In this case the network size is small and the clustering procedure is not needed to solve the sensor placement problem. Thus, just step 2 of the methodology outlined in the section ‘Nominal sensor placement methodology’ has been directly applied. Table 1 provides the resulting leak locatability matrices. At the top row, the optimal sensor locations for each scenario are provided.

Table 1

Leak locatability matrices for case study 1

(a) Leak magnitude uncertainty analysis
S1* = {1,4}S2* = {1,4}S3* = {3,8}S4* = {1,4}S5* = {1,4}
Scn1 50.00 50.00 48.03 50.00 50.00
Scn2 50.00 50.00 49.24 50.00 50.00
Scn3 50.00 50.00 50.00 50.00 50.00
Scn4 50.00 50.00 50.00 50.00 50.00
Scn5 50.00 50.00 50.00 50.00 50.00
(b) Operating point variation analysis
S1* = {1,9}S2* = {3,8}S3* = {3,8}S4* = {1,4}S5* = {1,4}
Scn1 50.00 49.57 49.57 47.73 47.73
Scn2 49.63 49.97 49.97 48.03 48.03
Scn3 43.50 50.00 50.00 50.00 50.00
Scn4 42.79 50.00 50.00 50.00 50.00
Scn5 43.03 50.00 50.00 50.00 50.00
(a) Leak magnitude uncertainty analysis
S1* = {1,4}S2* = {1,4}S3* = {3,8}S4* = {1,4}S5* = {1,4}
Scn1 50.00 50.00 48.03 50.00 50.00
Scn2 50.00 50.00 49.24 50.00 50.00
Scn3 50.00 50.00 50.00 50.00 50.00
Scn4 50.00 50.00 50.00 50.00 50.00
Scn5 50.00 50.00 50.00 50.00 50.00
(b) Operating point variation analysis
S1* = {1,9}S2* = {3,8}S3* = {3,8}S4* = {1,4}S5* = {1,4}
Scn1 50.00 49.57 49.57 47.73 47.73
Scn2 49.63 49.97 49.97 48.03 48.03
Scn3 43.50 50.00 50.00 50.00 50.00
Scn4 42.79 50.00 50.00 50.00 50.00
Scn5 43.03 50.00 50.00 50.00 50.00

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