# A Survey on Fault Diagnosis of Rolling Bearings
## 3 Rolling Bearing Fault Detection
### Decomposition-Based Fault Detection Methods  
The decomposition-based detection method involves decomposing the raw vibration signal into several components, such as the fault-related pulse, the noise, and the harmonic interference. Analyzing only the fault-related pulses can simplify the process of detecting the fault. In 1998, [PERSON] et al. [56; 57] proposed the empirical mode decomposition (EMD) method, which provides a new idea for analyzing non-stationary signals. [PERSON] [58] utilized EMD to decompose a bearing vibration signal into a series of eigenmode components with inherent oscillation attributes and then conducted envelope spectral analysis to realize bearing fault detection. The EMD method achieved promising performance, but it also hasa number of deficiencies, such as end effect, modal aliasing, and over/under envelope, that limit its applications. [PERSON] et al. (2019) proposed ensemble empirical mode decomposition (EEMD), where Gaussian white noise is introduced in EMD to assist signal decomposition. [PERSON] et al. (2018) used EEMD to analyze bearing signals and extract bearing fault features effectively. Even though EEMD can overcome the mode aliasing problem to some degree, it still suffers from problems, such as low decomposition efficiency and the inability to determine white noise amplitude adaptively. [PERSON] et al. (2019) proposed complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), where Gaussian white noise is adaptively added to each stage of the decomposition process. CEEMDAN can improve computing efficiency and reduce construction errors and was successfully applied to detect rolling bearing faults ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). In 2005, [PERSON] et al. (2005) proposed the local mean decomposition (LMD), which gradually decomposes a non-stationary signal into a linear combination composed of multiple product function components through the moving average method. In essence, LMD is to separate the pure FM signal and envelope signal from the original signal and multiply the pure FM signal and envelope signal to obtain the product function component with instantaneous frequency and physical significance. LMD shows good performance for bearing fault detection, i.e., can avoid some over/under envelopes and has better signal local characteristics and fewer decomposition components than EMD ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). However, the LMD method can encounter several problems in practical application, such as signal mutation, modal aliasing, and computational inefficiency ([PERSON] et al., 2019). In 2007, [PERSON] et al. (2019) proposed the intrinsic time scale decomposition (ITD), which can obtain the baseline signal by linear transformation and can adaptively decompose a complex vibration signal into a combination of several proper rotation components (PRCs) and a residual. ITD for bearing fault diagnosis displays significant advantages in end effect, envelope error, and calculation speed over EMD. However, the components decomposed by ITD produce burrs, resulting in distortion of the instantaneous amplitude and frequency ([PERSON] et al., 2019; [PERSON] et al., 2020). Local characteristic-scale decomposition (LCD) was proposed by [PERSON] et al. (2017); [PERSON] et al. (2017) in 2012, which simultaneously considers the position information of non-stationary signals in the time domain and the frequency domain, avoiding the frequency confusion of EMD and the signal mutation of ITD ([PERSON] et al., 2020). Although LCD overcomes the shortcomings of EMD and ITD, there are still some drawbacks, such as the end effect, which often affect the processing results ([PERSON] et al., 2020). All the EMD, LMD, ITD, and LCD methods adopt the idea of recursive decomposition, which shares several similar defects.