On the Probability Distribution of Mooring Line Tensions in a Directional Environment

2011 ◽  
Author(s):  
Jan Mathisen ◽  
Siril Okkenhaug ◽  
Kjell Larsen
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Extreme Value ◽  
Mooring Line ◽  
Large Set ◽  
Short Term ◽  
Reliability Method ◽  
Line Design

A joint probabilistic model of the metocean environment is assembled, taking account of wind, wave and current and their respective heading angles. Mooring line tensions are computed in the time domain, for a large set of short-term stationary conditions, intended to span the domain of metocean conditions that contribute significantly to the probabilities of high tensions. Weibull probability distributions are fitted to local tension maxima extracted from each time series. Long time series of 30 hours duration are used to reduce statistical uncertainty. Short-term, Gumbel extreme value distributions of line tension are derived from the maxima distributions. A response surface is fitted to the distribution parameters for line tension, to allow interpolation between the metocean conditions that have been explicitly analysed. A second order reliability method is applied to integrate the short-term tension distributions over the probability of the metocean conditions and obtain the annual extreme value distribution of line tension. Results are given for the most heavily loaded mooring line in two mooring systems: a mobile drilling unit and a production platform. The effects of different assumptions concerning the distribution of wave heading angles in simplified analysis for mooring line design are quantified by comparison with the detailed calculations.

Prediction of Mooring Line Tensions for Hurricane Conditions in the Gulf of Mexico

2014 ◽  
Author(s):  
Jan Mathisen ◽  
Torfinn Hørte
Keyword(s):  
Short Interval ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Time Domain Analysis ◽  
Extreme Value ◽  
Value Distribution ◽  
Mooring Line ◽  
Response Analysis ◽  
Short Term ◽  
Tension Distribution

A probabilistic metocean model for hurricane conditions is briefly described. The model is based on site-specific, hindcast data and defines the time variation of the metocean conditions during the realisation of a hurricane at the site. The annual extreme value distribution of mooring line tension for a large, semi-submersible, mobile drilling unit is computed. Time domain analysis is applied to obtain the short-term, extreme value distribution of line tension, conditional on stationary metocean conditions. A large number of different conditions are considered. A response surface is used to interpolate on the short-term distribution parameters in order to describe the tension response during the varying conditions associated with the passage of a hurricane. The hurricane duration is split into a sequence of 15-minute intervals such that the conditions can be assumed stationary during each such short interval. The tension distribution, conditional on the realisation of a hurricane, is accumulated across the sequence of short intervals. The distribution of hurricanes is taken into account to obtain the tension distribution in a random hurricane. Finally, the frequency of hurricanes is taken into account to give the annual extreme distribution of line tension. The characteristic tension computed using 10-year return conditions and the ISO 19901-7 design standard is found to correspond to a return period of 29 years in the test case. The effects of various assumptions in the design analysis are investigated. Sensitivities to simplifications of the metocean model are considered. The effects of uncertainties in the response calculation and in the distribution of peak significant wave height during hurricanes are quantified and included in the response analysis.

NorMoor JIP: On Safe Mooring Line Design

2012 ◽  
Author(s):  
Siril Okkenhaug ◽  
Jan Mathisen ◽  
Torfinn Hørte
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Line Tension ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Extreme Value ◽  
Mooring Line ◽  
Safety Factors ◽  
Line Design

DNV is currently running a Joint Industry Project, “NorMoor JIP”, on calibration of safety factors for mooring lines together with several oil companies, engineering companies, rig-owners, manufacturers of mooring line components and Norwegian authorities. Our motivation for initiating a study on mooring line safety factors started out with questions raised with regards to the safety level given by the Norwegian regulations. However, this is equally important for other mooring regulations like ISO, API and class-regulations. What we see is that the mooring standards are interpreted and applied in different ways. The reliability level implied by the regulations is not known, and the present safety factors were set when frequency domain analysis was prevalent while time domain analysis is often applied today. DNV carried out the DeepMoor JIP [9] during 1995–2000 using frequency domain analysis and reliability-based calibration. Now, a decade later, the increase in computing capacity makes it feasible to carry out a similar calibration for time-domain analysis of the mooring systems. The objective of the project work is to investigate and compare the characteristic line tension calculated according to design standards with the annual extreme value distribution of the line tension. Further, to calibrate safety factors for mooring line design for the ultimate limit state (ULS) as a function of the target probability of failure. The original proposal for this JIP included calculations for chain and wire rope moorings on a typical drill rig and a turret moored FPSO at three different water depths at Haltenbanken. However, since this JIP has been very well received in the industry, the scope has been extended to include calculations for a production semisubmersible, for fibre rope systems and for Gulf of Mexico environmental conditions. This paper will focus on the reasons for doing this calibration study, and the importance of seeking to agree on unified calculation recipes and requirements. Preliminary results for characteristic tension and annual extreme value distributions of tension for some designs are presented and discussed. The calibration of safety factors will be carried out later in the project when all designs are finalized.

How Should We Combine Long and Short Term Wave Height Distributions?

2008 ◽  
Author(s):  
George Z. Forristall
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Ocean Engineering ◽  
Short Term ◽  
Method Of Calculation ◽  
Individual Wave ◽  
Long Time ◽  
Wave Heights ◽  
The Individual

Estimating the maximum wave or crest height that will occur in a long return interval is one of the fundamental problems for ocean engineers. Long time series of individual wave heights are not available. The calculations must start with measured or hindcast time series of significant wave heights. An extreme value distribution is fit to that data. The resulting long term distribution is then combined with a short term distribution for the individual heights. This study is concerned with finding the most accurate methods for that calculation. The basic tool is the Borgman integral, but it has been applied in many different ways. Theoretical derivations do not clearly indicate which method is most accurate, and time series of measurements long enough for accurate tests do not exist. These problems were circumvented in this study by constructing very long simulated time series with known distributions. Both initial value and storm based methods were tested. The correct method of calculation depends on what question is being asked. The distribution of the maximum wave heights in a six hour interval is different than the distribution of the maxima of all of the waves. The distribution of the maxima in a storm is different than the distribution of the maxima in an interval. We believe that the finding the maximum in a storm is the most appropriate question for ocean engineering design. The Tromans and Vanderschuren (1995, Proc. Offshore Tech. Conf., OTC 7683) method accurately matches the results from our storm simulations.

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.

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.

scholarly journals Extreme Storm Surge estimation and projection through the Metastatistical Extreme Value Distribution

2021 ◽  
Author(s):  
Maria Francesca Caruso ◽  
Marco Marani
Keyword(s):  
Time Series ◽  
Sea Level ◽  
Return Period ◽  
Extreme Value Distribution ◽  
Storm Surges ◽  
Extreme Value ◽  
Value Distribution ◽  
Sample Sizes ◽  
Sea Levels ◽  
Calibration Sample

Abstract. Accurate estimates of the probability of extreme sea levels are pivotal for assessing risk and the design of coastal defense structures. This probability is typically estimated by modelling observed sea-level records using one of a few statistical approaches. In this study we comparatively apply the Generalized Extreme Value (GEV) distribution, based on Block Maxima (BM) and Peak-Over-Threshold (POT) formulations, and the recently Metastatistical Extreme Value Distribution (MEVD) to four long time series of sea-level observations distributed along European coastlines. A cross-validation approach, dividing available data in separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation. To address the limitations posed by the length of the observational time series, we quantify the estimation uncertainty associated with different calibration sample sizes, from 5 to 30 years. Focusing on events with a high return period, we find that the GEV-based approaches and MEVD perform similarly when considering short samples (5 years), while the MEVD estimates outperform the traditional methods when longer calibration sample sizes (10-30 years) are considered. We then investigate the influence of sea-level rise through 2100 on storm surges frequencies. The projections indicate an increase in the height of storm surges for a fixed return period that are spatially heterogeneous across the coastal locations explored.

Neural Probabilistic Forecasting of Symbolic Sequences With Long Short-Term Memory

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Michael Hauser ◽  
Yiwei Fu ◽  
Shashi Phoha ◽  
Asok Ray
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Short Term Memory ◽  
Probability Distributions ◽  
Series Data ◽  
Model Parameters ◽  
Short Term ◽  
Term Memory ◽  
Experimental Apparatus ◽  
Long Short Term Memory

This paper makes use of long short-term memory (LSTM) neural networks for forecasting probability distributions of time series in terms of discrete symbols that are quantized from real-valued data. The developed framework formulates the forecasting problem into a probabilistic paradigm as hΘ: X × Y → [0, 1] such that ∑y∈YhΘ(x,y)=1, where X is the finite-dimensional state space, Y is the symbol alphabet, and Θ is the set of model parameters. The proposed method is different from standard formulations (e.g., autoregressive moving average (ARMA)) of time series modeling. The main advantage of formulating the problem in the symbolic setting is that density predictions are obtained without any significantly restrictive assumptions (e.g., second-order statistics). The efficacy of the proposed method has been demonstrated by forecasting probability distributions on chaotic time series data collected from a laboratory-scale experimental apparatus. Three neural architectures are compared, each with 100 different combinations of symbol-alphabet size and forecast length, resulting in a comprehensive evaluation of their relative performances.

scholarly journals STATISTICAL INTERPRETATION OF HYDROMETEOROLOGICAL EXTREME VALUES

1972 ◽  
Vol 3 (4) ◽  
pp. 199-213 ◽  
Author(s):  
B. SAMUELSSON
Keyword(s):  
Stream Flow ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Statistical Characteristics ◽  
Statistical Interpretation ◽  
Short Term ◽  
Frequency Distributions ◽  
Low Probability ◽  
Term Data

The application of Jenkinson's method to extremal distributions for low probability annual extremes of rainfall and stream flow is studied and discussed. A statistical method devised by Jenkinson has been examined and compared with other methods of fitting extreme value distributions to observed data. The Jenkinson method, being strictly objective, has the particular advantage of taking into account the extreme part of the extreme value distribution. The author shows, by applying the Jenkinson method to extreme values which significantly belong to several different kinds of frequency distributions, that this method could be applied as a standard one. Finally, the author indicates the possibility of using the Jenkinson method to extrapolate statistical characteristics from a series of statistically unstable short-term data.

The Effect of Mooring Line Pre-Tension on FDPSO’s Motion

2016 ◽  
Author(s):  
Yanlong Sun ◽  
Huilong Ren ◽  
Zhendong Liu ◽  
Liu Yan ◽  
Zepeng Guo
Keyword(s):  
Time Series ◽  
Model Test ◽  
Time Domain ◽  
Prediction Method ◽  
Line Tension ◽  
Mooring Line ◽  
Floating Platform ◽  
Motion Response ◽  
Drilling Unit ◽  
Environment Condition

As a multifunction floating platform, Floating Drilling, Production, Storage and Offloading (FDPSO) combining the well-known Floating Production, Storage and Offloading (FPSO) with a drilling unit. For the environment condition of deep-water oilfield is very severe, the motion response and mooring line tension of FDPSO is a worthy topic of studying. In this study, the numerical time-domain coupled prediction method for the mooring line tension and motion response of FDPSO system is constructed by ANSYS AQWA software. Furthermore, the results of a model test conducted in Harbin Engimeering University are used to investigate the feasibility and validity of the commercial simulation. The effect of mooring line pre-tension on the response of FDPSO is studied by varying the pre-tension of mooring line during the calculation. The time series curve of the mooring line tension and motion response, and the comparison of motion spectrum and mooring line tension spectrum are provided in this article.

Detecting hazardous rivers: the physically-based extreme value distribution (PHEV!)

2020 ◽  
Author(s):  
Stefano Basso ◽  
Andrea Domin ◽  
Ralf Merz ◽  
Gianluca Botter ◽  
Arianna Miniussi
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Flood Frequency ◽  
Value Distribution ◽  
Alternative Methods ◽  
Frequency Curve ◽  
Engineering Structures ◽  
Empirical Observation ◽  
Physically Based

<p>Flood frequency curves are the basis to design ordinary engineering structures and devise strategies aimed at mitigating an increasing flood risk. Moreover, they are a crucial tool of risk assessment for insurance and reinsurance purposes. This work is concerned with the presence of abrupt increases of the flood frequency curve (i.e., sudden increments of streamflow magnitudes for a certain return period, named step changes), and investigate their occurrence by means of the physically-based extreme value distribution (PHEV!) of streamflow. This is an analytic probability distribution of extremes, which emerges from a lumped mechanistic-stochastic description of runoff generation and rainfall, soil moisture and discharge dynamics.</p><p>In the study, long synthetic time series of streamflow for river catchments exhibiting step changes have been generated and randomly resampled to construct sub-series of decreasing length. These shorter series are then used to test the performance of the PHEV!, of standard purely statistical distributions of the extremes, and of empirical observation-based estimates of the flood frequency curve in detecting the existence of a step change in the long time series from scarce data. Findings show that the PHEV! robustly detects the occurrence of step changes also when only short time series (e.g., 10 years) are used for parameter estimation. Conversely, the alternative methods tested mostly fails in this objective. These results indicate that the PHEV! might be a reliable tool for detecting the propensity of rivers to generate extreme floods in regions lacking long series of discharge observations.</p>

Sign in / Sign up

Export Citation Format

Share Document