This research introduces an inverse transientbased optimization approach to automatically detect potential faults, such as leaks, partial blockages, and distributed deteriorations, within pipelines or a water distribution network (WDN). The optimization approach is named the Pipeline Examination Ordinal Symbiotic Organism Search (PEOS). A modified steady hydraulic model considering the effects of pipe aging within a system is used to determine the steady nodal heads and piping flow rates. After applying a transient excitation, the transient behaviors in the system are analyzed using the method of characteristics (MOC). A preliminary screening mechanism is adopted to sift the initial organisms (solutions) to perform better to reduce most of the unnecessary calculations caused by incorrect solutions within the PEOS framework. Further, a symbiotic organism search (SOS) imitates symbiotic relationship strategies to move organisms toward the current optimal organism and eliminate the worst ones. Two experiments on leak and blockage detection in a single pipeline that have been presented in the literature were used to verify the applicability of the proposed approach. Two hypothetical WDNs, including a smallscale and largescale system, were considered to validate the efficiency, accuracy, and robustness of the proposed approach. The simulation results indicated that the proposed approach obtained more reliable and efficient optimal results than other algorithms did. We believe the proposed fault detection approach is a promising technique in detecting faults in field applications.
Water distribution networks (WDNs) in modern cities are usually largescale, with complex systems and limited instrumentation. Water may be lost due to system aging, poor maintenance, and improper operations. The effective management of a water supply may be a serious engineering problem faced by cities, and rapid urbanization and infrastructure aging are expected to intensify in the future [
Due to different data collection methods, the fault identification problem may be classified into the following two categories: Steadystate methods and transient analysis. Steadystate methods, such as vibration analysis, pulseecho analysis, and acoustic reflectometry, were developed in previous studies for leak isolation [
The heuristic algorithm is capable of searching for global optimal solutions [
Blockage detection is a crucial issue in aged pipelines and pipe networks in energy, chemical, and water industries. A blockage consists of chemical or physical depositions [
The condition of the pipe wall in pressurized pipelines changes with their age or operating condition. Pipe wall deterioration may be due to corrosion, material erosion, and external pressures with system aging. At present, the transientbased approach is recognized as a potential tool for the noninvasive detection of discrete and distributed deterioration in pressurized pipelines [
Multiple fault detection in pipeline systems or WDNs using ITA is considered to be a troublesome issue because a large amount of input data and computation time is required. Moreover, the computation time and searching space in the optimization process may be enormous, especially for a complicated WDN with multiple faults. This paper presents a novel and efficient transientbased approach for multiple fault detection, including leak detection, partial blockage identification, and distributed deterioration determination, in a single pipeline or a WDN. An ITAbased hybrid heuristic approach called the Pipeline Examination Ordinal Symbiotic Organism Search (PEOS) was developed based on a combination of an ordinal optimization algorithm (OOA) and a symbiotic organism search (SOS). The proposed approach can simultaneously determine information on various faults via inverse calculation. Two experimental single pipeline cases and two numerical tests with different pipe network configurations were considered to examine the performance and capability of the proposed approach. The performance of PEOS was further compared to different optimization algorithms to demonstrate its accuracy and efficiency in predicting fault information. The reliability and robustness of the proposed approach for fault detection in a complicated WDN (considering data collection issues) was further validated.
EPANET is a widely used public software package for modeling hydraulic and water quality behavior in pressurized pipe systems. However, it needs an external functionality to model water leakage in a system in simulations [
For a new installed pipe (i.e.,
The unsteady pressurized flow in a pipe network with a known steadystate nodal head and flow rate can be described by a pair of partial differential equations, written as [
Three kinds of faults (i.e., leaks, partial blockages, and distributed deterioration) are considered and discussed. Both leaks and blockages could be described by the simple orifice equation and implemented as an internal boundary condition in the MOC analysis as [
The volumetric flow rate
Similarly, a discrete (partial) blockage is treated as an inline valve with a constant opening area. The upstream and downstream of the blockage satisfy the continuity conditions of the head and flux. The volumetric flow rate
Deterioration (e.g., pipe wall damage or pipeline corrosion) often introduces a decrease in pipe wall thickness, which in turn introduces a change in the pipeline impedance and wave speed, defined as [
Ho et al. [
The SOS algorithm [
In short, the organisms (solutions) in the ecosystem are guided toward the current best organism in mutualism and commensalism states, while the parasitism state is used to prevent the organisms trapping in a local optimal solution. These three states are repeated until the stopping criterion is achieved. Details about the SOS algorithm are given in the
The ITA introduced by Pudar and Liggett [
The PEOS is a hybrid heuristic algorithm combining the screening procedure of OOA and the heuristic algorithm SOS to automatically determine fault information in WDNs. The overall operational architecture and steps of PEOS are briefly given below (also in
Import the network configurations;
Randomly generate candidate solutions (CASes) with different fault information consisting of the unknown variables listed in
Rearrange the network configurations, since the new fault points (leaks and blockages) and/or new fault pipe reaches (deterioration parts) are added;
Use PNSOS to calculate the optimal steadystate nodal heads and piping flow rates within a given WDN for each CAS;
Generate hydraulic transient events and apply the MOC to obtain the transient head distribution of each CAS;
Utilize Equation (14) to calculate the CASes’ objective function values (OFVs) and rank them. The top 5% of CASes with smaller OFVs are selected for the next step;
Consider the selected CASes to be initial organisms for the ecosystem of the SOS used in the pipe examination;
Execute the fault detection procedure, in which the organisms containing fault information continually move forward to the current best solution (
Check whether the optimization process satisfies the stopping criterion. If so, the fault detection procedure is then terminated and moves to the next step. Otherwise, the searching process goes on.
The first stopping criterion is defined as the absolute difference between two successive optimal OFVs (in Equation (14)), which is always less than 10^{−4} within four iterations. The second criterion for fault detection is the iteration reaching the specified maximum limit.
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 algorithmbased 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 bestknown position and is also guided toward the global bestknown positions in the search space. The readers may refer to References [
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 [
The second case was carried out at the Water Engineering Laboratory (WEL) at the University of Perugia, Italy [
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
The temporal head distributions predicted by the PEOS for the IC and WEL pipeline systems were respectively displayed in
A synthetic benchmark WDN (pipe network A) was adopted from Reference [
In the following section, the performance of the proposed approach is validated and compared to the other evolutionary algorithmbased approaches mentioned in
The steadystate nodal heads and piping flow rates of pipe network A were solved by PNSOS in 52 s. The transient head distributions were further predicted by three benchmark algorithms and the proposed approach. Temporal transient perturbations were observed at N8 by applying different approaches with the various
The present techniques were further executed five times to guarantee the reproducibility of the predicted result and to test its efficiency, accuracy, and robustness for obtaining the optimal solution. The
PEOS further demonstrated its accuracy and robustness in fault detection on a largescale drinking WDN by considering different data collection issues.
N1 was the first reservoir with a constanthead of 138.9 m, and the second reservoir N2 had a constanthead of 91.4 m. The inflow rates at nodes N9 and N31 were both 1620.33 L/s. The consumption rates at nodes N10, N14, N17, N21, N25, N30, N32, N37, N45, N46, and N47 were respectively 23.15, 17.36, 162.04, 74.07, 104.17, 12.73, 92.59, 138.88, 254.63, 196.76, and 16.2 L/s. Three leaks were separately located at different pipes. Leak L1 was at the middle of P19 and was 1150 m away from N36. Leak L2 was located at P32, 0 m away from N22, implying that leak L2 occurred exactly at N22. Leak L3 was 960 m away from N12 and was located at P41. The
Three cases were selected to test the capability of PEOS in fault detection in a complex pipe network such as pipe network B, considering the effects of limited observations, measurement errors, and inappropriate transient operation. Case 1 used less data, with a low frequency of 0.1 s (i.e., 10% of the original sampling frequency) to represent instrument limitations in the field survey, and thus 601 data points were collected and used in the simulation of case 1. In case 2, measurement errors were added to the 601 lowfrequency data points to depict the uncertainty in data collection. Notice that the white noise
Case 3 was designed under the same sampling frequency as case 1, but the transient operation time was extended to 10 s to address the effects of an inappropriate transient operation. There were 601 data points collected after 10 s of transient operation that were used in the simulations of case 3.
In order to evaluate the effects of limited observations and measurement errors on the results predicted by the proposed approach, two error criteria, the standard error of the estimate (SEE) and mean error (ME), were considered. The SEE is a measure of the accuracy of predictions, defined as the square root of the sum of squared errors between the observed and predicted heads divided by the number of degrees of freedom, which equals the number of observed data points minus the number of unknowns. The criterion ME is the average of the sum of errors between the observed and simulated heads.
The steadystate hydraulics of pipe network B were predicted by PNSOS in 309 s, and the transient event was then generated by closing the valve at N17. The transient head distributions for cases 1–3 were therefore measured at N17.
In case 3, leaks, blockages, and deterioration segments were also accurately determined by PEOS, with its associated parameters listed in
This paper demonstrates an inverse transientbased heuristic optimization approach called PEOS for pipe examination in a pipeline or pipe network system. The application of PEOS was verified by two experimental RPV systems in the literature, and PEOS was further applied to identify fault information in synthetic pipe networks. PEOS was used to detect faults in an experimental pipeline (carried out at Imperial College London) and in a pipeline at the Water Engineering Laboratory at the University of Perugia. The head distributions predicted by PEOS agreed well with those from the experiments reported in the literature. The leak and blockage information in both systems was accurately determined by the proposed approach. The results indicated that PEOS provided good predictions in fault detection in a real pipeline system.
The proposed approach was further compared to three evolutionarybased algorithms in fault detection in a synthetic benchmark pipe network. Temporal head distribution and fault information were accurately predicted by PEOS and agreed well with the actual ones, even when using only 10 initial input organisms. PEOS on average took about 50.6 min and 1382 iterations to obtain the optimal results, which is significantly faster than other algorithms. The results indicated that the OOA made the proposed approach avoid most unnecessary calculations of incorrect solutions and quickly converge to the optimal result via three states of SOS. In other words, PEOS not only provided predictions with better accuracy and robustness, but also performed better at computational efficiency. The proposed approach with these two advantages obviously outperformed other algorithms.
To illustrate the applicability of PEOS in fault detection in realworld problems, a largescale WDN with three data collection statuses was considered as a field study to represent practical issues. The results indicated that PEOS performed well in solving the fault detection problem, considering the effects of limited observations and measurement errors in a complicated WDN. The effect of limited observations on the estimated result was not significant, but the measurement errors induced some inaccuracy. When the observations contained measurement errors, the predicted
In summary, we demonstrated via the simulations that PEOS has the ability to simultaneously detect various faults in a pipeline and pipe networks and can outperform other existing evolutionarybased algorithms. Another superiority of PEOS over competing algorithms is the small number of parameters that must be tuned. Fault information can be precisely predicted even when observations are collected with issues. The cases presented in this study were for relatively simple pipe system configurations and operations. Extending the current work from numerical simulations to solving the problems of realworld complicated WDNs would be an interesting direction for further research.
The details of the SOS algorithm are available online at
C.C.L. designed the numerical experiment, analyzed the data, and wrote the paper. H.D.Y. is the supervisor of the proposed research.
The authors would like to thank the editor and three anonymous reviewers for their valuable and constructive comments, which greatly improved the manuscript.
The authors declare no conflict of interest.
Flowchart of the Pipe Examination Ordinal Symbiotic Organism Search (PEOS).
The simulated head distributions at the valve for (
Configuration of pipe network A with a sectional view of P1.
Temporal transient perturbations at N8 of pipe network A predicted by (
Impedance and wave speed along (
Configuration of the largescale WDN (pipe network B).
Fault information to be determined.
Variable  Description 




Leak pipe number 

Leak location 

Discharge coefficient times the leak area of the orifice 



Blockage pipe number 

Blockage location 

Discharge coefficient times the open orifice area of the blockage 



Deterioration pipe number 

Deterioration location 

Length of 

Wave speed of 

Pipe crosssectional area of 
Specific parameters for each algorithm, with
PEGA  PEPSO  PESOS and PEOS 

No specific parameters required  
 
Note:
The predicted and actual fault information for the two pipeline systems.













Actual  2  15.95  1.21 × 10^{−5}    3  46.32  1.50 × 10^{−5}    
PEOS  2  16  1.23 × 10^{−5}  1.65  3  46  1.52 × 10^{−5}  1.33  








Actual  2  38.96  1.18 × 10^{−3}    
PEOS  2  38  1.20 × 10^{−3}  1.69  
Note:
The characteristics of the synthetic water distribution network (WDN) (pipe network A).
Pipe  Node  Diameter (mm)  Length (m)  Impedance (s/m^{2})  Year Used (year)  

From  To  
P1  N1  N2  300.0  1000.0  1442.60  10  108.2 
P2  N2  N3  300.0  1000.0  1442.60  15  90.2 
P3  N3  N4  250.0  1100.0  2077.35  10  105.7 
P4  N1  N4  400.0  1250.0  811.47  15  92.2 
P5  N4  N5  200.0  500.0  3245.86  5  112.1 
P6  N5  N6  400.0  400.0  811.47  5  114.2 
P7  N7  N6  200.0  500.0  3245.86  5  112.1 
P8  N4  N7  350.0  400.0  1059.87  5  113.6 
P9  N7  N8  350.0  600.0  1059.87  5  113.6 
P10  N8  N9  300.0  1100.0  1442.60  10  108.2 
P11  N3  N9  300.0  1250.0  1442.60  15  90.2 
Determined fault information of pipe network A.

Method  L1  B1  D1  





Actual  11  300  2.50 × 10^{−4}  10  200  5.60 × 10^{−2}  1  200  80  800  1148.98  
10  PEGA  2  650  3.27 × 10^{−4}  Not detected  Not detected  
PEPSO  11  830  3.19 × 10^{−4}  Not detected  3  510  100  805  1156.16  
PESOS  11  300  2.49 × 10^{−4}  10  200  5.58 × 10^{−2}  1  200  80  800  1148.98  
PEOS  11  300  2.51 × 10^{−4}  10  200  5.61 × 10^{−2}  1  200  80  800  1148.98  
20  PEGA  11  510  3.34 × 10^{−4}  Not detected  3  490  70  805  1156.16  
PEPSO  11  300  2.49 × 10^{−4}  10  200  5.61 × 10^{−2}  3  700  70  805  1156.16  
PESOS  11  300  2.50 × 10^{−4}  10  200  5.59 × 10^{−2}  1  200  80  800  1148.98  
PEOS  11  300  2.50 × 10^{−4}  10  200  5.60 × 10^{−2}  1  200  80  800  1148.98  
50  PEGA  11  300  2.49 × 10^{−4}  10  200  5.60 × 10^{−2}  1  200  80  800  1148.98 
PEPSO  11  300  2.49 × 10^{−4}  10  200  5.60 × 10^{−2}  1  200  80  800  1148.98  
PESOS  11  300  2.50 × 10^{−4}  10  200  5.59 × 10^{−2}  1  200  80  800  1148.98  
PEOS  11  300  2.50 × 10^{−4}  10  200  5.60 × 10^{−2}  1  200  80  800  1148.98 
The performances of the four algorithms.
Method  Round  CPU Time (min)  Average Time (min)  Iterations  Average Iterations 

PEGA  1  325  331.2  8021  8072 
2  346  8216  
3  322  8124  
4  324  7983  
5  339  8016  
PEPSO  1  310  302.2  7502  7604 
2  308  7551  
3  312  7669  
4  294  7606  
5  287  7710  
PESOS  1  101  105.4  3789  3882 
2  107  4012  
3  108  3883  
4  110  3810  
5  101  3915  
PEOS  1  56  50.6  1415  1382 
2  49  1371  
3  46  1337  
4  52  1396  
5  50  1391 
Note: CPU time is the computation time.
The characteristics of the largescale WDN (pipe network B).
Pipe  Node  Diameter (mm)  Length (m)  Impedance (s/m^{2})  Year Used (year)  

From  To  
P1  N48  N1  950.0  240.0  143.86  5  120.5 
P2  N34  N33  900.0  60.0  160.29  10  113.5 
P3  N2  N46  1450.0  1830.0  61.75  0  130.0 
P4  N43  N2  1150.0  3550.0  98.17  0  130.0 
P5  N41  N45  1450.0  1220.0  61.75  0  130.0 
P6  N45  N46  1450.0  640.0  61.75  0  130.0 
P7  N42  N43  900.0  60.0  160.29  10  113.5 
P8  N41  N43  900.0  60.0  160.29  10  113.5 
P9  N44  N43  1000.0  50.0  129.83  10  114.6 
P10  N42  N2  900.0  3660.0  160.29  10  113.5 
P11  N41  N42  900.0  60.0  160.29  10  113.5 
P12  N42  N44  1000.0  60.0  129.83  10  114.6 
P13  N40  N42  900.0  800.0  160.29  10  113.5 
P14  N37  N41  1450.0  3140.0  61.75  0  130.0 
P15  N38  N43  1150.0  3140.0  98.17  0  130.0 
P16  N39  N44  1650.0  3140.0  47.69  0  130.0 
P17  N38  N36  900.0  60.0  160.29  10  113.5 
P18  N38  N39  1000.0  60.0  129.83  10  114.6 
P19  N36  N40  800.0  2300.0  202.87  10  112.8 
P20  N38  N37  900.0  60.0  160.29  10  113.5 
P21  N35  N38  1150.0  4050.0  98.17  0  130.0 
P22  N36  N37  900.0  60.0  160.29  10  113.5 
P23  N33  N36  800.0  4050.0  202.87  10  112.8 
P24  N34  N37  1150.0  4050.0  98.17  0  130.0 
P25  N33  N35  900.0  60.0  160.29  10  113.5 
P26  N34  N35  900.0  60.0  160.29  10  113.5 
P27  N25  N32  800.0  2150.0  202.87  10  112.8 
P28  N32  N33  800.0  180.0  202.87  10  112.8 
P29  N23  N34  1450.0  2980.0  61.75  0  130.0 
P30  N25  N35  1450.0  2980.0  61.75  0  130.0 
P31  N31  N30  1650.0  12,000.0  47.69  0  130.0 
P32  N22  N24  950.0  670.0  143.86  10  114.0 
P33  N29  N28  1000.0  60.0  129.83  10  114.6 
P34  N30  N29  1650.0  13400.0  47.69  0  130.0 
P35  N13  N11  900.0  80.0  160.29  10  113.5 
P36  N11  N15  950.0  4290.0  143.86  5  120.5 
P37  N12  N14  900.0  4290.0  160.29  5  115.7 
P38  N13  N12  50.0  60.0  51,933.76  10  102.6 
P39  N10  N11  970.0  2590.0  137.99  5  120.5 
P40  N11  N12  50.0  60.0  51,933.76  10  102.6 
P41  N6  N12  900.0  2960.0  160.29  5  115.7 
P42  N7  N13  1150.0  2960.0  98.17  0  130.0 
P43  N9  N8  1150.0  2280.0  98.17  0  130.0 
P44  N8  N10  950.0  370.0  143.86  5  120.5 
P45  N8  N7  1000.0  90.0  129.83  0  130.0 
P46  N6  N7  50.0  60.0  51,933.76  10  102.6 
P47  N5  N6  900.0  1610.0  160.29  5  115.7 
P48  N6  N8  50.0  60.0  51,933.76  10  102.6 
P49  N3  N5  950.0  1350.0  143.86  5  120.5 
P50  N4  N8  50.0  2960.0  51,933.76  10  102.6 
P51  N47  N3  950.0  6530.0  143.86  5  120.5 
P52  N3  N4  900.0  60.0  160.29  10  113.5 
P53  N48  N47  950.0  230.0  143.86  5  120.5 
P54  N48  N4  950.0  7200.0  143.86  5  120.5 
P55  N27  N26  1000.0  60.0  129.83  10  114.6 
P56  N29  N27  1150.0  3200.0  98.17  0  130.0 
P57  N26  N25  1450.0  4300.0  61.75  0  130.0 
P58  N28  N26  1150.0  3200.0  98.17  0  130.0 
P59  N22  N23  800.0  80.0  202.87  10  112.8 
P60  N23  N25  750.0  90.0  230.82  0  130.0 
P61  N18  N23  950.0  2050.0  143.86  5  120.5 
P62  N21  N22  800.0  2380.0  202.87  10  112.8 
P63  N20  N23  1150.0  3050.0  98.17  0  130.0 
P64  N19  N21  50.0  670.0  51,933.76  5  105.8 
P65  N18  N19  50.0  60.0  51,933.76  10  102.6 
P66  N19  N20  50.0  60.0  51,933.76  10  102.6 
P67  N17  N19  800.0  1830.0  202.87  10  112.8 
P68  N18  N20  900.0  60.0  160.29  10  113.5 
P69  N14  N17  800.0  1950.0  202.87  10  112.8 
P70  N15  N18  950.0  3780.0  143.86  5  120.5 
P71  N16  N14  50.0  60.0  51,933.76  5  105.8 
P72  N16  N15  900.0  60.0  160.29  10  113.5 
P73  N13  N16  1150.0  4290.0  98.17  0  130.0 
P74  N14  N15  50.0  60.0  51,933.76  5  105.8 
The optimal fault information of pipe network B predicted by PEOS for three cases.
Case  Leak  Blockage  Deterioration  

No. 

No. 

No. 


Actual  L1  19  1150  2.00 × 10^{−4}    B1  23  200  4.00 × 10^{−1}    D1  62  400  40  800  163.2  
L2  32  0  1.00 × 10^{−4}    B2  39  600  6.00 × 10^{−1}    D2  67  600  30  600  122.4  
L3  41  960  1.20 × 10^{−4}          
Case 1  L1  19  1150  1.98 × 10^{−4}  1.00  B1  23  190  3.98 × 10^{−1}  0.50  D1  62  400  40  799.2  163.0  
L2  32  0  1.01 × 10^{−4}  1.00  B2  39  600  6.04 × 10^{−1}  0.67  D2  67  600  30  603.1  123.0  
L3  41  950  1.18 × 10^{−4}  1.67        
Case 2  L1  19  1160  1.88 × 10^{−4}  6.00  B1  23  200  3.79 × 10^{−1}  5.25  D1  62  390  40  794.3  162.0  
L2  32  0  0.98 × 10^{−4}  2.00  B2  39  610  5.75 × 10^{−1}  4.17  D2  67  610  30  595.8  121.5  
L3  41  950  1.11 × 10^{−4}  5.83      
Case 3  L1  19  1150  1.96 × 10^{−4}  2.00  B1  23  190  3.94 × 10^{−4}  1.50  D1  62  400  40  798.5  162.9  
L2  32  0  0.99 × 10^{−4}  1.00  B2  39  600  6.07 × 10^{−4}  1.16  D2  67  600  30  598.2  122.1  
L3  41  950  1.17 × 10^{−4}  2.50       
Note:
The prediction errors for three cases. ME: mean error; SEE: standard error of the estimate.
Case  Prediction Errors  

ME (m)  SEE (m)  
1  3.41 × 10^{−6}  1.27 × 10^{−4} 
2  1.73 × 10^{−4}  6.35 × 10^{−2} 
3  3.29 × 10^{−6}  1.12 × 10^{−4} 