# A Survey on Fault Diagnosis of Rolling Bearings
## 4 Rolling Bearing Fault Type Recognition
### Traditional Fault Type Recognition Methods  
Traditional rolling bearing fault type recognition methods usually include three steps: feature extraction, feature reduction, and classification. (1) Feature extraction  
Extracting fault-related features from vibration signals is the first step to perform rolling bearing fault type recognition. It is necessary to map the original bearing signals to statistical features to reflect the health status of bearings. Early work on feature extraction of rolling bearing vibration signals mainly focused on calculating various types of time-domain or frequency-domain statistical descriptive indexes [94; 95], such as root mean square, kurtosis, skewness, average frequency, and root mean square frequency. These indexes are easy to calculate and intuitive to understand; their values vary with the running state of the rolling bearing. Complexity can describe the dynamic characteristics of bearing signals under different running conditions. More and more attention is paid to applying various complexity evaluation indexes to fault type recognition. [PERSON] et al. [96] used fractal dimension (FD) to evaluate bearing signals, but the calculation speed of FD is slow, which limits its use in online diagnosis. [PERSON] et al. [97] calculated the Lyapunov exponent of bearing vibration signal as a feature, but its stability is vulnerable to noise interference. The entropy of a time series is an index commonly used to quantify the degree of uncertainty or irregularity. Approximate entropy (AE), sample entropy (SE), fuzzy entropy (FE), permutation entropy (PE), and dispersion entropy (DE) were applied to fault type identification [98; 99; 100; 101; 102]. AE has good anti-noise performance when analyzing signals with more data points, but it may cause inaccurate estimation when analyzing signals with fewer data points [103; 104]. As an improved form of AE, SE has the advantage of low dependence on the signal length and improved immunity to interference from noise. The disadvantage of SE is that its computation cost is high, and it may not be appropriate for analyzing signals containing similar information [103]. Based on SE, FE introduced a fuzzy membership function and was capable of assessing signal uncertainty more effectively [105]. PE offers simplicity, high robustness to dynamic noise, and a fast calculation speed and can effectively analyze non-stationary signals with complex components [106]. [PERSON] and [PERSON] [107] developed  
Figure 5: Summary of rolling bearing fault type recognition methods. DE and proved that it was reliable in quantifying the complexity and uncertainty of time signals through the comparative test of various time series. The computational efficiency of DE is significantly better than that of SE, FE, and PE. Instantaneous energy distribution (IED) of bearing vibration signals can describe the time-varying process between fault states. Based on these characteristics, instantaneous energy distribution permutation entropy (IED-PE) [108] and instantaneous energy distribution permutation dispersion entropy (IED-DE) [109] were developed to enhance the accuracy of identifying fault types. As performing the single-scale analysis of bearing vibration signals with complexity and uncertainty may lead to loss of information, multiscale analysis is introduced to entropy calculation to more accurately evaluate the vibration signals [110; 111; 112; 113; 114; 115]. [PERSON] et al. [110] and [PERSON] et al. [113] used the coarsening method to calculate the entropy of signals on multiple scales and proposed multi-scale sample entropy (MSE) and multi-scale permutation entropy (MPE), respectively. MSE and MPE investigate the irregularity of bearing vibration signals from multiple scales and have made significant progress toward fault diagnosis. In addition, when MSE and MPE are used to analyze signals with fewer data points, their calculation values will fluctuate with the increase in the scale factor, potentially leading to evaluation results instability. [PERSON] et al.