# A Hybrid Heuristic Optimization Approach for Leak Detection in Pipe Networks Using Ordinal Optimization Approach and the Symbiotic Organism Search

## Abstract

**:**

## 1. Introduction

_{d}A (discharge coefficient multiplies area opening of the orifice) in the pipe network, with optimum transient perturbations. A hybrid heuristic approach, called leak detection ordinal symbiotic organism search (LDOSOS), is developed based on the ordinal optimization algorithm (OOA) and symbiotic organism search (SOS) for automatically determining leak information in a leaking pipe network. In order to examine the performance of the proposed approach, two synthetic leaking scenarios with different pipe network configurations are considered. The ability of convergence compared with different optimization algorithms pertaining to the detection results is addressed in first scenario. Furthermore, the use of the optimum transient generation is demonstrated in the second scenario.

## 2. Methodology

#### 2.1. Flow Simulation Model

_{ij}) in the Hazen-Williams equation for a pipe is defined as [38]:

_{ij}is the length (m) of the pipe, C

_{ij}is the Hazen-Williams friction coefficient depending on the pipe material [36], and D

_{ij}is the pipe diameter (m). Based on Equation (1), the flow rate Q

_{ij}in each pipe can be expressed as

_{ij}is the frictional head loss in a pipe. The equation of mass conservation at node i can be written as

_{i}is the demand or the source at node i. The flow rate is positive for flowing out of node i and negative for flowing into node i, while QI

_{i}is positive for inflow and negative for outflow. Therefore, the objective function used in the PNSOS is defined as

#### 2.2. Hydraulic Transient Model

_{L}is the volumetric flow rate of the leak, C

_{d}A is the discharge coefficient times the effective area of orifice, and ΔH is the head loss caused by the orifice.

#### 2.3. Excitation Procedure for Transient Generation

_{i0}is the initial steady head, H

_{its}is the piezometric head at node i at time step t

_{s}, nt is number of transient modelling time steps, H

_{r}is the reservoir head, Pe

_{its}is the penalty factor to impose pressure constraints, H

_{max}and H

_{min}are, respectively, the maximum and the minimum permissible heads in system.

#### 2.4. Ordinal Optimization Approach

#### 2.5. Symbiotic Organism Search (SOS)

#### 2.5.1. Mutualism State

_{i}and X

_{j}are randomly selected from an ecosystem for interaction. Both organisms interact to mutual benefit in order to increase chances of survival in the ecosystem. Hence, the new candidate solutions for X

_{i}and X

_{j}are modified based on the mutualistic mechanism between X

_{i}and X

_{j}, and is illustrated as:

_{M}is a vector of random numbers range from 0 to 1, X

_{best}is the current best organism with the best OFV in the ecosystem, MV is the mutual vector defined as MV = (X

_{i}+ X

_{j})/2, and BF

_{1}, and BF

_{2}are the benefit factors randomly as either 1 or 2.

#### 2.5.2. Commensalism State

_{j}is randomly chosen from the ecosystem to interact with another random organism X

_{i}. X

_{i}gains benefit from X

_{j}, but X

_{j}is not affected by this relationship. The new X

_{i}can be modified as:

_{C}is the vector of random numbers range from −1 to 1.

#### 2.5.3. Parasitism State

_{P}is generated by cloning and mutating it from X

_{i}in random dimensions, using a random number with a range between given lower and upper bounds. A parasite X

_{P}tries to replace the random host organism X

_{j}. Both X

_{P}and X

_{j}are then evaluated for their fitness (OFVs). If the parasite has a better OFV, the host organism will be immediately replaced by the parasite. If the OFV of X

_{j}is better, then X

_{j}will survive and kill the parasite X

_{P}.

#### 2.6. Development of LDOSOS

_{oij}and H

_{sij}are ith observed, and simulated heads at the observation point j, respectively. The LDOSOS can automatically determine the leak information based on the minimization of Equation (15). The procedures of LDOSOS are summarized in Figure 4. The LDOSOS can be used to determine the optimal leak location, leak size, and the number of leaking pipes simultaneously. The procedure for detecting the leaks using LDOSOS is given below:

- Import the network configurations.
- Use SOS to determine the optimal transient generating point with its corresponding operating parameters (i.e., y: duration of outflow change, z: amount of nodal consumption variation) by maximizing Equation (10). The optimum solution is obtained when the OFV of Equation (10) does not change within four iterations.
- For the pipe sifting procedure in OOA, successively generate a temporary leak which is located at the middle of each pipe; the location and C
_{d}A of the orifices are treated as temporary solutions. - Since the temporary leak solutions are available, PNSOS is then used to calculate the steady-state nodal heads and flow rates in the network.
- Generate a hydraulic transient event at the optimal generation point and apply Equations (7) and (8) to simulate the head distribution in the network.
- Apply Equation (15) to calculate the temporary OFV for the temporary solution of each pipe.
- Arrange all of the pipes according to the values of temporary OFVs. A quarter of pipes with smaller OFVs are chosen as candidate pipes (CAPs). Only the CAPs will be used in the further steps.
- Randomly generate 200 CASs with the information of a leaking pipe, leak location and C
_{d}As of the orifices, and calculate their OFVs. The top 5% CASs would then be selected for the next step. - Consider the best 5% CASs as the initial organisms for the ecosystem.
- Execute a searching process using SOS. In general, mutualism and commensalism states are used to guide the organisms toward the current best organism, and the parasitism state is applied to avoid the organism becoming stuck in a local optimal solution.
- Check whether the optimization process satisfies the stopping criterion or not. If so, the LDOSOS is then terminated; otherwise, the searching process goes on and back to the tenth step.

_{best}which are all less than 10

^{−4}within four iterations. The second criterion is that the iteration reaches 10,000 times.

## 3. Results and Discussion

#### 3.1. Pipe Networks Setting

^{3}/min). Two potential leaks, denoted as L1 and L2, are both in P6 and are at 300 and 310 m from N5, respectively, with the same C

_{d}A = 0.00025 m

^{2}and same Q

_{L}= 0.5 m

^{3}/min. The downstream valve is the only outflow of pipe network A. Hence, the optimum operation point is located at the valve. In order to compare the proposed approach with the work of [25], the operation parameters y and z are fixed to 1 s and −5 m

^{3}/min, respectively, for the simulation of a sudden closure of the valve. The characteristics of the nodes and pipes of the pipe network A are listed in Table 1.

^{3}/min and constant head of 120 m. Seven outflow nodes N2, N3, N4, N5, N6, N8, and N9 continuously discharge 5, 2.5, 2.2, 2.2, 2.5, 5 and 5 m

^{3}/min, respectively. The leak L1 is in P11 and 300 m away from N3, while the leak L2 is at the middle of P7 and 250 m away from N6. The C

_{d}A and Q

_{L}of L1 are 0.00025 m

^{2}and 0.5 m

^{3}/min and C

_{d}A and Q

_{L}of L2 are 0.0001 m

^{2}and 0.1 m

^{3}/min. In pipe network B, N2, N8, and N9 are available as candidate transient generation points with larger discharges. The optimal operation point (i.e., N2, N8 and N9) and the optimal parameters, y and z, must be determined.

#### 3.2. Applicability of LDOSOS to Leak Detection

_{d}A. However, the searching space in SA may be enormous and required a large computing time to find the optimal solution. By contrast, OOA is adopted in the LDOSOS to sift through the searching space. Based on the search procedure, P6 and P7 in pipe network A are first sifted and ranked as the CAPs; the top 5% CASs from CAPs with different leak information are sifted by calculating all CASs’ OFV (Equation (15)). More specifically, the top 10 best CASs ($200\times 0.05=10$) are sifted as the initial organisms for LDOSOS.

_{d}As. The convergence and efficiency of LDOSOS is greatly enhanced as a result of the sifting procedure OOA. The computing efficiency of LDOSOS is approximate 86 and 58% better than that of LDSA and LDSOS. The LDOSOS obtained the optimum solution after about 1500 iterations which is significantly less than the other two approaches. Obviously, the performance of LDOSOS is much more efficient than the other two algorithms.

#### 3.3. Leak Determination in WDN with Optimal Transient Operation

^{3}/min, with all of the nodal heads being greater than 0 and less than 160 m. The maximum value of Equation (10) with the optimal parameters for each candidate node is listed in Table 4. The overall maximum value reaches to 1978, while using N8 as the transient generation point. The optimum operation duration time y is determined as 2.7 s, while the discharge change z is estimated as −2.58 m

^{3}/min. The maximum transient energy of N8 is higher than that of N2 and N9. Thus, the N8 with its relevant parameters is the best point to generate the transient fluctuations for S2. Furthermore, N8 and N9 are considered as the observation and generation point in LDOSOS to compare the leak detection results using different operation points with its relevant parameters. The transient pressures are sampled for 30 s after the excitation.

#### 3.4. Measurement Error Analysis

## 4. Conclusions

_{bes}

_{t}) with the smallest OFV.

_{d}As are accurately predicted and agreed well with those from the other two algorithms. When these three algorithms are compared, LDOSOS had an approximately 86 and 58% better computing efficiency than LDSA and LDSOS. Moreover, the LDOSOS only takes about 50 min and 1469 iterations to obtain the optimal solution, implying that the searching space is largely reduced by the elimination procedure OOA, and the solutions quickly converged to the optimal solution during iterations. The simulation results show that LDOSOS not only greatly enhances the computation efficiency but also increases the convergence ability. On the other word, LDOSOS significantly outperforms LDSA and LDSOS.

## Acknowledgments

## Conflicts of Interest

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Pipe | Node | Diameter (mm) | Length (m) | |
---|---|---|---|---|

Number | From | To | ||

P1 | N1 | N2 | 305.0 | 1000.0 |

P2 | N2 | N3 | 305.0 | 1000.0 |

P3 | N3 | N4 | 250.0 | 1100.0 |

P4 | N1 | N4 | 405.0 | 1250.0 |

P5 | N4 | N5 | 355.0 | 1000.0 |

P6 | N5 | N6 | 305.0 | 1100.0 |

P7 | N3 | N6 | 305.0 | 1250.0 |

P8 | N6 | Valve | 500.0 | 1000.0 |

Pipe | Node | Diameter (mm) | Length (m) | |
---|---|---|---|---|

Number | From | To | ||

P1 | N1 | N2 | 305.0 | 1000.0 |

P2 | N2 | N3 | 305.0 | 1000.0 |

P3 | N3 | N4 | 250.0 | 1100.0 |

P4 | N1 | N4 | 405.0 | 1250.0 |

P5 | N4 | N5 | 200.0 | 500.0 |

P6 | N5 | N6 | 400.0 | 400.0 |

P7 | N7 | N6 | 200.0 | 500.0 |

P8 | N4 | N7 | 355.0 | 400.0 |

P9 | N7 | N8 | 355.0 | 600.0 |

P10 | N8 | N9 | 305.0 | 1100.0 |

P11 | N3 | N9 | 305.0 | 1250.0 |

Header | L1 | L2 | CPU Time (min) | Iterations | ||||
---|---|---|---|---|---|---|---|---|

Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | |||

Actual | 6 | 300 | 2.5 | 6 | 310 | 2.5 | - | - |

LDSA | 6 | 300 | 2.5 | 6 | 310 | 2.5 | 372 | 9815 |

LDSOS | 6 | 300 | 2.5 | 6 | 310 | 2.5 | 120 | 3481 |

LDOSOS | 6 | 300 | 2.5 | 6 | 310 | 2.5 | 50 | 1469 |

Node | y (s) | z (m^{3}/min) | E_{Max} |
---|---|---|---|

N2 | 7.2 | −5.0 | 1239 |

N8 | 2.7 | −2.58 | 1978 |

N9 | 3.6 | −3.22 | 1843 |

Header | N8 | N9 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

L1 | L2 | L1 | L2 | |||||||||

Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | Pipe No. | Location (m) | C_{d}A × 10^{−4} (m^{2}) | |

Actual | 11 | 300 | 2.5 | 7 | 250 | 1 | 11 | 300 | 2.5 | 7 | 250 | 1 |

LDOSOS | 11 | 300 | 2.499 | 7 | 250 | 1 | 11 | 300 | 2.479 | 7 | 250 | 0.964 |

Prediction Errors | ||
---|---|---|

Scenario 1 | ME (m) | SEE (m) |

Case 1 | −1.76 $\times $ 10^{−6} | 4.11 $\times $ 10^{−4} |

Case 2 | 1.35 $\times $ 10^{−5} | 5.63 $\times $ 10^{−2} |

Scenario 2 | ME (m) | SEE (m) |

Case 1 | 6.13 $\times $ 10^{−6} | 8.13 $\times $ 10^{−4} |

Case 2 | 7.41 $\times $ 10^{−5} | 6.58 $\times $ 10^{−2} |

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**MDPI and ACS Style**

Lin, C.-C.
A Hybrid Heuristic Optimization Approach for Leak Detection in Pipe Networks Using Ordinal Optimization Approach and the Symbiotic Organism Search. *Water* **2017**, *9*, 812.
https://doi.org/10.3390/w9100812

**AMA Style**

Lin C-C.
A Hybrid Heuristic Optimization Approach for Leak Detection in Pipe Networks Using Ordinal Optimization Approach and the Symbiotic Organism Search. *Water*. 2017; 9(10):812.
https://doi.org/10.3390/w9100812

**Chicago/Turabian Style**

Lin, Chao-Chih.
2017. "A Hybrid Heuristic Optimization Approach for Leak Detection in Pipe Networks Using Ordinal Optimization Approach and the Symbiotic Organism Search" *Water* 9, no. 10: 812.
https://doi.org/10.3390/w9100812