The fault features of rolling bearing under time-varying speed conditions are often submerged in strong noise. For one thing, the system parameters of stochastic resonance (SR) need to match the change fault feature frequency of non-stationary signals, which makes the process very complex. Order analysis converts the non-stationary signals into a stationary angular domain signal, and the fault feature order does not change with time in the order spectrum. Because the system parameters only need to match a single order of stationary angular domain signals, and the process becomes simpler and more efficient. For another, the dual-tree complex wavelet packet transform decomposes the angle domain signal into a series of frequency band components. We select the frequency band containing more fault information (optimal frequency band) using statistical complexity measures (SCM). This operation suppresses the interference of strong noise on the output effect of SR. In addition, we also demonstrate that SCM has better stability than other indexes (kurtosis, Gini index, harmonic noise ratio) under different noise intensities. Finally, a piecewise tri-stable SR system is constructed to effectively avoid the saturation problem, and to improve the performance of the system in signal enhancement. Through an adaptive frequency-shifted SR method, we effectively extract the fault feature information of rolling bearing under time-varying speed conditions. The robustness of the proposed method is verified by theoretical research, simulation, and the collected experimental data.

Recurrence-plot (RP) analysis is a graphical tool to visualize and analyze the recurrence of nonlinear dynamic systems. By combining the advantages of the RP and a convolutional neural network (CNN), a fault-classification scheme for planetary gear sets is proposed in this paper. In the proposed approach, a vibration is first picked up from the planetary-gear test rig and converted into an angular-domain quasistationary signal through computed order tracking to eliminate the frequency blur caused by speed fluctuations. Then, the signal in the angular domain is divided into several segments, and each segment is processed by the RP to constitute the training sample. Moreover, a two-dimensional CNN model was developed to adaptively extract faulty features. Experiments on a planetary-gear test rig with four conditions under three operating speeds were carried out. The results of measured vibration demonstrated the validity of CNN and recurrence plot analysis for the fault classification of planetary-gear sets.