# Rolling-Element Bearing Fault Diagnosis Using Advanced Machine Learning-Based Observer
## 1 Introduction
However, recently the trend in KB-based approaches has been shifted toward artificial intelligence techniques that are used for automatically extracting valuable features and making decisions about the fault conditions of the system [8, 18, 19]. To address the issues of model-based approaches and knowledge-based techniques, hybrid fault diagnosis can be introduced for bearing fault diagnosis. In the hybrid approach, various algorithms from different groups can be used in parallel to improve the performance of the fault diagnosis method. In this research, a robust hybrid fault diagnosis algorithm is presented using a machine learning-based advanced fuzzy sliding mode observer for the REB. The main challenge in designing the procedure of sliding mode observer is system modeling. The mathematical-based system modeling and system identification are the main frameworks for modeling the complex (e.g., bearing) systems [5,6]. In the mathematical-based system modeling, the Lagrange technique can be used for modeling the REBs [6]. Apart from the reliability and accuracy of physical system modeling, this technique has drawbacks in uncertain and noisy conditions. To address this issue, the system identification techniques are widely applied as indicated in [5,20,21]. To estimate the system using system identification technique, various orthonormal procedures such as Auto Regressive with eXogenous input (ARX), orthonormal function bases (OFB), and generalized orthonormal bases (GOB) methods have been used [20,21]. Apart from several advantages of orthonormal techniques compared to the classical algorithms, these techniques have two important drawbacks. The first one is related to the challenge of finding the optimal orthonormal values and the second problem is related to the restrictions in decoupled systems [6; 7; 20; 21]. To address these issues, ensure an efficient complexity reduction and reduce the system's estimation order, the ARX-Laguerre technique has been applied in [20; 21]. Apart from the advantage of complexity reduction in ARX-Laguerre, it has a challenge related to estimation accuracy in nonlinear systems. To increase the accuracy in the ARX-Laguerre technique, the T-S fuzzy ARX-Laguerre (FAL) technique is presented in the literature [5]. In our work, this technique is used to estimate the vibration signals of REBs. One of the main model-based techniques that can be used for FEDI is the observation technique [1]. The observation techniques can be categorized into two main groups: (a) The linear observers (e.g., proportional-integral (PI) and proportional multi integral (PMI)) and (b) nonlinear observers (e.g., feedback linearization observer (FLO), sliding mode observer (SMO), and fuzzy observer (FO)). To reduce the observation error, the linear observer only uses the feedback term. Robustness and reliability in uncertain conditions are the main drawbacks of linear observers [21; 22]. Regarding the nonlinear observers, they can be designed based on driving the dynamic system's behavior in parallel with the linear observer to increase the robustness and reliability of the linear observer for fault estimation [6; 7]. In this research nonlinear observer is used for FEDI. Despite the improvement of the accuracy obtained from using the FLO, robustness is the main issue of this technique [7]. The extended FLO and SMO have been presented by researchers to improve the robustness of observers [5; 6; 7]. The SMO is a robust technique for FEDI for nonlinear and complex systems (e.g., rolling bearings) which operate in uncertain and noisy conditions. The nonlinear switching function in the SMO is defined to converge the output estimation error toward zero. This technique can perform FEDI according to adaptive updates of the observer parameters, which can significantly improve the performance of FEDI in nonlinear systems [23; 24]. Though the SMO increases the robustness, this scheme unfortunately suffers from the chattering phenomenon and reduced fault estimation accuracy in the presence of uncertainties and unknown conditions.