• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1070-1077
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• 2006

In the present study, sizing and shape optimizations are performed based on the reduced system of large-scaled problem. In the analysis part to achieve efficiency and reliability of computation, two-level condensation scheme is applied. In the construction of reduced system of large scaled problems, it is much more efficient to use sub-domain method. Thus, in the present paper, two-level reduction method combined with sub-domain method is employed. Once the reduced system is constructed, it is straightforward to obtain design sensitivities from the analysis results of the reduced system We use semi-analytic method to obtain design sensitivities. Performance of the efficiency and reliability of the present reduction method in the structural optimization problem is demonstrated through the numerical examples. The present framework of reduction method should serve as a fast and reliable design tool in analysis and design of large-scaled dynamic problems.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.453-458
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• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1062-1069
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• 2006

Reduction schemes approximate the lower eigenvalues that represent the global behavior of the structures. But, they are not efficient to be applied to large-scaled problems because these schemes require considerable amount of computing time in constructing reduced one from the original large-scaled systems. In addition, the selection of the primary degrees of freedom might be localized to cause the excessive emphasis of the lower mode or lost of the important modes. In the present study, a new reduction method combined with the subdomain method is proposed. For the construction of the final reduced system the system of each domain subdivided into primary, slave and interface degrees of freedom. It is remarkably efficient and accurate comparable to full-scale system. Numerical examples demonstrate that the proposed method saves computational cost effectively and provides a reduced system which predicts accurate eigen-pairs of global system.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.10
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• pp.4411-4417
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• 2012

The present study proposes the optimization of wing structure base on reduced model which assures the solution accuracy and computational efficiency. Well-constructed reduced model assures the accurate result in the eigenvalue problem, dynamic analysis or sensitivity of design optimization. Reduced system is classified into the reduce-order model based on structural modes and the reduced system based on degrees of freedom. Because this study uses the reduced system based on degrees of freedom, it is important to select the dominant degrees of freedom properly. For this work, robust selection method, two-level selection scheme, is employed and IRS(Improved Reduced System) is applied to construct the final reduced system. In the optimization process based on the reduced system, all of the equivalent stress, eigenvalue and design sensitivities are calculated from the reduced system. Through a numerical example, it is shown that the present optimization methodology based on the reduction method can provide an optimal results for objective function satisfying constraint condition.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.2 s.48
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• pp.21-29
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• 2006

It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reduced order control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reduced order system is updated repeatedly until a desired one is obtained, the accuracy of the reduced order system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. An eigenvalue shilling technique is applied to accelerate the convergence of Iteration. Two schemes to establish the reduced order system by using the proposed method are also presented and discussed in this paper. The results for a tail building with active tuned mass damper show that the proposed method is efficient for the reduced order modelling and the accuracy is very close to exact only after two iterations.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.491-496
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• 2003

In sensitivity analysis, semi-analytical method(SAM) reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Recently such errors of SAM resulted by the finite difference scheme have been improved by the separation of rigid body mode. But the eigenvalue should be obtained first before the sensitivity analysis is performed and it takes much time in the case that large system is considered. In the present study, by constructing a reduced one from the original system, iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The sensitivity analysis is performed by the eigenvector acquired from the reduced system. The error of SAM caused by difference scheme is alleviated by Von Neumann series approximation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.7
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• pp.98-104
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• 2002

System condensation technique improves the efficiency of the inverse perturbation method of damage detection developed in the previous work. The technique is applied to transform the unmeasured DOFs to the measured DOFs. This approach makes it possible to eliminate the unmeasured DOFs, which accelerates the computational efficiency. The numerical instability problems due to the system condensation technique are also resolved by updating the transformation matrix for each step, and also by adopting the accelerated improved reduced system(AIRS) condensation method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.173-179
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• 2009

Reduction scheme is remarkably useful in the case requiring the repeated calculation procedure. Recently, the efficiency of the reduction scheme has been improved by combining scheme of sub-domain method. But, when the global domain is partitioned into a few sub-domains, sub-domains without constraints can be produced. it is needed to extract the ritz vector from each sub-domain to construct the reduced system of each sub-domain. it is easy to extract the ritz vector from sub-domain with constraint. on the other hand, pseudo inverse method should be employed to extract the ritz vector from sub-domain without constraint. generally, the pseudo inverse takes a large number of computing time to obtain a reduced system of a sub-domain without boundary condition. This trouble can be overcome by the reduced pseudo inverse scheme which proposed in this study. This scheme is based on the static condensation that is not related with selection of the primary degrees of freedom. Numerical examples demonstrate that present method saves computational cost effectively. In addition, it is shown that the reduced system based on the proposed scheme predicts the accurate eigenvalues of global system.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.753-758
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• 1988

In this paper, we propose a new method of designing a reduced-order controller for a linear discrete-time system. Firstly, we study a design problem for a two-degree-of-freedom control system with a feedforward controller. Secondly, in order to obtain a reduced-order controller, frequency-weighted least squares approximation problems are considered. Thirdly, we propose a synthesis procedure of a reduced-order controller. Finally, an example is given to illustrate the effectiveness of this proposed method.