# Bayesian Uncertainty Inferencing for Fault Diagnosis of Intelligent Instruments in IoT Systems
## 7 Sensitivity Analysis Overview of Information Uncertainties in Bayesian Networks  
A sensitivity analysis was used to determine how the root node fault state affected the intermediate and top nodes [38,39]. The top event was treated as the target node, and a sensitivity analysis was performed by changing the fault state of the root nodes. The results of the sensitivity analysis are presented in Figures 10-12. Figure 10 shows that the sensitivity of the nodes could be divided into 4 levels. The influence of the nodes on the top node state was divided into 5 levels; the results are listed in Table 8. For example, in the monitored node layer, monitored nodes had different effects on the fault state of the top node. M21, M22, and M23 were the most influential nodes; M11, M32, M41, M51, and M61 were the second-most influential nodes; and M12 and M31 were the third-most influential nodes. In addition, regarding nodes at higher levels, we must pay more attention to their use and maintenance.  
Figure 9: BN model when x23 and x15 nodes are in failure state.  
Figure 11: Sensitivity analysis of M3 node fault probability.  
Figure 10: Sensitivity analysis of IPT top node fault probability.  
Sensitivity analysis could also be used for the module nodes, as shown in Figure 11. It revealed that different root fault events will affect the whole functional module's fault state.  
In the established model, monitored nodes are important performance parameters for the corresponding functional modules. If any of these key parameters are in an abnormal or fault state, the possible root event fault probability and overall fault state of the IPT, can be diagnosed. Figure 12 shows the fault probability performance of the root nodes and the top IPT node, when the monitored node M21 was in the fault state. Therefore, the most probable fault type and its qualitative probability can be determined when abnormal data are detected by the IoT.  
As mentioned previously, the most influential performance parameters can also be determined through the established BN model. Therefore, the second application of the proposed method is in the identification of important nodes and their influence on the top node fault. This is helpful in the development of a preventive maintenance strategy to reduce possible fault rates. Although an OR gate was used in this study, when the fault probability of the influential nodes and modules decreased, the IPT fault probability also decreased. Therefore, preventive control or more frequent monitoring measures for these node data can be implemented in order to minimize fault probability and improve the stability and reliability of the IPT instrument.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Influential Level** & **1 st Level** & **2 nd Level** & **3 rd Level** & **4 th Level** & **5 th Level** \\ \hline \multirow{2}{*}{The module layer} & M1, M2, M3, & & & \\  & M4, M5, M6 & & & \\  & M21, M22, & M11, M32, M41, & & \\  & M23 & M51, M61 & & \\  & & & M231 & M321 & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Nodes’ influential levels.  
Figure 12: BN model when M21 is in fault state.