## 1 Introduction  
In the context of the increasingly complex maritime strategic environment, submarines, as the core equipment of modern naval forces, play a crucial role in underwater warfare, with their safety being of paramount importance [1]. Enhancing the magnetic stealth capabilities of submarines is vital to ensure their concealment and survivability in underwater environments, which is a significant consideration in submarine design and operations [2]. The extremely-low-frequency (ELF) magnetic fields of submarines exhibit diverse characteristics, including a wide range of sources and multidimensional and multimodal features. The threats posed by these ELF fields to submarine safety are multifaceted and represent a comprehensive system engineering challenge. In the context of this study, ELF magnetic fields primarily refer to magnetic fields with frequencies below 30 Hz. In recent years, major military powers around the world have begun to research various ELF magnetic fields, primarily focusing on the mechanisms of and control strategies for individual types of ELF magnetic fields [3]. For instance, Canada's Department of National Defence and the UK's Ultra Electronics have been concentrating on the corrosion-related shaft frequency magnetic fields of ships, designing software for Beasy boundary element simulation to model and analyze their distribution [4]. Russia and the US's Cortana Corporation have been researching the Debye magnetic fields generated by the ion separation motion in submarine wakes and exploring the feasibility of using these fields for submarine detection [5]. Ship magnetic control mainly involves measures taken against individual magnetic sources and the conditions that allow for the existence of ship magnetic fields. The shaft frequency electric field control system developed jointly by Canada's Davis Company and the Pacific Defense Research Institute of Canada's Department of National Defence has been applied to newly built ships in multiple countries. Davis Company has provided shaft frequency electric field control systems for the US Navy's \"Seawolf\" class SSN-21 and SSN-22 nuclear submarines [6]. Vickers Shipbuilding and Engineering Technology Limited has also developed a shaft frequency electric field control system, which has been equipped on the British Navy's \"Trafalgar\" and \"Turbulent\" class nuclear submarines. The Polish Navy Technical Research and Development Center has tested shaft-based ELF electric fields and studied a short-circuit slip ring device, which can effectively reduce shaft-based ELF magnetic fields [7; 8; 9]. Russia has developed a ship magnetic field compensation system called \"Kackal-s\". This system is designed to counteract the magnetic fields of ships. Ships equipped with the \"Kackal-s\" system have effective insulation. This insulation prevents any contact with dissimilar metals. The system uses magnetic modulation sensors to measure something important: the shaft frequency current characteristic parameters. To eliminate shaft frequency magnetic fields, reverse currents are applied. These currents are directed through the tail anode. [10]. In practical scenarios, the magnetic field as the main component changes dynamically with different frequency bands, distances, environments, and operating conditions. Consequently, it cannot be measured in isolation and is necessary to estimate the contribution rates based on the measurement signals of the overall ELF magnetic fields. However, comprehensive research on the various causes of ELF fields in submarines and the assessment of their threat contribution rates remain nascent. Therefore, it is imperative to clarify the relationships among various ELF fields and, in conjunction with detection scenarios, quantitatively assess the systemic contribution rates of each ELF field to inform effective stealth strategies and countermeasures [11].