• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.607-613
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• 2007

Eigenstructure assignment provides the advantage of allowing great flexibility in shaping the closed-loop system responses by allowing specification of closed-loop eigenvalues and corresponding eigenvectors. But, the general eigenstructure assignment methodologies cannot guarantee stability robustness to parameter variations of a system. In this paper, we present a novel method that has the capability of exact assignment of an eigenstructure which can consider the probability of instability for LTI (Linear Time-Invariant) systems. The probability of instability of an LTI system is determined by the probability distributions of the closed-loop eigenvalues. The stability region for the system is made probabilistically based upon the Monte Carlo evaluations. The proposed control design method is applied to design a flight control system with probabilistic parameter variations to confirm the usefulness of the method.

• Journal of Labour Economics
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• v.28 no.3
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• pp.111-139
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• 2005

This study analyzed employment instability, defining the increase of employment instability as 'a greater possibility of losing a job and a declining possibility of re-employment'. Flow variable measurements showed that the extent of employment instability was higher post 2000 compared to the period of before financial crisis. When considering the status of workers, such an increase in employment instability can be characterized by a greater possibility of unemployment for daily workers. If this is examined in conjunction with job creation and destruction, employment instability is increased not because there are less jobs being created but because there is an actual decline in the number of jobs and also because the jobs that are being created are mostly temporary. On the other hand the increased instability is due to the large-scaled public work policy under the financial crisis.

• Journal of the Korean Geotechnical Society
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• v.18 no.2
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• pp.97-105
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• 2002

Random properties of discontinuities were attributed to the limitation of test methods and lack of obtained data. Therefore, the uncertainties are pervasive and inevitable in rock slope engineering as well as other geotechnical engineering fields. The probabilistic analysis has been proposed to deal properly with the uncertainty. However, previous probabilistic approaches do not take account of the condition of kinematic instability but consider only kinetic instability. In this study, in order to overcome the limitation of the previous studies, the geometric characteristics as well as the shear strength characteristics in discontinuities are taken account into the probabilistic analysis. Then, the new approach to evaluate the probability of failure is suggested. The results of the deterministic analysis which was carried out to compare with the result of the probabilistic analysis, are somewhat different from those of the probabilistic approach. This is because the selected and used data in the deterministic approach do not take account of the random properties of discontinuities.

• Journal of Microbiology and Biotechnology
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• v.4 no.1
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• pp.13-19
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• 1994

A model equation to describe the plasmid instability in recombinant Escherichia coli fermentation is proposed. The equation allows one to estimate easily the two model parameters; (1) the difference in the specific growth rates between plasmid-free cells and plasmid-harboring cells ($\delta$), and (2) the probability of plasmid loss by plasmid-harboring cells ($\rho$). The estimated values of $\delta and \rho$ were in the range of 0.02-0.07 and $10^{-3}-10^{-5}$, respectively, and were strongly dependent on the dilution rate. As another parameter, the ratio of specific growth rates of plasmid-free cells and plasmid-harboring cells ($\alha$) was calculated and the result showed the highest value of 1.28 at the lowest dilution rate of 0.075 $hr^{-l}$, examined in this work. By the sensitivity analyses on the estimates of $\delta and \rho$, it was found that the growth rate difference ($\delta$) affected the plasmid instability more seriously than the probability of plasmid loss ($\rho$). Furthermore, the profound instability of plasmid at low dilution rate could be explained by the high values of $\alpha and \rho$.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.58-64
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• 1998

An analysis method for the reliability of ceramic structures subjected to thermal shocks is presented. Flaws with the size of given probability distribution function are assumed to be distributed at random with a certain density per unit volume in the structures. Criterions for crack instability are derived for brittle solids under general thermal stresses. A probabilistic failure model is presented to study the probability of crack instability for brittle solids containing cracks with uncertain size. The reliabilities of brittle structures are evaluated based on the weakest-link hypothesis, which states that a structure fails when the cracks in any differential volume become unstable. A numerical example is given to demonstrate the application of the proposed method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.954-958
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• 1996

An analysis method for the reliability of ceramic structures subjected to thermal shocks is presented, Flaws with the size of given probability distribution function are assumed to be distributed at random with a certain density per unit volume in the structures. Criterions for crack instability are derived for brittle solids under general thermal stresses. A probabilistic failure model is presented to study the probability of crack instability for blittle solids containing cracks with uncertain crack size. The reliabilities of brittle structures are evaluated based on the weakest-link hypothesis, which states that a structure fails when the cracks in any differential volume become unstable. A numerical example is given to demonstrate the application of the proposed method.

• 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 Electrical Engineering and Technology
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• v.1 no.2
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• pp.129-136
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• 2006

This paper proposes a probabilistic evaluation for the transient stability of electrical power systems incorporating FACTS devices. The uncertainties of the fault location and relay operation time play important keys in power system instability evaluation. The TCSC and SVC are employed for the reduction of system instability probability. This method is demonstrated by the WSCC test system and the results are compared with and without FACTS by means of Monte Carlo simulation.

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.1
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• pp.15-29
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• 2010

Spalling is a kind of instability phenomenon of surrounding rock around underground openings subjected to high in-situ stress according to the development of extension fractures. Three kinds of spalling criteria have been presented so far; however, all spalling criteria have the range of values so that the fuzziness and vagueness of spalling criterion cannot be avoided. In this study, a new fuzzy probability model is proposed to predict the probability of spalling in a systematic way by using fuzzy probability theory. Many of the underground opening projects worldwide are evaluated with the proposed method. Prediction results expressed as the spalling probability agree well with the in-situ observations. In particular, a new fuzzy probability model considering all three evaluation indices of spalling by adopting weighting factors based on relative reliability among three evaluation indices is able to resolve erroneous prediction of spalling by choosing only one prediction method. Moreover, the more reasonable value of spalling probability could have been obtained by adopting the modified damage index to the newly proposed fuzzy probability model.

• Geomechanics and Engineering
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• v.34 no.3
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• pp.285-301
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• 2023

During the construction of E75 highway through Grdelica gorge in Serbia, a major failure occurred in the zone of reinforced rock slope. Excavation was performed in highly anisotropic Paleozoic schist rock formation. The reinforcement consisted of the two rows of micropile wall with pre-stressed anchors. Forces in anchors were monitored with load cells while benchmarks were installed for superficial displacement measurements. The aim of the study is to investigate possible causes of instability considering different probability distributions of the strength of discontinuities and anchor bond strength by applying different optimization techniques for finding the critical failure surface. Even though the deterministic safety factor value is close to unity, the probability of failure is governed by variability of shear strength of anisotropic planes and optimization method used for locating the critical sliding surface. The Cuckoo search technique produces higher failure probabilities compared to the others. Depending on the assigned statistical distribution of input parameters, various performance functions of the factor of safety are obtained. The probability of failure is insensitive to the variation of bond strength. Different sampling techniques should yield similar results considering that the sufficient number of safety factor evaluations is chosen to achieve converged solution.