## 3 Signal Processing Techniques Applied to Wind Turbine Failure Detection
Furthermore, since the transient state of the induction motor can offer very useful information for the detection of electromechanical faults, such as the dynamic eccentricity, the signal is sampled during startup. The detection of failures of loads coupled to the induction machine using the MCSA has also been extensively studied, such as in reference [65], where this methodology is used to detect gearbox failures caused by broken gears or broken teeth. The use of GCSA for this purpose in WTs has not received the same attention, especially in regard to studies based on real data. In the time-frequency analysis, both variables are dependent, and according to the Heisenberg uncertainty principle, it is not possible to know exact values but only intervals [66]. The autocorrelation and power spectrum function does not provide all the necessary information, such as phase coupling or bicoherence, whereas the STFT has the drawback of temporal resolution. For this reason, in the case of non-Gaussian and nonlinear signals and signals whose spectrum is made up of a large number of frequencies, SA must be implemented using high-resolution or higher-order-spectrum (HOS) techniques [67]. Among these techniques is an approach using the bispectrum, which, being a complex number, consists of magnitude and phase. The bispectrum can be used to analyze the relationship between the frequencies of two sinusoids and the result obtained due to the modulation between them. For each set of three frequencies, the signal power and phase are calculated; if the phase shift between the two sinusoids tends to zero, then both have the same origin. Otherwise, the phase shift provides an indication of failure [68]. According to reference [69], given a signal \(X(K)\), its second-order statistical characterization can be represented by the autocorrelation and power spectrum function. For the same signal, with zero mean, its third-order moment is given by (44). If the signal is not stationary, Equation (44) depends on three parameters (\(k\), \(\tau_{1}\), \(\tau_{2}\)), while for stationary signals, the function contains only \(\tau_{1}\) and \(\tau_{2}\). The FT of the second-order momentum is the power spectrum that we have seen previously, while the bispectrum is the double FT of the third-order momentum and is defined by Equation (45). The degree of coupling between frequencies of different phases is measured by the bicoherence index, Equation (46), whose magnitude varies from zero to one. The greater the value, the greater is the coupling [70]. According to reference [26], the bispectrum technique allows us to represent the FFT of both the phase and the amplitude of the signal. Since the magnitude of the dominant component is a function of the level of the fault, when this technique is applied to the current of induction motors, the spectrum of the current signal allows the detection of electrical faults. The theoretical and mathematical foundations of HOSs are addressed in reference [71; 72; 73; 74; 75]. \[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]3  
\[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]4  
\[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]5  
Other HOS techniques used are frequency estimators based on eigen analysis. This methodology divides the RM autocorrelation matrix into two vector subspaces, one representing the signal and another representing noise, as shown in Equation (47). The order of the matrix and its eigenvalues are given by (48). Among the frequency estimators developed based on this methodology, multiple signal classification (MUSIC) and root MUSIC can be mentioned, which, as addressed in [76], are high-resolution models that allow for the detection of frequencies in signals with low signal-to-noise ratios.