**2. Materials and Methods**

## *2.1. Methodology*

The application of machine learning regression methods to predict the dynamics of a rolling bearing cage requires data representing the correlation between the varied parameters and the calculated cage dynamics. The starting point was the multi-body simulation model defined in the software Caba3D [22,23]. The calculation parameters of the model such as initial and boundary conditions, friction models, and elastic modeling of the cage are described in Section 2.2. The geometry of the cage as well as the bearing load and rotational speed were modified with the help of a comprehensive simulation plan using the design of experiment, see Section 2.3. A Latin hypercube sampling was used to ensure that the varied parameters are distributed uniformly in the entire mathematical space defined by previously specified boundaries [24]. The limits of the simulation plan were chosen so that the operating conditions prevailing in reality are mainly covered. On the basis of the uniformly distributed parameter values in the simulation plan, the correlations between the parameters can be efficiently learned by the algorithm. After performing the calculations, the simulation results were used to determine the input and output parameters and thus the data sets for machine learning, see Section 2.4. Characteristic values such as the Cage Dynamics Indicator (CDI) defined by Schwarz et al. [21] were derived from the calculated time series, which can be used for the assessment of the cage dynamics and as target values for machine learning. Artificial neural networks (ANN) [25], random forest (RF) [26], and XGBoost [27] were applied to predict the target variables based on the varied calculation parameters, see Section 2.5. The optimization of the hyperparameters of the used algorithms was performed as part of the training process using an evolutionary algorithm (EA) [28]. Finally, the predictions of the optimized models for test data sets were compared so that the most suitable algorithm could be selected. Figure 1 illustrates the procedure for generating a regression model for the prediction of characteristic values representing cage dynamics.

**Figure 1.** Procedure in this study, starting with the dynamics simulation and the design of experiments, followed by the creation of a database, the training of the machine learning models, and analysis of the predictions.
