*3.2. PEOS Simulation*

In the PEOS application, the IC pipeline system was divided into six series segments with seven nodes. Each segment was assigned a pipe number from 1 to 6 from upstream to downstream. The first five segments had the same length, 50 m, and the last segment had a length 22 m. Two leaks, L1 and L2, which occurred 65.95 m and 146.32 m from the upstream end, were respectively placed in segments

2 and 3. The WEL pipeline system was partitioned into four series segments with five nodes. From upstream to downstream, the segments were given a pipe number from 1 to 4. Segments 1 to 3 had the same length, 50 m, and the last one was 14.93 m. A blockage named B1 was located at segment 2 and was 88.96 m from upstream. A valve was set at the last downstream node for measurement and transient generation for both pipeline systems. The distance interval (Δ*x*) was considered to be 2 m to divide each segment for PEOS to search for leaks. The simulation durations for the IC and WEL pipeline systems were selected to be 15 and 5 s, respectively.

The temporal head distributions predicted by the PEOS for the IC and WEL pipeline systems were respectively displayed in Figure 2a,b. Both predicted temporal head distributions exhibited oscillatory patterns almost identical to the experimental data, indicating that the transient events in the IC and WEL pipeline systems could be precisely simulated by PEOS. Fault information was successfully identified, with the initial values listed in Table 3. In the IC pipeline system, L1 and L2 were respectively detected at 66 m in segment 2, with *CdAs* = 1.23 <sup>×</sup> 10−<sup>5</sup> m2, and at 146 m in segment 3, with *CdAs* <sup>=</sup> 1.52 <sup>×</sup> <sup>10</sup>−<sup>5</sup> <sup>m</sup>2. Blockage B1 in the WEL pipeline system was identified at 88 m in segment 2, with *CdBAB* = 1.20 <sup>×</sup> 10−<sup>3</sup> m2. The leak and blockage locations in both systems were accurately determined by the proposed approach. The largest relative difference (*E*) between the actual *CdLALs*/*CdBAB* and the predicted one was 1.69% for detecting blockage B1 in the WEL pipeline system. The relative differences were insignificant in both systems. The success of PEOS in fault detection indicated that PEOS performs excellently in a pipeline system.

**Figure 2.** The simulated head distributions at the valve for (**a**) the Imperial College (IC) pipeline and (**b**) the Water Engineering Laboratory (WEL) pipeline.


**Table 3.** The predicted and actual fault information for the two pipeline systems.

Note: *E* = relative difference between the predicted *CdLAL*/*CdBAB* and the actual one.
