE rotordynamic model is also provided and found to be in close agreement with the existing solutions.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.161-166
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• 1998

In this paper, an approach to the reduced order H$_{\infty}$ controller synthesis is proposed. This approach employs the frequency weighted model reduction whose frequency weights are deduced from the closed-loop system regarding the controller order reduction errors as uncertainties in a plant, while the resultant reduced order H$_{\infty}$ controller guarantees prescribed H$_{\infty}$ control performances.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.121-122
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• 2006

In the case of mechanical control systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete mechanical control system models and used for system-level dynamic simulation. In this paper, a moment-matching based model order reduction (MOR) which reduces the number of degrees of freedom of an original finite element model via the Arnoldi process is considered to study the dynamic responses of a HDD actuator and suspension system.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.150-154
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• 1987

A new mixed approximation method is proposed for the model reduction of high order linear and time-invariant dynamic systems. This method makes allowance for stability and feature retention simultaneously. After defining dominant frequency range which affects relative stability of systems, a part of denominator is obtained using the energy dispersion method and tests are obtained using dominant frequency response matching method. The proposed method reflects the characteristic of the original system more faithfully and guarantees absolute stability of the reduction model.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.4
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• pp.413-419
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• 1998

A novel order-reduction technique for model predictive control(MPC) is proposed based on the singular value decomposition(SVD) of a pulse response circulant matrix(PRCM) of a concerned system. It is first investigated that the PRCM (in the limit) contains a complete information of the frequency response of a system and its SVD decomposes the information into the respective principal directions at each frequency. This enables us to isolate the significant modes of the system and to devise the proposed order-reduction technique. Though the primary purpose of the proposed technique is to diminish the required computation in MPC, the clear frequency decomposition of the SVD of the PRCM also enables us to improve the robustness through selective excitation of frequency modes. Performance of the proposed technique is illustrated through two numerical examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.9
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• pp.878-885
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• 2009

One of important factors in designing MEMS resonators for RF filters is obtaining a desired frequency response function (FRF) within a specific frequency range of interest. Because various array-type MEMS resonators have been recently introduced to improve the filter characteristics such as bandwidth, pass-band, and shape factor, the degrees of freedom (DOF) of finite elements for their FRF calculation dramatically increases and therefore raises computational difficulties. In this paper the Krylov subspace-based model order reduction using moment-matching with non-zero expansion points is represented as a numerical solution to perform the frequency response analyses of those array-type MEMS resonators in an efficient way. By matching moments at a frequency around the specific operation range of the array-type resonators, the required FRF can be efficiently calculated regardless of their operating frequency from significantly reduced systems. In addition, because of the characteristics of the moment-matching method, a minimal order of reduced system with a prearranged accuracy can be determined through an error indicator using successive reduced models, which is very useful to automate the order reduction process and FRF calculation for structural optimization iterations. We also found out that the presented method could obtain the FRF of a $6\times6$ array-type resonator within a seventieth of the computational time necessary for the direct method and in addition FRF calculation by the mode superposition method could not even be completed because of a data overflow with a half after calculation of 9,722 eigenmodes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.685-688
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• 2011

본 논문에서는 다양한 음향 가진에 따른 음향 응답을 유한 요소법을 통하여 효과적으로 계산하기 위한 새로운 모델 축소법을 제안한다. 일반적인 유한 요소법을 통한 기계구조물의 응답을 구하기 위해서는 음향 방정식의 강성 및 행렬을 구한 뒤 이들의 조합을 통한 동적 강성행렬을 구한 뒤 역행렬을 구하여 다양한 주파수 응답을 구하게 된다. 현재 컴퓨터 하드웨어의 발전과 소프트 웨어의 발전에 의하여 더 많은 유한 요소를 사용할 수 있게 되었고 이로 인하여 더욱 정확하고 넓은 대역의 음향 응답을 구할 수 있게 되었다. 그러나, 아직까지도 아주 복잡한 구조물의 음향 응답을 구하기 위하여 유한 요소를 무한정으로 증가할 수 없는 경우가 많다. 이를 해결하기 위하여 일반적으로 모델 축소법(Model order reduction) 기법을 사용한다. 이 모델 축소법은 기본적으로 전체 행렬을 아주 작지만 효율적인 작은 행렬로 바꾸어 응답을 예측하는 기법으로 mode superposition method, ritz vector method, quasi-static ritz vector method등이 있다. 기존의 모델 축소법은 기본적으로 질량 및 강성행렬이 가진 주파수에 영향을 받지 않는 행렬이라 가정한다. 그렇기 때문에 경계조건이나 다공성 재료를 모델링할 경우 가진 주파수에 영향을 받는 강성행렬과 질량행렬이 만들어지게 되어 기존의 모델 축소법은 효과적이지 못하게 된다. 이런 문제점을 해결하기 위하여 이 논문에서는 Quasi-static ritz vector method의 기본적인 개념을 확장하여 여러 개의 중심 주파수(Center frequency)에서 기저를 계산하고 이를 동시에 이용하는 Multi-frequency quasi-static ritz vector method를 제안한다.