# A Method for Broken Rotor Bars Diagnosis Based on Sum-Of-Squares of Current Signals
## 1 Introduction  
Induction motors (IMs), which provide most of the power for the factory, are significant power components of industrial production equipment [1, 2]. The health condition of IMs not only affects the quality of products but also causes serious security threats to operators and equipment [3, 4, 5]. Broken rotor bar (BRB) is a typical fault mode of IMs. Its fault proportion is only lower than that of bearing faults and winding faults, accounting for 7% of the total fault types [6]. The fault diagnosis of BRBs plays a vital role in improving the reliability of induction motors. Broken rotor bars will cause periodic fluctuations in motor output torque, and the periodic fluctuations not only make the motor periodically vibrate but also change the motor current and magnetic field periodically. These results make it possible to diagnose the BRBs of IMs through different kinds of signals. The diagnosis methods based on vibration signals are popular in the fault diagnosis of rotating machinery, and they are also applied in the fault diagnosis of IMs. [PERSON] et al. [7] used cyclic modulation spectral analysis of the vibration signal to diagnose the broken rotor bars of the IMs. [PERSON] et al. [8] use improved cyclic modulation spectral analysis based on the continuous wavelet transform to process the vibration signal for BRB detection of IMs. [PERSON] et al. [9] extract the higher-order statistics of vibration signals for the diagnosis approach based on machine learning. [PERSON] et al. [10] improve the Hilbert-Huang transform for vibration signal processing to detectBRBs of IMs. Although the BRBs have an impact on the vibration signals of IMs, they have a greater impact on the magnetic and electrical signals of IMs [11]. [PERSON] et al. [12] use flux signals to detect BRBs of IMs. [PERSON] et al. [13] diagnose BRBs of IMs through air-gap rotational magnetic field signals. Although these methods have good effects, these kinds of detection methods are usually invasive. On the contrary, the current signals are widely used because of their convenient measurement and obvious fault signature. In fact, the number of studies using current signals for fault diagnosis of IMs is the largest. Motor current signature analysis (MCSA) methods are widely used in the fault diagnosis of IMs [14; 15; 16]. BRBs will stimulate the signature frequency components in the current signals. MCSA methods detect BRBs by extracting the signature frequency components of current signals [6]. The methods based on Fast Fourier Transform (FFT) of MCSA try to find the signature frequency components directly in the spectrum of the single-phase current signal [17; 18]. FFT-based methods are simple, but the signature frequency components often cannot be found due to the spectrum leakage of the fundamental frequency and the influence of the noise [17; 19]. To solve this problem, many popular MCSA methods extract the signature frequency components by removing the fundamental frequency component of the current signal. The Hilbert transform amplitude demodulation (HT) [20; 21; 22], [PERSON]' s vector modulus [23; 24; 25], d-q transform demodulation [1; 26], and Teager energy operator (TEO) [27; 28] are the most popular among these MCSA methods. HT can obtain the demodulation signal by extracting the envelope of the single-phase current signal using the Hilbert transform. The envelope reflects the torque ripple of the induction motor and is related to the BRBs. [PERSON]'s vector and d-q transform are essentially based on coordinate transformation. After coordinate transforming, new current vector signals are obtained which contain fault information and are less influenced by fundamental frequency and noise. The TEO method extracts the energy operator of the single-phase current signal which is modulated by BRBs. However, they all have complicated principles and high calculation costs, which are not conducive to understanding and online diagnosis of IMs.