## 5 Case Study
The total cost of the sensory system also reduced from the saturated sensing's value of 3020 and DG's value of 1810 to the BN's value of 1740. Thus, it is concluded that, with the inclusion of the causal features of BNs and quantitative information of the sensory system, BNs with SFLA-based sensor deployment modeling effectively enhance the accuracy of parameter estimation and the economy of sensor layout. The following reasons could account for this: while allocating the sensors, the DG with greedy-based \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Sensors Selects (\(S\))**} & \multirow{2}{*}{\
\begin{tabular}{c} **Accuracy** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Sensor** \\ **Failure Rate** \\ **(7/\%)** \\ \end{tabular} } & \multirow{2}{*}{**Cost (\(S\))**} & \multirow{2}{*}{**Sensing Location (\(SL\))**} & \multirow{2}{*}{**Physical Parameters (\(P\))**} \\ \hline
1 & S\({}_{10}\): Ultrasonic sensor & 0.5 & 0.02 & 200 & SL\({}_{102}\): Ultrasonic sensing station & Fi: Bead filling rate \\
2 & & & & & & F\({}_{2}\): Motor critical speed \\
3 & S\({}_{11}\): Laser caliper sensor & 0.1 & 0.5 & 200 & SL\({}_{11}\): Laser caliper station & Fi: Bead diameter \\
4 & & & & & & F\({}_{2}\): Griding power \\
5 & S\({}_{2}\): Concentration sensor & 0.3 & 0.2 & 300 & SL\({}_{2}\): Concentration sensing station & Fi: Saturday concentration \\
6 & S\({}_{21}\): Viscosity sensor & 1 & 0.1 & 100 & SL\({}_{21}\): Viscosity sensing station & Fi: Saturday viscosity \\
7 & S\({}_{21}\): Liquid flow sensor & 1 & 0.1 & 240 & SL\({}_{21}\): Liquid flow sensing station & Fi: Saturday flow \\
8 & & & & & F\({}_{2}\): Diphragm pump outlet pressure \\
9 & S\({}_{1}\): Gas flow sensor & 1 & 0.1 & 120 & SL\({}_{21}\): Gas flow sensing station & Fi: Air consumption \\
10 & & & & & F\({}_{21}\): Air supply pressure \\
11 & & & & & F\({}_{11}\): Bead density \\
12 & S\({}_{2}\): Torque sensor & 0.1 & 0.1 & 300 & SL\({}_{2}\): Torque sensing station & Fi: Motor torque \\
13 & S\({}_{2}\): Speed sensor & 0.1 & 0.1 & 50 & SL\({}_{21}\): Speed sensing station & Fi: Motor speed \\
14 & S\({}_{2}\): Power meter & 1 & 0.02 & 40 & SL\({}_{21}\): Power sensing station & Fi: Motor power \\
15 & S\({}_{2}\): Pressure sensor & 0.5 & 0.1 & 50 & SL\({}_{21}\): Pressure sensing station & Fi: Pressure in grinding drum \\
16 & S\({}_{2}\): Temperature sensor & 0.1 & 0.01 & 60 & SL\({}_{21}\): Temperature sensing station & Fi: Saturday temperature \\
17 & S\({}_{2}\): Accelerometer & 1 & 0.01 & 150 & SL\({}_{21}\): Vibration sensing station & Fi: Bead–wall impact energy \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sensors and physical parameters for the wet-grinding system. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Approach**} & \multirow{2}{*}{**Sensors Selected**} & \multirow{2}{*}{ \begin{tabular}{c} **No. of Selected** \\ **Sensors** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Maximum Data** \\ **Output Deviation** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Average** \\ **Deviation Index** \\ \end{tabular}  } & \multirow{2}{*}{**Cost Utilized**} \\ \cline{4-5}  & & & & & & \\ \hline BN with SFLA & \{S\({}_{2}\), S\({}_{3}\) (2), S\({}_{2}\), S\({}_{7}\), S\({}_{8}\) (2), S\({}_{9}\), S\({}_{11}\)\} & 10 & 0.505 & 0.2827 & 1740 \\ DG with ready & \{S\({}_{1}\), S\({}_{2}\), S\({}_{3}\), S\({}_{4}\), S\({}_{5}\), S\({}_{6}\), S\({}_{7}\), S\({}_{8}\), S\({}_{9}\), S\({}_{11}\), S\({}_{12}\)\} & 12 & 1.1 & 0.6018 & 1810 \\ Saturated sensing & \{S\({}_{1}\), S\({}_{2}\) (2), S\({}_{3}\), S\({}_{4}\) (2), S\({}_{5}\), S\({}_{6}\) (2), S\({}_{7}\) (2), S\({}_{8}\) (2), S\({}_{9}\) (2), S\({}_{10}\) (2), S\({}_{11}\), S\({}_{12}\) (2)\} & 20 & 1.1 & 0.4321 &sensor deployment always tries to select the sensor node with the most edge connections with the physical parameter nodes. If the other sensors also cover the physical parameter nodes, the arcs connected to these sensors must be deleted.