A coupled Unscented Kalman Filter and modified Error in Constitutive Relation technique for structural dynamics identification

This work arises from an industrial need for EDF (the French electric power company) to study the dynamics of complex structures, for which (noisy) measurements are used in an effort to alleviate the presence of Finite Element model uncertainties. Our work aims at formulating and implementing a strategy allowing optimal estimation of the structure dynamics and model parameters from available, imperfect, modelling and experimental information. One of the motivations of this work is to consider evolving model parameters. This introduces additional difficulties in the identification strategy, especially when evolution laws are a priori unknown. In the present work we propose a strategy to tackle with the above mentioned problem based in combining both the modified Error in Constitutive Relation (mECR) technique and the Unscented Kalman Filter (UKF). A numerical example of a reinforced concrete beam is presented to show how this strategy gives particularly good results to both locate and identify model errors such as structural damage and boundary conditions misspecification. Furthermore, we illustrate how this approach is adapted for the case of evolving damage with no prior knowledge of the evolution law.