# Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes
## 4 Industrial Application  
The four approaches described above are applied to the injection moulding process of car pedals in a local automotive industry. The implementation is carry out in a plastic injection machine with the capability to produce four pieces per cycle and save the relevant information in each run i.e., the parameters used to produce such pieces are automatically stored in a database. Subsequently, the pieces are classified as good or bad through several quality tests carry out by the technical staff. The injection moulding process involves 36 variables listed in Table 1. This data set was selected by the expert personnel of the process and consists of variables of diverse nature like temperatures, pressure,  
Figure 1: Fault detection system. time, etc., corresponding to several machine operational features such as heating power, mold position, and injection time. Since this machine just recently started operating, the primary data provided by the company include 154 observations of normal operation mode. Once the data are cleaned up and structured, the training of the one-class classifier takes place. As soon as the algorithm is trained in order to determine the system's capability, 64 new observations provided by the company are tested. This new data set includes observations corresponding to machine faults, that is, measurements where the injection process does not meet the quality standards. Then, the F1 score metric is calculated and the metaheuristics tune the SVDD hyper-parameters in order to achieve a better F1 score. The parameters of the different metaheuristics were selected according to their authors and the corresponding values are specified in Table 2. The number of iterations was selected in experimental testing where it was determined as the maximum amount of iterations that produced changes in the results. The search range is from 0.001 to 600 for the hyper-parameters. Table 3 shows the different values and descriptive statistics of the F1 score metric and the computational times corresponding to 30 runs using each of the four approaches. As it can be seen, the SHO algorithm reaches the highest mean value of F1 score (0.9702) with a small variability i.e., standard deviation (std) equal to 0.0074. \begin{table}
\begin{tabular}{l|l} \hline \hline \multicolumn{2}{c}{**Description**} \\ \hline \(x_{f1}\) & [F\({}^{\text{c}}\)], Nozzle 1 \\ \(x_{f2}\) & [F\({}^{\text{c}}\)], Nozzle 2 \\ \(x_{f3}\) & [Percent], Heating power zone 1 \\ \(x_{f4}\) & [Percent], Heating power zone 2 \\ \(x_{f5}\) & [Percent], Heating power zone 3 \\ \(x_{f6}\) & [Percent], Heating power zone 4 \\ \(x_{f7}\) & [Percent], Heating power zone 5 \\ \(x_{f8}\) & [Percent], Heating power zone 6 \\ \(x_{f9}\) & [in], Mold position value \\ \(x_{f10}\) & [in], Opening run \\ \(x_{f11}\) & [US ton], Closing force peak value \\ \(x_{f12}\) & [US ton], Closing force real value \\ \(x_{f13}\) & [s], Mold protection time \\ \(x_{f14}\) & [F\({}^{\text{c}}\)], Oil temperature \\ \(x_{f15}\) & [F\({}^{\text{c}}\)], Traverse \\ \(x_{f16}\) & [s], Cooling time \\ \(x_{f17}\) & [psi], Backpressure \\ \(x_{f18}\) & [in\({}^{3}\)], Volume end screw \\ holding pressure \\ \(x_{f19}\) & [psi], Holding pressure \\ \(x_{f20}\) & [in\({}^{3}\)/s], Dosage power \\ \(x_{f21}\) & [psi], Pressure at Switchover \\ \(x_{f22}\) & [s], Cycle time \\ \(x_{f23}\) & [lbf-ft], Mean spin \\ \(x_{f24}\) & [lbf-ft], Peak value at spin \\ \(x_{f25}\) & [psi], Specific injection pressure \\ \(x_{f26}\) & [in\({}^{3}\)], Dosage volume \\ \(x_{f27}\) & [in\({}^{3}\)], Injection volume \\ \(x_{f28}\) & [s], Dosing time \\ \(x_{f29}\) & [s], Injection time \\ \(x_{f30}\) & [F\({}^{\text{c}}\)], Cylinder zone 1 \\ \(x_{f31}\) & [F\({}^{\text{c}}\)], Cylinder zone 2 \\ \(x_{f32}\) & [F\({}^{\text{c}}\)], Cylinder zone 3 \\ \(x_{f33}\) & [F\({}^{\text{c}}\)], Cylinder zone 4 \\ \(x_{f34}\) & [ft/s], Revolutions \\ \(x_{f35}\) & [Wh], Injection work \\ \(x_{f36}\) & [in\({}^{3}\)], Switching volume \\ \hline \hline \end{tabular}
\end{table}