## 4 Results and Analysis
### Fault Detection and Fault Identification
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**Algorithm 1** Support vector machined (SVM)-based adaptive neuro variable structure observer for fault diagnosis and fault-tolerant control of the robot manipulator. In Figure 5, there is a clear difference among residual signals used for differentiating normal and abnormal signals for fault detection and identification. In view of Figures 3-5, the ANHVSO algorithm allows more accurate and more differentiable residual signals compared with the ones obtained through the NHVSO and VSO algorithms. The energies of torque and position residual signals are illustrated in Figure 6. Based on this figure, in the normal condition, the residual signals of position and torque are lower than the ones corresponding to abnormal conditions. In sensor faulty conditions, the position residual signal is bigger than the one corresponding to the actuator fault, but the torque residual signal is smaller than the one corresponding to the actuator fault. For fault detection and classification, the types of faults such as actuator fault, sensor fault and actuator-sensor fault, SVM is used in this research. Therefore, the SVM+VSO, SVM+NHVSO and SVM+ANHVSO methods are used for fault detection and identification. The results are presented in Figure 7 and Table 3. The confusion matrices from Figure 7 demonstrate that all of the methods show high fault detection accuracies (i.e., differentiating between normal and abnormal states). Regarding the fault identification (i.e., differentiating between types of faults), it can be seen that the SVM+ANHVSO method resulted in the smallest numbers of misclassified samples for all of the signal classes in comparison with the SVM+VSO and SVM+NHVSO methods. Figure 2: Torque and position of robot manipulator’s joint in normal and faulty actuator conditions. The results shown in Table 3 indicate that the SVM+ANHVSO method outperforms the SVM+VSO and SVM+NHVSO techniques in terms of average accuracy with a value of 98.7%. Moreover, from Table 3, it can be observed that for all of the signal classes, the accuracy of fault detection and identification through the SVM+ANHVSO method is higher compared to the one of the aforementioned methods. Overall, it can be concluded that the SVM-based ANHVSO (SVM+ANHVSO) method is highly effective in detecting and identifying the operating conditions of the robot manipulator. The best results shown by the ANHVSO technique outperform the best results achieved by the NHVSO and VSO approaches by 27% and 29.2%, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & **ANHVSO** & **NHVSO** & **VSO** \\ \hline Normal State & 100\% & 95.7\% & 96.6\% \\ Actuator Fault & 97.4\% & 72.4\% & 60\% \\ Sensor Fault & 99.1\% & 55.2\% & 59.5\% \\ Actuator–sensor Fault & 98.3\% & 63.8\% & 62.1\% \\ \hline Average & 98.7\% & 71.7\% & 69.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fault diagnosis results for the robot manipulator based on ANHVSO, NHVSO and VSO. Figure 3: Torque and position residual signals of robot manipulator’s joints in normal and faulty conditions based on the variable structure observer (VSO) algorithm. In addition, we compare our proposed approach with the following state-of-the-art methods: ARX-Laguerre fuzzy PID observer (ALFPIDO) [2], fuzzy ARX-Laguerre fuzzy extended feedback linearization observer (FALFEFLO) [8], ARX-Laguerre fuzzy extended PI observer (ALFEPIO) [10], fuzzy PI feedback linearization observer (FPIFLO) [29] and ARX-Laguerre extended PI observer (ALEPIO) [30] in terms of performance. As shown in Table 4, the proposed method for robot fault diagnosis outperforms the state-of-the-art ALFPIDO method, FALFEFLO technique, ALFEPIO procedure, FPIFLO algorithm and ALEPIO method, yielding average performance improvements of 13.2%, 5.5%, 7.8%, 13.1% and 15.6% for three faults, respectively.