Ground settlement prediction during the process of mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two paradigms are existing: a physics-driven approach utilizing process-oriented computational simulation models for the tunnel-soil interaction and the settlement prediction, and a data-driven approach employing machine learning techniques to establish mappings between influencing factors and the ground settlement. To integrate the advantages of both approaches and to 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 of 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 characteristics 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 information provided by the numerical simulations and accurately fit measured data as well. Remarkably, even with very limited noisy monitoring data, the proposed model can achieve rapid, accurate, and robust predictions of the full-field ground settlement in real-time during mechanized tunnel excavation.

翻译：机械化隧道施工过程中的地层沉降预测至关重要，且始终是一个具有挑战性的研究课题。通常存在两种范式：一种是物理驱动方法，利用面向过程的计算模拟模型描述隧道-土体相互作用并预测沉降；另一种是数据驱动方法，采用机器学习技术建立影响因子与地层沉降之间的映射关系。为整合两种方法的优势并融合多源数据，我们提出一种基于近期发展的算子学习方法的低保真/高保真深度算子网络（DeepONet）框架。该框架包含两个组成部分：捕获有限元模拟所得基本地层沉降模式的低保真子网络，以及学习数值模型与真实工程监测数据间非线性关系的高保真子网络。具体采用因果预处理策略考虑隧道开挖过程中沉降的时空特性，并利用迁移学习降低低保真子网络的训练成本。结果表明，该方法能有效捕获数值模拟提供的物理信息，同时精确拟合实测数据。值得注意的是，即使在仅有极少量含噪声监测数据的情况下，该模型仍可在机械化隧道掘进过程中快速、准确且鲁棒地实现全场地层沉降实时预测。