We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to a part of the state variables of the reduced-order model. In recent years, such nonlinear approximation ansatzes have gained more and more attention especially due to their effectiveness in the context of model reduction for transport-dominated systems which are challenging for classical linear model reduction techniques. We demonstrate that port-Hamiltonian reduced-order models can often be obtained by a residual minimization approach where a suitable weighted norm is used for the residual. Moreover, we discuss sufficient conditions for the resulting reduced-order models to be stable. Finally, the methodology is illustrated by means of two transport-dominated numerical test cases, where the ansatz functions are determined based on snapshot data of the full-order state.
Data-driven reduced order modeling methods that aim at extracting physically meaningful governing equations directly from measurement data are facing a growing interest in recent years. The HAVOK-algorithm is a Koopman-based method that distills a forced, low-dimensional state-space model for a given dynamical system from a univariate measurement time series. This article studies the potential of HAVOK for application to mechanical oscillators by investigating which information of the underlying system can be extracted from the state-space model generated by HAVOK. Extensive parameter studies are performed to point out the strengths and pitfalls of the algorithm and ultimately yield recommendations for choosing tuning parameters. The application of the algorithm to real-world friction brake system measurements concludes this study.
Surrogate models are a must-have in a scenario-based safety simulation framework to design optimally integrated safety systems for new mobility solutions. The objective of this study is the development of surrogate models for active human model responses under consideration of multiple sampling strategies. A Gaussian process regression is chosen for predicting injury values based on the collision scenario, the occupant's seating position after a pre-crash movement and selected restraint system parameters. The trained models are validated and assessed for each sampling method and the best-performing surrogate model is selected for restraint system parameter optimization.
Frontiers in Applied Mathematics and Statistics
Harnessing Optimal Control for Eco-Epidemic Stability: A Vision for Future Ecosystems