• Ocean and Polar Research
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• 제43권1호
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• pp.1-14
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• 2021

In this study, extreme wind speeds in the Western North Pacific (WNP) were estimated using reanalysis wind fields synthesized with an empirical typhoon vortex model. Reanalysis wind data used is the Fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) data, which was deemed to be the most suitable for extreme value analysis in this study. The empirical typhoon vortex model used has the advantage of being able to realistically reproduce the asymmetric winds of a typhoon by using the gale/storm-forced wind radii information in the 4 quadrants of a typhoon. Using a total of 39 years of the synthesized reanalysis wind fields in the WNP, extreme value analysis is applied to the General Pareto Distribution (GPD) model based on the Peak-Over-Threshold (POT) method, which can be used effectively in case of insufficient data. The results showed that the extreme analysis using the synthesized wind data significantly improved the tendency to underestimate the extreme wind speeds compared to using only reanalysis wind data. Considering the difficulty of obtaining long-term observational wind data at sea, the result of the synthesized wind field and extreme value analysis developed in this study can be used as basic data for the design of offshore structures.

• Wind and Structures
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• 제33권6호
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• pp.423-435
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• 2021

Although existing algorithms can predict wind speed using historical observation data, for engineering feasibility, most use moment methods and probability density functions to estimate fitted parameters. However, extreme wind speed prediction accuracy for long-term return periods is not always dependent on how the optimized frequency distribution curves are obtained; long-term return periods emphasize general distribution effects rather than marginal distributions, which are closely related to potential extreme values. Moreover, there are different wind speed parent sample types; how to theoretically select the proper extreme value distribution is uncertain. The influence of different sampling time intervals has not been evaluated in the fitting process. To overcome these shortcomings, updated steps are introduced, involving parameter sensitivity analysis for different sampling time intervals. The extreme value prediction accuracy of unknown parent samples is also discussed. Probability analysis of mean wind is combined with estimation of the probability plot correlation coefficient and the maximum likelihood method; an iterative estimation algorithm is proposed. With the updated steps and comparison using a Monte Carlo simulation, a fitting policy suitable for different parent distributions is proposed; its feasibility is demonstrated in extreme wind speed evaluations at Longhua and Chuansha meteorological stations in Shanghai, China.

• 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.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.55-67
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• 2020

The common practice to predict the characteristic structural load effects (LEs) in long reference periods is to employ the extreme value theory (EVT) for building limit distributions. However, most applications ignore that LEs are driven by multiple loading events and thus do not have the identical distribution, a prerequisite for EVT. In this study, we propose the composite extreme value modeling approach using clustering to (a) cluster initial blended samples into finite identical distributed subsamples using the finite mixture model, expectation-maximization algorithm, and the Akaike information criterion; (b) combine limit distributions of subsamples into a composite prediction equation using the generalized Pareto distribution based on a joint threshold. The proposed approach was validated both through numerical examples with known solutions and engineering applications of bridge traffic LEs on a long-span bridge. The results indicate that a joint threshold largely benefits the composite extreme value modeling, many appropriate tail approaching models can be used, and the equation form is simply the sum of the weighted models. In numerical examples, the proposed approach using clustering generated accurate extrema prediction of any reference period compared with the known solutions, whereas the common practice of employing EVT without clustering on the mixture data showed large deviations. Real-world bridge traffic LEs are driven by multi-events and present multipeak distributions, and the proposed approach is more capable of capturing the tendency of tailed LEs than the conventional approach. The proposed approach is expected to have wide applications to general problems such as samples that are driven by multiple events and that do not have the identical distribution.

• Smart Structures and Systems
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• 제21권5호
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• pp.549-559
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• 2018

The dynamic behaviors of the bridge structures have great effects on the comfortability and safety of running high-speed trains, which can also reflect the structural degradation. This paper aims to reveal the characteristics of the dynamic behaviors induced by train loadings for a combined highway and railway bridge. Monitoring-based analysis of the acceleration and dynamic displacement of the bridge girder is carried out. The effects of train loadings on the vertical acceleration of the bridge girder are analyzed; the spatial variability of the train-induced lateral girder displacement is studied; and statistical analysis has been performed for the daily extreme values of the train-induced girder deflections. It is revealed that there are great time and spatial variabilities for the acceleration induced by train loadings for the combined highway and railway cable-stayed bridge. The daily extreme values of the train-induced girder deflections can be well fitted by the general extreme value distribution.

• 물과 미래
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• 제26권4호
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• pp.73-83
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• 1993

본 연구에서는 우리나라 강우자료에 대한 분리효과를 검토하였다. 2변수 대수정규분포, 3변수 대수정규분포등, TYPE-극치분포, 2변수 Gamma 분포, 3변수 Gamma 분포, Log-Pearson Type-분포, GEV분포 등 7개 분포함수를 선정하고, Monte C미개 실험을 이용하여 과거 강우기록 자료로부터 얻은 왜곡도의 평균과 표준편차와 각 분포형들로부터 모의된 왜곡도의 평균과 표준편차와 차이를 분석하였다. 그 결과 우리나라 강우자료는 3변수 Gamma 분포를 제외한 나머지 6개 분포형에서 분리현상을 보였다.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.289-297
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• 1997

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권12호
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• 응용통계연구
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• 제23권5호
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• pp.835-844
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• 2010

극단값 통계 분석의 도구로는 전통적인 연간 최대값 방법과 현대적인 분계점 방법, 그리고 분계점 방법을 개선한 변형체 등으로 분류할 수 있다. 연간 최대값 방법은 시계열자료의 연간 최대값들에 대하여 일반화극단값분포를 적합시키는 것이고, 분계점 방법은 충분히 큰 하나의 분계점을 넘어서는 초과값들의 초과여분들에 대하여 일반화파레토분포를 적합시키는 것이다. 분계점 방법의 한 변형체로서 본 논문에서는 분계점 방법에 추가적으로 초과값들의 전체 개수가 포아송분포를 따른다고 가정하는 포아송-GPD 방법을 다루고, 이를 1988.01.04부터 2009.12.31까지 수집된 서부텍사스산중질유의 현물가격 자료로부터 계산된 일일 상승율과 일일 하락율에 적용한다. 이에 따르면 일일 상승율과 일일 하락율의 분포는 정규분포와 달리 두터운 꼬리를 갖는 분포로 나타났는데, 이는 오늘날의 많은 금융 자료분석에서 나타나는 일반적인 현상과 잘 부합하는 것이다.

• 대한안전경영과학회지
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• 제9권5호
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• pp.43-48
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• 2007

This paper is to present linkage parameter to integrate statistical models and physical models for accelerated life test. Statistical models represent the relationship of probability distribution and life. Physical models show the relationship of life and stress. Moreover, this study proposes the four steps for construction of integrated models for accelerated life test using linkage parameter. Finally, this paper develops new integrated models such as extreme value distribution-general Eyring, linearly increasing failure rate function-general Eyring, etc., and estimates various reliability measures.