Cyclostationary Analysis of Irregular Statistical Cyclicity and Extraction of Rotating Speed for Bearing Diagnostics With Speed Fluctuations

Abstract

Mechanical fault diagnosis under nonstationary conditions is one of the hotspots in the condition monitoring research field, presenting still several difficulties. Vibration signals of faulty bearings exhibit second-order cyclostationarity when rotating speed and load are constant. Due to the time-varying rotating speed, the original cyclostationary signal becomes a special type of nonstationary signal. Considering the superiority of cyclostationary analysis in bearing fault diagnosis, it is interesting to extend the cyclostationary paradigm to make it suitable for particular signals that show irregular statistical cyclicity (ISC). Modeling bearing vibrations with speed fluctuation, however, is a controversial topic, which further sparked a debate on how to process bearing signals with ISC. Therefore, in this article, a detailed comparison of two signal models is made, the pace irregularity and the time warping, to illustrate the advantages and disadvantages of the modeling ideas. Based on these models, two novel tacholess diagnostic methods, the synchronization-sequence method and the dewarping method, are proposed for bearing diagnosis in nonstationary operations. By identifying the impact points with the same cyclic feature, the synchronization-sequence method shifts the impulse patches to the same interval, so the signal becomes cyclostationary. Using another strategy, the dewarping method recovers the regular statistical property by maximizing the squared modulus of the cyclic autocorrelation of specific feature points. The results show that both models can help diagnose local bearing faults, and the classical cyclostationary diagnostic tools become more powerful when extending to nonstationary operation conditions. In addition, the speed fluctuation curve can also be estimated by the two methods without using a tachometer. The characteristic of the proposed methods for speed estimation is that only the second-order cyclostationary information is utilized. Besides, the methods are robust to noise, so they are suitable for processing bearing data in the incipient failure stage. Numerical simulations and experimental data analyses corroborate the theoretical results.