*2.7. Benchmark Evolutionary Algorithms*

To validate the ability of the proposed approach in obtaining global optimal fault information, the performance of PEOS will be further compared in a later section to other evolutionary algorithm-based approaches, including a pipe examination genetic algorithm (PEGA), pipe examination particle swarm optimization (PEPSO), and a pipe examination symbiotic organism search (PESOS).

PEGA and PEPSO are benchmark pipe examination techniques that were developed based on the evolutionary algorithms of GA and PSO. A GA and PSO are employed as optimization tools to substitute the algorithm SOS uses in PESOS. PEGA uses a process involving selection, crossover, and mutation to evolve a population of potential solutions toward improved solutions. In PEPSO, the potential solutions, called particles, fly through the problem space by following the current optimum particle. Each particle's movement is influenced by its local best-known position and is also guided toward the global best-known positions in the search space. The readers may refer to References [29,60] for detailed discussions on the use of GAs. In addition, more detail about the application of PSO can be obtained in References [32,61]. The other benchmark approach is PESOS, which is a simplified fault detection approach similar to PEOS but without the preliminary elimination procedure (i.e., the OOA) for the initial organisms. The initial solutions of PEGA, PEPSO, and PESOS are randomly generated from feasible solution domains with corresponding upper and lower bounds. The control and specific parameter settings for each algorithm are listed in Table 2.

**Table 2.** Specific parameters for each algorithm, with *NP* = 10, 20, or 50, and *Miter* = 10,000 or 20,000.


Note: *NP* = population size/ecosystem size; *Miter* = maximum iteration; *m* = mutation rate; *c* = crossover rate; *g* = generation gap; *w* = inertia weight; *v* = limit of velocity.

#### **3. Laboratory Experiments and PEOS Simulations**

#### *3.1. Experiment Configurations*

Two cases of experimental reservoir pipe valve (RPV) systems with leaks or blockages that have been reported in the literature were adopted to verify the applicability of PEOS. The first case was carried out in a specially constructed RPV system at Imperial College (IC), London [62]. The system had a pump and tank upstream and a valve at the downstream end. The valve was a transient generation point, and pressure signals were also measured there at the same time. The IC pipe was made of high-density polyethylene (HDPE) with an inner diameter of 50.6 mm and a length of 272 m. Two leaks with different orifice sizes of 1.21 <sup>×</sup> 10−<sup>5</sup> m2 and 1.50 <sup>×</sup> 10−<sup>5</sup> m2 occurred at the locations of 65.95 m and 146.32 m, respectively: This was measured from upstream. These two leak orifices were very small, and the discharge coefficient was considered to be one. Thus, the *CdLALs* for the two leaks was respectively 1.21 <sup>×</sup> <sup>10</sup>−<sup>5</sup> <sup>m</sup><sup>2</sup> and 1.50 <sup>×</sup> <sup>10</sup>−<sup>5</sup> m2. The initial flow rate downstream was 1 L/s.

The second case was carried out at the Water Engineering Laboratory (WEL) at the University of Perugia, Italy [63]. A pressurized tank upstream of the system supplied the pipe, and a valve was located at the downstream end for data measurement and transient generation. The WEL pipe was also made of HDPE, with an inner diameter of 93.3 mm and a length of 164.93 m. A partial blockage was located at 88.96 m, measured from upstream. The partial blockage was simulated by an inline valve with a diameter of 38.8 m, and thus the *CdBAB* was 1.18 <sup>×</sup> 10−<sup>3</sup> m2. The initial flow rate downstream was 2.57 L/s.
