• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.35-37
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• 2014

We examine a question raised in [1] regarding existence and uniqueness of the steady-state solution of certain type of Kolmogorov forward equation in this paper, and prove that the question holds for $S^1$ by giving an explicit solution.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.679-681
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• 2013

In this paper, we raise a question regarding existence and uniqueness of the steady-state solution of a type of Kolmogorov forward equation. We prove that the question has a positive answer for trivial vector fields, and also provide examples which show that the compactness assumption is necessary.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.706-709
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• 2007

일반적으로 알려진 시스템 규명은 시스템의 입/출력 관계를 이용하여 시스템을 규명하고 그 파라미터를 구하고 있다. 그러나 많은 경우에 시스템이 불규칙한 외란에 노출된 경우에는 알려져 있는 시스템의 규명방법이 없다. 이에 그 특성이 알려져 있지 않은 미지의 시스템이 미지의 불규칙한 외란에 노출되었을 때에 그 시스템을 규명하는 방법을 연구 개발하였다. 여기서는 시스템의 출력이 정상적(Stationary)일 때만 이를 확률영역에서 고려하였다. 확률 영역에서 시스템의 응답은 시스템 파라미터의 영향을 크게 받는바 시스템모멘트응답을 시스템 파라미터와의 관계로 구성할 수 있다. 이로부터 시스템의 출력만을 이용하여 시스템 파라미터의 규명이 가능하게 되었다. 본 연구에서는 실 물리영역에서의 출력을 확률영역에서의 모멘트 응답으로 변환시킨 후 역변환 개념으로 미지의 불규칙 외란에 노출되어진 미지의 2차 선형 확률시스템의 파라메타를 성공적으로 규명하였다.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.918-922
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• 2007

Most of the study on system identification has been carried out using input/output relation in physical domain. However identification concept of stochastic system has not been reported up to now. Interest is focused to identify an unknown dynamic system under random external disturbances which is not possible to measure. A concept to identify the system parameters in stochastic domain is proposed and implemented in terms of simulation. Attempt has been made to identify the system parameters in inverse manner in stochastic domain based on system output only. Simulation is conducted to reveal quite noticeable performance of the proposed concept.

• Wind and Structures
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• v.36 no.2
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• pp.133-147
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• 2023

The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.