A New Approach to the Degradation Stage Prediction of Rolling Bearings Using Hierarchical Grey Entropy and a Grey Bootstrap Markov Chain

Abstract

Degradation stage prediction, which is crucial to monitoring the health condition of rolling bearings, can improve safety and reduce maintenance costs. In this paper, a novel degradation stage prediction method based on hierarchical grey entropy (HGE) and a grey bootstrap Markov chain (GBMC) is presented. Firstly, HGE is proposed as a new entropy that measures complexity, considers the degradation information embedded in both lower- and higher-frequency components and extracts the degradation features of rolling bearings. Then, the HGE values containing degradation information are fed to the prediction model, based on the GBMC, to obtain degradation stage prediction results more accurately. Meanwhile, three parameter indicators, namely the dynamic estimated interval, the reliability of the prediction result and dynamic uncertainty, are employed to evaluate the prediction results from different perspectives. The estimated interval reflects the upper and lower boundaries of the prediction results, the reliability reflects the credibility of the prediction results and the uncertainty reflects the dynamic fluctuation range of the prediction results. Finally, three rolling bearing run-to-failure experiments were conducted consecutively to validate the effectiveness of the proposed method, whose results indicate that HGE is superior to other entropies and the GBMC surpasses other existing rolling bearing degradation prediction methods; the prediction reliabilities are 90.91%, 90% and 83.87%, respectively.

Keywords: degradation stage prediction; grey bootstrap Markov chain; hierarchical grey entropy; rolling bearing.

Figure 1

Hierarchical decomposition of Y with four scales.

Figure 2

(a) Temporal waveform of 1/f noise. (b) Temporal waveform of Gaussian white noise.

Figure 3

GE values of 1/f noise according to different embedding dimension q values.

Figure 4

GE values of 1/f noise according to different similarity tolerance e values.

Figure 5

HGE with different embedding dimension q values.

Figure 6

HGE with different similarity tolerance e values.

Figure 7

HGE analysis of 1/f noise and WG noise.

Figure 8

HFE analysis of 1/f noise and WG noise.

Figure 9

HSE analysis of 1/f noise and WG noise.

Figure 10

Flowchart of the proposed degradation stage prediction method.

Figure 11

The test rig.

Figure 12

Time domain wave of the vibration signal (case 1).

Figure 13

The HGE, HFE and HSE of rolling bearing vibration signal (case 1).

Figure 14

The HGE and kurtosis of rolling bearing vibration signal (case 1).

Figure 15

Large sample sequence of the degradation stages (case 1).

Figure 16

Histogram of large sample sequences of degradation stages (case 1).

Figure 17

Prediction results and dynamic evaluation of rolling bearing degradation stages based on GBMC model (case 1).

Figure 18

Prediction results of rolling bearing degradation stages based on GB model (case 1).

Figure 19

Prediction results of rolling bearing degradation stages based on AR method (case 1).

Figure 20

Time domain wave of the vibration signal (case 2).

Figure 21

The HGE, HFE and HSE of rolling bearing vibration signal (case 2).

Figure 22

The HGE and kurtosis of rolling bearing vibration signal (case 2).

Figure 23

Large sample sequence of the degradation stages (case 2).

Figure 24

Histogram of large sample sequences of degradation stages (case 2).

Figure 25

Prediction results and dynamic evaluation of rolling bearing degradation stages based on GBMC model (case 2).

Figure 26

Prediction results of rolling bearing degradation stages based on GB model (case 2).

Figure 27

Prediction results of rolling bearing degradation stages based on AR method (case 2).

Figure 28

Schematic of the bearing test rig.

Figure 29

Time domain wave of the vibration signal (case 3).

Figure 30

The HGE, HFE and HSE of rolling bearing vibration signal (case 3).

Figure 31

The HGE and kurtosis of rolling bearing vibration signal (case 3).

Figure 32

Large sample sequence of the degradation stages (case 3).

Figure 32

Large sample sequence of the degradation stages (case 3).

Figure 33

Histogram of large sample sequences of degradation stages (case 3).

Figure 33

Histogram of large sample sequences of degradation stages (case 3).

Figure 34

Prediction results and dynamic evaluation of rolling bearing degradation stages based on GBMC model (case 3).

Figure 35

Prediction results of rolling bearing degradation stages based on GB model (case 3).

Figure 36

Prediction results of rolling bearing degradation stages based on AR method (case 3).