There has been extensive research on corrosion electric fields because of their special characteristics. There are apparent distribution characteristics corresponding to different coating damage regions of a vessel. To accurately detect where the coating damage region is located on vessels using underwater electric field signature, in this study, a method called “refined composite multivariate multiscale fluctuation reverse dispersion entropy (RCMMFRDE)” was proposed. This method effectively extracted the multichannel signal in a complex environment of poor stability and high noise. By combining RCMMFRDE and hierarchical prototype (HP), a novel coating damage detection method was developed. First, the accumulated differential value was calculated to determine the side on which the vessel had the damaged coating. Second, RCMMFRDE was used to extract the features of electric field signals. Then, feature vector dimensionality reduction was carried out using pair-wise feature proximity (PWFP). The low-dimensional features were given as input to the HP classifier to detect the damaged region. Finally, a series of numerical and physical scale experiments were conducted to validate the feasibility of the proposed method. The damaged region was efficiently predicted, achieving satisfactory accuracy of 96.67% and 92.00% in numerical and measurement data respectively; thus, it is a suitable alternative to conventional methods, especially when there is a lack of previous environmental information.

The theoretical basis for a multi-physics coupling modeling involving a turbulence flow field and a ship’s electric field was analyzed using the principles of electrochemistry and hydrodynamics. Considering the mass transfer of oxygen in the cathode reaction of electrochemical corrosion, the boundary element method was adopted to construct a corrosion electric field model for a multi-shaft ship under navigation. After dissecting the equivalent circuit resistance of the mechanical structure of a ship’s shaft, the initial phase difference of the equivalent resistance between different shafting systems of a multi-shaft ship was analyzed to reveal the regularity of variation of the ship corrosion mixed electric field, when the contact positions of the shaft grounding device were different. A ship model experiment was conducted to verify the correctness of the simulation model. As shown in the results, when the initial phase difference of two-shaft ship shafting equivalent resistance increased from 0° to 45°, 90°, 135°, and 180°, the amplitude of the ship’s mixed electric field varied by less than 3.7%, which was practically negligible. However, the amplitude of the ship’s shaft-rate electric field decreased by 8.30%, 25.4%, 50.2%, and 88.0%, respectively. Moreover, the minimum value of the shaft-rate electric field accounted for 4.11% of the maximum value. This significantly increased the difficulty of marine target detection based on electric field sensors.

Due to strong noises from the marine environment and measurement devices, the vessel’s electric field signature would become weak, posing a detection challenge. To accurately extract the characteristics of the vessel’s electric field signature, this paper proposed a line-spectrum extraction method combining successive variational mode decomposition (SVMD) with adaptative asymmetric mixed potential stochastic resonance (AAMPSR) based on the equilibrium optimizer (EO) algorithm. The SVMD decomposed the original signal into multiple components, and then AAMPSR was utilized to absorb the noise energy in order to enhance the information signal. The EO algorithm was employed to optimize the potential function parameter settings, resulting in an improvement in the signal-to-noise ratio (SNR). Numerical and physical scale experiments were conducted to validate the feasibility of the proposed method. The results verify that the proposed method is effective in extracting the shaft rate frequency of the ship electric field signal and has much superiority over traditional methods in processing weak signals, thereby offering valuable applications in engineering.

Accurate localization of coating damage is crucial for timely repairs and protection against related threats. The complexity of corrosion electric field signals increases with the presence of multiple coating damages, making detection more challenging. To address this issue, this study proposes a novel multi-coating damage detection method by integrating the improved dung beetle optimizer (IDBO) with a machine learning-based approach. First, IDBO was employed to decompose the multi-coating damage electric field signals into a superposition of individual single damage signals using equivalent point charge calculations. Next, refined composite multivariate multiscale fluctuation reverse dispersion entropy (RCMMFRDE) was utilized for feature extraction. These feature vectors were subsequently input into the hierarchical prototype (HP) classifier to detect the damaged regions. Numerical experiments demonstrated that the proposed method detection accuracies of 94.0% or two damages and 88.0% for three damages. Physical scale experiments further validated these findings, with accuracies of 90.1% and 84.3% for two and three damages, respectively. The results confirm that the proposed method reliably detects coating damages, contributing to enhanced vessel vessel defense and surveillance.