## 3 Signal Processing Techniques Applied to Wind Turbine Failure Detection
\[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]6  
\[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]7  
As described in reference [76], although the relevant techniques generally deal with the detection of a fault, in induction motors, it is most likely to find the presence of several faults, and for its detection, a high-resolution model is proposed that combines a bank of infinite impulse responses and MUSIC. According to the authors, this method is capable of detecting broken bars, imbalance, and defects in the outer bearing race. Another approach that MUSIC uses is described in reference [77]. Although signal sampling is generally performed during machine operation and in some approaches during startup, in that work, signal sampling is performed when the machine is disconnected from the network since, according to reference [75], as the terminal voltage is produced by the rotor currents, the presence of broken bars is reflected in the spectrum of the stator voltage. On the other hand, according to reference [78], the disadvantage of MUSIC is that by increasing the correlation matrix to find more frequencies, the required computational effort increases. To overcome this drawback, that work proposes applying an algorithm similar to the zoom-FFT (ZFFT) method that focuses on certain frequencies regardless of the total frequency range while applying zoom-MUSIC (ZMUSIC). According to the authors, very good results are obtained with the proposed method, comparable to those obtained with ZFFT but requiring less sampling time and less memory capacity. Other models used for HOS fault monitoring and detection include estimation of signal parameter via rotational invariance technique (ESPRIT) and PRONY. ESPRIT belongs to the subspace parametric spectrum estimation methods expressed by Equations (52) and (53) [79], whereas according to reference [80], the PRONY method is used to model the sampled data of a signal using a linear system of complex exponential functions. As described in reference [81], the extensive use of the power converter when the DFIG works below the synchronous speed causes the current to have a high content of interharmonics that can cause resonance, in addition to damage to capacitors, insulation, control elements, and protection. According to the authors, the identification of these harmonics can be performed using the PRONY and ESPRIT methods, although the latter has a lower resolution than the former. According to reference [82], to overcome spectral leakage, high-resolution analysis should be applied, but since this implies a longer sampling time, the spectrum varies both in frequency and in amplitude, making diagnosis difficult. From this, it can be deduced that there are no stable conditions that are required to apply the FFT and that its use does not guarantee the identification of the frequency components. The DWT allows for better spectral resolution. However, in general, the proposed signal techniques are not efficient at low slips, such as 1%. Based on the foregoing, reference [82] proposed using ESPRIT in combination with an improved Hilbert's modulus method, which was successful in detecting broken bars even with a slip as small as 0.33%, using only the one-phase signal and short sampling time. When the same experiments were performed using MUSIC, satisfactory results were not obtained, demonstrating the superiority of ESPRIT. Another technique that has been widely used to diagnose faults in electrical machines is [PERSON]'s vectors. According to [PERSON]'s theorem, a triphasic system can be represented as the sum of the components as a zero or homopolar, positive sequence and negative sequence, as expressed in Equation (49) [83]. For three-phase induction motors, the three phases can be represented in the 2D \(dq\) plane with Equations (3) and (4), known as Park vectors or Concordia patterns.