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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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