Nonlinear System Identification in Structural Dynamics: A Short (and Biased) History

Although linear systems are now very well-understood in the context of structural dynamics, this is not at all the case for nonlinear systems. In particular, despite huge advances in the mathematical theory of nonlinear dynamical systems, progress in the difficult field of nonlinear system identification (learning of models from measured input/output data) has largely remained fairly slow and incremental. This is not to say that there have been no major successes in the field in its comparatively short history, and the objective of this paper is to present some of the highlights, as perceived by the authors, and to pave the way for a second paper discussing new developments and possibilities for the future