## 4 Results and Analysis
### Fault-Tolerant Control  
After designing an SVM-based ANHVSO for fault detection and identification, an active modern adaptive fuzzy backstepping variable structure controller (AMFBVSC) is designed for fault tolerance. Figure 8 shows the performance of the algorithm: AMFBVSC, FBVSC and VSC, in abnormal conditions. It is clear from the figure as to the efficiency of the AMFBVSC method in reducing the effects of the FBVSC and VSC techniques. Figure 8: Fault-tolerant control algorithm based on the proposed active modern fuzzy backstepping variable structure controller (AMFBVSC), fuzzy backstepping variable structure controller (FBVSC) and backstepping variable structure controller BVSC. Figure 7: Confusion matrices for the ANHVSO, NHVSO and VSO algorithms based on the SVM technique. From Figure 8 and Equation (42), it can be seen that the BVSC method is weak regarding the properties of robustness and accuracy, especially in faulty conditions. To improve the robustness and accuracy, FBVSC is applied in the study. According to the power of fault-tolerant control computed through Equations (42,55) and demonstrated in Figure 8, we can see that the BVSC and FBVSC have problems reducing the effect of actuator-sensor fault in the joint position. Based on Figure 8 and Equation (57), the proposed fault-tolerant control algorithm (AMFBVSC) has effectively reduced the effect of the fault. Regarding Figure 8, the fault-tolerant control algorithm based on the AMFBVSC method is more powerful compared to the BVSC and FBVSC methods. The efficiencies under various faulty conditions of the fault-tolerant control algorithms based on the AMFBVSC, FBVSC and BVSC are presented in Figures 9-11. Figure 9 shows the error of the position for the fault-tolerant control based on the AMFBVSC, FBVSC and BVSC methods in the presence of an actuator fault. It is evident that the AMFBVSC method is more robust than the other two. According to this figure, the difference between the normal and actuator faulty joint position when using the algorithm based on the AMFBVSC is close to zero (e.g., \(\cong 0.2\times 10^{-3}\)). Figure 10 shows the performance of the three fault-tolerant control algorithms in reducing the effects of a sensor fault in the robot manipulator. The effectiveness of the sensor fault tolerant control in the robot manipulator when using the AMFBVSC is higher compared to the one corresponding to the other two methods. According to Figure 10, the difference between the normal and sensor faulty joint position when using the algorithm based on the AMFBVSC is about \(1\times 10^{-3}\). Figure 11 shows the actuator-sensor (multi) fault reduction in the robot manipulator for the algorithms based on the AMFBVSC, FBVSC and BVSC. As in the previous cases, it can be seen that the power of actuator-sensor fault reduction based on the AMFBVSC algorithm is better than the one of the other two methods. According to Figure 11, the difference between the normal and actuator-sensor faulty joint position when using the algorithm based on the AMFBVSC is close to zero (\(\cong 0.25\times 10^{-3}\)). Overall, it can be concluded that the AMFBVSC is highly-effective in controlling various types of faults (e.g., actuator fault, sensor fault and actuator-sensor fault) in the robot manipulator. The use of the ANHVSO improved the average fault identification performance for various types of faults by about 27% and 29.2% compared with the NHVSO and VSO, respectively. All of the authors contributed equally to the conception of the idea, the design of experiments, the analysis and interpretation of results, as well as the writing of the manuscript. All authors have read and agreed to the published version of the manuscript. This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry and Energy (MOTIE) of the Republic of Korea (20192510102510). In this section you can acknowledge any support given which is not covered by the author contribution or funding sections.