A novel underwater weak signal detection method based on High-order double-coupled duffing oscillator, Empirical wavelet transform and Hilbert transform

The increasing complexity of marine noise environments and advancements in stealth technology have significantly weakened the continuous spectrum of underwater signals, rendering traditional random signal analysis methods inadequate for weak signal detection amidst complex noise backgrounds. To address the challenge of detecting underwater weak signals at ultra-low Signal-to-Noise Ratios (SNR), we propose a novel detection method that integrates high-order double-coupled Duffing oscillator, Empirical Wavelet Transform (EWT), and Hilbert Transform. This approach begins with the introduction of a novel high-order double-coupled Duffing oscillator, whose dynamic behavior is thoroughly analyzed using nonlinear techniques, including Lyapunov exponents, bifurcation analysis, and entropy measures. The analysis proves that the improved Duffing oscillator has excellent robustness to different noise. Then, combined with the constructed geometric frequency array and the scale transformation, a new weak signal detection array that can detect any frequency is constructed. The system discerns the presence of underwater signals by monitoring changes in the attractor trajectory, specifically transitions from chaotic behavior to large-period or intermittent chaos. Finally, a novel frequency extraction method that leverages EWT and Hilbert Transform is proposed, which can achieve noise reduction and kurtosis optimization for intermittent chaotic signals, thereby extracting the actual frequency of underwater weak signals. Experimental results confirm that the proposed detection array effectively identifies underwater weak signals submerged in complex noise environments, achieving a detection SNR of -38.42 dB and an extracted signal frequency error of <1 %. The simulation results meet the stringent accuracy requirements for underwater sonar applications.