Detection method of ship-radiated noise based on fractional-order dual coupling oscillator

The popularly known integer-order chaotic oscillators are widely used to detect ship-radiated noise (S-RN). However, the current integer-order oscillators exhibit low accuracy in detecting complex S-RN. In this study, a method is proposed to detect ship-radiated noise based on double complexity and fractional-order dual coupling Duffing system to address the challenge. Firstly, embedding the integer derivative, we put forward a fractional-order dual coupling Duffing oscillator, a novel chaotic oscillator that considers the derivative changes. Secondly, determining the critical threshold of the system is to combine a double complexity algorithm with phase trajectory observation. The double complexity algorithm is utilized to determine the critical threshold and reduce the error in phase trajectory observation. Then, studying the dynamic behavior of the fractional-order dual coupling Duffing system, we demonstrate that the critical threshold of the fractional-order system is lower than the integer-order system and changes more drastically near the critical threshold. Finally, measured and analog signals are used to verify the performance of the proposed detection method. We empirically show that the method has a fine detection performance. Analyzing the system performance under the same detection signal and noise distribution, the signal-to-noise ratio threshold of the proposed detection method is −43.01 dB. This research generalizes the Duffing oscillator, aiming to explore the practical application of the fractional chaotic system.