Comparing Two Strategies to Model Uncertainties in Structural Dynamics

Abstract

In the modeling of dynamical systems, uncertainties are present and they must be taken into account to improve the prediction of the models. Some strategies have been used to model uncertainties and the aim of this work is to discuss two of those strategies and to compare them. This will be done using the simplest model possible: a two d.o.f. (degrees of freedom) dynamical system. A simple system is used because it is very helpful to assure a better understanding and, consequently, comparison of the strategies. The first strategy (called parametric strategy) consists in taking each spring stiffness as uncertain and a random variable is associated to each one of them. The second strategy (called nonparametric strategy) is more general and considers the whole stiffness matrix as uncertain, and associates a random matrix to it. In both cases, the probability density functions either of the random parameters or of the random matrix are deduced from the Maximum Entropy Principle using only the available information. With this example, some important results can be discussed, which cannot be assessed when complex structures are used, as it has been done so far in the literature. One important element for the comparison of the two strategies is the analysis of the samples spaces and the how to compare them.

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