• Steel and Composite Structures
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• 제8권2호
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• pp.129-144
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• 2008

This paper demonstrates an application of the perturbation based stochastic finite element method (SFEM) for predicting the performance of structural systems made of composite sections with random material properties. The composite member consists of materials in contact each of which can surround a finite number of inclusions. The perturbation based stochastic finite element analysis can provide probabilistic behavior of a structure, only the first two moments of random variables need to be known, and should therefore be suitable as an alternative to Monte Carlo simulation (MCS) for realizing structural analysis. A summary of stiffness matrix formulation of composite systems and perturbation based stochastic finite element dynamic analysis formulation of structural systems made of composite sections is given. Two numerical examples are presented to illustrate the method. During stochastic analysis, displacements and sectional forces of composite systems are obtained from perturbation and Monte Carlo methods by changing elastic modulus as random variable. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.

• Structural Engineering and Mechanics
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• 제26권2호
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• pp.163-178
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• 2007

In practical engineering, the uncertain concept plays an important role in the control problems of the vibration structures. In this paper, based on matrix perturbation theory and interval finite element method, the closed-loop vibration control system with uncertain parameters is discussed. A new method is presented to develop an algorithm to estimate the upper and lower bounds of the real parts and imaginary parts of the complex eigenvalues of vibration control systems. The results are derived in terms of physical parameters. The present method is implemented for a vibration control system of the frame structure. To show the validity and effectiveness, we compare the numerical results obtained by the present method with those obtained by the classical random perturbation.

• 전산구조공학
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• 제5권3호
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• pp.119-126
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• 1992

교량, 발전소, 해양구조물과 같은 토목구조물은 사용기간중에 지진, 바람, 파랑하중등에 의해 구조적 손상을 받기 쉽다. 장기간에 걸쳐 구조물에 손상이 누적되면 구조물 전체의 파괴를 초래할 수도 있다. 따라서 현존하는 구조물의 안전성을 분석하기 위한 구조물의 손상도를 추정하는 방법이 필요하다. 본 논문에서는 Inverse Modal Perturbation기법을 이용하여 구조물의 손상도를 추정하는 방법에 대하여 연구하였다. Perturbation식은 구조물의 강성 및 질량행렬의 변화량과 구조물의 고유진동수와 모우드형상의 변화량의 식으로 구성된다. 또한 구조물의 손상은 강성행렬의 변화량으로 표현하였다. 본 연구에서는 구조물의 손상도추정의 효율성을 증대시키기 위하여 2차-Perturbation식을 구성하고, 이것을 반복적인 절차를 거쳐 해를 구하는 방법에 대하여 연구하였다. 제안된 방법의 효율성은 일련의 예제해석을 통하여 검증하였으며, 추정된 결과로 부터 본 방법이 구조물의 손상을 적절히 산정함을 알 수 있었다.

• 제어로봇시스템학회논문지
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• 제1권2호
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Journal of Mechanical Science and Technology
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• 제17권5호
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• pp.637-646
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• 2003

In the previous study, the inverse perturbation method was used to identify structural damages. Because all unmeasured DOFs were considered as unknown variables, considerable computational effort was required to obtain reliable results. Thus, in the present study, a system condensation method is used to transform the unmeasured DOFs into the measured DOFs, which eliminates the remaining unmeasured DOFs to improve computational efficiency. However, there may still arise a numerically ill-conditioned problem, if the system condensation is not adequate for numerical Programming or if the system condensation is not recalibrated with respect to the structural changes. This numerical problem is resolved in the present study by adopting more accurate accelerated improved reduced system (AIRS) as well as by updating the transformation matrix at every step. The criterion on the required accuracy of the condensation method is also proposed. Finally, numerical verification results of the present accelerated inverse perturbation method (AIPM) are presented.

• Structural Engineering and Mechanics
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• 제13권3호
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• pp.299-312
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• 2002

In this paper, a new method to solve the dynamic response problem for structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an optimum scheme is adopted when there are many interval structural parameters. With the interval algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are developed. Based on the matrix perturbation theory and interval extension of function, the upper and lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to illustrate the validity of the present method.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1181-1188
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• 2017

This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton-Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.696-699
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• 1997

In this paper, we presents that for discrete system with matched perturbation of uncertain parameters in the state coefficient matrix A(i.e., with perturbation of A in the range of the input matrix B), the poles of the perturbed closed loop system can be placed into the preassigned circle by the static-state feedback. We discuss the robust stabilization of the system satisfying the matching condition and application to the controller design problem.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.105-108
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• 1997

This paper proposes a new approach of balanced model reduction using matrix pencil. The algorithm presented in this paper is to convert full-rank high-order system into rank-deficient system using perturbation made by matrix pencil method. Then the system can be truncated to a low-order system that we want via balanced realization. We discuss the comparison with other methods and the various observations by simulations.

• 대한전자공학회논문지
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• 제19권2호
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• pp.1-6
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• 1982

본 논문에서는 런덤파라미터를 포함하는 선형 시스템의 실제 해석에 perturbation 이론의 응용을 보이고 있다. 시스템의 출력의 통계치가 시스템의 파라미터와 입력의 통계치들에 의해 (perturb된 선형 연산자 방정식에 의해) 구해졌고, perturb된 state 변환 매트릭스도 유도되었다. 간단한 일차, 이차 선형 시스템 모델을 가지고, 정확한 해와 perturbation 결과사이의 정확도가 비교되어 졌고 perturbation series의 수렴도도 조사되어 졌다.