Data- and experience-driven neural networks for long-term settlement prediction of tunnel

In recent years, machine learning methods have been widely used to predict the long-term settlement of tunnels. However, data -driven models for long-term settlement prediction often suffer from poor out -of -distribution generalization. Consequently, data -driven models cannot satisfy the requirements of tunnel engineering. This study aims to develop an innovative machine learning methodology with strong out -of -distribution generalization for long-term settlement prediction of tunnel. To implement the data and experience -driven neural networks, we propose two methods: Empirical Formula Based Neural Network (EFBNN) and Empirical Information Constrained Neural Network (EICNN). EFBNN uses an explicit empirical formula to calculate the predicted value, while EICNN calculates it directly. Both methods employ a neural network, but EFBNN estimates the undetermined parameters of the formula, and EICNN constrains the network parameters and loss function with empirical information as prior information. Based on the 20 -year settlement monitoring data of a shield tunnel section in Shanghai, the out -of -distribution generalization of EFBNN and EICNN are compared with BPNN. The results show that not all multi -driven methods could improve the out -of -distribution generalization. EFBNN has better temporal out -of -distribution generalization, but worse spatial out -of -distribution generalization, and is sensitive to the choice of empirical formula. EICNN has significant temporal and spatial out -of -distribution generalization. This method can improve the usability of monitoring data, and summarize a model with out -of -distribution generalization. It is a suitable machine learning method for predicting the long-term settlement of tunnels affected by countless and uncertain factors.