*2.1. Experiments*

The investigations are based on structure-borne sound measurement data, which is recorded on a rolling bearing test rig. The concept of the FE9 test rig used was originally designed for testing rolling bearing greases. An electric motor drives the test head shaft via a belt. On one side of the shaft, an ancillary bearing is mounted, which is provided with circulating oil lubrication. The grease-lubricated test bearing, the wear of which is to be examined, is located on the other side of the shaft. In order to accelerate grease aging and thus, its wear, the test bearing is heated. An axial load is applied with the aid of a spring preload. The test head of the FE9 test rig can be seen in Figure 2.

**Figure 2.** Test head of the FE9 test bench, adapted with permission from [22].

In the case of the tests evaluated in this work, the test bearings used are of type 6206- C-C3 (Schaeffler AG, Herzogenaurach, Germany) and lubricated with a low-temperature grease. The grease is used beyond the limits of its specification due to the applied thermal load, which is why the operating life is greatly reduced. A constant speed of 6000 rpm is present at the test head shaft. The axial load is 1500 N and the temperature of the heater on the test bearing is set to 140 ◦C. The sensor used is a three-axis piezo accelerometer of type PCB-356A15 (PCB Piezotronics, Depew, NY, USA). The sensor is mounted close to the test bearing, as shown in Figure 3.

**Figure 3.** Placement of the accelerometer on the test bench, adapted with permission from ref. [20].

For the investigations carried out here, only data from the sensor's *X*-axis, which is aligned radially to the bearing, is analyzed. The data is acquired at a sampling rate of 20 kHz. An imc CRONOSflex (imc Test & Measurement GmbH, Berlin, Germany) data acquisition system is used in the measuring chain with an 8th order Cauer LP anti-aliasing filter having a cut-off frequency of 8 kHz. The amplitude is resolved with 24 bits. The measurement data is recorded at intervals of 1 s with intervening pauses of 59 s. A total of nine endurance runs are investigated. A threshold value in the power consumption of the driving electric motor is defined as a termination criterion for the experiments. This leads to test run times ranging from 10 h to 20 h. At the end of the tests, the test bearings show very similar damage patterns in the form of pitting. Figure 4 shows an example of the inner ring of one bearing after endurance testing.

**Figure 4.** Pitting on a ball bearing inner ring after its test run, reprinted with permission from ref. [20].

## *2.2. Data and Labeling*

The aim of the procedure used here is to directly infer the bearings remaining useful life from the trained ML model. Therefore, a supervised learning approach in terms of a regression is used. The label must represent the progressive bearing damage. As already shown in [20], a label that linearly increases from 0 to 1 is used for this purpose. A similar labeling approach has also been presented in [23]. Figure 5 shows the label based on the structure-borne sound signals of a single test run. From a mathematical point of view, the label can be described as the normalized test run duration. The value 0 represents the original condition of the bearing, while 1 indicates the end of its useful life.

**Figure 5.** Measurement and assigned label for an exemplary test run.

#### *2.3. Feature Engineering*

A wide variety of feature-engineering methods have already been described in the literature [13,24]. The focus of the research conducted here is on the comparison of different feature-engineering methods that consider the temporal past in the context of feature generation. As a basis, the so-called averaged-frequency-band (afb) features are used, which have already been shown in [20] to be particularly performant and computationally efficient compared to the features proposed by Lei et al. [21]. The studies in [20] were based on the same data set also used for the present work. Starting from the afb features, additional features are now to be generated, which contain the information of the temporal past. The influence of these processed features on the RUL prediction is to be investigated.
