Physics-enhanced multi-fidelity neural ordinary differential equation for forecasting long-term creep behavior of steel cables

• A novel machine-learning model for predicting the long-term creep of cables is proposed. • Combination of viscoelastic and data-driven models for prediction. • Multi-fidelity modeling is used to enhance the prediction performance. In spatial structures, prestressed steel cables experience creep behavior when subjected to tensile stress, resulting in stress relaxation, reduced stiffness, and potential structural failure. Consequently, the accurate assessment of creep is vital for the design and evaluation of prestressed cable structures. However, assessing the creep behavior of steel cables is challenging due to the absence of long-term creep data. To tackle this challenge, a novel framework called physics-enhanced multi-fidelity neural ordinary differential equation (PMNODE) is introduced, which integrates the viscoelastic model into the neural ordinary differential equation (NODE) model to forecast the long-term creep behavior of steel cables. Within this framework, the NODE is adopted to identify the underlying system dynamics by learning the derivative of the input-to-output transformation concerning time from a multi-fidelity model. The multi-fidelity model is designed to facilitate prediction by training NODE using both low-fidelity data from a physical model and high-fidelity measurement data. To verify the accuracy of the proposed framework, results from three commonly employed models including the physical model, the long short-term memory (LSTM) model, and the original NODE model are compared with those of PMNODE. The results illustrate that the proposed PMNODE framework can deliver higher accuracy predictions than other models and it is a valuable approach for forecasting the long-term creep behavior of steel cables.