Application of the envelope peaks over threshold (EPOT) method for probabilistic assessment of dynamic stability

This paper reviews the research and development of the Envelope Peaks over Threshold (EPOT) method that has taken place in the last three years. The EPOT method is intended for the statistical extrapolation of ship motions and accelerations from time-domain numerical simulations, or possibly, from a model test. To model the relationship between probability and time, the large roll angle events must be independent, so Poisson flow can be used. The method uses the envelope of the signal to ensure the independence of large exceedances. The most significant development was application of the generalized Pareto Distribution (GPD) for approximation of the tail, replacing the previously used Weibull distribution. This paper reviews the main aspects of modeling the GPD, including its mathematical justification, fitting the parameters of the distribution, and evaluating the probability of exceedance and its confidence interval.

[1]  Richard L. Smith.  Estimating tails of probability distributions , 1987 .

[2]  Woei-Min Lin,et al.  Split-time method for estimation of probability of capsizing caused by pure loss of stability , 2016 .

[3]  Armin W. Troesch,et al.  Statistical Estimation of Extreme Roll in Head Seas , 2014 .

[4]  Charles Turner,et al.  Parametric Investigation on the Influence of GM, Roll Damping, and Above-Water Form on the Roll Response of Model 5613 , 2005 .

[5]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[6]  Vladas Pipiras,et al.  On the Application of the Generalized Pareto Distribution for Statistical Extrapolation in the Assessment of Dynamic Stability in Irregular Waves , 2014 .

[7]  Aaron Dinovitzer,et al.  Capsize risk of intact frigates in irregular seas. Discussion. Authors' closure , 2000 .

[8]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[9]  Kevin McTaggart.  Ongoing work examining capsize risk of intact frigates using time domain simulation , 2000 .

[10]  R. Reiss,et al.  Statistical Analysis of Extreme Values-with applications to insurance , 1997 .

[11]  H. N. Nagaraja,et al.  Order Statistics, Third Edition , 2005, Wiley Series in Probability and Statistics.

[12]  Vladas Pipiras,et al.  Confidence intervals for exceedance probabilities with application to extreme ship motions , 2015 .

[13]  J. Hüsler,et al.  Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields , 2007 .

[14]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[15]  David Taylor,et al.  Hybrid Models for Fast Time-Domain Simulation of Stability Failures in Irregular Waves With Volume-Based Calculations for Froude-Krylov and Hydrostatic Forces , 2013 .

[16]  Dennis D. Boos,et al.  Essential Statistical Inference: Theory and Methods , 2013 .