Affiliations: Mechanical Engineering Department, PUC-Rio, Rua
Marquês de São Vicente, 225, Gávea, RJ, CEP: 22453-900,
Brazil | Applied Mathematics Department, Graduate Program in
Telecommunications Engineering, Universidade Federal Fluminense, Rua
Mário Santos Braga, S/N, Centro, Niterói, RJ, CEP: 24120-040,
Brazil
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.
