## 4 Experiments and Evaluation
### PM-Based Adaptive Scheduling vs. A Rule-Based Preventive System  
In conventional systems, rule-based and preventive approaches are used to detect and recover from abnormal behaviors. In general, our system adds more fine-grained control over such conventional approaches thanks to the predicted operational deviations calculated in real-time. Hence, to demonstrate the effectiveness of incorporating PM analysis into such automated control systems, we compare our approach (with the selected settings of \(speed\ interval=0.5\ r/\min\), \(\alpha=0.55\), \(\beta=0.45\), see in Sections 4.5.1 and 4.5.2) with a rule-based mechanism as a baseline. We run the two mechanisms on the digital twin motor to be able to simulate harsh abnormal conditions. The experimented rule-based mechanism, as its name suggests, slows down the motor speed based also on PM analysis and on certain rules. In our experiment settings, we set the rule as follows: when the power exceeds 1.5 times of the expected power, the speed drops to 50% of the originally requested speed. If it is more severe, then the system stops. The rule is set as the base performance of our adaptive control mechanism, that is, with a very high speed interval size in chromosomes (13 r/min) that in theory should resemble a rule-based approach. As discussed in Section 4.5.2, when the interval size becomes relatively large, the system is expected to respond to predicted anomalies with a poor sensitivity. The selection of the interval of 13 r/min is due to the available speed range (from 6 to 30 r/min), where there are only two chromosomes generated, one recommending a center speed of 12.5 r/min. This is exactly 50% of the initially requested speed of 25 r/min; hence, we obtain a similar behavior to the rule-based mechanism. The results of the speed performance in Figure 11a indicate that our adaptive control with the interval of 0.5 has a very a sensitive adaptation that it can react fast to torque increase, starting at 5.414 s (seconds). Rule-based mechanism reacts first at 15.786 s after the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Interval size** & 0.25 & 0.5 & 1 & 2 & 8 \\ \hline
**Efficiency (\%)** & 74.5 & 74.6 & 72.8 & 68.7 & 57.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The efficiency values under different chromosome designs, i.e., different speed intervals. predefined power threshold is reached. We note that the rule-based mechanism's reaction speed purely depends on the power threshold, a smaller threshold would lead to a shorter reaction time; however, it would show less tolerance to the power increase by directly dropping the speed. On the other hand, our PM-based adaptive control mechanism at the interval of 13 r/min reacts the slowest, at 19.275 s, since the error calculation has a very large threshold. Even though the PM algorithm throws a notification, as the same PM algorithm runs in the case of \(interval=0.5\), a large interval indicates a large threshold, and so a longer waiting time. This shows that although a PM algorithm detects problems earlier, the system behaves just like a rule-based preventive mechanism with the lack of a fine-grained adaptive control, leading to a slow response and a poor protection. Figure 11: Performances of our PM-based adaptive control with \(interval=0.5\) r/m, 13 r/m and the rule-based system. In addition, the rule-based exhibits bad flexibility in terms of speed, that is, the operational speed is not restored back when the disturbance is withdrawn. This is because a rule-based mechanism is usually designed fail-safe to protect a machine. The same effect is also observable with \(interval=13\) due to its large error threshold (in Figure 11a). This indicates that such preventive and/or coarsely designed adaptation mechanisms causes longer downtimes on a system even though the disturbance is withdrawn and despite they run a PM. Whereas, our fine-grained PM-based adaptive control mechanism recovers well after the abnormal torque is withdrawn even for a short time (between 40 s and 60 s).