# Bayesian Uncertainty Inferencing for Fault Diagnosis of Intelligent Instruments in IoT Systems
## 6 BN Model Example for IPT in an IoT Network
The first expert specializes in researching faults in industrial instruments, another is responsible for the operation and maintenance of the IoT system in which IPTs are located, a third is an instrument engineer working on-site with IPT, a fourth is an operator who works with IPT on-site, and the fifth is technical personnel from the manufacturer of the IPT. Their opinions were expressed using a seven-level linguistic term. The linguistic terms and their corresponding TrIFNs are listed in Table 1. The linguistic evaluation results are presented in Table 4. Their corresponding TrIFNs were used to determine the qualitative fault probability, using the steps outlined in Section 3. Table 5 displays the experts' weight calculations, and the calculated root node fault joint probabilities are shown in Table 6 as the expected values. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**ID** & **E1** & **E2** & **E3** & **E4** & **E5** & **ID** & **E1** & **E2** & **E3** & **E4** & **E5** \\ \hline x1 & L & L & EL & RH & M & x18 & H & M & RH & L & EL \\ x2 & RL & L & RH & M & M & x19 & RH & RL & L & RL & RL \\ x3 & M & L & M & M & RH & x20 & RL & RL & EL & L & L \\ x4 & RH & M & EL & L & L & x21 & M & M & VH & EL & EL \\ x5 & M & RL & RL & L & RL & x22 & RL & L & M & RL & RL \\ x6 & M & RL & M & L & L & x23 & M & RL & EL & M & M \\ x7 & RH & RL & H & L & M & x24 & RH & RL & EL & M & M \\ x8 & VH & RL & H & RL & RL & x25 & VH & RL & EL & RL & RL \\ x9 & VH & RL & RL & RL & RL & x26 & H & RL & H & M & M \\ x10 & VH & RL & VH & L & L & x27 & H & M & H & L & L \\ x11 & H & M & H & M & M & x28 & H & M & L & M & RL \\ x12 & RH & RL & EL & RL & RL & x29 & H & RH & L & M & M \\ x13 & H & RL & RH & L & L & L & x30 & M & M & VH & L & L \\ x14 & VH & RL & EL & EL & EL & x31 & RL & M & EL & EL & RL \\ x15 & H & RL & H & EL & L & x32 & RH & RH & H & L & L \\ x16 & VH & RL & EL & EL & EL & x33 & M & M & H & L & EL \\ x17 & L & RH & EL & EL & L & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experts’ opinions of the joint fault probability of basic events in root nodes. Figure 6: IPT fault tree structure and its layers. After obtaining the joint probability, the CPT of the intermediate and top nodes was calculated using the leaky OR gate. For example, node M11 had 3 child nodes: x1, x2, and x3. After obtaining the joint probabilities of x1, x2, and x3, as shown in Table 6, M11's CPT could be calculated using Equation (15), as presented in Table 7.  
The IPT BN model was established using GeNle software, as shown in Figure 7, where the IPT denotes the top node, M1 to M6 are module nodes, the light green nodes are monitored nodes, M231 and M321 are intermediate nodes, and x1-x33 are the root nodes. When the IPT was in the fault state, its fault state was set to \"0\" in GeNle, and then, the fault probability of related intermediate nodes and the top node, could be calculated automatically, as shown in Figure 8. A BN model was used to conduct the simulations. When fault states occurred in the root nodes, the fault occurrence probability of the top and intermediate nodes could be obtained, as shown in Figure 9. This demonstrates how the fault states of root nodes x23 and x15, affected the fault states of the related intermediate and top nodes.