• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.583-589
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• 1987

A new approximation method is proposed for the linear model reduction of high order dynamic systems. This mehtod is based upon the denominator table(D-table) and time moment-matching technique. The denominator table(D-table) is used to obtain the denominator polynomial of reduced-order model, and the numerator polynomial is obtained by time moment-matching method. This proposed method does not require the calculation of the alpha-beta expansion and reciprocal transformation which should be calculadted by Routh approximation method. The advantages of the proposed method are that it is computationally every attractive better than Routh approximation method and the reduced model is stable Il the original system is stable.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1018-1023
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• 1992

In this paper we proposed the systematic method of reducing the order of controller with robustness. State space formulae for all controllers is found by solving two coupled J-lossless coprime factorizations and model reduction problem. To reduce the order of controller, balanced truncation and Hankel approximation are used.

• 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.

• KIPE Magazine
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• v.25 no.4
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• pp.44-49
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• 2020

• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.36-48
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• 2022

As a valid numerical method to obtain a high-resolution result of a flow field, computational fluid dynamics (CFD) have been widely used to study coolant flow and heat transfer characteristics in fuel rod bundles. However, the time-consuming, iterative calculation of Navier-Stokes equations makes CFD unsuitable for the scenarios that require efficient simulation such as sensitivity analysis and uncertainty quantification. To solve this problem, a reduced-order model (ROM) based on proper orthogonal decomposition (POD) and machine learning (ML) is proposed to simulate the flow field efficiently. Firstly, a validated CFD model to output the flow field data set of the rod bundle is established. Secondly, based on the POD method, the modes and corresponding coefficients of the flow field were extracted. Then, an deep feed-forward neural network, due to its efficiency in approximating arbitrary functions and its ability to handle high-dimensional and strong nonlinear problems, is selected to build a model that maps the non-linear relationship between the mode coefficients and the boundary conditions. A trained surrogate model for modes coefficients prediction is obtained after a certain number of training iterations. Finally, the flow field is reconstructed by combining the product of the POD basis and coefficients. Based on the test dataset, an evaluation of the ROM is carried out. The evaluation results show that the proposed POD-ROM accurately describe the flow status of the fluid field in rod bundles with high resolution in only a few milliseconds.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.75.1-75
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• 2002

Several model order reduction methods for large RLC circuits have been developed in the last few years. Krylop subspace based methods are extremely effective for generating the low order models of large system but there is no optimal theory for the resulting models. Alternatively, methods based truncated balanced realization have an optimality property but are too computationally expensive to use on complicated problems such as large RLC circuits. In this paper, we present a method for improving time domain response of reduced order RLC circuits. The method used here is based on combing Krylop subspace based method and truncated balanced realization method plus residualization. The metho...

• Journal of the Computational Structural Engineering Institute of Korea
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• v.37 no.1
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• pp.9-16
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• 2024

Using the proper orthogonal decomposition (POD) based intrusive reduced order model (ROM), the total degrees of freedom of the structural system can be significantly reduced and the critical time step satisfying the conditional stability increases in the explicit time integrations. In this study, therefore, the changes in the critical time step in the explicit time integrations are investigated using both the POD-ROM and Voronoi-cell lattice model (VCLM). The snapshot matrix is composed of the data from the structural response under the arbitrary dynamic loads such as seismic excitation, from which the POD-ROM is constructed and the predictive capability is validated. The simulated results show that the significant reduction in the computational time can be achieved using the POD-ROM with sufficiently ensuring the numerical accuracy in the seismic analyses. In addition, the validations show that the POD based intrusive ROM is compatible with the Voronoi-cell lattice based explicit dynamic analyses. In the future study, the research results will be utilized as an elemental technology for the developments of the real-time predictive models or monitoring system involving the high-fidelity simulations of structural dynamics.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.1
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• pp.9-15
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• 2003

To improve the performance of PID controller of high order systems by model reduction, we proposed two model reduction methods. One, Original model with two point $({\angle}G(jw)=\;-{\pi}/2,\;-{\pi})$ in Nyquist curve used gradient base method and genetic algorithm. The other, Original model without two point$({\angle}G(jw)=\;-{\pi}/2,\;-{\pi})$in Nyquist curve used to add very small dead time. This method has annexed very small dead time on the base model for reduction, and we remove it after getting the reduced model, and , we improved Smith-predictor for a dead-time compensator using genetic algorithms. This method considered four points$({\angle}G(jw)=0,\;-\pi/2,\;-\pi,\;-3\pi/2)$ in the Nyquist curve to reduce steady state error between original and reduced model. It is shown that the proposed methods have more performance than the conventional method.

• Journal of Institute of Convergence Technology
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• v.5 no.2
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• pp.37-42
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• 2015

This paper presents the effects of the computational time-varying delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a computational time-varying delay model. In this paper, the maximum of the computational time-varying delay is assumed to be as much as the sampling time. Using the simulation, it is analyzed how the sample-hold methods and the computational time-varying delay affect the maximum available stiffness. As the maximum of computational time-varying delay increases, the maximal available stiffness of a virtual wall model is reduced.