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.
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 |