Entropy-driven characterization of acoustic emission precursors for rockbursts: a systematic comparison of four entropy metrics and early warning verification

Rockburst early warning in deep coal mines is challenged by the strong noise, nonstationarity, and limited interpretability of raw acoustic emission (AE) intensity series. This study develops a feature-oriented early-warning framework that integrates four entropy metrics—Information Entropy, Approximate Entropy, Fuzzy Entropy, and Permutation Entropy—with sliding-window analysis and downstream forecasting validation. Using minute-level AE-intensity data from a coal mine in Liaoning Province, the window length and step size were optimized by grid search. Warning performance was evaluated under an operational protocol using precision, recall, F1-score, false alarm rate, and lead time, together with non-event interval comparison, event-aligned confidence-interval analysis, and benchmark tests against simpler amplitude-based baselines and classical change-detection methods. The results show that Information Entropy achieved the best overall warning balance whereas raw AE and sliding-mean baselines failed to provide useful true-positive warning windows. Non-event comparison and event-aligned analysis indicate that the precursor stage is better characterized as temporal reorganization rather than as a uniform entropy decrease. Proxy-based analysis further suggests increasingly persistent and temporally clustered high-intensity AE episodes before failure. In downstream forecasting, entropy-based inputs generally reduced training cost and improved test performance; for Informer, the test mean squared error decreased from 0.441 to 0.413 while training time was reduced by 11.2%. These findings indicate that entropy-based representations can transform noisy AE-intensity fluctuations into more discriminative and interpretable warning features for rockburst monitoring.