## 1 Introduction  
Micro-seisms (MEs) and electromagnetic radiation (EMR) represent forms of energy released during the deformation and rupture of coal and rock masses under stress [1; 2]. To delve into the destruction process and mechanism of coal and rock mass under static loads, researchers employ various technical means to monitor and analyze a series of physical parameters during the destruction process. Their objective is to pinpoint the most effective early warning methods, including acoustic emission/micro-seismic [3], EMR [4], and others. The EMR method, particularly suited for complex underground environments, offers more information about rock fractures and remains unaffected by fractures, making it a non-contact monitoring method. However, the mechanism of EMR remains incompletely understood, limiting the further development and widespread application of EMR technology in deformation monitoring [5]. The EMR mechanism in rock materials can be understood from multiple perspectives. Rock experiments suggest two perspectives on EMR mechanisms: rupture and non-rupture. These perspectives provide microscopic and specific explanations for seismic EMR [6]. Scholars have dedicated significant efforts to understanding the generation mechanism of EMR [7; 8]. [PERSON] et al. [9] experimentally verified the piezoelectric effect mechanism proposed by early scholars for rock materials. They posit that when rocks containing quartz and other piezoelectric materials fracture, polarization occurs within the material, creating positive and negative charges on its opposing surfaces. The generation mechanism of EMR is typically related to the movement of charged objects [10]. Therefore, irregular work or vibration of electric charges can be considered the basic condition for the EMR generated by rock fractures. [PERSON] et al. and [PERSON] et al. [11] developed a new electromagnetic vector three-axis sensor, laying the foundation for EMR positioning and enabling the preliminary development of EMR monitoring technology from prediction to positioning. By analyzing the EMR signals of sandstone samples with different water contents under uniaxial compression, [PERSON] et al. [12] proposed that the inhomogeneity of EMR signals and the frequency mutations of the minimum and maximum signals should be regarded as precursors of rock failures. Scholars found that EMR and AE signals are synchronized in time series, and although they share low-frequency components, their average dominant frequencies differ significantly [13]. [PERSON] et al. discussed crack propagation, AE, and EMR laws, as well as the response characteristics of coal with different diameters and strengths during the failure process. Ref. [14] concluded that the hole diameter significantly affects the axial load limit. ME refers to the stress wave released when coal and rock mass lose stability under external loads. It is a form of energy release usually accompanied by crack vibrations [15]. [PERSON] et al. [16] found good synchronicity in the time domain between the ME, EMR signals, and the generated crack area by conducting static load tests on coal briquettes with different particle sizes. [PERSON] et al. [17] proposed a comprehensive prediction index based on the principle of dynamic and static load superposition to predict large energy events and affected areas. Crack vibration refers to the mechanical movement of cracks or fissures, similar to the EMR physical quantity generated during and after the local mechanical movement of an object [18]. However, due to the unknown and complex nature of the coal mining process, actual time series observations are often irregular and noisy, making it increasingly important to analyze and process complex data to obtain more accurate information [19].