4. Finally, both the row and column associated with node 10, are removed from the graph.
This is done to all the graphs in the attributed graph data.
Nodes 4 & 10 are also summarized with the MATLAB® code. Table C.7 contains the NSM reduced by implementing Technique 5 in Excel® and Table C.8 contains the NSM reduced by implementing Technique 5 in MATLAB®.
Since the reduced matrices produced by Excel® match the reduced matrices produced with the MATLAB® code, the implementation of all five graph reduction techniques have been verified.
Table C.1: Reduced attributed graph produced by implementing Technique 2 in Excel.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.16E+07 -9.70E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.04E+08 -3.90E+07 0.00 0.00 -3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3.51E+06 -5.85E+05 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
4.34E+08 4.44E+07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.19E+08
-5.94E+07 6.40E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.93E+04 3.51E+06 8.45E+05 0.00 0.00
3.82E+06 3.85E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 0.00 3.51E+06 0.00 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -8.45E+05 0.00 0.00 0.00 6.48E+05 -1.43E+05
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 0.00 1.43E+05 0.00 0.00
157
Table C.2: Reduced attributed graph produced by implementing Technique 2 in Matlab.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.16E+07 -9.70E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.04E+08 -3.90E+07 0.00 0.00 -3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3.51E+06 -5.85E+05 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
4.34E+08 4.44E+07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.19E+08
-5.94E+07 6.40E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.93E+04 3.51E+06 8.45E+05 0.00 0.00
3.82E+06 3.85E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 0.00 3.51E+06 0.00 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -8.45E+05 0.00 0.00 0.00 6.48E+05 -1.43E+05
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 0.00 1.43E+05 0.00 0.00
158
Table C.3: Reduced attributed graph produced by implementing Technique 3 in Excel.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.16E+07 -9.70E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.04E+08 -3.90E+07 0.00 0.00 0.00 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 0.00 -3.51E+06 0.00 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 -4.92E+06 0.00 6.47E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 -6.47E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.82E+08
4.34E+08 4.44E+07 0.00 0.00 0.00 0.00 0.00 -4.92E+06 0.00 0.00 2.15E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.15E+06 0.00 0.00 0.00 0.00 0.00 0.00 1.19E+08
-5.94E+07 6.40E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.57E+06 0.00 0.00 0.00 3.51E+06 8.45E+05 0.00 0.00
3.82E+06 3.85E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 0.00 3.51E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 -8.45E+05 0.00 0.00 0.00 6.48E+05 0.00
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 0.00 0.00 0.00 0.00
159
Table C.4: Reduced attributed graph produced by implementing Technique 3 in Matlab.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.16E+07 -9.70E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.04E+08 -3.90E+07 0.00 0.00 0.00 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 0.00 -3.51E+06 0.00 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 -4.92E+06 0.00 6.47E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 -6.47E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.82E+08
4.34E+08 4.44E+07 0.00 0.00 0.00 0.00 0.00 -4.92E+06 0.00 0.00 2.15E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.15E+06 0.00 0.00 0.00 0.00 0.00 0.00 1.19E+08
-5.94E+07 6.40E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.57E+06 0.00 0.00 0.00 3.51E+06 8.45E+05 0.00 0.00
3.82E+06 3.85E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 0.00 3.51E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 -8.45E+05 0.00 0.00 0.00 6.48E+05 0.00
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 0.00 0.00 0.00 0.00
160
Table C.5: Reduced attributed graph produced by implementing Technique 4 in Excel.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 2.76E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 5.50E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.16E+07 -9.70E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.55E+05 0.00 0.00
-3.04E+08 -3.90E+07 -2.76E+05 -5.50E+05 0.00 0.00 4.92E+06 0.00 0.00 -3.51E+06 -5.85E+05 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 -4.92E+06 0.00 6.57E+06 0.00 0.00 0.00 0.00 0.00
4.34E+08 4.44E+07 0.00 0.00 0.00 0.00 -4.92E+06 0.00 6.57E+06 0.00 0.00 0.00 0.00
-5.94E+07 6.40E+06 0.00 0.00 0.00 0.00 0.00 -6.57E+06 0.00 3.51E+06 8.45E+05 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 3.51E+06 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 -1.55E+05 4.92E+06 0.00 0.00 -8.45E+05 0.00 0.00 6.48E+05 -1.43E+05
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.43E+05 0.00 0.00
161
Table C.6: Reduced attributed graph produced by implementing Technique 4 in Matlab.
-5,80E+07 -3,06E+05 0,00 0,00 0,00 2,76E+05 0,00 0,00 0,00 0,00 0,00 0,00 0,00
-5,36E+07 -2,89E+05 0,00 0,00 0,00 5,50E+05 0,00 0,00 0,00 0,00 0,00 0,00 0,00
-5,16E+07 -9,70E+05 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,55E+05 0,00 0,00
-3,04E+08 -3,90E+07 -2,76E+05 -5,50E+05 0,00 0,00 4,92E+06 0,00 0,00 -3,51E+06 -5,85E+05 0,00 0,00
6,42E+07 7,37E+06 0,00 0,00 0,00 -4,92E+06 0,00 6,57E+06 0,00 0,00 0,00 0,00 0,00
4,34E+08 4,44E+07 0,00 0,00 0,00 0,00 -4,92E+06 0,00 6,57E+06 0,00 0,00 0,00 0,00
-5,94E+07 6,40E+06 0,00 0,00 0,00 0,00 0,00 -6,57E+06 0,00 3,51E+06 8,45E+05 0,00 0,00
-3,05E+08 -3,07E+07 0,00 0,00 0,00 3,51E+06 0,00 0,00 -3,93E+04 0,00 0,00 0,00 0,00
-1,45E+07 -6,85E+06 0,00 0,00 -1,55E+05 4,92E+06 0,00 0,00 -8,45E+05 0,00 0,00 6,48E+05 -1,43E+05
1,69E+08 2,56E+06 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 -6,48E+05 0,00 0,00
0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,43E+05 0,00 0,00
162
Table C.7: Reduced attributed graph produced by implementing Technique 5 in Excel.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 2.76E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 5.50E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.11E+08 5.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.57E+06 0.00 3.93E+04 3.51E+06 1.00E+06 0.00 0.00
-3.04E+08 -3.90E+07 -2.76E+05 -5.50E+05 -3.89E+03 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 -3.51E+06 -5.85E+05 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 -4.92E+06 0.00 6.47E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 -6.47E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.82E+08
4.34E+08 4.44E+07 0.00 0.00 0.00 6.57E+06 0.00 -4.92E+06 0.00 0.00 2.15E+06 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.15E+06 0.00 0.00 0.00 0.00 0.00 1.19E+08
3.82E+06 3.85E+05 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 -3.93E+04 3.51E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 -1.00E+06 4.92E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.48E+05 -1.43E+05
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 1.43E+05 0.00 0.00
163
Table C.8: Reduced attributed graph produced by implementing Technique 5 in Matlab.
-5.80E+07 -3.06E+05 0.00 0.00 0.00 0.00 2.76E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-5.36E+07 -2.89E+05 0.00 0.00 0.00 0.00 5.50E+05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-7.77E+05 -2.51E+04 0.00 0.00 0.00 0.00 3.89E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.11E+08 5.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.57E+06 0.00 3.93E+04 3.51E+06 1.00E+06 0.00 0.00
-3.04E+08 -3.90E+07 -2.76E+05 -5.50E+05 -3.89E+03 0.00 0.00 4.92E+06 0.00 0.00 0.00 0.00 -3.51E+06 -5.85E+05 0.00 0.00
6.42E+07 7.37E+06 0.00 0.00 0.00 0.00 -4.92E+06 0.00 6.47E+06 6.57E+06 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -1.03E+07 0.00 0.00 0.00 0.00 0.00 -6.47E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.82E+08
4.34E+08 4.44E+07 0.00 0.00 0.00 6.57E+06 0.00 -4.92E+06 0.00 0.00 2.15E+06 0.00 0.00 0.00 0.00 0.00
0.00 -3.43E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -2.15E+06 0.00 0.00 0.00 0.00 0.00 1.19E+08
3.82E+06 3.85E+05 0.00 0.00 0.00 -3.93E+04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-3.05E+08 -3.07E+07 0.00 0.00 0.00 -3.93E+04 3.51E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
-1.45E+07 -6.85E+06 0.00 0.00 0.00 -1.00E+06 4.92E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.48E+05 -1.43E+05
1.69E+08 2.56E+06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -6.48E+05 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.04E+08 0.00 6.18E+07 0.00 0.00 1.43E+05 0.00 0.00
164
Appendix D
Performance of the FDI methods applied to the GTLP
This appendix contains the detection and isolation rates of all three FDI methods applied to the attributed graph data of the GTLP. The detection and isolation rates of all the fault conditions after applying the distance parameter, the eigendecomposition, and the residual- based FDI methods to the GTLP can be seen in Tables D.1, D.2, & D.3 respectively.
Table D.1: Detection and isolation rates of the distance pa- rameter FDI method applied to the GTLP.
Main F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 DR (%) 100 100 75 75 75 100 75 75 75 100 100 100
IR (%) F1 75 75 0 0 0 25 0 0 0 0 0 0 0
IR (%) F2 75 0 75 0 0 0 0 25 0 0 0 0 0
IR (%) F3 75 0 0 75 0 0 0 0 0 0 0 0 0
IR (%) F4 75 0 0 0 75 0 0 0 0 0 0 0 0
IR (%) F5 75 0 0 0 0 75 0 0 0 0 0 0 0
IR (%) F6 75 0 0 0 0 0 75 0 0 0 0 0 25
IR (%) F7 75 0 0 0 0 0 0 75 0 0 0 0 0
IR (%) F8 75 0 0 0 0 0 0 0 75 0 0 0 0
IR (%) F9 75 0 0 0 0 0 0 0 0 75 0 0 0
IR (%) F10 50 0 0 0 0 0 25 0 0 0 50 0 25
IR (%) F11 75 0 0 0 0 25 0 0 0 0 0 75 0
IR (%) F12 50 0 0 0 0 0 0 25 0 0 25 0 50
Table D.2: Detection and isolation rates of the (modified) eigendecomposition FDI method applied to the GTLP.
Main F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 DR (%) 100 100 100 100 75 100 100 100 75 100 100 100
IR (%) F1 75 75 0 0 0 0 0 0 0 0 25 0 0
IR (%) F2 25 25 25 0 0 0 25 0 0 0 0 0 25
IR (%) F3 25 0 0 25 25 25 0 0 0 0 0 25 0
IR (%) F4 25 0 0 50 25 0 0 25 0 0 0 0 0
IR (%) F5 75 0 0 0 0 75 0 0 0 0 0 0 0
IR (%) F6 50 0 25 0 0 0 50 0 0 0 25 0 0
IR (%) F7 25 0 0 0 25 50 0 25 0 0 0 0 0
IR (%) F8 75 0 0 0 0 0 0 0 75 25 0 0 0
IR (%) F9 50 0 0 0 0 0 0 25 0 50 0 0 0
IR (%) F10 25 0 0 0 25 0 25 0 0 0 25 0 25
IR (%) F11 50 0 25 25 0 0 0 0 0 0 0 50 0
IR (%) F12 50 25 25 0 0 0 0 0 0 0 0 0 50
Table D.3: Detection and isolation rates of the residual-based FDI method applied to the GTLP.
Main F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 DR (%) 100 100 100 100 100 100 100 100 75 100 100 100
IR (%) F1 75 75 0 0 0 0 0 25 0 0 0 0 0
IR (%) F2 100 0 100 0 0 0 0 0 0 0 0 0 0
IR (%) F3 0 0 75 0 0 0 0 25 0 0 0 0 0
IR (%) F4 0 0 75 0 0 0 0 25 0 0 0 0 0
IR (%) F5 0 0 100 0 0 0 0 0 0 0 0 0 0
IR (%) F6 75 25 0 0 0 0 75 0 0 0 0 0 0
IR (%) F7 25 0 75 0 0 0 0 25 0 0 0 0 0
IR (%) F8 0 0 100 0 0 0 0 0 0 0 0 0 0
IR (%) F9 25 25 0 0 0 0 0 0 0 25 0 0 25
IR (%) F10 50 25 0 0 0 0 0 0 0 0 50 25 0
IR (%) F11 100 0 0 0 0 0 0 0 0 0 0 100 0
IR (%) F12 25 25 0 0 0 0 0 0 0 0 0 50 25
Appendix E
Performance of the FDI methods using the GTLP graph data as reduced by all the reduction techniques
The purpose of this appendix is to provide the results of the experimental process conducted in Chapter 7. Each graph reduction technique is applied incrementally to the graph data of the GTLP, and the FDI performance is recorded with each increment. The percentage attribute reduction increases with each increment. The results of Technique 1 to 5 can be seen in Tables E.1 - E.5.
Table E.1: Performance of all three FDI methods using the GTLP graph data as reduced by Tech- nique 1.
Distance FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 87.50 87.50 87.50 87.50 85.42 83.33 83.33 100.00 100.00 97.92 Overall Isolation Rate (%) 70.83 70.83 68.75 70.83 70.83 72.92 68.75 56.25 56.25 22.92 Attribute Reduction (%) 0.00 0.00 25.00 27.78 38.89 50.00 66.67 83.33 84.72 93.06 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 0.00 Isolation rate of Fault 10 (%) 50.00 50.00 50.00 75.00 75.00 75.00 75.00 0.00 0.00 0.00 Isolation rate of Fault 12 (%) 50.00 50.00 50.00 75.00 75.00 75.00 75.00 50.00 50.00 0.00
Eigen FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 95.83 100.00 100.00 95.83 93.75 97.92 97.92 97.92 85.42 Overall Isolation Rate (%) 43.75 45.83 50.00 52.08 43.75 43.75 47.92 43.75 43.75 18.75 Attribute Reduction (%) 0.00 0.00 25.00 27.78 38.89 50.00 66.67 83.33 84.72 93.06 Isolation rate of Fault 1 (%) 75.00 75.00 50.00 75.00 50.00 50.00 75.00 75.00 25.00 25.00 Isolation rate of Fault 5 (%) 75.00 75.00 75.00 50.00 75.00 75.00 100.00 75.00 50.00 50.00 Isolation rate of Fault 8 (%) 75.00 75.00 50.00 50.00 75.00 50.00 0.00 75.00 50.00 25.00
Residual FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 97.92 97.92 97.92 100.00 100.00 97.92 100.00 95.83 0.00 Overall Isolation Rate (%) 39.58 39.58 37.50 33.33 45.83 41.67 29.17 22.92 22.92 0.00 Attribute Reduction (%) 0.00 0.00 25.00 27.78 38.89 50.00 66.67 83.33 84.72 93.06 Isolation rate of Fault 1 (%) 75.00 75.00 50.00 25.00 0.00 100.00 100.00 100.00 100.00 0.00 Isolation rate of Fault 2 (%) 100.00 100.00 100.00 100.00 100.00 0.00 0.00 0.00 0.00 0.00 Isolation rate of Fault 11 (%) 100.00 100.00 0.00 0.00 100.00 100.00 0.00 0.00 0.00 0.00
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Table E.2: Performance of all three FDI methods using the GTLP graph data as reduced by Tech- nique 2.
Distance FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 87.50 87.50 87.50 85.42 83.33 85.42 89.58 89.58 93.75 93.75 Overall Isolation Rate (%) 70.83 70.83 68.75 66.67 64.58 66.67 70.83 68.75 68.75 68.75 Attribute Reduction (%) 0.00 2.78 8.33 13.89 16.67 22.22 25.00 30.56 36.11 38.89 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 Isolation rate of Fault 10 (%) 50.00 50.00 50.00 50.00 50.00 50.00 75.00 50.00 50.00 50.00 Isolation rate of Fault 12 (%) 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00
Eigen FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 91.67 93.75 97.92 100.00 100.00 91.67 97.92 100.00 91.67 Overall Isolation Rate (%) 43.75 45.83 47.92 45.83 37.50 37.50 41.67 52.08 45.83 52.08 Attribute Reduction (%) 0.00 2.78 8.33 13.89 16.67 22.22 25.00 30.56 36.11 38.89 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 50.00 75.00 75.00 25.00 50.00 100.00 75.00 Isolation rate of Fault 5 (%) 75.00 50.00 75.00 50.00 50.00 75.00 50.00 50.00 50.00 50.00 Isolation rate of Fault 8 (%) 75.00 50.00 75.00 50.00 50.00 25.00 50.00 75.00 50.00 50.00
Residual FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 97.92 97.92 97.92 97.92 97.92 97.92 100.00 100.00 100.00 Overall Isolation Rate (%) 39.58 39.58 39.58 37.50 35.42 35.42 35.42 35.42 31.25 33.33
Attribute Reduction (%) 0.00 2.78 8.33 13.89 16.67 22.22 25.00 30.56 36.11 38.89 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 50.00 50.00 75.00 75.00 25.00 100.00 100.00 Isolation rate of Fault 2 (%) 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Isolation rate of Fault 11 (%) 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 75.00
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Table E.3: Performance of all three FDI methods using the GTLP graph data as reduced by Tech- nique 3.
Distance FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 87.50 87.50 87.50 87.50 87.50 83.33 83.33 83.33 85.42 83.33 Overall Isolation Rate (%) 70.83 68.75 68.75 68.75 68.75 66.67 68.75 68.75 75.00 70.83 Attribute Reduction (%) 0.00 5.56 11.11 13.89 19.44 25.00 30.56 36.11 41.67 47.22 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 Isolation rate of Fault 10 (%) 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 Isolation rate of Fault 12 (%) 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 100.00 75.00
Eigen FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 97.92 91.67 100.00 100.00 93.75 97.92 91.67 95.83 93.75 Overall Isolation Rate (%) 43.75 41.67 37.50 43.75 50.00 43.75 43.75 39.58 37.50 50.00 Attribute Reduction (%) 0.00 5.56 11.11 13.89 19.44 25.00 30.56 36.11 41.67 47.22 Isolation rate of Fault 1 (%) 75.00 25.00 75.00 75.00 75.00 75.00 75.00 50.00 50.00 75.00 Isolation rate of Fault 5 (%) 75.00 50.00 75.00 50.00 75.00 50.00 75.00 75.00 75.00 75.00 Isolation rate of Fault 8 (%) 75.00 75.00 25.00 50.00 50.00 50.00 50.00 25.00 50.00 50.00
Residual FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 93.75 100.00 100.00 100.00 97.92 100.00 100.00 100.00 100.00 Overall Isolation Rate (%) 39.58 47.92 50.00 50.00 45.83 45.83 41.67 39.58 33.33 18.75
Attribute Reduction (%) 0.00 5.56 11.11 13.89 19.44 25.00 30.56 36.11 41.67 47.22 Isolation rate of Fault 1 (%) 75.00 50.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Isolation rate of Fault 2 (%) 100.00 50.00 50.00 50.00 100.00 0.00 0.00 0.00 0.00 0.00 Isolation rate of Fault 11 (%) 100.00 100.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
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Table E.4: Performance of all three FDI methods using the GTLP graph data as reduced by Tech- nique 4.
Distance FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 87.50 87.50 87.50 87.50 87.50 87.50 87.50 89.58 89.58 100.00 Overall Isolation Rate (%) 70.83 70.83 72.92 72.92 72.92 72.92 72.92 72.92 72.92 62.50
Attribute Reduction (%) 0.00 22.22 38.89 44.44 55.56 66.67 75.00 83.33 88.89 94.44 Isolation rate of Fault 1 (%) 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 75.00 Isolation rate of Fault 10 (%) 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 Isolation rate of Fault 12 (%) 50.00 50.00 50.00 50.00 100.00 100.00 100.00 100.00 100.00 25.00
Eigen FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 93.75 89.58 91.67 97.92 95.83 89.58 95.83 89.58 95.83 Overall Isolation Rate (%) 43.75 37.50 43.75 45.83 47.92 50.00 45.83 37.50 37.50 37.50 Attribute Reduction (%) 0.00 22.22 38.89 44.44 55.56 66.67 75.00 83.33 88.89 94.44 Isolation rate of Fault 1 (%) 75.00 50.00 75.00 75.00 75.00 50.00 75.00 75.00 50.00 75.00 Isolation rate of Fault 5 (%) 75.00 25.00 50.00 75.00 100.00 75.00 75.00 50.00 25.00 75.00 Isolation rate of Fault 8 (%) 75.00 25.00 25.00 25.00 0.00 25.00 50.00 75.00 25.00 50.00
Residual FDI Method
Percentiles 0th 10th 20th 30th 40th 50th 60th 70th 80th 90th
Overall Detection Rate (%) 97.92 97.92 97.92 100.00 100.00 100.00 100.00 100.00 31.25 0.00 Overall Isolation Rate (%) 39.58 56.25 58.33 52.08 47.92 50.00 31.25 16.67 2.08 0.00 Attribute Reduction (%) 0.00 22.22 38.89 44.44 55.56 66.67 75.00 83.33 88.89 94.44 Isolation rate of Fault 1 (%) 75.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 0.00 0.00 Isolation rate of Fault 2 (%) 100.00 50.00 75.00 75.00 75.00 100.00 100.00 0.00 0.00 0.00 Isolation rate of Fault 11 (%) 100.00 100.00 25.00 0.00 0.00 100.00 0.00 0.00 0.00 0.00
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