The stochastic resonance (SR) in a bistable system driven by nonlinear frequency modulation (NLFM) signal and strong noise is studied. Combined with empirical mode decomposition (EMD) and piecewise idea, an adaptive piecewise re-scaled SR method based on the optimal intrinsic mode function (IMF), is proposed to enhance the weak NLFM signal. At first, considering the advantages of EMD for dealing with non-stationary signals, the segmented NLFM signal is processed by EMD. Meanwhile, the cross-correlation coefficient is used as the measure to select the optimal IMF that contains the NLFM signal feature. Then, the spectral amplification gain indicator is proposed to realize the adaptive SR of the optimal IMF of each sub-segment signal and reconstruct the enhanced NLFM signal. Finally, the effectiveness of the proposed method is highlighted with the analysis of the short-time Fourier transform spectrum of the simulation results. As an application example, the proposed method is verified adaptability in bearing fault diagnosis under the speed-varying condition that represents a typical and complicated NLFM signal in mechanical engineering. The research provides a new way for the enhancement of weak non-stationary signals. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

中文翻译：

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噪声 NLFM 信号驱动的双稳态系统中的自适应随机共振：现象与应用

研究了非线性调频(NLFM)信号和强噪声驱动的双稳态系统中的随机共振(SR)。结合经验模态分解(EMD)和分段思想，提出了一种基于最优固有模态函数(IMF)的自适应分段重标度SR方法来增强弱NLFM信号。首先，考虑到 EMD 在处理非平稳信号方面的优势，对分段后的 NLFM 信号进行 EMD 处理。同时，以互相关系数作为度量选择包含NLFM信号特征的最优IMF。然后，提出频谱放大增益指标，实现各子段信号最优IMF的自适应SR，重构增强后的NLFM信号。最后，通过对仿真结果的短时傅立叶变换谱的分析，突出了所提出方法的有效性。作为一个应用实例，该方法在代表机械工程中典型且复杂的NLFM信号的变速条件下的轴承故障诊断中得到了验证。该研究为弱非平稳信号的增强提供了一种新途径。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。该研究为弱非平稳信号的增强提供了一种新途径。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。该研究为弱非平稳信号的增强提供了一种新途径。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。