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

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.23 no.11 s.170
• /
• pp.2007-2013
• /
• 1999

A Newly proposed control methodology applied to the aeroelastic system experiencing flutter is investigated and its performance is verified experimentally. The flexible cantilever beam slicked 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. It is shown experimentally that the vibration of beam 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 the new control method, called Heo-stochastic control technique, has better performance as a controller.

• Journal of the Korean Statistical Society
• /
• v.28 no.1
• /
• pp.93-106
• /
• 1999

In this paper we consider estimation of a real valued parameter in the drift coefficient of a Hilbert space valued Ito stochastic differential equation. First we consider observation of the corresponding diffusion in a fixed time interval [0, T] and prove the Bernstein - von Mises theorem concerning the convergence of posterior distribution of the parameter given the observation, suitably normalised and centered at the MLE, to the normal distribution as Tlongrightarrow$\infty$. As a consequence, the Bayes estimator of the drift parameter becomes asymptotically efficient and asymptotically equivalent to the MLE as Tlongrightarrow$\infty$. Next, we consider observation in a random time interval where the random time is determined by a predetermined level of precision. We show that the sequential MLE is better than the ordinary MLE in the sense that the former is unbiased, uniformly normally distributed and efficient but is latter is not so.

• Nuclear Engineering and Technology
• /
• v.43 no.6
• /
• pp.523-530
• /
• 2011

In a previous study, the stochastic space-dependent kinetics model (SSKM) based on the forward stochastic model in stochastic kinetics theory and the Ito stochastic differential equations was proposed for treating monoenergetic space-time nuclear reactor kinetics in one dimension. The SSKM was tested against analog Monte Carlo calculations, however, for exemplary cases of homogeneous slab reactors with only one delayed-neutron precursor group. In this paper, the SSKM is improved and evaluated with more realistic and complicated cases regarding several delayed-neutron precursor groups and heterogeneous slab reactors in which the extraneous source or reactivity can be introduced locally. Furthermore, the source level and the initial conditions will also be adjusted to investigate the trends in the variances of the neutron population and fission product levels across the reactor. The results indicate that the improved SSKM is in good agreement with the Monte Carlo method and show how the variances in population dynamics can be controlled.

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

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.129-136
• /
• 2001

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1501-1509
• /
• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.

• International Journal of Reliability and Applications
• /
• v.4 no.1
• /
• pp.1-12
• /
• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.