## 1 Introduction  
Induction motor (IM) is one of the most popular pieces of mechanical equipment and plays an important part in industrial applications. However, the harsh operation environment and gradual wearing make it be liable to failure. Broken rotor bar (BRB) in IMs represents 8-9% of IM faults but they bring serious breakdown and lead to loss of productivity [1]. This needs to be solved, otherwise it can cause multiple BRB faults, mechanical eccentricity, and thermal stress because of localized heating. The detection of this type of fault has been a key issue of studies which aims to develop more advanced techniques to minimize the breakdown and maintenance cost of IMs. Several sensing techniques have been researched in the field of BRB fault diagnosis. For example, motor current signature analysis (MCSA) [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] is the mainstream technique, and the motor vibration signature analysis (MVSA) [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32] technique is commonly used for diagnosing the presence of BRB failures. However, the sound measurement [32], temperature measurement [33], and magnetic field analysis [34] have been used less due to the inference of external factors. Among them, vibration signature analysis has become an effective tool in the field of condition monitoring and fault diagnosis of rotating machinery [35]. Also, the vibration signature of the motor under different loads is easy to measure and can provide rich dynamic information reflecting BRB health status. Some authors proposed that vibration signal can be the fault symptom as well as electric signal [36; 37]. Like other rotating machinery, the vibration signals of IMs with BRB faults generally include modulation components that are the culprit of BRB failures and have close connection with fault diagnosis. This type of modulation signal is non-stationary, thus useful methods need to effectively extract the modulation components reflecting the BRB faults. In recent years, many advanced techniques for BRB fault detection in IMs have been developed based on the vibration signature analysis and obtained good diagnostic results. For instance, the authors proposed an approach based on the use of frequency sliding and wavelet (WT) analysis to isolate the contribution of the BRB fault characteristics issued from vibration signals [25]. [PERSON] et al. [27] presented the analysis of BRB faults in a three-phase squirrel cage IM using an artificial intelligence method. [PERSON] et al. [28] applied the sparse representation methodology to the detection of BRB fault based on the vibration signals from IMs. Also, [PERSON], et al. [29] presented the development of analytical equations for vibration detection under successive broken bars and showed the relation between the number of broken bars and the vibration amplitudes. In addition, the orthogonal matching pursuit algorithm (OMP) in [30] was used for the decomposition of signals, which demonstrated that the detection accuracy is higher. Also, researchers in [31] developed a technique based on the vibration magnitudes of electromagnetic force for the rotor bar breakages detection in a squirrel-cage IM. Furthermore, [PERSON] et al. [32] used the complete ensemble empirical mode decomposition (CEEMD) for the fault diagnosis of BRB faults based on vibration analysis, which solved the drawback of ensemble empirical mode decomposition (EEMD) and the empirical mode decomposition (EMD) in signal processing. The above vibration detection methods are based on the non-stationary level for the BRB fault diagnosis. Meanwhile, cyclostationary analysis has been proven to be effective for the analysis of second order cyclostationary (CS2) signals based on cyclostationary level. Cyclostationary analysis is a kind of special \"time-frequency\" demodulation tool, where the time axis represents the cyclic or modulation frequency domain, and the frequency axis denotes the carrier frequency domain.