A Fracture Mode-Constrained Physics-Informed Machine Learning Framework for Predicting Acoustic Emission Energy of Coal Gangue Backfill

Coal gangue backfill serves as a primary supporting structure for overlying strata in mined-out areas, and its internal damage evolution is directly associated with the safety and stability of mining operations. Acoustic emission (AE) technology provides an effective approach for investigating damage evolution by capturing transient strain energy release events within materials in real time. However, conventional AE analysis methods predominantly rely on statistical interpretations of individual parameters, making them insufficient for revealing the underlying physical mechanisms governing the influence of fracture characteristics on energy evolution pathways. To address the aforementioned limitations, this paper proposes a fracture mode-informed physics-enhanced machine learning framework for predicting acoustic emission energy evolution in coal gangue backfill. First, based on the AE monitoring data of coal gangue backfill under uniaxial compression (a total of 18,992 valid AE events from three parallel specimens with identical mix proportion), the RA–AF parameters combined with the K-means unsupervised clustering algorithm were employed to automatically identify tensile and shear fracture modes, thereby constructing physically meaningful fracture mode labels. Second, the fracture mode information was integrated with AE statistical features, including rise time, duration, amplitude, counts, peak frequency, and center frequency. After selecting the most informative features using the minimum-redundancy, maximum-relevance (mRMR) algorithm, a Bayesian optimization-based support vector regression (BO-SVR) model was developed for AE energy prediction. The results demonstrated that after incorporating the fracture mode-based physical labels, the proposed model achieved a coefficient of determination (R2) of 0.9027 on the testing dataset, with an RMSE of 0.1562 and an MAE of 0.1204. Ablation experiments further confirmed that the introduction of fracture mode labels improved the R2 value by approximately 3.4% compared with the model without physical constraints. Fivefold cross-validation yielded an average R2 of 0.9460 with a standard deviation of 0.0023 for the SVR model. Furthermore, per-specimen independent holdout validation yielded an average R2 of 0.9044 with a standard deviation of 0.0512 across three independent specimens, confirming the excellent stability and repeatability of the proposed framework. The original single-specimen results (4083 events, R2 = 0.9727) are provided as a baseline reference. Mechanistic analysis revealed that the average energy release associated with shear fractures was approximately 739 times that of tensile fractures, demonstrating that fracture mode information provides physically consistent mechanical constraints for the machine learning model. This study provides an effective new method for the stability evaluation and intelligent monitoring of coal gangue filling materials.