Fusing simulation and monitoring data for real-time settlement prediction during tunnel construction: A multi-fidelity deep operator network (DeepONet)

Ground settlement prediction during the process of mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two different paradigms have been created: a physics-driven approach utilizing advanced process-oriented numerical models for settlement prediction, and a data-driven approach employing machine learning techniques to establish mappings between influencing factors and ground settlement. To integrate the advantages of both approaches and assimilate the data from different sources, we propose a multi-fidelity deep operator network (DeepONet) framework, leveraging the recently developed operator learning methods. The presented framework comprises two components: a low-fidelity subnet that captures the fundamental ground settlement patterns obtained from finite element simulations, and a high-fidelity subnet that learns the nonlinear correlation between numerical models and real engineering monitoring data. A pre-processing strategy for causality is adopted to consider the spatio-temporal characteristic of the settlement during tunnel excavation. Transfer learning is utilized to reduce the training cost for the low-fidelity subnet. The results show that the proposed method can effectively capture the physical laws presented by numerical simulations and accurately fit measured data as well. Remarkably, even with very limited noisy monitoring data, our model can achieve rapid, accurate, and robust prediction of the full-field ground settlement in real-time mechanized tunneling.