Prediction of non-revenue water ratio in water distribution systems

Abstract

Keywords: ANFIS; ANN; Modeling; Non Revenue Water; Water Distribution Systems

Introduction

Considering global warming and climate change, the management of water resources and especially water losses should be one of the most significant issues for the countries which are located in the Mediterranean basin, a weak basin in terms of water. The amount of water loss in the water distribution systems (WDSs) is a crucial issue to consider [1, 2]. The water losses and leakage activities are caused by many factors related to physical instances like water measurement

errors, illegal water use, network age, and network pressure as well as the environmental reasons which depend on the topography and the state of the floor; the consumption habits and so on [3, 4]. To use water resources more efficiently and effectively, water utilities should calculate the Non-Revenue Water (NRW) quantities, a significant indicator for water leakages, and monitor them monthly by using water balance budget tables which were standardized by American Water Works Association (AWWA) and the International Water

*Corresponding author. *E-mail address: bkiziloz@isu.gov.tr This paper was recommended for publication in revised form by Editor in Chief Ahmet Selim DAlkilic Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Association (IWA). The high levels of the NRW ratio have negative impacts on the budgets and the future investment plans of the administrations. Recently, studies on NRW have increased in the literature. Among these studies, there are many different methods, analyses, and methodologies to estimate and decrease the NRW, through calculations with the risk evaluation approaches, and define its components [5- 9]. The NRW ratio performances in different regions of Kocaeli have been evaluated through methodologies based on risk [10, 11]. [12] developed various models in order to predict the NRW ratio, using the parameters in the WDSs with the methods of artificial neural network (ANN) and the multiple regression analysis (MRA). When the obtained results of the used models are compared, it is seen that the ANN (R2=0.6318) model has a higher prediction accuracy than the MRA (R2=0.1906). Incheon (Republic of Korea) developed a model with the ANN method in order to predict the NRW ratio using some of the specific parameters that are influential on the leaks in the WDSs [13]. The models are developed by using 10, 20 and 30 neurons in the hidden layer, and it reached to its best model correlation as R2=0.3973 with 20 neurons in the hidden layer. Various models have been developed to predict the NRW par [14] using ANN and ANFIS methods. According to one of the model results, the highest model accuracy is R2=0.65 with ANN, and R2=0.50 with ANFIS for the combination of WSQ/NL-ST/WM. In another study conducted on NRW

ratio prediction, the ANN and Kriging methods have been preferred [15]. When the model results have been analyzed, the highest model performance has been obtained for the combinations with three variables, ST/NJ-NL-MAP (R2=0.76) and NL-SCL-MPN (R2=0.76). According to the Kriging model results, the combinations with two inputs, SIV-NJ/MPN (R2=0.95) and SIV-NJ/MAP (R2=0.94) have been quite successful. In another study on the NRW prediction conducted by [16] through ANN and Kriging methodologies, the model performance for two inputs of WSQ/ SCL-MAP variables is R2=0.397, and this one is R2=0.89 for the Kriging model performance. [17] have used the Serial Triple Diagram Model (STDM) approach in another study and have obtained the model accuracy in the R2=0.99 level for the NRW ratio model predictions. In this study, the NRW ratios of WDS of Kocaeli’s twelve regions are modeled through ANN and Adaptive NeuroFuzzy Inference System (ANFIS) approaches. Within the scope of this study, NRW predictions have been evaluated for the first time in our country with i) ANFIS models with three and four-input combinations, ii) ANN models with four-input combinations, iii) ANN models with NNF variables, and finally, iv) ANFIS models with four-input with WM variable.

Study Area and Data Kocaeli is located between the 29° 22’-30° 21’ east-west longitudes and the 40° 31’- 41° 13’ north-south latitude. It is a metropolitan city with a total surface area of 3,623 km2 (Figure 1).

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Figure 2. The NRW ratio changes of the regions. It has 12 different regions in terms of water and sewerage administration. The water distribution system of the city has a total length of 8,936 km and the number of customers is 796,577 [15]. The total water consumption in the city is 163,627,918 m3 for the year 2018 [18]. There are 195 drinking water storages, which are controlled via the SCADA system, 105 drinking water elevation centers and 11 potable water treatment facility in the Kocaeli [15]. NRW ratio was 28% at the end of 2022. The physical losses are at a very high level of 24.79% and this is followed by the 6.03% of apparent losses and 1.49% of unbilled authorized consumption in Kocaeli. The 4.85% of authorized consumption errors component shows its impact on the NRW. In this study, the authorized consumption errors component, which has an impact on the NRW ratio, is included in the model study. The water balance components of 12 regions are also given separately in the Figure 2.

Figure 2 shows that Kartepe has the highest ratio of NRW, while Çayırova region has the lowest one. It is clear from the figure that the real loss component is much more efficient over the NRW ratio. Apparent loss component is another parameter that is influential over the NRW ratio.

Materials And Methods

The NRW ratio is predicted for the 12 regions of Kocaeli by models using the ANFIS and the ANNs methods in this study. Models are developed with single input and single output (SISO), two inputs and single output (TISO), three inputs and single output (T3ISO), and finally, four inputs and single output (FISO). As the input, the factors that represent the WDS are used such as the water supply quantity, the network length, the service connection length, the mean pipe diameter,

Table 1. Range of input-output parameters Parameters Abbreviation

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the number of service connection, the number of network failure, water meter, the number of junctions, the domestic water storage tank, the failure ratio, and the number of failures (Table 1). In the study, the ANN NRW ratio models are developed as training data (55%), validation data (35%) and testing data (10%). The Levenberg Marquad (LM) back-propagation training algorithm is used. In all the models, sigmoid activation function is used in the hidden layer with a threelayer feed forward back propagation network (FFBP). The best model results are obtained when there are four neurons in the hidden layer. Sugeno fuzzy logic (FL) System Inference principle is taken into account for the ANFIS models. In the models, grid partition method is used in order to generate the rules and categorize the input data. For all prediction models, the most appropriate MFs are selected. MFs of all models, linguistic terms such as “low”, “medium” and “high” are considered. Hybrid learning algorithm has been used in order to get the best prediction in all models. In order to prevent over-learning, the number of epochs is selected as 20 in the models. More detailed information about the ANN and ANIFS methodologies which are preferred frequently in the literature can be obtained from various resources [20, 21, 22]. The statistical operators below (correlation coefficient, R2, root mean square error, RMSE, mean absolute error, MAE, and scatter index, SI, and bias) are used in order to compare the NRW ratio prediction results with actual results and also to evaluate the best model performances.

where, Pi is the predicted data, n is the total number of − − data points, and Pi is the actual data. Finally, P and A are the means of the prediction and actual data.

Results And Discussion

ANN In this study, of all the collected datasets, the 55% (80 data) is randomly divided as training datasets, the 35% (50 data) for validation datasets, and 10% (14 data) for testing datasets. ANN models’ performance is given for each validation data set in Tables 2, 3, 4, and 5 for the prediction of the NRW ratio. The developed four-input models have generally higher model performance. In order to predict the NRW ratios a total of 146 ANN models are developed of which the 24 is single-input (SISO), 32 is two-input (TISO), 48 is three-input (T3ISO), and 42 is four-input (FISO) models. When the SISO models in Table 2 are analyzed, it is seen that the components of WDSs, such as the domestic water storage tank, water supply quantity, water meter, number of junctions, number of service connection, mean pipe diameter, network length and number of failures are the variables that have an impact on the NRW ratio. The estimated NRW ratio scatter graph to the measured NRW ratio is also drawn in Figures 3 and 4. It is seen that the best model is the ANN-1.12. Upon a close look at the 36 TISO models in Table 3, it is seen that the domestic water storage tank, number of junctions in water distribution networks and network length are variables that have an influence on the NRW ratio. The estimated NRW ratio scatter graph corresponding to the measured NRW ratio is drawn in Figures 5 and 6. It is seen that the best model is the ANN-2.27 Additionally, the number of inputs increases in the models, the performance of the models improves as well. The T3ISO models in the Table 4 show that water supply quantity, number of junctions in water distribution networks, network length, water meter and number of failures are the effective on the NRW ratio. When the estimated NRW ratio scatter graph corresponding to the actual NRW ratio is drawn in Figures 7 and 8, one can see that the best two models are ANN-3.34 and ANN-3.37. The FISO models in Table 5 show that water supply quantity, number of junctions in water distribution system, network length, mean pipe diameter and number of failures are the influential ones. The estimated NRW ratio scatter graph corresponding to the actual NRW ratio is drawn in Figures 9 and 10. Additionally, it is seen that the best two models are ANN-4.29 and ANN-4.34. The WDS consist of different uncertain components and each component is effective on the NRW ratio. Several 146 ANN models are developed with different combinations in the study and the results show that the all component has

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ANN-2.1 ANN-2.2 ANN-2.3 ANN-2.4 ANN-2.5 ANN-2.6 ANN-2.7 ANN-2.8 ANN-2.9 ANN-2.10 ANN-2.11 ANN-2.12 ANN-2.13 ANN-2.14 ANN-2.15 ANN-2.16 ANN-2.17 ANN-2.18 ANN-2.19 ANN-2.20 ANN-2.21 ANN-2.22 ANN-2.23 ANN-2.24 ANN-2.25 ANN-2.26 ANN-2.27 ANN-2.28 ANN-2.29 ANN-2.30 ANN-2.31 ANN-2.32 ANN-2.33 ANN-2.34 ANN-2.35 ANN-2.36

WSQ/NL–DWST/NSC WSQ/NL–DWST/SCL WSQ/NL–DWST/WM WSQ/NL–DWST/NJ WSQ/NL–DWST/MPD WSQ/NL–NL/WM WSQ/NL– NL/SCL WSQ/NL– NL/NSC WSQ/NL–MPD WSQ/NL–NNF WSQ/NL–FR WSQ/NL–WM [15] WSQ/NJ–WSQ/WM WSQ/NJ–WSQ/MPD WSQ/NJ–WSQ/NF WSQ/NJ–DWST/WM WSQ/NJ–DWST/MPD WSQ/NJ–DWST/NF WSQ/NJ–MPD [15] WSQ/NJ–FR WSQ/NJ-NL DWST/NJ–DWST/MPD DWST/NJ–MPD DWST/NJ–NL [15] DWST/NJ–FR [15]

Wsq-Nf Wsq-Fr

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ANN-3.1 ANN-3.2 ANN-3.3 ANN-3.4 ANN-3.5 ANN-3.6 ANN-3.7 ANN-3.8 ANN-3.9 ANN-3.10 ANN-3.11 ANN-3.12 ANN-3.13 ANN-3.14 ANN-3.15 ANN-3.16 ANN-3.17 ANN-3.18 ANN-3.19 ANN-3.20 ANN-3.21 ANN-3.22 ANN-3.23 ANN-3.24 ANN-3.25 ANN-3.26 ANN-3.27 ANN-3.28 ANN-3.29 ANN-3.30 ANN-3.31 ANN-3.32 ANN-3.33 ANN-3.34 ANN-3.35 ANN-3.36 ANN-3.37 ANN-3.38 ANN-3.39 ANN-3.40 ANN-3.41 ANN-3.42 ANN-3.43 ANN-3.44 ANN-3.45 ANN-3.46 ANN-3.47 ANN-3.48 ANN-3.49 ANN-3.50

WSQ/NL–DWST/NSC-DWST/WM WSQ/NL–DWST/NS -DWST/NJ WSQ/NL–DWST/NSC-DWST/MPD WSQ/NL–DWST/NSC-NL/WM WSQ/NL–DWST/NSC-WM WSQ/NL–DWST/NSC-MPD WSQ/NL–DWST/NSC-FR WSQ/NL–DWST/SCL-DWST/WM WSQ/NL–DWST/SCL-DWST/NJ WSQ/NL–DWST/SCL-DWST/MPD WSQ/NL–DWST/SCL-MPD WSQ/NL–DWST/SCL-NF WSQ/NL–DWST/SCL-WM WSQ/NL–DWST/SCL-FR WSQ/NL–DWST/WM-MPD WSQ/NL–DWST/WM-NF WSQ/NL–DWST/WM-FR WSQ/NL–DWST/NJ-MPD WSQ/NL–DWST/NJ-WM WSQ/NL–MPD-NF WSQ/NL–MPD-FR WSQ/NL–MPD-WM WSQ/NL–WM-FR WSQ/NL–WM-NF WSQ/NL–WSQ/WM-WSQ/MPD WSQ/NL–WSQ/WM-WSQ/NF WSQ/NJ–WSQ/WM-WSQ/MPD WSQ/NJ–WSQ/WM-WSQ/NF WSQ/NJ–DWST/WM-MPD WSQ/NJ–DWST/MPD-WM WSQ/NJ–MPD-WM WSQ/NJ–MPD-FR WSQ/NJ-NL-MPD WSQ/NJ-NL-WM WSQ/NJ-NL-NF

Wsq–wm-Nf

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ANN-4.1 ANN-4.2 ANN-4.3 ANN-4.4 ANN-4.5 ANN-4.6 ANN-4.7 ANN-4.8 ANN-4.9 ANN-4.10 ANN-4.11 ANN-4.12 ANN-4.13 ANN-4.14 ANN-4.15 ANN-4.16 ANN-4.17 ANN-4.18 ANN-4.19 ANN-4.20 ANN-4.21 ANN-4.22 ANN-4.23 ANN-4.24 ANN-4.25 ANN-4.26 ANN-4.27 ANN-4.28 ANN-4.29 ANN-4.30 ANN-4.31 ANN-4.32 ANN-4.33 ANN-4.34 ANN-4.35 ANN-4.36 ANN-4.37 ANN-4.38 ANN-4.39 ANN-4.40 ANN-4.41 ANN-4.42

WSQ/NL–DWST/NSC-DWST/WM-DWST/NJ WSQ/NL–DWST/NSC-DWST/MPD-DWST/NJ WSQ/NL–DWST/NSC-DWST/MPD-DWST/WM WSQ/NL–DWST/NSC-NL/WM-MPD WSQ/NL–DWST/NSC-WM-MPD WSQ/NL–DWST/NSC-MPD-FR WSQ/NL–DWST/NSC-WM-FR WSQ/NL–DWST/SCL-DWST/WM-MPD WSQ/NL–DWST/SCL-DWST/NJ-WM WSQ/NL–DWST/SCL-DWST/MPD-WM WSQ/NL –DWST/SCL-WM-MPD WSQ/NL–DWST/SCL-WM-FR WSQ/NL–DWST/SCL-MPD-FR WSQ/NL–DWST/WM-MPD-FR WSQ/NL–DWST/NJ MPD-WM WSQ/NL–DWST/NJ-MPD-FR WSQ/NL–MPD-WM-FR WSQ/NL–WSQ/WM-WSQ/MPD-WSQ/NF WSQ/NJ–WSQ/WM -WSQ/MPD-WSQ/NF WSQ/NJ–DWST WM-MPD-FR WSQ/NJ–DWST/MPD-WM-FR WSQ/NJ–MPD -WM-FR WSQ/NJ -NL-MPD-WM WSQ/NJ -NL-WM-FR WSQ/NJ -NL-MPD-FR WSQ/NJ-MPD-WM

Wsq–nsc-Mpd-Nf Wsq–nsc–wm-Nf

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Figure 9. Scatter graph for WSQ-NJ-NL-NF model. an impact on the NRW. Each component in the water distribution networks is evaluated by separate modeling, and its impact on the NRW ratio is studied. With the developed plenty of ANN models, the NRW ratios can be predicted at the partly acceptable levels.

Anfis

In order to predict the NRW ratio, ANFIS method is also used in this investigation and the results compare with the ANN model. The data used in the ANN method are also preferred for the ANFIS. Here, 66% of the total data is separated for the training, while the 34% testing for the validation. Starting from one input, and increasing the number of inputs one by one; the models are developed with the ANFIS until the four-input (see Tables 6, 7, 8, 9). In this part of the research, the most meaningful models are selected among all the ANN models, and total 57 ANFIS

Figure 10. Scatter graph for WSQ-NL-MPD-NF model model including 8 single-input, 15 two-input, 23 three-input and 11 four-input have been developed. The SISO ANFIS models and their performance in Table 6 has been presented. The estimated NRW ratio scatter graph corresponding to the actual NRW ratio is drawn in Figures 11 and 12. It is seen that the best model is ANFIS1.3. ANN models with single input are better than ANFIS model performances. The TISO ANFIS models in Table 7 show that the WSQ, NL, DWST, WM, NJ and FR are the variables, which have an impact on the NRW ratio. When the estimated NRW ratio scatter graph corresponding to the actual NRW ratio is drawn in Figures 13 and 14, one can see that the best model is ANFIS-2.8. It is seen that as the number of input increases as the correlation coefficient increases, while the scatterings decrease. The ANN method is better than the ANFIS method for model performances with two-input model combinations.

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Figure 11. Scatter graph for DWST/WM model [14] The T3ISO ANFIS models in Table 8 show that WSQ, NL, DWST, WM, NJ, SCL and FR are the variables, which have an impact on the NRW ratio. When the estimated NRW ratio scatter graphs corresponding to the actual NRW ratio are drawn in Figures 15 and 16; the best two models are ANFIS-3.2 and ANFIS-3.7. When the ANFIS model performances with TISO given in Table 7 are compared with the model performances with T3ISO given in Table 8, it is seen that there is no significant improvement. In conclusion, when the ANFIS models with FISO are analyzed, the FISO ANFIS model in Table 9 indicates that the WSQ, NL, WM, NJ, and MPD are the variables that

Figure 12. Scatter graph for MPD model are most effective on the NRW ratio. When the estimated NRW ratio scatter graphs corresponding to the actual NRW ratios are drawn in Figures 17 and 18; them the best two models are ANFIS-4.2 and the ANFIS-4.7. As the number of inputs in the models increases, the correlation coefficient little increases, while the scatterings decrease. The best performance among the ANFIS models has been obtained for the model combination with four-input (WSQ-NJ-NL-MPD). Out of all several ANN and ANFIS models that have been developed within the study ANN-4.29 and ANFIS-4.2 have the highest correlation coefficient and the smallest root mean square errors for the ANN and ANFIS methodologies

ANFIS-2.1 ANFIS-2.2 ANFIS-2.3 ANFIS-2.4 ANFIS-2.5 ANFIS-2.6 ANFIS-2.7 ANFIS-2.8 ANFIS-2.9 ANFIS-2.10 ANFIS-2.11 ANFIS-2.12 ANFIS-2.13 ANFIS-2.14 ANFIS-2.15 ANFIS-2.16

WSQ/NL–DWST/SCL WSQ/NL–DWST/WM [14] WSQ/NL–MPD WSQ/NL–WM WSQ/NJ–DWST/WM DWST/NJ–DWST/MPD DWST/NJ–NL DWST/NJ–FR

Wsq–nl Wsq-Wm

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ANFIS-3.1 ANFIS-3.2 ANFIS-3.3 ANFIS-3.4 ANFIS-3.5 ANFIS-3.6 ANFIS-3.7 ANFIS-3.8 ANFIS-3.9 ANFIS-3.10 ANFIS-3.11 ANFIS-3.12 ANFIS-3.13 ANFIS-3.14 ANFIS-3.15 ANFIS-3.16 ANFIS-3.17 ANFIS-3.18 ANFIS-3.19 ANFIS-3.20 ANFIS-3.21 ANFIS-3.22 ANFIS-3.23

WSQ/NL–DWST/NSC-DWST/MPD WSQ/NL–DWST/NSC-WM WSQ/NL–DWST/NSC-MPD WSQ/NL–DWST/SCL-DWST/WM WSQ/NL–DWST/SC -DWST/MPD WSQ/NL–DWST/SCL-WM WSQ/NL–DWST/SCL-FR WSQ/N –DWST/WM-MPD WSQ/NL–DWST/JUC-WM WSQ/NJ–WSQ/WM-SIV/MPD WSQ/NJ–DWST/WM-MPD WSQ/NJ-NL-MPD WSQ/NJ-MPD-WM WSQ/NJ-MPD-NF

19. It should be noted that there is an amount of difference

in the method among the model scatterings in which model results are compatible with each other. The results of this study are also compared with the earlier studies in Table 10. It is seen in Table 10 that the ANN,

Kriging, STDM, and ANFIS methodologies have been used in the literature to predict NRW ratios. As a result, the best ANN and ANFIS models have been determined by forming NRW ratio prediction models over many model input variables combinations.

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Figure 15. Scatter graph for WSQ/NL-DWST/NSC-WM model Figure 16. Scatter graph for WSQ/NL-DWST/SCL-FR model

ANFIS-4.1 ANFIS-4.2 ANFIS-4.3 ANFIS-4.4 ANFIS-4.5 ANFIS-4.6 ANFIS-4.7 ANFIS-4.8 ANFIS-4.9 ANFIS-4.10 ANFIS-4.11

Wsq–nsc-Mpd-Nf

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combinations. The best model accuracy is obtained by the (R2=0.606) combination of the ANFIS approach. Both models have average correlation and a small error to predict the NRW ratio. There is some amount of slight difference between the models due to a difference in method. Predicting and interpreting the NRW ratio is so difficult due to uncertainties. One of the leading causes of uncertainties is the inability to measure and monitor WDS parameters and variables with sufficient accuracy. Technological investments are needed to reduce NRW and to monitor accurately. These investments are only possible with an additional budget. It is expected that this study and its developed models can guide NRW ratio predictions for water utilities with relatively limited resources and prioritize their future investments accordingly. In conclusion, it is also expected that the developed models can serve as a model for the future studies of experts and researchers studying this subject. Figure 19. Compare of the best ANN and ANFIS models for this study.

Authorship Contributions

All authors contributed to the study conception and design. The data analysis was performed by B.K. initiated the research. The first draft of the manuscript was written by B.K., E.Ş., and all authors commented on and added to the following versions of the manuscript. All authors read, review, editing and approved the final manuscript.

Anfis

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Anfis

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

Within this study, research is operated on the NRW ratios in the WDSs through ANN and ANFIS models. A total of new 216 models are developed as SISO, TISO, T3ISO and FISO. The best prediction model with a maximum accuracy by both methods is researched. Among the methods, the best ones are obtained using the FISO variables. When all models are evaluated; it is seen that the WSQ, NL, DWST, NJ, MPD, NF, SCL and WM variables have an impact on the NRW ratio and that they should be taken into account in prediction models. The best ANN model is obtained by using the WSQNJ-NL-NF (R2=0.794) input parameters. Any prediction accuracy on ANN methodology could not be achieved with ANFIS models which are formed with various

There are no ethical issues with the publication of this manuscript.

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