*2.5. RUL Prediction*

To infer the predicted remaining useful life RULpred based on the predictions of the label within the regression, the following equation is used:

$$\text{RUL}\_{\text{pred}} = \frac{t}{y\_{\text{pred}}} \cdot \left(1 - y\_{\text{pred}}\right) \tag{1}$$

Here, *t* is the current operating time and *y*pred is the label predicted at the corresponding time. The described mathematical relationship results from the background of the selected label, which corresponds to the normalized test-run time. At the beginning of the measurement, where the predicted label *y*pred is close to zero, RUL prediction is not practical due to large inaccuracies, which can be directly justified by Equation (1). Dividing by small *y*pred then leads to very large fluctuations in the RUL prediction, caused by only slight variations in the predicted label. For this reason, RUL prediction is evaluated exclusively for the second half of the test runs. The result evaluation by means of the RUL-based MAE is also performed exclusively on the second half of the test runs.

In order to compare the predicted with the true remaining useful life RULtrue, the latter must also be calculated. This is performed using the total operating time until bearing failure *T* and the true label at the respective time *y*true:

$$\text{RUL}\_{\text{true}} = T \cdot (1 - y\_{\text{true}}) \tag{2}$$
