Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

Noise would give rise to incorrect filtering frequency-band selection in signal filtering-based methods including fast kurtogram, teager energy operators and wavelet packet transform filters and meanwhile would result in incorrect selection of useful components and even mode mixing, end effects, etc., in signal decomposition-based methods including empirical mode decomposition, singular value decomposition and local mean decomposition. On the contrary, noise in stochastic resonance (SR) is beneficial to enhance weak signals of interest embedded in signals with strong background noise. Taking into account that nonlinear systems are crucial ingredients to activate the SR, here we investigate the SR in the cases of overdamped and underdamped harmonic-Gaussian double-well potential systems subjected to noise and a periodic signal. We derive and measure the analytic expression of the output signal-to-noise ratio (SNR) and the steady-state probability density (SPD) function under approximate adiabatic conditions. When the harmonic-Gaussian double-well potential loses its stability, we can observe the antiresonance phenomenon, whereas adding the damped factor into the overdamped system can change the stability of the harmonic-Gaussian double-well potential, resulting that the antiresonance behavior disappears in the underdamped system. Then, we use the overdamped and underdamped harmonic-Gaussian double-well potential SR to enhance weak useful characteristics for diagnosing incipient rotating machinery failures. Theoretical and experimental results show that adjusting both noise intensity and system parameters can activate overdamped and underdamped harmonic-Gaussian double-well potential SR in which there is a bell-shaped peak for the SNR. Additionally, the underdamped harmonic-Gaussian double-well potential SR is independent of frequency-shifted and rescaling transform to process large machine parameter signals and outperforms the overdamped one. Finally, comparing the advanced robust local mean decomposition (RLMD) method based on signal decomposition and the wavelet transform method based on noise cancellation or infogram method based on signal filtering, the overdamped or underdamped harmonic-Gaussian double-well potential SR methods characterize a better performance to detect a weak signal. Fault characteristics in the early stage of failures are successful in improving the incipient fault characteristic identification of rolling element bearings.