• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.296-300
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• 1997

Recently, the genetic algorithm has been applied to the various types of optimization problems and these attempts have very successfully. However, in most cases on these approaches, there is not given by investigator about to the theoritical analysis. The reason that the analysis of the dynamics for genetic algorithm is not clear, is the probablitic aspect of genetic algorithm. In this paper, we investigate the analysis of the internal dynamics for genetic algorithm using stochastic differential method. In addition, we provide a new genetic algorithm, based on the study of the convergence property for the genetic algorithm.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.1-12
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• 2013

In this paper, we introduce a continuous-time risk model where the surplus follows a diffusion process with positive drift while being subject to two types of claims. We assume that the sizes of both types of claims are exponentially distributed and that type I claims occur more frequently, however, their sizes are smaller than type II claims. We obtain the ruin probability that the level of the surplus becomes negative, by establishing an integro-differential equation for the ruin probability. We also obtain the ruin probabilities caused by each type of claim and the probability that the level of the surplus becomes negative naturally due to the diffusion process. Finally, we illustrate a numerical example to compare the impacts of two types of claim on the ruin probability of the surplus with that of the diffusion process in the risk model.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.83-91
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• 2004

Nonlinear system responses of an impact system under randomly perturbed harmonic excitations are predicted in the probability domain by adopting the semi-analytical procedure previously developed. The semi-analytical procedure is obtained by solving the Fokker-Planck equation corresponding to the stochastic differential equation of the given impact system by utilizing the path-integral solution. The evolutionary joint probability density functions are generated by using the method, and the characteristics of nonlinear dynamic response behaviors of the system are examined. Noise effects on the responses are also examined. It Is found that the semi-analytical method can provides the accurate information of the responses via the joint probability functions for the impact system. It is found that the noises weaken and eventually terminate the chaos in the responses, but it is also found that the chaotic signatures reside in the presence of the external noise with relatively high intensity. The joint probability density function shows that the ensemble of the system responses are weakly stationary.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1292-1297
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• 2000

For dynamic system under the external irregular disturbance, a performance of the controller designed by using of the 'Heo-stochastic control methodology' is investigated by simulations and experiments. MIMO Flexible cantilever beam, sticked with piezoceramics used as a sensor and actuator, under the irregular disturbance at bottom is modelled in physical domain. Dynamic moment equation about the system is derived through both the Ito's stochastic differential equation and Fokker-Planck-Kolmogoroff equation and also system's characteristics in stochastic domain is analyzed. In this study, the controller suppresses the amplitude of the system's moment response to the external disturbance. MIMO PI controller('Heo-stochastic MIMO PI controller') is designed in the stochastic domain and the response characteristics are investigated in the time domain

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.801-811
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• 2008

Modeling financial phenomena with diffusion processes is a commonly used methodology in the area of modern finance. Recently, various types of diffusion models have been suggested to explain the specific financial processes, and their related inference methodology have been also developed. In particular, likelihood methods for the efficient and accurate inference have been explored in various ways. In this paper, we review the mathematical properties of an approximated likelihood method, which is obtained by linearizing the drift coefficient of a diffusion process.

• Journal of KSNVE
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• v.9 no.3
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• pp.502-508
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• 1999

Newly developed control methodology applied to dynamic system under random disturbance is investigated and its performance is verified experimentall. Flexible cantilever beam sticked with piezofilm sensor and piezoceramic actuator is modelled in physical domain. Dynamic moment equation for the system is derived via Ito's stochastic differential equation and F-P-K equation. Also system's characteristics in stochastic domain is analyzed simultaneously. LQG controller is designed and used in physical and stochastic domain as wall. It is shown experimentally that randomly excited beam on the base is controlled effectively by designed LQG controller in physical domain. By comparing the result with that of LQG controller designed in stochastic domain, it is shown that new control method, what we called $\ulcorner$Heo-stochastic controller design technique$\lrcorner$, has better performance than conventional ones as a controller.

• Computational Structural Engineering
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• v.4 no.2
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• pp.111-117
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• 1991

The analysis method calculating the mean and standard deviation for the eigenvalue of complicated structures in which the limit state equation is implicitly expressed is formulated and applied to the buckling analysis by combining probabilistic finite element method with direct differential method which is a kind of sensitivity analysis technique. Also, the probability of buckling failure is calculated by combining classical reliability techniques such a MVFOSM and AFOSM. As random variables external load, elastic modulus, sectional moment of inertia and member length are chosen and Parkinson's iteration algorithm in AFOSM is used. The accuracy of the results by this study is verified by comparing the results with the crude Monte Carlo simulation and Importance Sampling Method. Through the case study of some structures the important aspects of buckling reliability analysis are discussed.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.691-725
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• 1998

무한차원 상공간에서의 디리클레 형식과 이에 관계된 확산과정에 대한 일반 이론을 소개하고, 이 이론을 물리학의 통계역학 모델에 적용하였다. 구체적으로, 고전 비유계 스핀계에 대한 통계역학적인 모델, 연속체 공간에서 상호 작용하는 무한 입자계에 대한 통계역학적인 모델에 응용하였다. 아울러서 확률 미분 방정식과 같은 디리클레 형식에 관련된 연구분야에 대해서도 간단히 알아보았다.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.477-489
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• 2021

COVID-19 has spread seriously around the world in 2020 and it is still significantly affecting our whole daily life. Currently, the whole world is still undergoing the pandemic and South Korea is no exception to it. During the pandemic, South Korea had several events that prevented or accelerated its spread. To establish the prevention policies for infectious diseases, it is very important to evaluate the intervention effect of such events. The susceptible-infected-removed (SIR) model is often used to describe the dynamic behavior of the spread of infectious diseases through ordinary differential equations. However, the SIR model is a deterministic model without considering the uncertainty of observed data. To consider the uncertainty in the SIR model, the Bayesian approach can be employed, and this approach allows us to evaluate the intervention effects by time-varying functions of the infection rate in the SIR model. In this study, we describe the time trend of the spread of COVID-19 in South Korea and investigate the intervention effects for the events using the stochastic SIR model based on the Bayesian approach.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.6
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• pp.55-64
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process for the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.