## 2 Mechanisms for Generating Shaft Frequency Signals of Vessels  
When a vessel travels through seawater, the metal hull's electrochemical corrosion and anti-corrosion measures generate a static electric field and an Extremely Low-Frequency Electric Field (ELFE). The ELFE, characterized by its low frequency, long underwater propagation distance, and distinct spectral features, is widely utilized for long-range underwater target detection [27]. Figure 1 illustrates the shaft frequency electric field's generation principle and equivalent circuit diagram, where ICCP represents the impressed current cathodic protection system. Due to the potential of the metal hull being higher than that of the propeller, the hull, propeller, and seawater form a current loop. The equivalent impedance RB in the loop undergoes periodic changes with the rotation of propeller bearings. This leads to the demodulation of the current in the loop, generating a time-varying electric field signal around the vessel at the fundamental frequency of the propeller rotation, known as the shaft frequency signal [28]. Figure 1: Schematic diagram of shaft frequency electric field generation mechanism. The intensity of the shaft frequency electric field is correlated with variations in the grounding resistance of the shaft and the current density flowing through the propeller circuit. As a result, the magnitude difference in shaft frequency electric field signals between different types of vessels can be several times. Additionally, based on the propagation characteristics of the electric field in seawater, the intensity of the shaft frequency electric field is inversely proportional to the cube of the distance. The distance between the measurement point and the vessel target also determines the size of the shaft frequency electric field signal [29]. Therefore, in underwater electric field detection of vessels, the shaft-rate electric field serves as a critical characteristic signature. Figure 2 presents the shaft frequency signal recorded during the ship's transit. The experimental setup utilized an Ag/AgCl electrode-based electric field measurement system with a sampling frequency of 100 Hz, deployed at a water depth of approximately 10 m. To enhance the temporal resolution and energy representation of target signals in the time-frequency spectrum, a computational framework was implemented using a 512-point sliding time window with a 64-sample overlap increment. From the analytical results, the three orthogonal components of the shaft-rate electric field (denoted as \(E_{x}\), \(E_{y}\), and \(E_{z}\)) exhibit distinct spectral signatures. Notably, between 200 s and 580 s, a pronounced energy amplification of the 4.7 Hz harmonic component is observed across all three field dimensions. Furthermore, ambient electromagnetic noise induced by oceanic dynamics--including tidal currents, wave motion, and hydrodynamic turbulence--constitutes the dominant interference source, significantly compromising the detectability of target-specific spectral features. This stochastic noise floor fundamentally limits the discriminative capability for identifying distinct target signatures due to spectral overlap between environmental noise and vessel-generated signals under typical operational conditions. Figure 2: _Cont._  
3 Experimental Analysis Based on Feature Extraction of Vessel Shaft Frequency Electric Field Signals  
As per the findings in Section 1, it has been established that the shaft frequency electric field signal collected by the vessel's underwater electric field detection system contains a complex and random background noise signal from the marine environment. To study the characteristics of the shaft frequency signal itself, the experiment in this paper constructs a system that uses various modal decomposition techniques to extract signal features from both the time and frequency domains.