Fast nonlinear Hoyergram for bearings fault diagnosis under random impact interference

Random impact interference has always been an important subject in fault diagnosis. In the fast kurtogram (FK), kurtosis is a sparsity index used to locate optimal resonance frequency bands. However, the shortcomings of the kurtosis measure are a tendency to select the random impact with a large amplitude and a relatively weak sparse measure ability, which reduces the accuracy and anti-interference of the FK method. To overcome the effects of random impact interference, this paper proposes a novel bearing fault diagnosis method named the fast nonlinear Hoyergram (FNH), in which the nonlinear Hoyer index is employed to replace kurtosis to improve the fault representation capability under random impulse interference. Firstly, Z-score normalization and a generalized nonlinear sigmoid activation function are used for signal preprocessing, and the scale distribution of the signal is changed to weaken the impact of random impact interference. Secondly, the Hoyer index, which can be viewed as the normalized form of the l(2)/l(1) norm, is used to replace kurtosis to improve the sparsity measure capability. Thirdly, in the Hoyergram, the frequency band with the largest Hoyer value can be chosen as the best resonance frequency band for the squared envelope analysis. Finally, the proposed FNH is compared with the FK method through simulation and experimental signals, and the effectiveness of the proposed method is verified.