• 대한조선학회논문집
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• 제55권6호
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• pp.466-473
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• 2018

Most frequency domain-based approaches assume that structural response should be a Gaussian random process. But a lot of non-Gaussian processes caused by multi-excitation and non-linearity in structural responses or load itself are observed in many real engineering problems. In this study, the effect of non-Normality on fatigue damages are discussed through case study. The accuracy of four frequency domain methods for non-Gaussian processes are compared in the case study. Power-law and Hermite models which are derived for non-Gaussian narrow-banded process tend to estimate fatigue damages less accurate than time domain results in small kurtosis and in case of large kurtosis they give conservative results. Weibull model seems to give conservative results in all environmental conditions considered. Among the four methods, Benascuitti-Tovo model for non-Gaussian process gives the best results in case study. This study could serve as background material for understanding the effect of non-normality on fatigue damages.

• Ocean Systems Engineering
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• 제4권4호
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• pp.293-308
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• 2014

Unlike the traditional displacement type vessels, the high speed planing crafts are supported by the lift forces which are highly non-linear. This non-linear phenomenon causes their motions in an irregular seaway to be non-Gaussian. In general, it may not be possible to express the probability distribution of such processes by an analytical formula. Also the process might not be stationary or ergodic in which case the statistical behavior of the motion to be constantly changing with time. Therefore the extreme values of such a process can no longer be calculated using the analytical formulae applicable to Gaussian processes. Since closed form analytical solutions do not exist, recourse is taken to fitting a distribution to the data and estimating the statistical properties of the process from this fitted probability distribution. The peaks over threshold analysis and fitting of the Generalized Pareto Distribution are explored in this paper as an alternative to Weibull, Generalized Gamma and Rayleigh distributions in predicting the short term extreme value of a random process.

• Wind and Structures
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• 제35권6호
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• pp.419-430
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• 2022

In wind-resistant designs, wind velocity is assumed to be a Gaussian process; however, local complex topography may result in strong non-Gaussian wind features. This study investigates the non-Gaussian wind features over complex terrain under atmospheric turbulent boundary layers by the large eddy simulation (LES) model, and the turbulent inlet of LES is generated by the consistent discretizing random flow generation (CDRFG) method. The performance of LES is validated by two different complex terrains in Changsha and Mianyang, China, and the results are compared with wind tunnel tests and onsite measurements, respectively. Furthermore, the non-Gaussian parameters, such as skewness, kurtosis, probability curves, and gust factors, are analyzed in-depth. The results show that the LES method is in good agreement with both mean and turbulent wind fields from wind tunnel tests and onsite measurements. Wind fields in complex terrain mostly exhibit a left-skewed Gaussian process, and it changes from a softening Gaussian process to a hardening Gaussian process as the height increases. A reduction in the gust factors of about 2.0%-15.0% can be found by taking into account the non-Gaussian features, except for a 4.4% increase near the ground in steep terrain. This study can provide a reference for the assessment of extreme wind loads on structures in complex terrain.

• 한국해양공학회지
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• 제17권2호
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• pp.54-59
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• 2003

The characteristics of the parameters for the probability distribution of fatigue crack growth life, using the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length equals the number of cycle curves that are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratios of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Wiubull,, showing a slight dependence on specimen thickness and stress intensity level. The shape parameter, $\alpha$, does not show the dependency of thickness and stress intensity level, but the scale parameter, $\beta$, and location parameter, ${\gamma}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2002년도 추계학술대회 논문집
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• pp.301-306
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• 2002

The characteristics of parameters for the probability distribution of fatigue crack growth lives by the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length - the number of cycles curves are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratio of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth lives seems to follow the 3-parameter Wiubull and shows a slight dependence on specimen thickness and stress intensity level. The shape parameter, ${\alpha}$, does not show the dependency of thickness and stress intensity level, but the scale parameter, ${\beta}$, and location parameter, ${\upsilon}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• Wind and Structures
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• 제18권6호
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• pp.693-715
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• 2014

Stochastic processes are used to represent phenomena in many diverse fields. Numerical simulation method is widely applied for the solution to stochastic problems of complex structures when alternative analytical methods are not applicable. In some practical applications the stochastic processes show non-Gaussian properties. When the stochastic processes deviate significantly from Gaussian, techniques for their accurate simulation must be available. The various existing simulation methods of non-Gaussian stochastic processes generally can only simulate super-Gaussian stochastic processes with the high-peak characteristics. And these methodologies are usually complicated and time consuming, not sufficiently intuitive. By revealing the inherent coupling effect of the phase and amplitude part of discrete Fourier representation of random time series on the non-Gaussian features (such as skewness and kurtosis) through theoretical analysis and simulation experiments, this paper presents a novel approach for the simulation of non-Gaussian stochastic processes with the prescribed amplitude probability density function (PDF) and power spectral density (PSD) by amplitude modulation and phase reconstruction. As compared to previous spectral representation method using phase modulation to obtain a non-Gaussian amplitude distribution, this non-Gaussian phase reconstruction strategy is more straightforward and efficient, capable of simulating both super-Gaussian and sub-Gaussian stochastic processes. Another attractive feature of the method is that the whole process can be implemented efficiently using the Fast Fourier Transform. Cases studies demonstrate the efficiency and accuracy of the proposed algorithm.

• 대한수학회지
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• 제58권1호
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Structural Engineering and Mechanics
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• 제28권4호
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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.

• Journal of the Korean Statistical Society
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• 제12권1호
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• pp.10-17
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• 1983

Let $X^{(n)}_j, j=1,2,\cdots,n, n=1,2,\cdots$ be a triangular array of random variables which arise naturally in a study of ferromagnetism in statistical mechanics. This paper presents weak convergence of random function $W_n(t)$, an appropriately normalized partial sum process based on $S^{(n)}_n = X^{(n)}_i+\cdot+X^{(n)}_n$. The limiting process W(t) is shown to be Gaussian when weak dependence exists. At the critical point where the change form weak to strong dependence takes place, W(t) turns out to be non-Gaussian. Our results are direct extensions of work by Ellis and Newmam (1978). An example is considered and the relation of these results to critical phenomena is briefly explained.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2001년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2001
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• pp.243-250
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.