Análise comparativa de métodos para estimativa de valores extremos de processos aleatórios não-gaussianos

Abstract

This work makes a comparative study between four methods for extreme values estimation of non-Gaussian time series. The methods studied are: Hermite Moment Model, Shifted Generalized Lognormal Distribution (SGLD), Average Conditional Exceedance Rates (ACER) and Weibull Distribution Model. In the first two the process is transformed into an equivalent Standard Gaussian using the first four Statistical Moments of the time series. The last two procedures operate directly with the peaks observed in the time series regardless their statistical dependence, with only the ACER taking into account the statistical dependence between the peaks. Three case studies are presented to evaluate the performance of these methodologies and their accuracy as a function of the simulation time. In particular, the time series used are Utilization Factor series on the cross-section by the DnV-OS-F201 Standard for the steel risers design. It is shown that the Hermite Model has its applicability limited to some skewness-kurtosis combinations; the SGLD, due to its great versatility to cover the skewness-kurtosis combinations, is able to model any kind of distribution with high precision; the ACER and the Weibull models estimate efficiently the extreme values even for short simulation times. It is also observed that longer simulations are desirable to reduce the estimated values uncertainties.