An iterative fitting method based on a three-parameter distribution

In the last years, modelling structural systems with uncertain parameters, such as their geometrical or physical properties, has been the focus of intensive research. To assess structural reliability, uncertain parameters are to be defined in a probabilistic sense and Stochastic Finite Element Methods(SFEMs) offer the most popular tool for numerical modelling. In particular, some SFEMs attempt to estimate also high order statistics, with the aim of better characterizing the structural response by a three-parameter distribution. On one hand, this kind of distributions is able to provide for an optimal fitting in a very large number of structural problems, on the other hand, the parameters estimation with traditional methods is a very hard task. This drawback can be overcome with the proposed iterative fitting method for the Weibull’s distribution. However, even if recent SFEMs are capable to predict a skew probability density function of the response, some of them do not manage to ensure sufficient accuracy in determining the skewness. For this reason, a few SFEMs are analyzed, with the purpose of enlightening which characteristics are necessary for fitting a three-parameters curve. Finally, a new reliable stochastic method is presented.