Based on the noise-enhanced signal characteristics of stochastic resonance (SR), this paper proposes a nonlinear multi-order coupled SR model, aiming to make full use of nonlinear zero-order vibrational coupling and first-order damping coupling to enhance the detected signal-to-noise ratio (SNR) and increase the detection distance of the underwater passive sonar. First, the influence of nonlinear vibration coupling on the system potential function and output SNR is analyzed to obtain the optimal nonlinear coupling parameters under the selected potential function structure. Further for the coupling damping, the output SNR is used as the evaluation metric to explore the influence of self-coupling and mutual-coupling damping on the system performance. It is found that under the optimal vibration coupling parameters, when the two damping parameters are matched, the energy concentration effect occurs in the system. This effect maximizes noise energy transfer to the signal, concentrating spectral energy at the feature frequency. Furthermore, based on this energy concentration effect, the Rényi entropy is used as a metric to propose an adaptive feature frequency detection model without prior knowledge, and the simulation results show that this model can accurately extract the feature frequency even at an extremely low SNR of −40 dB. Finally, this model is demonstrated by detecting and extracting of weak feature signals in ocean background noise from a compact hydrophone at the Vigo harbor.

中文翻译：

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极低信噪比下的非线性多阶耦合随机共振建模


基于随机共振（SR）的噪声增强信号特性，该文提出了一种非线性多阶耦合SR模型，旨在充分利用非线性零阶振动耦合和一阶阻尼耦合来增强探测到的信噪比（SNR），增加水下被动声呐的探测距离。首先，分析非线性振动耦合对系统势函数和输出信噪比的影响，得到所选势函数结构下的最优非线性耦合参数。此外，对于耦合阻尼，输出 SNR 用作评估指标，以探索自耦合和互耦合阻尼对系统性能的影响。研究发现，在最优振动耦合参数下，当两个阻尼参数匹配时，系统内出现能量集中效应。这种效果使噪声能量传递到信号最大化，将频谱能量集中在特征频率上。此外，基于这种能量集中效应，以 Rényi 熵为度量，在没有先验知识的情况下提出了一个自适应特征频率检测模型，仿真结果表明，即使在 −40 dB 的极低 SNR 下，该模型也能准确提取特征频率。最后，通过检测和提取维戈港紧凑型水听器海洋背景噪声中的微弱特征信号来验证该模型。