Detecting weak underwater acoustic signal with the combination of composite second-order tristable coupled stochastic resonance and improved variational mode decomposition

Accurate detection of underwater acoustic signal presents a significant challenge in remote passive sonar for both detection and identification purposes. To address the challenge, this paper proposes a novel detection method for ship-radiated noise (S-RN) based on stochastic resonance (SR) and variational mode decomposition (VMD). At the outset, to address the problems of poor noise immunity and low signal-to-noise gain (SNRG) that existed in the previous SR, a composite second-order tristable coupled stochastic resonance (CSTCSR) is proposed, and the rich potential energy structure of the potential function of CSTCSR and the influence of parametric variation on particle transition are analyzed. Then, to achieve the best detection effect of CSTCSR, an improved particle swarm optimization (PSO) algorithm based on the refractive opposition learning, linear decreasing weight and compression factor improvement strategy, called RLCPSO, is proposed. RLCPSO obtains the optimal parameters of CSTCSR. Next, to achieve the best decomposition effect of VMD, an improved VMD based on the exponential distribution optimizer (EDO) algorithm and residual ratio, called ERVMD, is proposed. Finally, the proposed detection method is called ERVMD-RLCPSO-CSTCSR. The original signal is decomposed into several intrinsic mode functions (IMFs) by ERVMD, and the sensitive IMF, which contains the main feature information, is selected by mutual information (MI). The selected sensitive IMF is used as the input of CSTCSR, and CSTCSR obtains the detection result. The experiments on simulated signals and real S-RN signals show that the proposed detection method can complete signal detection under the signal-to-noise ratio (SNR) of - 40 dB, which verifies its effectiveness and accuracy. The SNRG of the proposed detection method can reach 38 dB, and its accuracy can reach 98.92%, which is greatly improved compared with the existing SR method. The proposed detection method can provide effective technical support for maritime defense and weak signal frequency measurement of maritime targets.