Combining integral transform and a generalized probabilistic approach of uncertainties to quantify model-parameter and model uncertainties in computational structural dynamics: The stochastic GITT method

Abstract

The current work combines the generalized probabilistic approach of uncertainties recently developed by Soize (2010)—with the generalized integral transform technique in order to take into account two types of uncertainties: (i) model-parameter uncertainties and (ii) model uncertainties induced by modelling errors. The generalized integral transform technique (or GITT) is a powerful meshless hybrid analytical-numerical approach based on eigenfunction expansions to solve systems of partial differential equations and has been progressively advanced during the last three decades. The current work advances the state-of-the-art of the GITT approach by rigorously taking into account both model-parameter uncertainties and model uncertainties to improve the predictive accuracy of computational models developed in the context of computational structural dynamics. The developed stochastic GITT method is flexible enough to handle parametric and non-parametric probabilistic methods to quantify both types of uncertainties. It is applied to the governing equations derived with the extended Hamilton’s variational principle for predicting the in-plane and out-of-plane bending vibrations of a slender flexible structure connected to a rotating rigid shaft, resembling many complex engineered structures. Stochastic dynamic analyses in both time- and frequency-domains under both types of uncertainties are firstly carried out. Finally, stochastic model updating is carried out with the maximum likelihood and Bayesian statistical methods in order to construct both the optimum prior stochastic models of uncertainties and the posterior stochastic model of model-parameter uncertainties, using the first natural frequencies as observed data.