• Structural Engineering and Mechanics
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• v.71 no.2
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• pp.197-210
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• 2019

Probabilistic buckling behavior of sandwich panel considering random system parameters using a radial basis function (RBF) approach is presented in this paper. The random system properties result in an uncertain response of the sandwich structure. The buckling load of laminated sandwich panel is obtained by employing higher-order-zigzag theory (HOZT) coupled with RBF and probabilistic finite element (FE) model. The in-plane displacement variation of core as well as facesheet is considered to be cubic while transverse displacement is considered to be quadratic within the core and constant in the facesheets. Individual and combined stochasticity in all elemental input parameters (like facesheets thickness, ply-orientation angle, core thickness and properties of material) are considered to know the effect of different degree of stochasticity, ply- orientation angle, boundary conditions, core thickness, number of laminates, and material properties on global response of the structure. In order to achieve the computational efficiency, RBF model is employed as a surrogate to the original finite element model. The stiffness matrix of global response is stored in a single array using skyline technique and simultaneous iteration technique is used to solve the stochastic buckling equations.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.155-165
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• 2000

In this paper, we propose some estimators of Kullback- Leibler Information functions using the data from three step stress accelerated life tests. This acceleration model is assumed to be a tampered random variable model. Some asymptotic properties of proposed estimators are proved. Simulations are performed for comparing the small sample properties of the proposed estimators under use condition of accelerated life test.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.11-17
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• 1995

Let ${\tau}_a$ be the first time that a perturbed random walk with extended real-valued independent and identically distributed (i.i.d.) random variables crosses a constant boundary $a{\geq}0$. For the stopping times ${\tau}_a$ we investigate some basic properties and obtain its limiting distribution as $a{\rightarrow}{\infty}$ and an upper bound of the expected stopping times E(${\tau}_a$).

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.639-645
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• 2010

We consider a subdiagonal bilinear model and give sufficient conditions for the associated Markov chain defined by Pham (1985) to be uniformly ergodic and then obtain the $\beta$-mixing property for the given process. To derive the desired properties, we employ the results of generalized random coefficient autoregressive models generated by a matrix-valued polynomial function and vector-valued polynomial function.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1097-1110
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• 2012

The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

• Geomechanics and Engineering
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• v.37 no.3
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• pp.253-262
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• 2024

Dynamic properties are pivotal in soil analysis, yet their experimental determination is hampered by complex methodologies and the need for costly equipment. This study aims to predict dynamic soil properties using static properties that are relatively easier to obtain, employing machine learning techniques. The static properties considered include soil cohesion, friction angle, water content, specific gravity, and compressional strength. In contrast, the dynamic properties of interest are the velocities of compressional and shear waves. Data for this study are sourced from 26 boreholes, as detailed in a geotechnical investigation report database, comprising a total of 130 data points. An importance analysis, grounded in the random forest algorithm, is conducted to evaluate the significance of each dynamic property. This analysis informs the prediction of dynamic properties, prioritizing those static properties identified as most influential. The efficacy of these predictions is quantified using the coefficient of determination, which indicated exceptionally high reliability, with values reaching 0.99 in both training and testing phases when all input properties are considered. The conventional method is used for predicting dynamic properties through Standard Penetration Test (SPT) and compared the outcomes with this technique. The error ratio has decreased by approximately 0.95, thereby validating its reliability. This research marks a significant advancement in the indirect estimation of the relationship between static and dynamic soil properties through the application of machine learning techniques.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.2
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• pp.473-480
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• 1996

Automatic fatigue crack length measuring system using DC electrical potential method and the system control program for automatic fatigue testing under random load condition were made in this study. And using these system and control program, fatigue tests were executed under constant and random load condition. As the result, the propagation of crack in random loading can be represented Paris equaiton and log normal probability function. But constant and random load test show different crack propagation properties.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.1
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• pp.98-103
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• 2005

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.

• Honam Mathematical Journal
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• v.9 no.1
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• pp.113-119
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• 1987

Random variables $X_1$, $X_1$, ..., $X_m$ are said to be weakly associated if whenever $\pi$ is a permutation of {1, 2,..., m}, $1{\leq}k<m$, and f: $R^{k}{\rightarrow}R$, g: $R^{m-k}{\rightarrow}R$ are coordinatewise nondecreasing functions then Cov $[f(X_{x(1)},...,\;X_{\pi(k)},\;g(X_{x(k+1)},...,\;X_{x(m)})]{\geq}0$, whenever the covariance is defined. An infinite collection of random variables is weakly associated if every finite subcollection is weakly associated. The basic properties of weak association and central limit theorem for weakly associated random variables are derived. We also extend this idea to point random fields and prove that a Cox process with a stationary weakly associated intensity rardom measure is weakly associated. Another inequalities and the fact that positive correlated normal random variables are weakly associated are also proved.