Non‐parametric–parametric model for random uncertainties in non‐linear structural dynamics: application to earthquake engineering

This paper deals with the transient response of a non-linear dynamical system with random uncertainties. The non-parametric probabilistic model of random uncertainties recently published and extended to nonlinear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The non-linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non-parametric-parametric formulation is developed in order to model all the sources of uncertainties in such a non-linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads.