Formation drillability characterization method based on multi-scale convolutional neural representation with stacking ensemble

Formation drillability characteristics are critical for optimizing drilling performance and designing bottom-hole assemblies. Accurate estimation of drillability parameters, including uniaxial compressive strength (σ_c), drillability grade (K_d), and abrasiveness index (I_a), is fundamental for safe and efficient drilling operations. To overcome the generalization constraints of conventional single models and their inability to capture multi-scale feature responses, this study proposes a novel data-driven framework, termed the multi-scale convolutional neural representation with stacking ensemble (MSCNR-SE), for accurately estimating σ_c, K_d, and I_a. The framework uses a three-stage strategy: (1) a multi-scale convolutional module extracts features across different spatial scales; (2) an ensemble of diverse base regressors (e.g., random forest (RF), gradient boosted decision tree (GBDT)) enhances representational capacity; and (3) extreme gradient boosting (XGBoost) is employed as a meta-learner to integrate the outputs of base regressors, thereby mitigating the risk of model-specific bias. This hierarchical deep-learning ensemble effectively captures complex nonlinear relationships intrinsic to formation properties. Experimental results show that MSCNR-SE accurately models depth-aligned drillability profiles, with strong agreement between predictions and measurements (the coefficient of determination, R² > 0.93 on the blind testing sequence). The MSCNR-SE model achieved superior predictive performance compared with other models across all three parameters. Specifically, MSCNR-SE reduced the mean absolute error (MAE) by approximately 3%–50%, the root mean squared error (RMSE) by 4%–64%, the mean absolute percentage error (MAPE) by 3%–59%, and increased the R² by 1%–32%. These results highlight the superior predictive accuracy and robustness of MSCNR-SE, underscoring its potential as a practical, highly efficient data-driven solution for real-time parameter estimation, monitoring, and control in complex drilling.