# Rolling-Element Bearing Fault Diagnosis Using Advanced Machine Learning-Based Observer
## 6 Conclusions  
This paper proposed a decision tree-based advanced fuzzy SMO (AFSMO) to perform reliable FEDI in a rotating machine. Rolling element bearing (REB) presents a nonlinear system that can now be analyzed in uncertain conditions. To improve the system modeling accuracy, the fuzzy ARX-Laguerre technique is presented in the first step. In the second step, the SMO is designed for the FEDI. To reduce the chattering and increase the estimation accuracy of the SMO, in the third step, the AFSMO is considered. To increase the fault estimation accuracy, the T-S fuzzy algorithm is applied to the AFSMO in the fourth step. To perform fault detection and identification in the presence of uncertainties, decision trees govern the AFSMO to find the exact solution for fault diagnosis under various crack types and motor speed conditions. The effectiveness of the proposed algorithm is validated using a publicly available vibration dataset of CWRU. The proposed decision tree-based AFSMO outperformed the ASMO and SMO in terms of classification accuracy. As a result, the proposed method improved the average fault identification performance by about 4.5%, 5.3%, and 4.8% compared with the ASMO for the crack sizes of 0.007, 0.014, and 0.021 inches, respectively. In addition, the AFSMO improved the average performance of fault identification by about 8.8%, 7.6%, and 8.1% compared with the SMO for the crack sizes of 0.007, 0.014, and 0.021 inches, respectively. Moreover, the proposed technique demonstrated its robustness while performing the tasks of REB fault detection and identification under changing operating conditions, such as variable load levels and variable rotating speeds. Based on the results we can conclude that the proposed methodology is highly efficient in diagnosing bearing faults. However, to ensure the robustness and efficacy in the industrial environment, it is crucial to reduce the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Algorithms** & **AFSMO (Proposed Method)** & \multicolumn{4}{c}{**ASMO**} & \multicolumn{4}{c}{**SMO**} \\ \hline
**Crack Diameters (in)** & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 \\
**Normal** & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 99\% & 99\% & 100\% \\
**BF** & 100\% & 99\% & 100\% & 95\% & 95\% & 95\% & 89\% & 88\% & 91\% \\
**OF** & 75\% & 99\% & 95\% & 81\% & 90\% & 92\% & 75\% & 79\% & 84\% \\
**IF** & 100\% & 99\% & 93\% & 93\% & 96\% & 91\% & 90\% & 91\% & 94\% \\
**ACA** & 93.8\% & 99.1\% & 97\% & 92.3\% & 95.25\% & 94.5\% & 88.3\% & 89.3\% & 92.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: The accuracy of the FEDI for the custom load-variant datasets.  
error of the system modeling. To address this issue, we will focus on developing an adaptive algorithm in our future work. Moreover, we will focus on exploring and evaluating the capabilities of applying the proposed methodology in conjunction with various vibration health indicators for a task of REB fault prognosis on run-to-failure experimental data.  
All authors contributed equally to the conception of the idea, the design of experiments, the analysis and interpretation of results, and the writing and improvement of the manuscript.  
It was supported in part by the Ministry of SMEs and Startups (MSS), Korea, under the \"Regional Specialized Industry Development Program (R&D, P0002964)\" supervised by the Korea Institute for Advancement of Technology (KIAT). This work was also partially supported a study on the \"Leaders in INdustry-university Cooperation +\" Project, supported by the Ministry of Education and National Research Foundation of Korea.  
The authors declare no conflict of interest.