Data and model uncertainties in complex aerospace engineering systems

ABSTRACT: The dynamical analysis of complex mechanical systems is in general very sensitive to random uncertainties. In order to treat the latter in a rational way and to increase the robustness of the dynamical predictions, the random uncertainties can be represented by probabilistic models. The structural complexity of the dynamical systems arising in these fields results in large finite element models with significant random uncertainties. Parametric probabilistic models capture the uncertainty in the parameters of the numerical model of the structure, which are often directly related to physical parameters in the actual structure, e.g. Young’s modulus. Model uncertainties would have to be modeled separately. On the other hand, the proposed nonparametric model of random uncertainties represents a global probabilistic approach which, in addition, takes directly into account model uncertainty, such as that related to the choice of a particular type of finite element. The uncertain parameters of the structure are not modeled directly by random variables (r.v.’s); instead, the probability model is directly introduced from the generalized matrices of a mean reduced matrix model of the structure by using the maximum entropy principle (Soize 2001). In this formulation the global scatter of each random matrix is controlled by one real positive scalar called dispersion parameter