# Bearing Health Monitoring Using Relief-F-Based Feature Relevance Analysis and HMM
## 3 Experimental Setup  
### Database and Preprocessing  
To test the proposed SFS approach, a publicly available bearing data collected by the Case Western Reserve University (K.A. Loparo, Bearing data center. Case Western Reserve University (2003)) (CWRU) is utilized in this paper. The experimental setup mainly included a three-phase induction  
Figure 1: Sketch of the proposed bearing fault diagnosis from vibration signals. Time, frequency, and time-frequency features are computed under a windowing scheme from vibration signals. Then, our Stochastic Feature Selection (SFS) applies a relief-F-based ranking, and a Hidden Markov Model to highlight relevant features and predict the signal label (bearing health condition).  
motor, a torque transducer/encoder, a dynamometer, and electronic control. SKF bearings under different states were attached to the motor shaft. Two accelerometers were attached to the housing with magnetic bases in both drive and fan end. The faults ranged in diameter and were seeded on the drive- and fan-end bearings (SKF deep groove ball bearings: 6205-2 RS JEM and 6203-2 RS JEM, respectively) of the motor using electro-discharge machining. The faults were seeded on the rolling elements and the inner and outer races, and each faulty bearing was reinstalled (separately) on the test rig. Further, it was run at a constant speed for motor loads of 0 to 3 horse-power. The database was acquired from the experimental test bench under the following bearing states: Normal, a fault in the inner race, a fault in the outer race, and a fault in rolling element (electro-discharge machining artificially produced fault states). Additionally, the failure states were produced with three levels of severity (0.007\({}^{\prime\prime}\), 0.014\({}^{\prime\prime}\), and 0.021\({}^{\prime\prime}\)) and three operation revolutions (1730, 1750, and 1797 [rpm]). As a consequence, 56 signals of 10 seconds (approximately) were acquired [63]. Although the CWRU provides vibration signals collected with a 16 channel DAT recorder using two different sample rate values (12 kHz and 48 kHz), we only considered the signals acquired with \(F_{\text{s}}=48\) kHz to cover the whole harmonic patterns of the bearing states following the recommendations in [64].  
Each vibration signal was pre-segmented using a rectangular window of 85.33 ms length (without overlapping); This value was selected following the [PERSON] et al. methodology in [65]. Therefore, an input matrix holding \(N=5610\) samples is calculated. Two different diagnosis/detection scenarios were considered for bearing condition monitoring by varying the label vector: (i) four-class problem (\(C=4\)), learning only the bearing state; and (ii) ten-class problem (\(C=10\)), which includes state diagnosis and fault severity detection, as shown in Table 3. To adjust the data set according to the methodology proposed, each signal is segmented using a Hamming window of 21.33 ms size and 50% overlapping. These values were chosen according to the approach presented by authors in [54,66]. As a consequence, \(W=7\) windows of analysis are studied.