Neural Network–Augmented Physics Models Using Modal Truncation for Dynamic MDOF Systems under Response-Dependent Forces

Accurate prediction of the dynamic response of a structure is crucial for its system identification, reliability analysis, and health monitoring. However, uncertainties in physics-based models and parameters may cause a significant discrepancy between predictions and actual responses. The neural network–augmented physics (NNAP) model aims to address this issue by augmenting physics-based models with deep-learning models trained by real data. While promising, such an approach has yet to be applied to large multi-degree-of-freedom (MDOF) structures under response-dependent forces. This paper presents a novel method incorporating modal truncation into the NNAP model for more accurate prediction of the dynamic responses of nonlinear MDOF systems. The proposed NNAP-m uses modal truncation to describe a physics-based model by lower-dimension coordinates and augments it with a neural network representing phenomena with more significant epistemic uncertainties. This hybrid modeling approach relies on information about mode shapes and natural frequencies to improve prediction capability. The proposed method is successfully verified using a numerical example of the Lysefjord bridge structure exhibiting nonlinear behaviors, including the interaction between wind loads and dynamic responses. The proposed approach is expected to provide accurate response predictions of real-world structures using measurement data and to promote the development of physics-based deep-learning approaches for complex structures with large DOFs.