## 2 IMS Bearing Dataset and Signal Analysis Techniques  
### Description of IMS Dataset 1  
As already mentioned, the signals that will be analyzed come from an open-access dataset released in 2014 by the NASA Center for Intelligent Maintenance Systems (IMS) [33]; the focus is on the results of the first of three run-to-failure experimental campaigns carried out at the University of Cincinnati, OH, USA, with support from Rexnord Corp., Milwaukee, MI, USA. The test rig included four rolling bearings installed on a common shaft, set in rotation at a constant speed of 2000 RPM by an AC motor coupled to the shaft via rub belts (Figure 1). The four double row bearings were of type Rexnord ZA-2115, force-lubricated by a circulation system that regulated the flow and the temperature and charged with a 26,690 N (6000 lbs) constant radial load applied by a spring mechanism. Eight PCB 353B33 High-Sensitivity Quartz ICP accelerometers were installed on the bearing housing (two sensors for each bearing, mounted orthogonally along the \(x\) and \(y\) axes), and the sampling frequency was set to 20,480 Hz. The dataset consists of individual files that are 1 s vibration signal snapshots recorded at specific intervals, every 5 (for the first 54 acquisitions) or 10 min, but it is sometimes subjected to a series of interruptions that make the time history not continuous (Figure 2). The experiment was stopped conventionally when the accumulation of debris on a magnetic plug exceeded a certain level, indicating the possibility of an impending failure. The resulting endurance duration was equal to 49,680 min (i.e., 34 days and 12 h), exceeding the bearing designed lifetime, which was more than 100 million revolutions. The most relevant experimental set-up characteristics and findings of IMS dataset 1 are reported in Table 1. It should be stressed that this dataset is particularly valuable because the bearing degradation was left to evolve naturally and was not artificially induced, as may often happen to speed up the experimental test. Figure 1: IMS test rig layout (from [13]). Figure 2: Raw signal and its actual time history for IMS dataset 1 (from [13]). Vibrational data collection was conducted with the National Instruments LabVIEW program thanks to a NI DAQ Card-6062E data acquisition, and the analysis that will be presented in this paper was developed with the software platform MATLAB 2021b by The MathWorks [34]. Considering the rolling bearing mechanical characteristics and working conditions of Table 2, it is possible to compute the value of the characteristic frequencies of the faults they are typically subjected to during their operating life, i.e., the fault signatures, by using the following formulas [1]:  
\[\text{BPFO}=\frac{nf_{r}}{2}\bigg{(}1-\frac{d}{D}\cos\phi\bigg{)} \tag{1}\]  
\[\text{BPFI}=\frac{nf_{r}}{2}\bigg{(}1+\frac{d}{D}\cos\phi\bigg{)} \tag{2}\]  
\[\text{FTF}=\frac{f_{r}}{2}\bigg{(}1-\frac{d}{D}\cos\phi\bigg{)} \tag{3}\]  
\[\text{BSF}=\frac{f_{r}D}{2d}\bigg{[}1-\bigg{(}\frac{d}{D}\cos\phi\bigg{)}^{2} \bigg{]} \tag{4}\]  
where:  
* BPFO (_BallPass Frequency_, _Outer Race_) is the frequency representing the fault signature on the outer race;
* BPFI (_BallPass Frequency_, _Inner Race_) is the frequency representing the fault signature on the inner race;
* FTF (_Fundamental Train Frequency_) is the frequency representing the fault signature on the bearing cage;
* BSF (_Ball Spin Frequency_) is the frequency representing the fault signature on the rolling element. See the rolling element bearing of Figure 3.