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Due to complex interactions between immersed tunnel and surrounding environment, it is difficult to apply theoretical analysis for axial displacement (DIS) of immersion joints. To develop a generalised model for DIS prediction, Deep Neural Network (DNN) could be considered. However, the spatial generalisation of black-box DNN models is not always convincible for small data. In this study, we proposed a novel hybrid physical data (HPD) informed DNN model with improved spatial generalisation for prediction of DIS. The physical mechanism of DIS is firstly analysed by correlation between DIS and other monitoring data. The HPD is then created based on the physical analysis and contributes to the DNN as a substituting feature rather than an additional feature. Three DNN models fed with different groups of features are compared, while the proposed HPD-DNN has outperformed others in terms of both prediction generalisation as well as accuracy. The permutation feature importance analysis reveals that HPD has effectively enhanced physical interpretation of DNN, which supports the results stated in physical analysis. The application of HPD is further verified to enhance the spatial generalisation of prediction for not only DNN but also other black-box models, which is promising for insufficient data problems in geotechnical engineering.

A hybrid physical data informed DNN in axial displacement prediction of immersed tunnel joint