# An Application of Instantaneous Spectral Entropy for the Condition Monitoring of Wind Turbines
## 4 The Experimental Case Study
The second part of Table 1 reports more details about these THs. For both signal #1 and #2, the data, originally reported in terms of \([g]\), were standardised (subtracting the mean and dividing by the standard deviation, for each recording separately) to remove any potential issue related to the different amplitudes. Figure 3 reports the Fast Fourier Transforms (FFT) of the five sets included in signal #2. One can notice that the multiple harmonic components of each acquisition do not allow for a simple comparison between the frequency content before and after the gearbox replacement. Thus, the common damage detection strategy based on the analysis of the frequency shift is hardly feasible in these circumstances. The same can be said for signal #1 as well since it comprises a subset of the segments of signal #2. Indeed, the limited reliability of FFT-based signal analysis for these typologies of bearing failure in wind turbine gearboxes was reported as well in [53]. Figure 2: The investigated signals: (**a**) #1, (**b**) #2. Data standardised as \(z(t)=(h(t)-\mu(h(t)))/\sigma(h(t))\). In (**a**), the dot-dashed vertical lines represent the three concatenated segments. In (**b**), the thick dot-dashed vertical lines enclose the segments considered for the training set, the two validation sets, and the two test sets, in this order (see Table 1). The single segments are separated by thin vertical lines. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Signal \#1**} \\ \hline ID & Period of & & & \\ number & recording & [years] & Rotational speed & Structural & Set \\  & [years] & [cpm] & conditions & \\ \hline
1588 & 1.9972 & 785.45 & Immediately & \\
1593 & 2.0040 & 783.61 & Immediately & \\  & & post-replacement & & \\
1594 & 2.0054 & 783.18 & Immediately & \\  & & post-replacement & & \\ \hline \multicolumn{4}{c}{**Signal \#2**} \\ \hline ID & Period of & & & \\ number & recording & [cpm] & & \\  & [years] & [cpm] & conditions & \\ \hline
785 & 0.7936 & 777.79 & More than one year & \\  & & & pre-replacement & \\
786 & 0.7988 & 714.90 & \(>\)1 year & \\  & & & pre-replacement & \\
787 & 0.7989 & 779.824 & \(>\)1 year & \\  & & & pre-replacement & \\
788 & 0.8080 & 708.74 & \(>\)1 year & \\  & & & pre-replacement & \\
789 & 0.8205 & 711.63 & \(>\)1 year & \\  & & & pre-replacement & \\
790 & 0.8208 & 785.33 & \(>\)1 year & \\  & & & pre-replacement & \\
791 & 0.8217 & 774.61 & \(>\)1 year & \\
1485 & 1.8480 & 768.34 & Immediately & \\  & & & pre-replacement & Validation \#2 \\
1486 & 1.8493 & 733.26 & Immediately & \\  & & & pre-replacement & \\
1487 & 1.8507 & 772.99 & Immediately & \\  & & & pre-replacement & \\
1488 & 1.8521 & 832.43 & \(>\)1 year & \\
1489 & 1.8537 & 706.29 & Immediately & \\  & & & pre-replacement & \\
1588 2 & 1.9972 & 785.45 & Immediately & Validation \#2 \\  & & & pre-replacement & \\
1593 3 & 2.0040 & 783.61 & \(>\)1 year & \\  & & & post-replacement & \\
1594 3 & 2.0054 & 783.18 & Immediately & \\  & & & post-replacement & \\
1595 & 2.0076 & 744.07 & Immediately & \\  & & & post-replacement & \\
2021 & 2.5995 & 786.29 & \(>\)1 year & \\  & & & post-replacement & \\
2022 & 2.6009 & 777.30 & \(>\)1 year & \\  & & & post-replacement & \\
2023 & 2.6023 & 772.13 & \(>\)1 year & \\  & & & post-replacement & \\
2024 & 2.6036 & 757.19 & \(>\)1 year & \\  & & & post-replacement & \\
2025 & 2.6050 & 836.38 & \(>\)1 year & \\  & & & post-replacement & \\ \hline \hline \end{tabular} \({}^{1}\) [[http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dkswidt=-2411](http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dkswidt=-2411)]([http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dkswidt=-2411](http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1244889&dkswidt=-2411)) (accessed on 24 June 2021).  
\({}^{2}\) Already included in signal #1 for training. \({}^{3}\) Already included in signal #1 for testing.  
\end{table} 
Table 1: The concatenated recordings, as reported in the experimental database \({}^{1}\).