AI-based state extension and augmentation for nonlinear dynamical first principles models

Nonlinear dynamics models derived using First Principles (FPs) often suffer from limited accuracy in relation to the complex physical systems they represent. Therefore, model updating may be employed to improve the accuracy of the FP model. In this work, an AI-based updating methodology is proposed where an existing FP model is extended by introducing new states (to capture, e.g., unmodeled modes or parasitic degrees of freedom) using a subspace encoder, and capture their governing equations of motion using a Recurrent Neural Network (RNN). Additionally, the retained FP equations of motion are augmented by additional RNNs to capture unmodeled dynamics (e.g. nonlinearities) or improper parameter values. Simultaneously training all neural networks such that an output prediction error-based loss is minimized yields an Extension and Augmentation-based (EA) model that significantly decreases the prediction error with respect to the FP model. This methodology is applied on two use cases, one of which uses measurements performed on an industrial wire bonder. These use cases demonstrate that, also when changes are made to the FP parameters, excitation signals, and controllers, the EA model still shows significant improvement in prediction capability over the FP model. This shows that by using the FP model as a basis for model updating, the extrapolation capabilities of the resulting model are improved. Furthermore, the EA model updating method is compared with a similar, yet fully black-box, subspace-encoder network method (Beintema et al. Automatica 158:111210). The EA model is shown to outperform such purely data-based models in terms of accuracy, training efficiency, and extrapolation capabilities. Finally, in contrast to the (purely data-based) subspace-encoder network method, the EA model updating method enables updating of unstable open-loop systems by embedding stabilizing controllers in the FP model.