# Rolling-Element Bearing Fault Diagnosis Using Advanced Machine Learning-Based Observer
## 1 Introduction
Figure 1 illustrates the complete block diagram of the proposed algorithm for FEDI of the bearing. This figure indicates that this algorithm has three main parts. In the first step, the system is modeled using the fuzzy ARX-Laguerre (FAL) technique. This part itself has three steps: (i) modeling the bearing based on the filtered ARX method, (ii) modifying the performance of the filtered ARX technique based on an orthonormal function and designing the ARX-Laguerre method, and (iii) improving the accuracy and performance of ARX-Laguerre bearing modeling based on the fuzzy ARX-Laguerre technique. In the second step, the AFSMO is designed for accurate fault estimation and improved performance of the decision component. The second step has three sub-blocks: (i) run the SMO, (ii) reduce the chattering and increase the robustness, in which the SMO is improved based on the advanced technique and the designed ASMO, and (iii) increase the fault estimation accuracy using the fuzzy algorithm and apply it to the ASMO. Apart from the advantages of the ASMO regarding robustness and reliability, it suffers from a suboptimal fault estimation accuracy. To address this issue, a fuzzy algorithm is used in parallel with the advanced SMO for the bearings. In the third step, the faults are detected and identified based on the DT machine learning algorithm. The decision-making for fault detection and identification of REBs contain three parts applied in sequence. These parts are the (i) residual generator, (ii) window characterization, and (iii) deriving the logical decision rules for fault detection and identification using DTs. In the residual generator, the residual signals are calculated in various (normal and abnormal) conditions. Next, these residual signals are cut into windows of equal size and the amplitude-dependent feature parameter is extracted to quantitively characterize these obtained windows. Finally, the fault detection and identification are accomplished by the logical decision rules delivered by the DT technique. Specifically, the decision about the fault condition is accomplished by comparing the value of the extracted feature parameter from the window of the residual signal with the learned threshold provided by the DT classification algorithm. This paper has the following contributions:  
1. Robust technique for modeling the vibration signals in bearings based on the fuzzy ARX-Laguerre approach is proposed. 2. The estimation accuracy of the higher-order sliding mode observer for vibration signals has been improved by the T-S fuzzy algorithm. 3. The performance of fault detection and identification by the proposed hybrid observer is improved by the decision tree technique and hence, new machine learning-based hybrid observer is introduced in this paper. The rest of this research paper is organized as follows: Section 2 provides insights into the Case Western Reserve University (CWRU) benchmark dataset used in this paper. In Section 3, the bearing is modeled based on the FAL procedure. Section 4 includes two main steps. In the first step, the AFSMO is utilized for fault estimation. In the second step, the decision tree algorithm is used for the fault detection and identification. In Section 5, fault detection, estimation, and identification results for the bearing are analyzed. Finally, the conclusions are provided in the last section.