Datagedreven modellering van niet-lineaire trillingen: Efficiënte rekenmethoden voor systeemidentificatie gericht op regeltechniek

The identification of nonlinear systems from experimental data remains a major challenge in engineering, primarily due to two factors: the difficulty of selecting an appropriate model structure among many possible nonlinear representations, and the intrinsic non-convexity of the associated parameter estimation problem, in which conventional gradient-based optimisation methods often converge slowly or become trapped in suboptimal solutions. The aim of this thesis is to develop a sequence of identification algorithms for modelling the nonlinear vibrations of electromechanical systems. The focus is on computational efficiency and robustness to local minima, while maintaining a balance with physical interpretability. Each proposed method progressively reduces the reliance on prior system knowledge, moving from approaches that require detailed physical insight towards more data-driven techniques that remain grounded in physical principles. All methods are built upon a nonlinear state-space framework that explicitly distinguishes between the linear dynamic behaviour and the nonlinear contributions, providing a flexible yet interpretable model structure suitable for subsequent control design. Three complementary approaches are developed, all based on the same sequential strategy: (i) identify a baseline model, (ii) infer the nonlinear residual dynamics nonparametrically, and (iii) subsequently parametrise the nonlinearities in a static and isolated setting.This separation bypasses the otherwise computationally demanding nonlinear optimisation over dynamic trajectories. The first method introduces a sliding-window approach to infer the nonlinear residual dynamics by exploiting the known physical structure of the system. The second method generalises this framework to arbitrary systems where no such prior knowledge is available. The third method merges the previously separate inference and learning steps into a single formulation, and does so in the frequency domain, which enables inherent parallelisation across frequencies that can be efficiently exploited on modern hardware. The proposed methods are validated on both simulated and experimental systems, yielding models that demonstrate accurate prediction while offering varying levels of physical interpretability. The corresponding identification algorithms show high computational efficiency and robustness to poor local minima. To promote openness and reproducibility, the thesis also provides an open-source Python package for frequency-domain state-space identification, along with a challenging new benchmark dataset for nonlinear system identification.