## 2 Materials and Methods
### Description of Data Evaluation  
The damage detection procedure includes three steps. First, the raw data is processed; the output serves as a basis for a subsequent feature generation that is finally assessed to evaluate the gear condition. Figure 4 depicts this process. The initial preprocessing stage entails the implementation of low-pass filtering, which is accomplished through the utilization of a Butterworth filter, characterized by a cut-off frequency of 6 kHz. This procedure is employed to attenuate high-frequency components, thereby ensuring that the subsequent processing stage is not influenced by these extraneous factors. The GMFs with higher orders and surrounding sidebands are damage-specific frequencies that are evaluated in the classification procedure. The first-order frequency is 700 Hz at the maximum speed of 2000 rpm. Therefore, 6 kHz is an appropriate cut-off frequency for the further processing of data. The subsequent preprocessing step entails ellipses fitting, a process that mitigates manufacturing and assembly deviations of the raw signal by compensating for the offset, phase, and amplitude to align with a sine wave [18]. The rotational angle is calculated via the atan2-function, which transforms the sine and cosine raw signals to a rotational angle [19]. The calculated rotational angle is then normalized to the rotational angle corresponding to one rotation of the gear wheel. The instantaneous angular speed (IAS) is calculated based on the rotational angle. Features are generated in the time and frequency domain as these have proven to be feasible for the condition monitoring of gear damages. The time domain features are calculated by first applying a time synchronous averaging (TSA) to the raw sensor signal and the IAS signal. Then, the statistical features of these two signals are calculated. The statistical features are classical features, i.e., the mean and standard deviation and so on, as well as gear-specific features, such as FM4 and FM0. Frequency features are calculated via an FFT of the raw and IAS signal, and gear-specific frequencies, such as the GMF and surrounding sidebands in the order domain, are extracted [20]. For the classification of the data, a random forest classifier is used. The random forest classifier has been shown to offer high accuracy and robustness by aggregating multiple decision trees. This process reduces the risk of overfitting and improves the classifier's ability to generalize to unseen data [21]. The _TreeBagger_ function in MATLAB R2023a was employed for classification with the random forest classifier. The classification process involved the generation of 100 trees, with a minimum of five leaves per tree. The hyperparameters were determined through an iterative process. As illustrated in Figure 5, the present publication delineates the various classifications. The seven damage classes are distributed over four pinions, with the first three classes being identical for all pinions. A total of 18 stationary operating conditions and 3 speed ramps were subjected to rigorous  
Figure 4: Data processing procedure. testing. Each test point is repeated twice, as previously outlined. The classification is performed with a five-fold cross validation and a split by repetitions. The classification is employed to evaluate the damage detection capabilities using the gear wheel sensor, as well as the transferability potential of the results. The features are calculated for one second of the signal, with an overlap of 90%, in order to increase the amount of data available for training and testing. The evaluation of classification capabilities is conducted in three stages. Initially, a five-fold cross-validation with an 80% training data and 20% test data split is employed as a reference for the classification process. Subsequently, a split according to the repetitions is implemented. In this manner, the classification algorithm is trained on the first repetition, and the classification accuracy is tested on the second repetition.