• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.97-109
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• 1998

In this paper, we propose a new approach to solve stochastic fluid flow models applied to the analysis of ceil loss of an ATM multiplexer. Existing stochastic fluid flow models have been analyzed by using linear differential equations. In case of large state space, however. analyzing stochastic fluid flow model without numerical errors is not easy. To avoid this numerical errors and to analyze stochastic fluid flow model with large state space. we develope a new computational algorithm. Instead of solving differential equations directly, this approach uses iterative and numerical method without calculating eigenvalues. eigenvectors and boundary coefficients. As a result, approximate solutions and upper and lower bounds are obtained. This approach can be applied to stochastic fluid flow model having general Markov chain structure as well as to the superposition of heterogeneous ON-OFF sources it can be extended to Markov process having non-exponential sojourn times.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.329-336
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• 2016

The optimal portfolio choice problem with a stochastic income is considered in continuous-time framework. We provide a novel approach to treat the stochastic income when the market is complete. The developed method is useful to obtain closed-form solutions of the problems under borrowing constraints.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.48-55
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• 2003

Hidden Markov Model(HMM) has a doubly embedded stochastic process with an underlying stochastic process that can be observed through another set of stochastic processes. This structure of HMM is useful for modeling vector sequence that doesn't look like a stochastic process but has a hidden stochastic process. So, HMM approach has become popular in various areas in last decade. The increasing popularity of HMM is based on two facts : rich mathematical structure and proven accuracy on critical application. In this paper, we applied continuous HMM (CHMM) approach with AR coefficient to detect and predict the chatter of lathe bite and to diagnose the wear of oil Journal bearing using rotor shaft displacement. Our examples show that CHMM approach is very efficient method for machine health monitoring and prediction.

• Geomechanics and Engineering
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• v.3 no.2
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• pp.153-167
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• 2011

Traditional design methods of bearing capacity of shallow foundations are deterministic in the sense that they do not explicitly consider the inherent uncertainty associated with the factors affecting bearing capacity. To account for such uncertainty, available deterministic methods rather employ a fixed global factor of safety that may lead to inappropriate bearing capacity predictions. An alternative stochastic approach is essential to provide a more rational estimation of bearing capacity. In this paper, the likely distribution of predicted bearing capacity of strip footings subjected to vertical loads is obtained using a stochastic approach based on the Monte Carlo simulation. The approach accounts for the uncertainty associated with the soil shear strength parameters: cohesion, c, and friction angle, ${\phi}$, and the cross correlation between c and ${\phi}$. A set of stochastic design charts that assure target reliability levels of 90% and 95%, are developed for routine use by practitioners. The charts negate the need for a factor of safety and provide a more reliable indication of what the actual bearing capacity might be.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.2
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• pp.86-95
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• 2016

We propose a new approach to the stochastic version of Lanchester model. Commonly used approach to stochastic Lanchester model is through the Markov-chain method. The Markov-chain approach, however, is not appropriate to high dimensional heterogeneous force case because of large computational cost. In this paper, we propose an approximation method of stochastic Lanchester model. By matching the first and the second moments, the distribution of each unit strength can be approximated with multivariate normal distribution. We evaluate an approximation of discrete Markov-chain model by measuring Kullback-Leibler divergence. We confirmed high accuracy of approximation method, and also the accuracy and low computational cost are maintained under high dimensional heterogeneous force case.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.153-163
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• 2009

Unlike the mean-variance approach, the stochastic dominance approach is to form a portfolio that stochastically dominates a predetermined benchmark portfolio such as KOSPI. This study is to search a set of portfolio weights for the first-order stochastic dominance with maximum expected return by managing the constraint set and the objective function separately. A nonlinear programming algorithm was developed and tested with promising results against Korean stock market data sets.

• Journal of the military operations research society of Korea
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• v.31 no.2
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• pp.28-44
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• 2005

The previous studies approach the field artillery fire scheduling problem as deterministic and do not explicitly include information on the potential scenario changes. Unfortunately, the effort used to optimize fire sequences and reduce the total time of engagement is often inefficient as the collected military intelligence changes. Instead of modeling the fire sequencing problem as deterministic model, we consider a stochastic artillery fire scheduling model and devise a solution methodology to integrate possible enemy attack scenarios in the evaluation of artillery fire sequences. The goal is to use that information to find robust solutions that withstand disruptions in a better way, Such an approach is important because we can proactively consider the effects of certain unique scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic model for the field artillery fire sequencing problem and offer revised robust stochastic model which considers worst scenario first. The robust stochastic model makes the solution more stable than the general two-stage stochastic model and also reduces the computational cost dramatically. We present computational results demonstrating the effectiveness of our proposed method by EVPI, VSS, and Variances.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.845-858
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• 2006

We present two approaches of the stochastic interest rate European option pricing model. One is a bond numeraire approach which is applicable to a nonzero value asset. In this approach, we assume log-normality of returns of the asset normalized by a bond whose maturity is the same as the expiration date of an option instead that of an asset itself. Another one is the expectation hypothesis approach for value zero asset which has futures-style margining. Bond numeraire approach allows us to calculate volatilities implied in options even though stochastic interest rate is considered.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.4
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• pp.432-446
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• 1996

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.