DETERMINATION OF EXTREME VALUES OF WAVES, WINDS CURRENTS, AND TIDES FOR THE DESIGN OF OFFSHORE INSTALLATIONS

1974 ◽  
Vol 14 (1) ◽  
pp. 166
Author(s):  
P. M. Aagaard
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Meteorological Data ◽  
Extreme Value Distribution ◽  
Relevant Information ◽  
Extreme Value ◽  
Distribution Functions ◽  
Design Parameters ◽  
Final Design ◽  
Wave Heights

Frequently the only relevant information available to a designer about a propective offshore platform site is its location, the water depth, and whatever can be gleaned from oceanographic atlases. In spite of this lack of data the platform designer is faced with the problem of selecting design parameters such that the proposed platform will not fail during its exposed life. He therefore needs to know what are the greatest wave height, current speed, etc., the platform will experience, and must specify studies that can provide the needed information on extreme values. This paper discusses methods used in such studies and their associated uncertainties.The method for acquiring extreme value data should be chosen on the basis of available oceanographic and meteorological data for the site, reliability requirements, time available before final design, and cost. Wave height is usually the most critical design parameter. Data over a long time span (e.g. greater than ten years) are needed to achieve reliable extreme values. Measured wave data covering such time spans are almost never available for a site of interest, and schedules seldom permit lengthy data-collection periods. Frequently the most reliable extreme wave heights can be obtained by calculating wave heights (i.e. hindcasting) from windfields derived from historical weather charts and fitting certain extreme-value distribution functions to the hindcast results. This preferred approach should include calibration of the wave height calculation method with local measured data. Alternative approaches, usually involving greater uncertainties in predicted extremes, are also appropriate for particular cases. Methods for determining extreme winds, currents, and tides are similar to those used for extreme waves, but some differences result from the nature of the phenomena and the type of data typically available.

Consideration of Epistemic Uncertainty in Extreme Wave Height Estimation

2014 ◽  
Author(s):  
Ryota Wada ◽  
Takuji Waseda
Keyword(s):  
Gulf Of Mexico ◽  
Observational Data ◽  
Wave Height ◽  
Extreme Values ◽  
Epistemic Uncertainty ◽  
Extreme Value Distribution ◽  
Predictive Distribution ◽  
Extreme Value ◽  
Posterior Predictive Distribution ◽  
Value Estimation

Extreme value estimation of significant wave height is essential for designing robust and economically efficient ocean structures. But in most cases, the duration of observational wave data is not efficient to make a precise estimation of the extreme value for the desired period. When we focus on hurricane dominated oceans, the situation gets worse. The uncertainty of the extreme value estimation is the main topic of this paper. We use Likelihood-Weighted Method (LWM), a method that can quantify the uncertainty of extreme value estimation in terms of aleatory and epistemic uncertainty. We considered the extreme values of hurricane-dominated regions such as Japan and Gulf of Mexico. Though observational data is available for more than 30 years in Gulf of Mexico, the epistemic uncertainty for 100-year return period value is notably large. Extreme value estimation from 10-year duration of observational data, which is a typical case in Japan, gave a Coefficient of Variance of 43%. This may have impact on the design rules of ocean structures. Also, the consideration of epistemic uncertainty gives rational explanation for the past extreme events, which were considered as abnormal. Expected Extreme Value distribution (EEV), which is the posterior predictive distribution, defined better extreme values considering the epistemic uncertainty.

scholarly journals Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

Atmosphere ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 257 ◽  
Author(s):  
Juan Pablo Molina-Aguilar ◽  
Alfonso Gutierrez-Lopez ◽  
Jose Angel Raynal-Villaseñor ◽  
Luis Gabriel Garcia-Valenzuela
Keyword(s):  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Generalized Extreme Value Distribution ◽  
Type I ◽  
Generalized Extreme Value ◽  
Heuristic Technique ◽  
Distribution Type

Due to its geographical position, Mexico is exposed annually to cold fronts and tropical cyclones, registering extremely high values that are atypical in the series of maximum annual flows. Univariate mixed probability distribution functions have been developed based on the theory of extreme values, which require techniques to determine their parameters. Therefore, this paper explores a function that considers three populations to analyze maximum annual flows. According to the structure of the Generalized Extreme-Value Distribution (GEV), the simultaneous definition of nine parameters is required: three of location, three of scale, and three of probability of occurrence. Thus, the use of a meta-heuristic technique was proposed (harmonic search). The precision of the adjustment was increased through the optimization of the parameters, and with it came a reduction in the uncertainty of the forecast, particularly for cyclonic events. It is concluded that the use of an extreme value distribution (Type I) structured with three populations and accompanied by the technique of harmonic search improves the performance in respect to classic techniques for the determination of its parameters.

DIscrepancy of Gear Tooth Allowable Bending Stress Using the Extreme Value Distribution From Different Test Methods

1991 ◽  
Author(s):  
Chienann A. Hou ◽  
Shijun Ma
Keyword(s):  
Gear Tooth ◽  
Extreme Value Distribution ◽  
Test Methods ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Test Method ◽  
Bending Stress ◽  
Gear Design ◽  
Experimental Approaches

Abstract The allowable bending stress Se of a gear tooth is one of the basic factors in gear design. It can be determined by either the pulsating test or the gear-running test. However, some differences exist between the allowable bending stress Se obtained from these different test methods. In this paper, the probability distribution functions corresponding to each test method are analyzed and the expressions for the minimum extreme value distribution are presented. By using numerical integration, Se values from the population of the same tested gear tooth are obtained. Based on this investigation it is shown that the differences in Se obtained from the different test methods are significant. A proposed correction factor associated with the different experimental approaches is also presented.

Tree-dependent extreme values: the exponential case

1990 ◽  
Vol 27 (01) ◽  
pp. 124-133 ◽  
Author(s):  
Vijay K. Gupta ◽  
Oscar J. Mesa ◽  
E. Waymire
Keyword(s):  
Branching Process ◽  
Extreme Values ◽  
Rooted Tree ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Extinction Time ◽  
Brownian Excursion ◽  
Weighted Trees

The length of the main channel in a river network is viewed as an extreme value statistic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses an interesting contrast to the classical independent theory. Equivalently, the distribution of the extinction time for a binary branching process given a large number of progeny is sought. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n–1/2 L given M = n is asymptotically distributed as the maximum of a Brownian excursion. When taken with an earlier result of Kolchin (1978), this makes the maximum of the Brownian excursion a tree-dependent extreme value distribution whose domain of attraction includes both the exponentially distributed and almost surely constant weights. Moment computations are given for the Brownian excursion which are of independent interest.

Extrapolation of Historical Storm Data for Estimating Design-Wave Heights

1971 ◽  
Vol 11 (01) ◽  
pp. 23-37 ◽  
Author(s):  
C. Petrauskas ◽  
P.M. Aagaard
Keyword(s):  
Wave Height ◽  
Distribution Functions ◽  
Extreme Value Statistics ◽  
Return Periods ◽  
Improved Method ◽  
Design Wave Height ◽  
Straight Line ◽  
Wave Heights ◽  
Computerized Procedures ◽  
Selection Of

Abstract An improved method is presented for selecting offshore structure design waves by extrapolating historical storm data to obtain extreme value statistics. The method permits flexibility in choice of distribution functions through use of computerized procedures, estimates extrapolated wave-height procedures, estimates extrapolated wave-height uncertainty due to small sample size, and includes criteria for judging whether or not given wave-height values can be represented by one or more of the distributions implemented in the method. The relevance of uncertainty to selection of design-wave heights is discussed and illustrated. Introduction The problem of selecting design-wave heights for offshore platforms has many facets, ranging from the development of oceanographic data to the selection of the prudent level of engineering risk for a particular installation. This paper deals only with part of the problem; it describes an improved method for using the small available amount of wave-height information to estimate the extreme value statistics and associated uncertainties for the large storm waves that have a very low probability of occurrence. probability of occurrence. Hindcast wave-height information for design-wave studies usually covers a period of historical record that is shorter than the return period selected for acceptable engineering risk. Return periods commonly used for selection design waves are 100 years or more, but good meteorological data, on Which the calculated wave heights are based, can rarely be obtained for periods covering more than 50 to 60 years. As a consequence, extrapolations to longer return periods are necessary. Present methods for making the extrapolation employ probablistic models through the use of special probability graph papers on which a family of distribution functions plot as straight lines. The wave heights are plotted vs their "plotting-position" return period, and a straight line fitted to the plotted data is extended beyond the data to estimate extreme wave heights for return periods of interest. The methods are described in periods of interest. The methods are described in numerous technical papers and books; Refs. 1 through 5 are examples. The shortcomings of the present commonly used methods are:the straight line drawn through the data is in most cases visually fit to the data, thus is subject to error; andno information is available on the uncertainty of the resulting extrapolation. These shortcomings have been discussed by many authors and many of their concepts influenced this study. The improved method presented in this paper offers:greater flexibility in the choice of distributions through computerized procedures,guidelines for picking the "best" distribution from several implemented in the method, andprocedures for estimating the uncertainty of procedures for estimating the uncertainty of extrapolated wave heights. CONDENSED CONCLUSIONS Procedures described in this paper for extrapolating hindcast storm-wave heights and estimating uncertainty intervals to the extrapolated values are recommended as aids in selecting the design-wave height. The results of the extrapolating procedure and related uncertainty considerations procedure and related uncertainty considerations are only aids to help the engineer assess the risks associated with his design. The actual selection of the design-wave height is a matter of engineering judgment. The choice is subjective and will vary according to the risk chosen for the design. Further consideration of ways to decrease the span of be uncertainty intervals is warranted. Increasing the number of years represented in the sample along with the number of storms is a direct way to decrease the span. In the areas of the world having poor weather records the sample size will be marginal for many years to come. SPEJ P. 23

Extreme values of phase-type and mixed random variables with parallel-processing examples

1999 ◽  
Vol 36 (01) ◽  
pp. 194-210 ◽  
Author(s):  
Sungyeol Kang ◽  
Richard F. Serfozo
Keyword(s):  
Parallel Processing ◽  
Asymptotic Distribution ◽  
Extreme Values ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Independent Random Variables ◽  
Phase Type

A basic issue in extreme value theory is the characterization of the asymptotic distribution of the maximum of a number of random variables as the number tends to infinity. We address this issue in several settings. For independent identically distributed random variables where the distribution is a mixture, we show that the convergence of their maxima is determined by one of the distributions in the mixture that has a dominant tail. We use this result to characterize the asymptotic distribution of maxima associated with mixtures of convolutions of Erlang distributions and of normal distributions. Normalizing constants and bounds on the rates of convergence are also established. The next result is that the distribution of the maxima of independent random variables with phase type distributions converges to the Gumbel extreme-value distribution. These results are applied to describe completion times for jobs consisting of the parallel-processing of tasks represented by Markovian PERT networks or task-graphs. In these contexts, which arise in manufacturing and computer systems, the job completion time is the maximum of the task times and the number of tasks is fairly large. We also consider maxima of dependent random variables for which distributions are selected by an ergodic random environment process that may depend on the variables. We show under certain conditions that their distributions may converge to one of the three classical extreme-value distributions. This applies to parallel-processing where the subtasks are selected by a Markov chain.

Metocean Design Criteria Considerations in South China Sea by Adopting Multivariate Extreme Value Theory

2017 ◽  
Author(s):  
Ping Li ◽  
Qi Zhu ◽  
Chunqi Zhou ◽  
Linbin Li ◽  
Hongtao Li
Keyword(s):  
Probability Distribution ◽  
South China Sea ◽  
Joint Probability ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Design Criteria ◽  
Joint Probability Distribution ◽  
Wind Speeds ◽  
Wave Heights ◽  
Significant Wave Heights

The proper determination of metocean design criteria is critical for offshore structures. We study in this paper the univariate and multivariate compound extreme value theories and their applications to metocean data. Firstly, we adopt Compound Extreme Value Distribution (CEVD) method to derive the marginal distributions of wind speeds and significant wave heights respectively. Modelling uncertainties are considered with different distribution models. Secondly, the basic theory of Bivariate Compound Extreme Value Distribution (BCEVD), especially Poisson Bivariate Gumbel Logistic Distribution (PBGLD) is reviewed and utilized to analyze the joint probability distribution of significant wave heights and the concomitant wind speeds. Thirdly, Extreme Water Level (EWL) which is defined as the combination of wave crest, surge height and tidal elevation, is analyzed. We treat astronomical tide as a deterministic phenomenon and estimate the joint probability distribution of crest heights and storm surges. Case studies are given for picked position points in Northern South China Sea with 40 years hindcasted data. The results of this paper could give some knowledge for the determination and refinement of metocean design parameters.

Bias and Uncertainty in the Estimation of Extreme Wave Heights and Crests

2009 ◽  
Author(s):  
Richard Gibson ◽  
Colin Grant ◽  
George Z. Forristall ◽  
Rory Smyth ◽  
Peter Owrid ◽  
...  
Keyword(s):  
North Sea ◽  
Extreme Value ◽  
Accurate Prediction ◽  
Design Parameters ◽  
Extreme Value Analysis ◽  
Extreme Wave ◽  
Data Set ◽  
Value Analysis ◽  
Design Values ◽  
Wave Heights

The accurate prediction of extreme wave heights and crests is important to the design of offshore structures. For example, knowledge of the extreme crest elevation is required to set the deck elevation of the topside of a jacket structure. However, methods of extreme value analysis have an inherent bias, and the manner in which they are applied affects this bias. Furthermore, there is uncertainty in the design parameters at the time of design and the possibility that the predictions will change during the life of the structure. This paper is concerned with the accurate prediction of design values that incorporate uncertainty. In the first part of this paper the details of commonly applied extreme value analysis techniques are examined. This is achieved through analysis of simulated data of known distribution. In particular it is the application of least squares minimisation routines that is investigated; however, comparisons are made with maximum likelihood estimation. From this, preferred approaches to the analysis are recommended and their advantages and disadvantages discussed. The methods are applied to the analysis of a North Sea data set and the implications for the design values ascertained. In the second part of the paper Bayesian inference is used to consider the effect of uncertainty in the predicted wave heights and crest elevations. The practical implications are determined by the analysis of a measured North Sea data set.

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.

Wave Distributions and Sampling Variability

2007 ◽  
Author(s):  
O̸istein Hagen
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Height Distribution ◽  
Short Term ◽  
Sea State ◽  
Sampling Variability ◽  
Wave Statistics ◽  
Individual Wave ◽  
Wave Heights ◽  
Crest Height

The paper describes the effect of sampling variability on the predicted extreme individual wave height and the predicted extreme individual crests height for long return periods, such as for the 100-year maximum wave height and 100-year maximum crest height. We show that the effect of sampling variability is different for individual crest or wave height as compared to for significant wave height. The short term wave statistics is modeled by the Forristall crest height distribution and the Forristall wave height distribution [3,4]. Samples from the 3-hour Weibull distribution are simulated for 100.000 years period, and the 100-year extreme values for wave heights and crest heights determined for respectively 20 minute and 3 hour sea states. The simulations are compared to results obtained by probabilistic analysis. The paper shows that state of the art analysis approaches using the Forristall distributions give about unbiased estimates for extreme individual crest or wave height if implemented appropriately. Direct application of the Forristall distributions for 3-hour sea state parameters give long term extremes that are biased low, and it is shown how the short term distributions can be modified such that consistent results for 20 minute and 3 hour sea states are obtained. These modified distributions are expected applicable for predictions based on hindcast sea state statistics and for the environmental contour approach.

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