Speaker
Description
The prediction of forced vibrations in nonlinear systems is typically based on solving differential equations derived from 'first principles'. Such modeling requires a high level of expertise, experience, and prior knowledge about the system and its relevant parameters. In cases where such in-depth understanding is not available but observations of the system's behavior are accessible, data-driven approaches offer a promising alternative, as they demand less user expertise and system-specific information.
This contribution introduces a data-driven approach employing stabilized autoregressive neural networks (s-ARNNs) to model nonlinear transfer behavior. The performance of these s-ARNNs is compared to that of long short-term memory (LSTM) and gated recurrent unit (GRU) architectures, as well as classical linear methods in both frequency and time domains. Particular attention is given to addressing stability issues inherent to autoregressive architectures. Additionally, it is demonstrated that performance can be significantly enhanced through a hybrid architecture, which incorporates frequency response functions (FRFs) as information about the linearized transfer behavior to enrich the dataset.
For demonstration and comparison, the proposed s-ARNNs, alongside the alternative approaches, are applied to a forced Duffing oscillator – as a well-documented reference example – and to data from a real-world application from automotive engineering. Across all time series in both examples, the s-ARNN approach consistently exhibits superior accuracy and an enhanced ability to handle nonlinear effects compared to the other methods. Moreover, the implemented stabilization technique ensures robustness, making the approach highly applicable beyond academic scenarios.
In the final step, aleatoric and epistemic uncertainties are estimated using a mean-variance approach combined with ensembling the outputs of the s-ARNNs. Validation of this method confirms that combining s-ARNN with FRF achieves the highest accuracy and reliability in both prediction performance and uncertainty quantification.
