Detection method of improved strongly coupled high-order Duffing-Van der Pol system for underwater acoustic signal

To address the challenges in underwater acoustic signal detection, where weak signals are easily masked by noise and conventional methods have limited detection accuracy, detection method of improved strongly coupled high-order Duffing-Van der Pol system (ISCHDVPS) for underwater acoustic signal is proposed. First, a high-order restoring force term and a nonlinear damping term are introduced into the Duffing oscillator, which is then strongly coupled with an improved Van der Pol oscillator to construct the ISCHDVPS. The system's equilibrium points, their stability, dissipative properties, and noise immunity are analyzed. By combining bifurcation diagram, Lyapunov exponent, and Simulink simulation, the chaos-period-chaos evolution law of the system under the change of driving parameters is revealed, thereby laying a robust theoretical groundwork for weak signal detection. Next, a multivariate joint analysis method (MJAM) is proposed to accurately determine the system's critical driving threshold by jointly analyzing four dimensions, namely bifurcation structure evolution, Lyapunov exponent variation, entropy mutation, and phase-space topology. Finally, depending on whether the target signal frequency is known, detection method of ISCHDVPS is categorized into two types: known frequency detection (KFD) and unknown frequency detection (UFD). KFD method determines the presence of signal through phase trajectory analysis. For UFD method, the proposed fata morgana algorithm-based adaptive successive variational mode decomposition (FATA-SVMD) is utilized to decompose the signal to be detected. The mode component with the highest energy ratio is selected as the optimal mode component and input into the oscillator train. After capturing the signal according to the intermittent chaos phenomenon, the output sequence is subjected to Hilbert transform to precisely estimate frequency. In the experimental verification of analog signal, actual ship radiated noise signal, and actual marine biological signal, it is demonstrated that KFD method achieves a minimum detectable signal-to-noise ratio threshold of −96.10 dB, which is significantly superior to traditional and improved Duffing systems, and the UFD method attains a detection accuracy of 99.94%, demonstrating the proposed method's high sensitivity and reliability under complex ocean noise environments.