Nowadays, predictions about non-linear dynamic systems are becoming more and more important, as the associated mathematical models can be expanded through new findings. Non-linear dynamic systems tend to result in periodic oscillations, which can lead to undesirable states of the system, e.g. due to inadmissible stress. In addition, more and more uncertainties of system variables are coming into focus. These can be, for example, scatter in material values or production inaccuracies. In non-linear systems, such changed parameters can lead to a completely different system behavior, which can limit or damage the function of the product.
In this research project, we are working at the interface between uncertainty quantification and non-linear dynamics. In order to make stochastic predictions about these systems, a system must be simulated very often for different parameter values. Depending on the complexity, this can be very time-consuming. For this reason, we are working on surrogate models which, on the one hand, represent the non-linear behavior and, on the other hand, ensure short calculation times for stochastic statements.
Lars de Jong, Paula Clasen, Michael Müller, Ulrich Römer, Uncertainty analysis of limit cycle oscillations in nonlinear dynamical systems with the Fourier generalized Polynomial Chaos expansion, Journal of Sound and Vibration, Volume 607, 2025, https://doi.org/10.1016/j.jsv.2025.119017
