An ISM-enhanced Bayesian network framework for tunnel deformation prediction

Accurate prediction of the ultimate deformation of the surrounding rock is pivotal for stability control and dynamic support design in tunneling. However, conventional predictive methods often struggle with data sparsity, missing values, and the complex, nonlinear interactions inherent in geological engineering and tunnel construction conditions. To address these challenges, this study proposes a novel probabilistic prediction framework based on Bayesian networks (BN), optimized with interpretive structural modeling (ISM) as a priori physical constrains. By integrating ISM-derived hierarchical dependencies with data-driven learning, two hybrid structure learning algorithms—ISM-K2-score and ISM-TAN—were developed comparatively to construct topologically robust networks. Based on a dataset of 130 tunnel cases, independent prediction models were established for crown settlement and horizontal convergence to account for their asynchronous deformation characteristics. Five-fold cross-validation results demonstrated that the ISM-K2-score BN model achieved the optimal performance, yielding an overall accuracy of 85.5% and F 1 -scores exceeding 83.5%. Comparative analysis confirmed that this framework significantly outperforms traditional support vector machine (SVM) and GA-BP neural network models, particularly in handling incomplete datasets. Furthermore, the model’s diagnostic inference capability was successfully applied to a practical engineering case, enabling the optimization of construction parameters to maintain deformation within safety limits. This research provides a rapid, efficient, and scientifically rigorous tool for data-driven decision-making in tunnel construction.