## 5 Case Study  
The zirconia powder production line of Root Industrial Co., Ltd. was used to validate the precision of the sensor-deployment approach proposed for parameter estimation in the wet-grinding system. Figure 3 shows the zirconia powder production process flowsheet. Zirconia powder and deionized water are first ground in a vertical ball mill to reach a certain initial product particle size, thoroughly mixed in a stirring tank, cooled by a heat exchanger, and pumped into a sand mill for grinding. After grinding, the slurry is returned to the stirring tank for mixing, and then to the grinding mill for circulating grinding after passing through the heat exchanger. When the product particle size meets the requirements, the slurry is sent to the drying tower for drying and storage. To provide high-precision, reliable, and relevant parameters for the online prediction of slurry product particle size, considering the causal relationship between the parameters and the spatial arrangement of the sensors, a total of 12 sensing stations are set up for the effective acquisition of these physical parameters (Figure 4). The graphical model of BNs is developed to portray linear causal relationships between the physical parameters. The path coefficient is calculated according to Equation (2), which illustrates the causal features of BNs (Figure 4). Due to the product particle size (F18) being a variable that must be predicted, there is no need to calculate the path coefficient. Table 1 presents the features of the sensors and the physical parameters. Sensor information about the wet-grinding system is taken from the accumulation of empirical data for actual industrial production at Root Industrial Co., Ltd. The table also shows that not every physical parameter requires a sensor to pick up relevant information owing to the inherent causal relationships among them. Figure 4: Causal features of Bayesian networks for the wet-grinding system. Figure 3: Zirconia powder production process flowsheet and sensing locations. The performance evaluation of a multi-objective optimized sensor layout requires further research. A systematic analysis should consider operability and economics [35]. Therefore, the data output deviation index and sensor cost are proposed as the optimization targets under the constraints of the mean shift detectability for each physical parameter in BNs. The aforementioned SFLA is used to accomplish this task, which is compared with two sensing layouts: the directed graph (DG), with a greedy-based approach, and saturated sensing. According to the actual industrial application monitoring requirements, the level of significance \(\alpha=0.05\), the mean shift \(\epsilon_{i}=3\), and the upper bound for \(\epsilon_{i}\), \(\Phi^{UI}_{1,\epsilon_{i}}=4\), are recommended by Root Industrial Co., Ltd. The basic parameters of SFLA are selected as follows. The number of memeplexes is 40, the number of frogs in each memeplex is 80, the number of frogs selected from each memeplex is 40, the local iteration number within each memeplex is 20, the maximum step size allowed to be adopted by a frog after being infected is 1, and the convergence criteria of SFLA are satisfied if at least one frog would carry the \"best memetic pattern thus far\" for 15 consecutive shuffles. Table 2 presents the results for all three sensing layouts. Comparisons are conducted from the perspectives of the maximum data output deviation index, the total cost of the selected sensors, and the average deviation index in the wet-grinding system. The cost utilized is simply a summation of all the sensor costs chosen in the deployment. The average deviation index is the data output deviation index per sensing location selected to arrange the sensors. Table 2 shows that the maximum data output deviation index in the wet-grinding system fell from the saturated sensing's and DG's value of 1.1, to the BN's value of 0.505; the average deviation index decreased from the saturated sensing's value of 0.4321 and DG's value of 0.6018 to the BN's value of 0.2827.