Extreme Values Models for the estimation of the maximum depth in pitting corrosion: Simulations Experiments

摘要

Perforation by pitting is one of the most common forms of localised corrosion likely to affect the lifetime of industrial construction as pipelines, tanks or nuclear vessels. Because of the stochastic behaviour of this physical phenomenon, extreme values theory provides a statistical treatment of pit depths to obtain an estimate of the maximum depth for a surface S from data collected on a smaller surface s. The most common approach is to use the Gumbel law as distribution of the maximum pit depth. In this work, simulations and experiments were combined to assess the relevancy of the Gumbel method in comparison with exceeding threshold methods in a view to reducing the uncertainties on the determination of the maximum pit depth. Experiment consists in measuring by optical microscopy the depths of more than 200 pits formed on an annealed aluminium sheet of 150 cm2 area immersed in a corrosive solution during 10 h. These measurements are used to determine the density of pits as well as the underlying distribution law of pit depths further considered in simulations. A chi-square test validates that data may come from Weibull distribution which belongs to the Gumbel Maximum Domain of attraction. Simulation consists in estimating the maximum pit depth and its related confidence intervals. Results are compared to the ones deduced from the usual Gumbel's method for various number and various area of analyse surfaces s (I.e. the return period T=S/s). A statistical test based on the analysis of quantile plot proved that our generated pitting corrosion phenomenon does not belong to the Gumbel attraction domain. Consequently the systematical use of this method as an estimator of pitting corrosion phenomena may be questionable. In order to reduce the error on the estimation of the distribution of pit depths, three statistical methods were also compared: the least-squares, the moments and the maximum of likelihood methods.