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.

翻译：机械化隧道施工过程中的地表沉降预测至关重要，且仍是一个具有挑战性的研究课题。通常，两种不同范式已被建立：一种是基于物理驱动的方法，利用先进的面向过程的数值模型进行沉降预测；另一种是数据驱动的方法，采用机器学习技术建立影响因素与地表沉降之间的映射关系。为融合两种方法的优势并整合不同来源的数据，我们提出了一种多保真度深度算子网络（DeepONet）框架，利用近期发展的算子学习方法。该框架包含两个组件：一个低保真子网络，用于捕捉由有限元模拟获得的基本地表沉降模式；以及一个高保真子网络，用于学习数值模型与真实工程监测数据之间的非线性相关性。采用因果预处理策略以考虑隧道开挖过程中沉降的时空特性。利用迁移学习降低低保真子网络的训练成本。结果表明，所提方法能够有效捕捉数值模拟呈现的物理规律，并精确拟合实测数据。值得注意的是，即使仅使用有限且含噪声的监测数据，我们的模型仍能在实时机械化隧道施工中实现全场地表沉降的快速、准确且鲁棒预测。