# An Application of Instantaneous Spectral Entropy for the Condition Monitoring of Wind Turbines
## 4 The Experimental Case Study  
The experimental recordings from a wind turbine have been used for the validation of the proposed entropy-based Condition Monitoring strategy. The dataset (describedin detail in [52]) originates from an undisclosed onshore wind farm, located in Northern Sweden and consisting of 18 2.5 MW Nordex N100 wind turbines [53]. The continuous monitoring was performed over 46 consecutive months, acquiring 1.28 s-long time series (16,384 data points for a sampling frequency \(f_{s}=12,800\)) approximately every 12 h.  
Specifically, Turbine #5 was considered here, as the only one (out of six installations included in the dataset) that suffered mechanical faults during the monitored timeframe. The vibration time series of interest were collected from an accelerometer, located and oriented as indicated by the black arrow in Figure 1 (which is based on the original schematics from [52]). This was mounted on the housing of the output shaft bearing of the turbine. The three-stage gearbox was made up of two sequential planetary gear stages, followed by a helical gear stage. The position of the bearing failure is highlighted in red in Figure 1. The damage consisted of an inner raceway failure on one of the four NSK RN2240 cylindrical roller bearings (CRBs) supporting one of the planets in the first planetary gear. From visual inspection after disassembly (refer to [52; 53]), the most probable cause was identified as rolling fatigue-induced flaking (according to the NSK definition [54]), with a loss of material and the consequent rough and coarse texture extended over most of the contact surface. This caused the entire gearbox to be replaced after two years of operation. Two signals of interest (portrayed in Figure 2) were defined by concatenating in chronological order some consecutive time histories (THs), recorded from Turbine #5 as described in Table 1 (the period column in Table 1 reports the time since the beginning of the continuous monitoring as year fractions). The concatenating procedure applied here reflects what was performed by [PERSON] et al. [55], to artificially generate a nonstationary experimental benchmark from stationary experimental recordings, emulating time-varying structural conditions with abrupt changes. For signal #1, three segments were considered. These correspond to one recording (the first one) shortly before replacement and two acquisitions (the remaining two thirds) shortly after. These latter two were chosen since they are consecutive recordings with very similar rotational speeds (i.e., very similar external input; reported as cycles per minute). Signal #1 was intended to study the effectiveness of the algorithm, presenting a discussion on parameter setting. For Machine Learning purposes, only the first tract was used as training data for the statistical modelling of the normal operating conditions (NOCs). The second and third parts of the signal provided the test points for the damage index. Figure 1: Schematics of the three-stage gearbox, with the damaged bearing highlighted in red and the position and direction of the output channels indicated by the black arrow. For signal #2, a larger set of acquisitions were included. In this latter case, by considering only the optimised algorithm parameters, the intent was to address the full capabilities of the proposed approach when trained on more than one tract. Thus, signal #2 was evaluated on data with (almost) comparable rotational speeds before and after bearing damage. Specifically, the following segments were used:  
1. seven consecutive tracts corresponding to 14 months before fault (the first five elements for training and the last two for validation),
2. the single tract already included in signal #1 plus five other nearby tracts immediately before fault (all included for further validation),
3. three recordings taken immediately after replacement, including the two already considered in signal #1 (all considered for testing),
4. other five segments acquired 7 months later (considered again for further testing).