Yang Chen, Yang Jianhua, Zhou Dengji, Zhang Shuai, Litak Grzegorz
School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China.
Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology, Xuzhou 221116, People's Republic of China.
Philos Trans A Math Phys Eng Sci. 2021 Mar 8;379(2192):20200239. doi: 10.1098/rsta.2020.0239. Epub 2021 Jan 18.
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)'.
研究了由非线性调频（NLFM）信号和强噪声驱动的双稳系统中的随机共振（SR）。结合经验模态分解（EMD）和分段思想，提出了一种基于最优本征模态函数（IMF）的自适应分段重标度SR方法，以增强微弱的NLFM信号。首先，考虑到EMD处理非平稳信号的优势，对分段后的NLFM信号进行EMD处理。同时，采用互相关系数作为度量来选择包含NLFM信号特征的最优IMF。然后，提出谱放大增益指标，实现各子段信号最优IMF的自适应SR，并重构增强后的NLFM信号。最后，通过对仿真结果的短时傅里叶变换谱分析，突出了所提方法的有效性。作为一个应用实例，在所提方法在变速条件下轴承故障诊断中的适应性得到了验证，变速条件代表了机械工程中典型且复杂的NLFM信号。该研究为微弱非平稳信号的增强提供了一种新途径。本文是主题为“驱动非线性系统中的振动和随机共振（第1部分）”的一部分。
