• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.974-974
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• 1995

• 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.

• East Asian Economic Review
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• v.25 no.4
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• pp.403-424
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• 2021

AdaBoost tweaks the sample weight for each training set used in the iterative process, however, it is demonstrated that it provides more correlated errors as the boosting iteration proceeds if models' accuracy is high enough. Therefore, in this study, we propose a novel way to improve the performance of the existing AdaBoost algorithm by employing heterogeneous models and a stochastic twist. By employing the heterogeneous ensemble, it ensures different models that have a different initial assumption about the data are used to improve on diversity. Also, by using a stochastic algorithm with a decaying convergence rate, the model is designed to balance out the trade-off between model prediction performance and model convergence. The result showed that the stochastic algorithm with decaying convergence rate's did have a improving effect and outperformed other existing boosting techniques.

• 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 Korean Data and Information Science Society
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• v.28 no.6
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• pp.1245-1255
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• 2017

The online learning is a process of obtaining the solution for a given objective function where the data is accumulated in real time or in batch units. The stochastic gradient descent method is one of the most widely used for the online learning. This method is not only easy to implement, but also has good properties of the solution under the assumption that the generating model of data is homogeneous. However, the stochastic gradient method could severely mislead the online-learning when the homogeneity is actually violated. We assume that there are two heterogeneous generating models in the observation, and propose the a new stochastic gradient method that mitigate the problem of the heterogeneous models. We introduce a robust mini-batch optimization method using statistical tests and investigate the convergence radius of the solution in the proposed method. Moreover, the theoretical results are confirmed by the numerical simulations.

• East Asian Economic Review
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• v.21 no.2
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• pp.167-197
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• 2017

I build a small open economy (SOE) dynamic stochastic general equilibrium (DSGE) model to investigate the effect of a heterogeneous wage contract between regular and temporary workers on a macroeconomic volatility in a financially fragile economy. The imperfect financial market condition is captured by a quadratic financial adjustment cost for borrowing foreign assets, and the labor market friction is captured by a Nash bargaining process which is only available to the regular workers when they negotiate their wages with the firms while the temporary workers are given their wage which simply equals the marginal cost. As a result of impulse responsesto a domestic productivity shock, the higher elasticity of substitution between two types of workers and the lower weight on the regular workers in the firm's production process induce the higher volatilities in most variables. This is reasoned that the higher substitutability creates more volatile wage determination process while the lower share of the regular workers weakens their Nash bargaining power in the contract process.

• IE interfaces
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• v.12 no.2
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• pp.312-318
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• 1999

This paper considers the cell loss probability(CLP) in a multiplexer with the superposition of heterogeneous ON/OFF sources. The input traffic is composed of k classes. Traffic of class i is the superposition of M_(i) ON/OFF sources. Recently, the method based on the Markov modulated deterministic process(MMDP) is presented. Basically, it is the discretized model of stochastic fluid flow process(SFFP) and gives the CLP very fast, but under-estimates the CLP especially when the value of estimated CLP is very low. This paper develops the discretized model of Markov modulated Poisson process(MMPP). It is a special type of switched batch Bernoulli process(SBBP). Combining the transition probability matrix of MMDP and SBBP according to the state which is characterized by the arrival rate, this paper presents hybrid algorithm. The hybrid algorithm gives better estimate of CLP than that of MMDP and faster than SBBP.

• Nuclear Engineering and Technology
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• v.25 no.1
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• pp.154-165
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• 1993

A stochastic method using continuous time Markov process is presented to model the one-dimensional convective nuclide transport in geologic media, which have usually heterogeneous feature in physical/geochemical parameters such as velocity, dispersion coefficient, and retardation factor resulting poor description by conventional deterministic advection-dispersion model. The primary desired quantities from a stochastic model are the mean values and variance of the state variables as a function of time. The time-dependent probability distributions of nuclides are presented for each discretized compartment given the volumetric groundwater flux and the intensity of transition. Since this model is discrete in medium space, physical/geochemical parameters which affect nuclide transport can be easily incorporated for the heterogeneous media as well as remarkably layered media having spatially varied parameters. Even though the Markov process model developed in this study was shown to be sensitive to the number of discretized compartments showing numerical dispersion as the number of compartments are increased, this could be easily calibrated by comparing with the analytical deterministic model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.6
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• pp.685-692
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• 2004

A stochastic approach has been presented for superplastic deformation of Ti-6Al-4V alloy, and probability functions are used to model the heterogeneous phase distributions. The experimentally observed spatial correlation functions are developed, and microstructural evolutions together with superplastic deformation behavior have been investigated by means of the two-point and three-point probability functions. The results have shown that the probability varies approximately linearly with separation distance, and deformation enhanced probability changes during the process. The stress-strain behavior with the evolutions of probability function can be correctly predicted by the model. The finite element implementation using Monte Carlo simulation associated with reconstructed microstructures shows that better agreement with experimental data of failure strain on the test specimen.

• Journal of the Korean Society of Groundwater Environment
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• v.1 no.2
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• pp.90-99
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• 1994

Heterogeneous hydraulic conductivity in a flow domain is generated under the assumption that it is a random variable with a lognormal, spatially-correlated distribution. The hydraulic head and the conductivity in a groundwater flow system are represented as a stochastic process. The method of Monte Carlo Simulation (MCS) and the finite element method (FEM) are used to determine the statistics of the head and the logconductivity. The second moments of the head and the logconductivity indicate that the cross-covariance of the logconductivity with the head has characteristic distribution patterns depending on the properties of sources, boundary conditions, head gradients, and correlation scales. The negative cross-correlation outlines a weak-response zone where the flow system is weakly responding to a stress change in the flow domain. The stochastic approach has a potential to quantitatively delineate the zone of influence through computations of the cross-covariance distribution.