# Fault Detection Algorithm Based on Dynamic Global-Local Preserving Projection
## 3 Fault Detection Based on DGLPP
### DGLPP Fault Detection Process  
The flowchart of using DGLPP for fault detection is shown in Figure 1. The process is mainly divided into two steps: offline modeling and online diagnosis. The specific steps are as follows. evaluation in the field of process monitoring [39; 40]. The process comprises five main units: reactor, compressor, condenser, gas-liquid separator, and product-refining tower. The TE process data used in this experiment include training datasets and 21 test datasets. The training dataset is sampled under normal conditions. It is also used for offline modeling of the monitoring method. The test set samples with faults are obtained during 48 h of running simulation and faults are introduced at 8 h. A total of 960 observation values are collected, with the first 160 observation values being normal data and the last 800 samples being fault data. The 21 types of faults are classified into six types. Table 1 describes the fault data types. Each dataset has 52 variables, consisting of 11 control variables and 41 measurement variables. The measurement variable comprises the process measurement variable and component measurement variable. Table 2 provides detailed descriptions of control variables and process measurement variables. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Fault Description** & **Type** \\ \hline
1 & A/C feed ratio, component B unchanged (stream 4) & Step \\
2 & Component B, A/C feed ratio unchanged (stream 4) & Step \\
3 & Material D temperature (stream 2) & Step \\
4 & Reactor cooling water inlet temperature & Step \\
5 & Condenser cooling inlet temperature & Step \\
6 & Material A feed loss & Step \\
7 & Material C pressure loss & Step \\
8 & A, B, C composition & Random variable \\
9 & Material D feed temperature & Random variable \\
10 & Material C temperature & Random variable \\
11 & Reactor cooling water inlet temperature & Random variable \\
12 & Condenser cooling water inlet temperature & Random variable \\
13 & Reaction kinetics parameters & Slow drift \\
14 & Reactor cooling water valve & Sticky \\
15 & Condenser cooling valve & Sticky \\ \hline \end{tabular}
\end{table} 
Table 1: TE process fault description. Figure 2: TE process flowchart. PCA, LPP, GLPP, and DGLPP methods are used for fault detection to verify the proposed method's effectiveness. The confidence level is 99%, the cumulative contribution rate is 85%, the delay is 1, and the number of neighbors is 5. The fault detection rates of 21 faults using the above methods are shown in Table 3. As shown in Table 3, the fault detection performance of the DGLPP method is superior to the fault detection performances of the other methods. Thus, the effectiveness of the proposed algorithm is verified. The DGLPP algorithm can detect all faults except faults 3, 9, and 15, indicating that the algorithm has a high fault coverage. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Fault Description** & **Type** \\ \hline
16 & Unknown & Unknown \\
17 & Unknown & Unknown \\
18 & Unknown & Unknown \\
19 & Unknown & Unknown \\
20 & Unknown & Unknown \\
21 & Logistics 4 valve position & Constant position \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._