Dynamic prediction model of tunnel surrounding rock deformation based on Bayesian network

Significant limitations and hysteresis are presented in dynamic prediction methods driven by on-site monitored displacement data for tunnel surrounding rock deformation. By comprehensively utilizing the physical information contained in tunnel construction project documents and the mathematical information from displacement time-series curves, a modelling method based on the dynamic Bayesian network (DBN) was developed using the concept of physical information machine learning (PIML) to achieve dynamic predictions of surrounding rock deformation. Through discretization processing and reconstruction of displacement time-series curves, a static sample database was established by combining physical information data with ultimate displacement data, while a dynamic sample database was created by integrating physical information data with displacement time-series curve data. Based on the characteristics of the static samples, the K2-score algorithm was improved to construct a static Bayesian network (BN) model for ultimate displacement prediction. Utilizing the static BN model and the characteristics of the dynamic samples, physical-data dual-drive modelling methods for the Markov DBN were derived by incorporating prior information, including the constraints of steady-state random processes and Markov process constraints. By integrating prior information for constraint-enhanced optimization, the optimized Markov DBN model was established. Five-fold cross-validation tests revealed that the prediction capability of the Markov DBN model decreased rapidly over time and that the network transition direction significantly affected this capability. In contrast, the prediction ability of the optimized Markov DBN model remained robust over time, was unaffected by the network transition direction, and significantly exceeded that of the Markov DBN model, as the optimized model enhanced constraint connections between target nodes and influencing factor nodes throughout the entire timeframe. Through engineering case analysis, it was concluded that before and during the early stages of tunnel construction, the optimized Markov DBN model could effectively predict displacement time-series curves, overcoming the limitations and hysteresis inherent in traditional methods. Furthermore, during construction, self-updating of the optimized Markov DBN model and dynamic predictions of surrounding rock deformation could be achieved by inputting the on-site monitored displacement data.