Water loss detection in water distribution networks by artificial immune systems-based on model calibration

Öz This study aims at the development of an optimization model based on a model calibration, using Artificial Immune Systems (AIS) for quantifying and locating water losses in water distribution networks (WDNs). The modified Clonal Selection Algorithm (modified Clonalg), a class of AIS, was used as a heuristic optimization technique in the model. EPANET 2 was used in conjunction with the model. The model was applied to two-loop virtual WDN under steady-state conditions in order to test its performance in the detection of water losses in both pipes and nodes. The results showed that the model appeared to be promising in terms of the water loss detection in WDNs. Bu çalışmada, su dağıtım şebekelerindeki su kayıplarının miktarları ve yerlerinin tespit edilmesi için Yapay Bağışıklık Sistemleri (YBS) kullanılarak model kalibrasyonuna dayalı bir optimizasyon modelinin geliştirilmesi amaçlanmıştır. Modelde sezgisel optimizasyon tekniği olarak YBS’ nin çeşitlerinden biri olan Modifiye edilmiş Klonal Seçim Algoritması kullanılmıştır. Model ile birlikte EPANET 2 simulatörü kullanılmıştır. Borularda ve düğüm noktalarındaki su kayıplarının tespit edilmesindeki performansını test etmek üzere model, sürekli (sabit) koşullar altında iki gözlü sanal bir su dağıtım şebekesine uygulanmıştır. Sonuçlar, su dağıtım şebekelerindeki su kayıplarının tespit edilmesi açısından modelin gelecek vadettiğini göstermiştir.


Introduction
Water is of vital importance for all living creatures due to being a life source.This also increases the economic value of water.In this regard, the detection of water losses comes into prominence to prevent them in water distribution networks (WDNs).Water losses in the WDNs consist of unauthorized water consumptions, meter inaccuracies, and leakages or bursts of pipes and nodes.Misiunas [1] and De Silva et al. [2] compiled the most commonly used leakage detection techniques in WDNs, which are Static Mass Balance [3]- [5], State Estimation [6]- [8], Transient Analysis [9]- [28], Acoustic Methods [29]- [45].Within these techniques, various sensors, meters, monitoring systems and measurements (flow rate, pressure and temperature sensors detecting quasi-static signals, acoustic sensors detecting sound waves/noises, electro-magnetic sensors, infrared thermography, transmitters emitting radio frequencies, manometers, flow meters, SCADA, tracing substances so on.)are used and installed into WDNs.Therefore, the water loss detection is an expensive and difficult task.In order to facilitate the task, an optimization model based on a model calibration, using Artificial Immune Systems (AIS) was developed in this study.The model minimizes number of required field measurements used in a model calibration (pressures are not used) for detecting water losses in pipes and nodes of WDNs.The model was applied to two-loop virtual WDN under steady-state conditions in order to test its performance in the water loss detection.The results showed that the model can detect both locations and amounts of water losses in the WDN.

Methodology and formulation
Model calibration is the process of minimizing the discrepancy between the model predictions and field observations of pressures and flows to determine the physical and operational characteristics of an existing system.These characteristics consist of model parameters such as pipe roughness, nodal demand, operation status of pipes, pumps, valves and tanks [46]- [50].Wu et.al.[48] defined model calibration as an implicit nonlinear optimization problem and used it for determining pipe roughness coefficients via Genetic Algoritm (GA).Model calibration is also utilized for detecting water losses or leaks in WDNs.Wu and Sage [49] presented an optimization-based approach using GA for simultaneously quantifying and locating water losses via the process of hydraulic model calibration.Prasad [51] proposed a model using Clonal Selection Algorithm (Clonalg) to determine model parameters including nodal demands, pipe roughness values, valve closures, pump controls and valve settings.Nasirian et al. [52] studied leak detection based on calibration in WDNs, and introduced a novel optimization method combining with GA to calibration and leakage detection in networks.In order to obtain model parameters in WDNs, model calibration process is optimized by minimizing the discrepancy between the model predicted and the field observed values of junction pressures and pipe flows under boundary conditions such as tank levels, control valve Pamukkale Univ Muh Bilim Derg, 23 (9)  +  (1) where Hobsnh is nh-th observed pressure, Hsimnh is nh-th simulated pressure, Fobsnf is nf-th observed flow rate, Fsimnf is nf-th simulated flow rate, Hpnt notes the hydraulic head per fitness point while Fpnt is the flow per fitness point, NH is the number of observed pressures, and NF is the number of observed pipe flows, wnh and wnf the weighting factors.Instead of Equation (1), Equation ( 2) was derived for detecting water losses in the WDN in this study: where Dobsnd is the nd-th observed junction (nodal) demand, Dsimnd is the nd-th model simulated junction demand.In this study, unauthorized water consumptions in nodes, and leakages in pipes were considered as water losses in WDNs.As applied by [8], all leakages in pipes were assumed as pseudo nodes and simulated as nodal demands.Unauthorized consumptions were added as a demand by demand multipliers to base demands in nodes [49].In the detection of water losses, the objective function is minimized by considering the following constraints: The equation of continuity has to be met for each node: where Qinf and Qoutf are inflow and outflow of a node, Qef is the external inflow or water demand at a node.The minimum pressure required for each node is formulated as the following: where Hj is the pressure head at node j, Hj min is a minimum required pressure head at node j, M is the number of nodes in WDN.The penalty function was defined in case of violating the constraints as follows: In this study, Hj min was assigned as zero so that negative pressures not occur in the nodes.EPANET 2 was used for hydraulic computations [53].The modified Clonalg was utilized for minimizing the objective function above.Eryigit [54] defined the modified Clonalg for optimization problems as follows: where Ab is an antibody population randomly generated, f is an antigenic affinity corresponding to the objective function of a given antibody, C is a set of antibodies cloned, C* is a set of matured (mutated) antibodies after the cloning process.
Description of Ab: where NAb is the total number of Ab, xij is a gene of Abi (decision variable of f), nd is the number of genes.In the study, xij corresponds to the nodal demand.The modified .Clonalg was coded in Matlab 2012a software in conjuction with EPANET 2.

Sample two-loop WDN
The network contains seven actual nodes including nodes 1-6, and a reservoir, eight pipes with two loops, and is fed by the gravity from a 75-m-head reservoir.Nodes 7-13 are pseudo nodes representing leakages in pipes.Also, unauthorized water consumptions were added to base demands in nodes 1-6 as water losses.Data and layouts of Two-loop WDN are given in Table 1, Table 2, and illustrated in Figure 2, and Figure 3, respectively.
As it is seen in Figure 2 and 3, leakages in pipes 1, 2 and 5 (pseudo nodes 9, 7 and 8, respectively) can be calculated by eq.
Although there is no leakage in pipe 3, it was assumed as a pseudo node (node 10) due to it's a leak candidate.

Results
The optimization model was run 20 times for Two-loop network.Random seed was carried out while constituting an initial set in each run.A PC with Intel I5 Core 2.5 Ghz (3.1 Ghz with Turbo Boost) and Matlab 2012a were used for the analysis.
The results of the model were given in Table 3 and Table 4.

Conclusions
The model can detect both locations and amounts of water losses in nodes and pipes of the WDN without using observed pressure data (see Equation ( 1)).Also, although there are four leakages (in pipes 3, 4, 6 and 7) in the WDN, which cannot be calculated by Equation (3) with observed data, they were detected successfully.These demonstrate that the model minimizes number of required field measurements used in a model calibration (pressures are not used) for detecting water losses in pipes and nodes of WDNs.The results showed that the model seems to be substantially successful and feasible for the water loss detection in WDNs.In next studies, a performance of the model should be tested for different WDNs.

Table 1 :
Data of Two-loop WDN.

Table 2 :
Operating data of two-loop WDN.
*All observed flow rates were assumed to be only measured at initial points of pipes in the WDN.

Table 3 :
Parameters and performance of the modified Clonalg for the objective function β: Multiplying coefficient for the cloning.ρ: Decay coefficient.

Table 4 :
Comparison of actual and predicted water losses in nodes and pipes.