## 2 Method
### Bearing Failure Cases  
From three bearing failure cases, datasets of stored vibration measurements from the condition monitoring system databases were extracted covering different frequency ranges and measurement lengths. These datasets were processed with the enveloping technique where bandpass filtering and rectifying extracts the repetition frequency of impact resonances yielding an early detection of the defect in a bearing [25], and fast Fourier transform (FFT). Thereafter, condition indicator (CI) values for each failing bearing was constructed by a summation of three characteristic bearing defect frequency harmonics, and the failure progression could be analysed. The characteristic bearing defect frequency is calculated by multiplying the bearing shaft rotational speed and a relation between the bearing dimensions [26]. As it was on the inner ring of the bearings which experienced the defects, the ball pass frequency of the outer inner ring (BPFI) was used. This is calculated as:  
\[BPFI=\frac{fn_{i}}{2}\bigg{(}1+\frac{D}{d_{m}}\cos{(\alpha)}\bigg{)} \tag{1}\]  
where \(f\) is the relative rotational frequency between the raceways, \(n_{i}\) number of rolling elements, \(D\) rolling element diameter, \(d_{m}\) pitch diameter, and \(\alpha\) is the contact angle. Additionally, as the defects are mounted on rotating components, shaft speed sidebands will appear on each side of the BPFI harmonics. Three harmonics of the shaft speed sidebands on each BPFI harmonic were also used when calculating the CI-values, as:  
\[CI_{n}=\sqrt{\sum_{i=1}^{k=3}\sum_{j=1}^{l=3}p_{i,j}^{2}}. \tag{2}\]  
Here, \(p_{i,j}\) is the specific peak acceleration amplitude level of \(k=3\) fault frequency harmonics and \(l=3\) shaft speed sideband harmonics where these theoretically should exist. An alternative method to convert the enveloped vibration measurements into the frequency domain which has previously shown to yield a higher CI-value increase, and in some cases at an earlier stage, is the wavelet packet transform (WPT). More information into this implementation and how it compares to the FFT, which is the standardized method in wind turbine drivetrain bearing monitoring to convert the enveloped measurements into the frequency domain, can be found in a previous study by the authors [27]. CI-values can therefore be calculated from two different spectra per measurement and trended over time. Henceforth, to differentiate between the two sets of CI-values these are denominated enveloped WPT and enveloped FFT CI-values. The three bearing failure cases consists of two gearbox output shaft bearing failures, cases 1 and 3, and one planet bearing failure, case 2. For all cases, defects appeared on the inner raceways. Note: case 1 is partially reproduced results from [27]. The relevant failure case information is compiled in Table 1. The specific envelope filters were determined to replicate the set filters in the vibration measurement systems mounted in the wind turbine drivetrains, as was the case in the authors previous study [27]. Comparative results between the enveloped FFT and the enveloped WPT CI-values for failure cases 1 and 2 can be seen in Figure 2a,b respectively with the enveloped FFT CI-values in blue and enveloped WPT CI-values in black trended over measurement number in the dataset as a parameter of time. For the gearbox output shaft bearing failure in case 1 show an increase of the normalized, by z-score using the first 20 measurements as a healthy reference, CI-values as the defect has appeared. The enveloped WPT CI-value results can both yield a higher as well as an earlier increase, which is important for the monitoring to be as sensitive as possible. For the planet bearing failure in case 2 however, no apparent increase of the CI-values can be seen. A small difference can be seen in the last 200 measurements where the spread has decreased.