*2.4. Machine Learning*

The goal of the machine learning is to approximate an unknown function, which maps the input features to the label. Since the label is defined in the form of a continuous variable, this is supervised learning in terms of a regression [26]. In the field of machine learning, there is a wide variety of regression algorithms [5]. A comprehensive overview of the available Deep Learning methods can be found in [27]. In [10], a random forest approach has already been used to detect the state of journal bearings. The aim of the present work is to show the influence of targeted feature engineering on RUL prediction performance. Therefore, traceability shall be as good as possible. For this reason, deep learning algorithms are not used here, instead, a random forest regressor is chosen. A random forest is an ensemble method based on decision trees [28]. It is considered to be very robust and to provide continuously good results compared to other regression algorithms.

In the workflow used here to investigate feature engineering, the machine learning algorithm is considered as a constant boundary condition. Therefore, the parameters of the random forest are kept fixed. Based on preliminary studies, the number of trees is set to 500, and the maximum tree depth is limited to 20. The models used in this work are implemented in Python using the numpy, pandas, scipy, and matplotlib libraries. Additionally, the library Scikit-learn is used for the implementation of the random forest and metrics for result evaluation.

To evaluate the models built with the different feature engineering methods, a 9-fold cross-validation is used. Out of the total nine endurance test runs available, eight endurance tests are used for training. The remaining test run is used for the test data set, which means that the test data is always completely separated from the training data. This is repeated a total of nine times so that the data from each test is used as independent test data once.

The quality of the prediction is evaluated using metrics. For this purpose, the MAE and the R2 are chosen. The MAE (Mean Absolute Error) provides a directly interpretable result of the regression quality in the context of the label used here. For example, an MAE of 0.05 means that the prediction of the current bearing condition is on average 5 % from the true value. Consequently, the MAE tends to 0 in case of a perfect model. In addition, the R2, which is called the coefficient of determination, provides a general measure of the

quality of a regression. It tends towards a maximum value of 1 for optimal predictions. The smaller the value, the worse the prediction [29]. For the overall evaluation in the results section below, the average value of the nine metrics calculated during cross-validation is considered. This ensures an evaluation of the model quality based on the entire data set.
