Hybrid modeling of multibody systems: Comparison of two discrepancy models for trajectory prediction

Abstract This study focuses on hybrid modeling approaches that combine physical and data-driven methods to create more effective dynamical system models. In particular, it examines discrepancy models, a type of hybrid model that integrates a physical system model with data-driven compensation for inaccuracies. The study applies two discrepancy modeling methods to a multibody system using discrepancies in the state vector and its time derivative, respectively. As an application example, a four-bar linkage with nonlinear damping is investigated, using a simplified conservative system as a physical model. The comparative analysis of the two methods shows that the continuous approach generally outperforms the discrete method in terms of accuracy and computational efficiency, especially for velocity prediction and prediction horizon. However, scenarios, where input signals for training and testing differ, present nuanced findings. When the continuous method is trained on complex signals (sine) and tested on simpler ones (stair), it struggles to deliver satisfactory results, exhibiting notably higher root mean square error (RMSE) values, particularly in angular velocity prediction. Conversely, training on simple signals (stair) and testing on complex ones (sine) surprisingly yields low RMSE values, indicating the continuous method’s adaptability. While the discrete method aligns more closely with expectations and performs better in certain scenarios, its results are consistently moderate, neither exceptional nor particularly poor. The study also introduces a selection framework for choosing the most suitable algorithm based on the specific characteristics of the modeling task. This framework provides guidance for researchers and practitioners in leveraging hybrid modeling effectively. Finally, the study concludes with an outlook on future research directions.