Research on Shaft-Rate Magnetic Field Detection Method for Underwater Targets Based on Differential High-Order Dual-Coupled Duffing Oscillators

To address the issues of low signal-to-noise ratios in detecting weak shaft-rate magnetic fields of underwater targets in complex marine environments, the poor identification capability of traditional detection methods, and difficulty in recognizing unknown frequency signals, this study proposes a differential high-order dual-coupled Duffing oscillator detection method. A dual-oscillator model containing a cubic coupling term was constructed, and common-mode interference was suppressed through a differential structure. Simultaneously, a scale-dispersion joint statistical feature quantity was designed to automatically determine the critical threshold of system phase transition. Combined with refined composite multiscale dispersion entropy to quantitatively determine intermittent chaotic states, the method enabled the detection of weak shaft-rate magnetic fields with unknown frequencies and high-precision frequency estimation. Both simulation and marine experimental results demonstrate that compared with traditional Duffing oscillator detection methods, this approach significantly improved detection accuracy and reduced false alarm rates, making it applicable to underwater target monitoring, port security, and related scenarios.