# Bearing Health Monitoring Using Relief-F-Based Feature Relevance Analysis and HMM
## 1 Introduction  
Due to the sector competitiveness, high demand for fuel, and increasing power consumption, the industry interests are mainly related to cost-efficient operations. Namely, American manufacturers spent around USD 600 bi-million in the maintenance of critical systems in the early 1980s, and such expenses doubled within just 20 years [1]. Concerning this, electric motors consume nearly the 70% of energy, and major industries related to oil, petrochemical, and gas, determined that motor bearings account for 51% of failure modes [2]. Hence, machinery fault diagnosis related to bearings appears as a strategy to mitigate current industry challenges, which favors the detection of abnormal states in their early stages and prevents the appearance of more severe failures [3]. Regarding this, machinery fault diagnosis can be carried out through model-based, signal-based, or knowledge-based approaches. Model-based techniques detect changes in the machine behavior using a mathematical model of the system [4]; nonetheless, their success depends upon deterministic models of the industrial processes holding assumptions that can not correspond to the real management. Signal-based algorithms utilize measured data rather than specific input-output models for fault diagnosis [5]. Although a signal-based method provides a more realistic way to assess the fault thanmodel-based ones, it depends on a symptom analysis from normal states, which is accomplished mainly by a field expert. Furthermore, finding a subset of useful sensors to record the signals is essential [6]. In turn, knowledge-based approaches deal with the diagnosis problem from a pattern recognition perspective, comprising: (i) a signal acquisition stage, (ii) a feature estimation procedure, and (iii) a fault assessment through learning algorithms [7]. In this context, the acquisition system should be both a non-invasive and non-destructive technique for extracting relevant information [8]. Recently, data acquisition systems-based on acoustic signals have gained demand over other non-contact measurement techniques. In particular, when the sensor locations on the machine are unavailable, or the measurement procedure has a risk for workers [9]. Notwithstanding, acoustic signals are more vulnerable to environmental noise than vibration responses [10]. Therefore, vibration signals are the most widely used method for machinery fault diagnosis, especially, from bearing [11]. Vibration signals from bearings are assumed to be quasi-stationary or non-stationary, with different fault diagnosis patterns even when data come from the same equipment [12]. Then, the signal characterization poses a challenge to code discriminative models. Commonly, feature estimation from vibration data comprises time, frequency, and time-frequency-based parameters [13,14]. Approaches devoted to time domain-based features focus on statistical measures. Still, they do not adequately reflect the change in frequency components as the progression of a fault develops [15]. Frequency-based features include the fast Fourier transform (FFT) and the power spectrum analysis. Authors in [16] introduced a power spectral density-based method to rotor fault detection from vibration signals. The technique can eliminate the influence of adverse disturbances on a diagnostic model of the machine. Likewise, authors in [17] propose a bearing health index based on the moving average cross-correlation of the power spectral density, which can track the health condition. Nevertheless, given the nature of the signals, such techniques are not suitable for identifying non-stationary events. Time-frequency features based on wavelet transform (WT) have obtained promising results in bearings fault diagnosis tasks [18]. Despite the advantage of the WT to deal with non-stationary patterns, only signal features that match with the wavelet shape can be detected [19].