Design optimization of quasi-rectangular tunnels based on hyperstatic reaction method and ensemble learning

The quasi-rectangular tunnel represents a novel cross-section design, intended to supersede the traditional circular and rectangular tunnel formats. Due to the limited capacity of the tunnel vault to withstand vertical loads, an interior column is often installed at the center to enhance its load-bearing capacity. This study aims to develop a hyperstatic reaction method (HRM) for the analysis of deformation and structural integrity in this specific tunnel type. The computational model is validated through comparison with the corresponding finite element method (FEM) analysis. Following comprehensive validation, an ensemble machine learning (ML) model is proposed, using numerical benchmark data, to facilitate real-time design and optimization. Subsequently, three widely used ensemble models, i.e. random forest (RF), gradient boosting decision tree (GBDT), and extreme gradient boosting (XGBoost) are compared to identify the most efficient ML model for replacing the HRM model in the design optimization process. The performance metrics, such as the coefficient of determination R² of about 0.999 and the mean absolute percentage error (MAPE) of about 1%, indicate that XGBoost outperforms the others, exhibiting excellent agreement with the HRM analysis. Additionally, the model demonstrates high computational efficiency, with prediction times measured in seconds. Finally, the HRM-XGBoost model is integrated with the well-known particle swarm optimization (PSO) for the real-time design optimization of quasi-rectangular tunnels, both with and without the interior column. A feature importance assessment is conducted to evaluate the sensitivity of design input features, enabling the selection of the most critical features for the optimization task.