# Bearing Fault Identification Using Machine Learning and Adaptive Cascade Fault Observer
## 1 Introduction  
Most countries are currently facing energy-related challenges. Generally, fossil fuels are a major source of energy in most countries. However, the use of fossil fuels causes many problems, such as greenhouse gas emissions like CO\({}_{2}\). In recent years, we have produced about 29 gigatons of CO\({}_{2}\) annually, and around 40% of this can be absorbed naturally. Therefore, we have issues with around 60% of the CO\({}_{2}\) we produce. Increasing CO\({}_{2}\) in the atmosphere causes several challenges, such as global warming and pollution. Heavy industries have played a large role in increasing the emission rate of CO\({}_{2}\). Numerous components are used in heavy industries, including various types of motors. Several factors can be analyzed in attempts to increase the efficiency of motors. Among these, condition monitoring and fault diagnosis of motors are important methods that can be taken advantage of to increase efficiency and reduce CO\({}_{2}\) emissions. Various kinds of faults have been introduced for motors, which can be divided into two main categories: (a) mechanical faults, such as bearing faults (around 69% of faults) and the other types of mechanical faults (around 10%) and (b) electrical faults (around 21%). Bearings are clearly a significant component in motors. Inner race faults (IRF), outer race faults (ORF), and ball faults (BLF) are the main fault types in bearings. Various kinds of condition monitoring have been used for fault diagnosis of bearings, such as methods based onvibration analysis, acoustic emission (AE) analysis, lubricant/debris analysis, power quality analysis and microscope analysis, and motor current signature analysis (MCSA) [1]. Various procedures have been recommended for fault diagnosis in bearings, including techniques based on signal processing procedures, methods based on data-driven techniques, techniques using model-based approaches, and mixtures of the above techniques using hybrid approaches [2; 3; 4; 5; 6; 7; 8]. Regarding the advantages of signal processing techniques, they have some challenges when used in uncertain conditions. Additionally, data-driven approaches have some limitations when used with large datasets, and model-based techniques have limitations in terms of accurate system modeling. To address the above issues a hybrid technique is recommended in this work. To analyze the vibration and AE signals, the signal processing techniques play an important role. A system with a bearing fault is identified as a complex nonlinear and non-stationary one [9]. Due to these issues and the limitation of the conventional time- and frequency-domain analysis, the researchers and engineers are forced to define two scenarios: (a) utilize complex time-frequency analysis (TFA) methods, and (b) utilize the hybrid approach for extracting valuable information about the mechanical fault and performing fault diagnosis. The most frequently used TFAs are empirical mode decomposition (EMD) [10] and its derivative methods, such as ensemble EMD (EEMD) [11; 12], and wavelet transform with its variations [13; 14; 15]. Apart from various positive points of these techniques for fault diagnosis in the bearing, these methods suffer some drawbacks in real industries including mode-mixing in the EMD [16], computational complexity in the EEMD, energy leakage and interference terms, and selection of the mother wavelet function the wavelet transform [17; 18; 19]. Due to the complexity and the problems of TFA signal analysis techniques for extracting discriminative fault features as well as the problems of the classical machine learning methods which are dependent on the quality of the feature, two scenarios have been recommended by researchers and engineers: the family of (machine/deep) learning approaches and the family of modern control algorithms.