Nonlinear dynamic analysis of new coupled Duffing-Van der Pol system and its application in underwater acoustic signal detection

Abstract

In the context of complex noise in the marine environment, with the continuous improvement of various stealth technologies for underwater target, the signal-to-noise ratio (SNR) of received signal is decreasing gradually, which makes underwater acoustic signal (UAS) detection a difficult problem in the development of underwater acoustics. To achieve underwater acoustic signal detection in complex marine environment, new coupled Duffing-Van der Pol system (NCDVPS) is proposed, its nonlinear dynamic behavior is analyzed, and its application in UAS detection is researched. To improve the SNR threshold, the interior of Duffing system is improved. The nonlinear term is extended to higher order, damping terms are introduced, and it is coupled with the Van der Pol system through derivative term. Thus, new coupled Duffing-Van der Pol system is proposed, its nonlinear dynamic behavior is analyzed, and its simulink model is built. To precisely determine the critical threshold, multi-dimensional threshold comprehensive judgment method is proposed based on bifurcation diagram, Lyapunov exponent, zero-crossing technique, and entropy measurement method. To realize underwater acoustic signal detection, two detection methods are proposed according to whether the frequency of the signal to be measured is known or not. If it is known, the signal is input into NCDVPS, and the signal detection is realized by observing the change of phase trajectory. This method is named D-KS. If it is unknown, firstly, successive variational mode decomposition based on moss growth optimization (MGO-SVMD) is used to decompose the signal to be measured. Then, the optimal decomposed component is selected and input into NCDVPS. Intermittent chaos and Hilbert transform are combined to realize more accurate detection of the signal frequency. This method is named D-US. In the experimental research, through simulation experiment and measured experiment on ship radiated noise signal and marine biological signal, it is demonstrated that SNR of D-KS can reach −89.49 dB, and the detection accuracy of D-US can reach 99.98 %. This research provides new ideas and methods for underwater acoustic signal detection.