# Fault Detection Algorithm Based on Dynamic Global-Local Preserving Projection
## 3 Fault Detection Based on DGLPP
### DGLPP Fault Detection Process
\begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Variable Description** & **No.** & **Variable Description** \\ \hline
1 & Material D feed amount & 22 & Separator grade \\
2 & Material E feed amount & 23 & Separator pressure \\
3 & Material A feed amount & 24 & Separator bottom flow (Flow 10) \\
4 & Material A and C feed amount & 25 & Stripper grade \\
5 & Compressor recirculation valve & 26 & Stripper pressure \\
6 & Discharge valve & 27 & Stripper bottom flow (Flow 11) \\
7 & Liquid flow of separator tank & 28 & Separator temperature \\
8 & Stripper liquid product flow & 29 & Separator grade \\
9 & Stripper flow valve & 30 & Changes in Material C temperature \\
10 & Reactor cooling water valve & 31 & Stripper temperature \\
11 & Condenser cooling water flow & 32 & Stripper flow rate \\
12 & Material A feed (Flow 1) & 33 & Compressor power \\
13 & Material D feed (Flow 2) & 34 & Reactor cooling water outlet temperature \\
14 & Material E feed (Flow 3) & 35 & Separator cooling water outlet temperature \\
15 & Total feed (Flow 4) & 36 & Stripper temperature \\
16 & Recirculation flow (Flow 8) & 37 & Stripper flow rate \\
17 & Reactor feed rate (Flow 6) & 38 & Compressor power \\
18 & Reactor pressure & 39 & Reactor cooling water outlet temperature \\
19 & Reactor class & 40 & Separator cooling water outlet temperature \\
20 & Reactor temperature & 41 & Separator cooling water outlet temperature \\
21 & Discharge rate (Stream 9) & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Variables of the TE process. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No. ** & **PCA** & & **LPP** & & **GLPP** & & **DGLPP** \\ \hline  & \(\mathbf{T^{2}}\) & **SPE** & \(\mathbf{T^{2}}\) & **SPE** & \(\mathbf{T^{2}}\) & **SPE** & \(\mathbf{T^{2}}\) & **SPE** \\ \hline
1 & 98.75 & 99.12 & 99.88 & 98.88 & 99.75 & 98.75 & 99.88 & 98.62 \\
2 & 98.0 & 98.5 & 98.88 & 98.25 & 98.88 & 97.50 & 99.12 & 97 \\
3 & 0.63 & 7. Fault 15 is viscous, and the process variable is described as condensate cooling water valve failure. Figure 3 shows the process monitoring diagrams for all methods of Fault 15. As the figure shows, PCA and LPP algorithms can hardly detect faults in this case, and the detection effect of the GLPP algorithm is not ideal. This scenario occurs because this fault is weak, and the measured variables are slightly affected. The changes in the mean, variance, or peak time are difficult to observe. The DGLPP algorithm is sensitive to faults and can detect faults continuously. The DGLPP algorithm can detect faults earlier and relatively higher detection rate than the other algorithms. Figure 3: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & \multicolumn{2}{c}{**PCA**} & \multicolumn{2}{c}{**LPP**} & \multicolumn{2}{c}{**GLPP**} & \multicolumn{2}{c}{**DGLPP**} \\ \hline  & **T\({}^{2}\)** & **SPE** & **T\({}^{2}\)** & **SPE** & **T\({}^{2}\)** & **SPE** & **T\({}^{2}\)** & **SPE** \\ \hline
10 & 18.62 & 36.75 & 91.13 & 16.38 & 91.25 & 2.13 & 93.5 & 0 \\
11 & 3 & 34.63 & 76.12 & 0.63 & 80.13 & 0.13 & 87.75 & 0 \\
12 & 90.25 & 93.63 & 99.88 & 90.75 & 99.88 & 76.5 & 100 & 51 \\
13 & 92.25 & 92.5 & 95.63 & 91.63 & 95.63 & 89.12 & 96.37 & 85.25 \\
14 & 0.13 & 71.88 & 100 & 10.50 & 100 & 0.25 & 100 & 0 \\
15 & 1.75 & 9.0 & 17.87 & 0.25 & 19 & 0 & 28.75 & 0 \\
16 & 8.13 & 34.88 & 93.75 & 6.25 & 94.5 & 0.37 & 96.63 & 0 \\
17 & 4.62 & 40.25 & 95.63 & 11 & 96.63 & 3.87 & 97.88 & 0 \\
18 & 87.88 & 88.5 & 90.87 & 87.75 & 91.37 & 87.5 & 92.13 & 85.12 \\
19 & 0.13 & 7.25 & 87.75 & 0 & 93.13 & 0 & 99.12 & 0 \\
20 & 4.62 & 40.25 & 90.75 & 13.75 & 91.13 & 4.5 & 91.75 & 0 \\
21 & 12.63 & 40.62 & 61.12 & 15.62 & 64.88 & 4.75 & 59.5 & 0 \\ MFDR & 36.62 & 55.11 & 81.60 & 39 & 82.52 & 33.73 & 84.49 & 30.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._In the case where Fault 2 is the example, the feed flow ratio of A/C is constant; however, the content of component B changes step by step. This phenomenon causes the total feed to change.