The exhaustive search of the section ‘Nominal sensor placement methodology’ is next applied to the reduced candidate sensor set provided by the clustering algorithm based on the extended FSM. Table 2 provides the resulting leak locatability matrices.

Table 2

Leak locatability matrices for case study 2

(a) Leak magnitude uncertainty analysis
S1* = {2, 8, 9, 83, 249}S2* = {2, 8, 9, 83, 249}S3* = {2, 8, 9, 83, 249}S4* = {2, 8, 9, 83, 249}S5* = {2, 8, 9, 83, 249}
Scn1 96,027 96,027 96,027 96,027 96,027
Scn2 100,165 100,165 100,165 100,165 100,165
Scn3 100,328 100,328 100,328 100,328 100,328
Scn4 100,186 100,186 100,186 100,186 100,186
Scn5 100,149 100,149 100,149 100,149 100,149
(b) Operating point variation analysis
S1* = {199, 243, 244, 245, 285}S2* = {199, 243, 244, 245, 285}S3* = {2, 8, 9, 83, 249}S4* = {9, 199, 206, 222, 285}S5* = {2, 9, 171, 222, 249}
Scn1 98,437 98,437 73,060 81,292 74,810
Scn2 99,086 99,086 79,696 80,116 78,817
Scn3 93,134 93,134 100,108 81,544 90,460
Scn4 41,328 41,328 42,355 49,105 46,728
Scn5 33,760 33,760 43,709 46,817 51,396
(a) Leak magnitude uncertainty analysis
S1* = {2, 8, 9, 83, 249}S2* = {2, 8, 9, 83, 249}S3* = {2, 8, 9, 83, 249}S4* = {2, 8, 9, 83, 249}S5* = {2, 8, 9, 83, 249}
Scn1 96,027 96,027 96,027 96,027 96,027
Scn2 100,165 100,165 100,165 100,165 100,165
Scn3 100,328 100,328 100,328 100,328 100,328
Scn4 100,186 100,186 100,186 100,186 100,186
Scn5 100,149 100,149 100,149 100,149 100,149
(b) Operating point variation analysis
S1* = {199, 243, 244, 245, 285}S2* = {199, 243, 244, 245, 285}S3* = {2, 8, 9, 83, 249}S4* = {9, 199, 206, 222, 285}S5* = {2, 9, 171, 222, 249}
Scn1 98,437 98,437 73,060 81,292 74,810
Scn2 99,086 99,086 79,696 80,116 78,817
Scn3 93,134 93,134 100,108 81,544 90,460
Scn4 41,328 41,328 42,355 49,105 46,728
Scn5 33,760 33,760 43,709 46,817 51,396

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