Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Accurate Estimate ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2013 ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights ◽  
Extreme Wind Speeds

In the reliability engineering and design of offshore structures probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as e.g. wave heights and wind speeds, application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the ACER method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method it is possible to provide an estimate of the exact extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the exact extreme value distribution. When this cascade has converged, an estimate of the exact distribution has been obtained. In this paper it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will also be demonstrated at the measured coupled wind speed and wave height data.

Prediction of Airgap Statistics for Fixed Offshore Platforms

2011 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai
Keyword(s):  
Time Series ◽  
Random Field ◽  
Wave Field ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Air Gap ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Offshore Platforms ◽  
Spatial Extremes

Air gap statistics for offshore platforms is directly related to the extreme value statistics of the random ocean wave field. The present paper describes a new method for predicting the extreme values of a random wave field in both space and time. The method relies on the use of data provided by measurements or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, a time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using recently developed techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This procedure is applied to the prediction of air gap statistics for a jacket structure.

Prediction of Extreme Tether Tension for a TLP

2009 ◽  
Author(s):  
A. Naess ◽  
C. T. Stansberg ◽  
O. Batsevych
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Alternative Methods ◽  
Scale Model ◽  
Statistical Dependence ◽  
Wave Basin ◽  
Extreme Response

The paper presents a study of the extreme value statistics related to measurements on a scale model of a large tension leg platform (TLP) subjected to random waves in a wave basin. Extensive model tests were carried out in three irregular sea states. Time series of the motion responses and tether tension were recorded for a total of 18 three hour tests (full scale). In this paper we discuss the statistics of the measured tether tension. The focus is on a comparison of two alternative methods for the prediction of extreme tether tension from finite time series records. One method is based on expressing the extreme value distribution in terms of the average upcrossing rate. The other is a novel method that can account for statistical dependence in the recorded time series by utilizing a cascade of conditioning approximations. Both methods rely on introducing a specific parametric form for the tail part of the extreme value distribution. This is combined with an optimization procedure to determine the parameters involved, which allows prediction of various extreme response levels.

Statistical Analysis of Ocean Environmental Conditions With PTGEVD

2004 ◽  
Author(s):  
Sheng Dong ◽  
Xiaoli Hao
Keyword(s):  
Environmental Conditions ◽  
Oil And Gas ◽  
Design Method ◽  
Discrete Distribution ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Extreme Value ◽  
Value Distribution ◽  
Design Criteria ◽  
Wind Speeds

Poisson Trivariate Gumbel Extreme Value Distribution (PTGEVD), a multivariate from of the Compound Extreme Value Distribution, is presented to solve for the ocean environmental design criteria in this paper. The proposed model is combined with a discrete distribution of storm frequency and a continuous trivariate extreme value distribution of environmental conditions simultaneously occurred in storm processes. Different from traditional univariate design method, the proposed design method with PTGEVD can reflect the combined effect of multi-loads on offshore structures and result in reasonable reduction of the design criteria. Validated with the synchronically measured significant wave heights, wind speeds and current velocities of 20 typhoon processes, PTGEVD model shows that it is easy to be applied and has considerable economic potential in the exploitation of ocean oil and gas, especially for marginal field.

Extreme Value Statistics of Wind Speed Data by the POT and AER Methods

2008 ◽  
Author(s):  
A. Naess ◽  
E. Haug
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
New Method ◽  
Extreme Value Statistics ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Wind Speed Data

The paper describes a new method for predicting the appropriate extreme value distribution derived from an observed time series. The method is based on introducing a cascade of conditioning approximations to the exact extreme value distribution. This allows for a rational way of capturing dependence effects in the time series. The performance of the method is compared with that of the peaks over threshold method.

Extreme Value Statistics of Wind Speed Data by the POT and ACER Methods

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
A. Naess ◽  
E. Haug
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Wind Speed Data ◽  
Novel Method

The paper describes a novel method for predicting the appropriate extreme value distribution derived from an observed time series. The method is based on introducing a cascade of conditioning approximations to the exact extreme value distribution. This allows for a rational way of capturing dependence effects in the time series. The performance of the method is compared with that of the peaks-over-threshold method.

Prediction of Extreme Tether Tension for a TLP by the AUR and ACER Methods

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
A. Naess ◽  
C. T. Stansberg ◽  
O. Batsevych
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Alternative Methods ◽  
Scale Model ◽  
Statistical Dependence ◽  
Wave Basin ◽  
Extreme Response

The paper presents a study of the extreme value statistics related to measurements on a scale model of a large tension leg platform (TLP) subjected to random waves in a wave basin. Extensive model tests were carried out in three irregular sea states. Time series of the motion responses and tether tension were recorded for a total of 18 three hour tests (full scale). In this paper we discuss the statistics of the measured tether tension. The focus is on a comparison of two alternative methods for the prediction of extreme tether tension from finite time series records. One method is based on expressing the extreme value distribution in terms of the average upcrossing rate (AUR). The other is a novel method that can account for statistical dependence in the recorded time series by utilizing a cascade of conditioning approximations obtained by defining the average conditional exceedance rates (ACER). Both methods rely on introducing a specific parametric form for the tail part of the extreme value distribution. This is combined with an optimization procedure to determine the parameters involved, which allows prediction of various extreme response levels.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (04) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (4) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

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