• Computers and Concrete
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• v.11 no.5
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• pp.411-440
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• 2013

Large fluctuations in surface strain at the level of steel are expected in reinforced concrete flexural members at a given stage of loading due to the emergent structure (emergence of new crack patterns). This has been identified in developing deterministic constitutive models for finite element applications in Ibrahimbegovic et al. (2010). The aim of this paper is to identify a suitable probability distribution for describing the large deviations at far from equilibrium points due to emergent structures, based on phenomenological, thermodynamic and statistical considerations. Motivated by the investigations reported by Prigogine (1978) and Rubi (2008), distributions with heavy tails (namely, alpha-stable distributions) are proposed for modeling the variations in strain in reinforced concrete flexural members to account for the large fluctuations. The applicability of alpha-stable distributions at or in the neighborhood of far from equilibrium points is examined based on the results obtained from carefully planned experimental investigations, on seven reinforced concrete flexural members. It is found that alpha-stable distribution performs better than normal distribution for modeling the observed surface strains in reinforced concrete flexural members at these points.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.6
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• pp.93-99
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• 2007

Robust nonlinear image denoising algorithms for the class of ${\alpha}$-stable distribution are introduced. The proposed amplitude-limited sample average filter(ALSAF) proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. The error norm for this estimator is equivalent to Huber#s minimax norm. It is optimal in the respect of maximizing the efficacy under the above noise environment. It is mired with the myriad filter to propose an amplitude-limited myriad filter(ALMF). The behavior and performance of the ALSAF and ALMF in ${\alpha}$-stable noise environment are illustrated and analyzed through simulation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.135-152
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• 2000

For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.1
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• pp.151-156
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• 2012

In this paper robust nonlinear image denoising algorithms are introduced for the distribution which is Gaussian in the center and Laplacian in the tails. The distribution is known as the least favorable ${\epsilon}$-contaminated normal distribution that maximizes the asymptotic variance. The proposed filter proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. It is optimal in the respect of maximizing the efficacy under the above noise environment. Another filter for reducing impulsive noise is proposed by mixing with the myriad filter to propose an amplitude-limited myriad filter. Extensive experiment is conducted with images corrupted with ${\alpha}$-stable noise to analyze the behavior and performance of the proposed filters.

• Journal of Communications and Networks
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• v.9 no.2
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• pp.185-191
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• 2007

Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in signal processing. This class of process has no closed form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in S$\alpha$SG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm Kalman filtering algorithm based on least p-norm of innovation process with infinite variances, and a new robust multiuser detection method based on least p-norm Kalman filtering. The simulation experiments show that the proposed new algorithm is more robust than the conventional Kalman filtering multiuser detection algorithm.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.1
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• pp.269-286
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• 2018

Signal detection in symmetric alpha-stable ($S{\alpha}S$) distributed noise is a challenging problem. This paper proposes a detector based on a decreasing exponential function (DEF). The DEF detector can effectively suppress the impulsive noise and achieve good performance in the presence of $S{\alpha}S$ noise. The analytical expressions of the detection and false alarm probabilities of the DEF detector are derived, and the parameter optimization for the detector is discussed. A performance analysis shows that the DEF detector has much lower computational complexity than the Gaussian kernelized energy detector (GKED), and it performs better than the latter in $S{\alpha}S$ noise with small characteristic exponent values. In addition, the DEF detector outperforms the fractional lower order moment (FLOM)-based detector in $S{\alpha}S$ noise for most characteristic exponent values with the same order of magnitude of computational complexity.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.101-123
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• 2001

For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

• Wind and Structures
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• v.19 no.6
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• pp.623-647
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• 2014

In this paper, a probability distribution which is consistent with the observed phenomenon at the roof corner and, also on other portions of the roof, of a low-rise building is proposed. The model is consistent with the choice of probability density function suggested by the statistical thermodynamics of open systems and turbulence modelling in fluid mechanics. After presenting the justification based on physical phenomenon and based on statistical arguments, the fit of alpha-stable distribution for prediction of extreme negative wind pressure coefficients is explored. The predictions are compared with those actually observed during wind tunnel experiments (using wind tunnel experimental data obtained from the aerodynamic database of Tokyo Polytechnic University), and those predicted by using Gumbel minimum and Hermite polynomial model. The predictions are also compared with those estimated using a recently proposed non-parametric model in regions where stability criterion (in skewness-kurtosis space) is satisfied. From the comparisons, it is noted that the proposed model can be used to estimate the extreme peak negative wind pressure coefficients. The model has an advantage that it is consistent with the physical processes proposed in the literature for explaining large fluctuations at the roof corners.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1635-1638
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• 1997

A measurement of conduction veloctiy of the action potentials along the muscle fibres has been applied to various diagnosis. When we measure muscle fiber conduction velocity, it occurs that not only change of conduction velocity but alos inclusion of mipulse component by physiological and experimental reason. So, robuster time delay estimation algorithm than general methods[1] is needed to find correct time delay form these signals. In this paper we, propose new time delay estimation algorithms, robust in impulsive noise, by using characteristic of .alpha.-stable distribution whcih defines impulsive noise well. Then we apply proposed algorthms to measure muscle fiber conduction velocity and compare them with other studies.