# Rolling-Element Bearing Fault Diagnosis Using Advanced Machine Learning-Based Observer
## 1 Introduction  
Rolling element bearings (REBs) have been extensively used in several industries, such as the automotive, steam and gas turbines, and power generation industries, to improve their efficiency by reducing friction [1, 2]. The complexities of the required tasks, with time-varying and nonlinear parameters in rolling bearings, make their fault estimation, detection, and identification highly challenging. The fault estimation, detection, and identification (further referred to as FEDI) are intransitive to prevent the bearing's destruction. Here, the fault estimation technique is used to estimate the signal (fault) to obtainthe valuable differentiation between various conditions of bearing, the fault detection algorithm is used to detect normal and abnormal conditions, and the fault identification technique is used to identify the specific types of faults in the REBs. Various types of failures have been representing in bearings, which are divided into four foremost groups, i.e., inner race faults, outer race faults, ball or rolling-element faults, and cage faults that in this research called IF, OF, BF, and CF, respectively. To analyze the faults conditions in a bearing, various REB condition monitoring techniques such as vibration, motor current signature analysis (MCSA), and acoustic emission (AE) measurements have been reported [3]. This research exploits the vibration measurements since these signals are suitable for FEDI. Numerous procedures have been recently presented for FEDI in various systems, which can be divided into four groups: (a) model-based (MB) techniques, (b) signal-based (SB) approaches, (c) knowledge-based (KB) procedures, and (d) hybrid methods [1,4]. Some recently published representative examples of model-based techniques have been reported in [1, 5, 6, 7]. Model-based techniques for fault diagnosis identify the faults by modeling the system's dynamics using mathematical modeling or system identification techniques using a small dataset. Apart from the various advantages of the MB method such as reliability and robustness, accuracy is the main drawback of this technique [1]. Signal-based fault diagnosis approaches extract fault features and differentiate the health conditions of the system by applying various signal processing techniques to the acquired signals. Some recently published representative examples of signal-based approaches can be found in [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. When using the traditional fault diagnosis frameworks (i.e., knowledge-based methods), it is crucial to select an appropriate signal processing technique that is useful for extracting the representative fault features that are used as inputs to the decision-making approaches. Recently, various types of advanced signal processing approaches were applied for rotating machinery fault diagnosis. These techniques include the conventional wavelet transform [9], wavelet-based kurtogram [10], empirical mode decomposition [11], ensemble empirical mode decomposition [12] and their modifications [13, 14, 15], as well as relatively new methods for detecting and extracting the repetitive transients caused by mechanical faults, such as spectral l2/l1 norm [16] and spectral Gini index [17]. These methods are essential for feature engineering; however, in the proposed methodology, the signal processing step is replaced by the observation technique (advanced fuzzy sliding mode observer) which is used to provide new insights and demonstrate the applicability of the control theory field for solving the problems of mechanical fault diagnosis. Knowledge-based approaches were based on the ideas of transferring the industrial knowledge and expertise in fault diagnosis from humans to the machine by creating algorithms that performed fault identification using decision tables and rules.