NONLINEAR EVOLUTION CHARACTERISTICS OF THE MUTUAL-EXCITING NETWORK OF ACOUSTIC EMISSION EVENTS AND THE MULTIFRACTAL EARLY WARNING MODEL

To improve the efficiency of early warning for rock failure, this study records acoustic emission (AE) events during the uniaxial compression of limestone. Within a point-process framework, a mutual-exciting network of AE events is constructed, and a spherical multifractal method is introduced to characterize its nonlinear evolution. On this basis, a data-driven multifractal early-warning model is developed. The results show that with increasing stress, the mutual-exciting network evolves from numerous isolated events to multiple localized clusters, and eventually to a connected global structure. The distribution of triggering probability first widens, then narrows, and widens again, indicating multiscale and multilevel interactions among AE events. The range of polar angles gradually becomes smaller and its median decreases, suggesting that AE events develop directionally along the axial direction, while the azimuth remains broadly distributed, implying continued lateral competition. The multifractal spectrum of the mutual-exciting network progressively broadens and shifts downward and leftward. Meanwhile, the evolution laws of the multifractal parameters [Formula: see text], [Formula: see text] and [Formula: see text] capture the transition of AE event triggering from random occurrence to localized clustering and finally global directional organization. Based on these findings, a multifractal early warning model is established, tested, and evaluated. The model achieves a false alarm rate of 4.28%, a recall of 91.55%, a hit rate of 95%, and an average first warning at 78.77% of [Formula: see text]. Compared with traditional early warning models based on [Formula: see text]-value and AE event rate, the proposed method demonstrates higher accuracy and reliability, offering significant practical value for engineering applications.