Up to journal
for Research & Developement
Journal of Materials Science: Materials in Electronics
Impact Factor
2000 - 2020
Open Access

Iranian Water Researches Journal
Evaluation of Wavelet Regression and Neuro-Fuzzy Models for Estimating Urban Water Consumption (Case Study: Kerman City)

 submission: 14/08/2019 | acception: 23/12/2019 | publication: 07/09/2020


Masoud Reza Hessami Kermani1*, Reza Valiparast Farkhani2

1-Shahid Bahonar University of Kerman،hessami@uk.ac.ir

2-Shahid Bahonar University of Kerman،r.valiparast@gmail.com



In the discussion of water demand management, it is important to have a predictive model of water consumption for the coming days. Such model can be useful in taking management decisions such as water rationing policies, water removal rates from wells and suitable timing for pumping water. Predicting water consumption in urban areas is of key importance for water supply management. Predictive modeling for water consumption can be used for planning water supply and expanding infrastructure for new developments and improving the control and operation of the water resources systems. In this research, the performance of Multi Linear Regression (MLR), Adaptive Neuro-Fuzzy Inference System (ANFIS), coupled Wavelet and MLR (WR) and coupled Wavelet and ANFIS (WANFIS) were evaluated in predicting water demand in Kerman City, Iran. For this purpose, weekly time series of water consumption and meteorological parameters including maximum temperature and total precipitation were used to predict weekly water consumption based on ۱۲ years data from ۲۰۰۶ to ۲۰۱۷. The data from ۲۰۰۶ to ۲۰۱۴ (۴۶۹ weeks) were considered for the training of MLR, WR, ANFIS and WANFIS models and the remaining data from ۲۰۱۵ to ۲۰۱۷ (۱۵۷ weeks) were used for the validation of various mentioned models. In WR and WANFIS wavelet-based models, the weekly time series of water consumption, maximum temperature and precipitation are decomposed by discrete wavelet transformation (DWT) to sub-series of approximations and details at various levels which are used as inputs of wavelet based models. The objective of multiple linear regression (MLR) analysis is to study the relationship between several independent or predictor variables and a dependent or criterion variable. The aim of this method is to determine the regression parameters by which the estimated values are efficient and consistent. Coupled Wavelet and Multi Linear Regression (WR) models are MLR models which use, as inputs, subseries components which are derived from the use of the Discrete Wavelet Transform (DWT) on the original time series data. Fuzzy Inference System (FIS) is a rule based system consisting of three components: (i) a rule-base, containing fuzzy if-then rules; (ii) a data-base, defining the membership functions (MF); and (iii) an inference system that combines the fuzzy rules and produces the system results. Fuzzy Logic (FL) is employed to describe human thinking and reasoning in a mathematical framework. The main problem with fuzzy logic is that there is no systematic procedure to define the membership function parameters. The construction of the fuzzy rule necessitates the definition of premises and consequences as fuzzy sets. On the other hand, an ANN has the ability to learn from input and output pairs and adapt to it in an interactive manner. In recent years, the ANFIS method, which integrates ANN and FL methods, has been developed. ANFIS has the potential benefits of both these methods in a single framework. ANFIS eliminates the basic problem in fuzzy system design, defining the membership function parameters and design of fuzzy if-then rules, by effectively using the learning capability of ANN for automatic fuzzy rule generation and parameter optimization. Coupled wavelet and Adaptive Neuro-Fuzzy Inference System (WANFIS) models are ANFIS models which use, as inputs, subseries components which are derived from the use of the Discrete Wavelet Transform (DWT) on the original time series data. In this comparative study, the performance of all predictive models was evaluated by statistical indices including coefficient of correlation (R), coefficient of determination (R۲), root mean square error (RMSE) and mean absolute error (MAE). The obtained results from this study suggest that the wavelet-based models including the WR model (for training: R۲ = ۰.۹۲, RMSE = ۳۴۱۵۱ m۳, MAE = ۲۳۹۰۸ m۳ and for simulation R = ۰.۹۷, RMSE = ۲۳۴۸۶ m۳, MAE = ۱۶۷۸۸ m۳) and the WANFIS (for training: R۲ = ۰.۹۴ RMSE = ۲۹۱۷۹ m۳, MAE = ۲۰۶۷۵ m۳ and for simulation: R = ۰.۹۲, RMSE = ۴۳۶۹۸ m۳, MAE = ۲۹۳۰۵ m۳) have much higher performance compared to the MLR and ANFIS models. By the results, it can be concluded that the best models for predicting weakly water consumption in Kerman City are those with the imputes of water consumption, maximum temperature, and total precipitation of last two weeks and data decomposition level of ۳ via discrete wavelet transformation method.


Discrete Wavelet Transformation  Urban Water demand  Prediction  Linear Regression  Neuro Fuzzy 

Download fulltext PDF

Open Access


حسامی کرمانی م. ر. و ولی‌پرست فرخانی ر. 1399. ارزیابی مدل‌های رگرسیونی و نروفازی موجکی در برآورد مصرف آب شهری (مطالعة موردی: شهر کرمان). مجله پژوهش آب ایران. 38: 71-84


Adamowski J. and Chan H. F. 2011. A wavelet neural network conjunction model for groundwater level forecasting. Journal of Hydrology. 407(1-4): 28-40

Adamowski J. and Karapataki C. 2010. Comparison of multivariate regression and artificial neural networks for peak urban water-demand forecasting: evaluation of different ANN learning algorithms. Journal of Hydrologic Engineering. 15(10): 729-743

Adamowski J. Chan H. F. Prasher S. O. Ozga‐Zielinski B. and Sliusarieva A. 2012. Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resources Research. 48(1): 1-14

Adamowski J. F. 2008. Peak daily water demand forecast modeling using artificial neural networks. Journal of Water Resources Planning and Management. 134 (2): 119-128

Altunkaynak A. and Nigussie T. A. 2017. Monthly water consumption prediction using season algorithm and wavelet transform–based models. Journal of Water Resources Planning and Management. 15(2): 177-181

Bougadis J. Adamowski K. and Diduch R. 2005. Short‐term municipal water demand forecasting. Hydrological Processes: An International Journal. 19 (1): 137-148

Campisi-Pinto S. Adamowski J. and Oron G. 2012. Forecasting urban water demand via wavelet-denoising and neural network models. Case study: city of Syracuse, Italy. Water resources management. 26(12): 3539-3558

Daubechies I. 1988. Time-frequency localization operators: a geometric phase space approach. IEEE Transactions on Information Theory. 34(4): 605-612

Firat M. Yurdusev M. A. and Turan M. E. 2009. Evaluation of artificial neural network techniques for municipal water consumption modeling. Water resources management. 23(4): 617-632

Gharabaghi S. Stahl E. and Bonakdari H. 2019. Integrated nonlinear daily water demand forecast model (case study: City of Guelph, Canada). Journal of Hydrology. 579: 124182

Grossmann A. and Morlet J. 1984. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM journal on mathematical analysis. 15(4): 723-736

Guo G. and Liu S. 2018. Short-term water demand forecast based on deep neural network. First International WDSA/CCWI Joint Conference Proceedings, Kingston, Ontario, Canada, July 23-25,Vol 1, 7 p

Haar A. 1910. Zur theorie der orthogonalen funktionensysteme. Mathematische Annalen. 69(3): 331-371

Han J. G. Ren W. X. and Sun Z. S. 2005. Wavelet packet based damage identification of beam structures. International Journal of Solids and Structures. 42(26): 6610-6627

Jang J. S. 1993. ANFIS: adaptive-network-based fuzzy inference system. IEEE transactions on systems, man, and cybernetics. 23(3): 665-685

Mohammed J. R. and Ibrahim H. M. 2012. Hybrid wavelet artificial neural network model for municipal water demand forecasting. ARPN Journal of Engineering and Applied Sciences. 7(8): 1047-1065

Rajaee T. 2011. Wavelet and ANN combination model for prediction of daily suspended sediment load in rivers. Science of the total environment. 409(15): 2917-2927

Shabri A. 2015. A hybrid model for stream flow forecasting using wavelet and least Squares support vector machines. Journal Teknologi. 73(1): 89-96

Yu T. C. Zhang T. Q. Mao G. H. and WU X. G. 2004. Study of artificial neural network model for forecasting urban water demand. Journal-Zhejiang University Engineering Science. 38(9): 1156-1161

عاقلی کهنه شهری ل. و آرام ع. 1390. ارائه­ی یک مدل ترکیبی برای پیش­بینی تقاضای روزانه آب شهری. مجله علمی پژوهشی اقتصاد مقداری. 9(1): 1-17.

تابش م. و دینی م. 1389. پیش­بینی تقاضای روزانه آب شهری با استفاده از شبکه عصبی مصنوعی، مطالعه موردی: شهر تهران. مجله آب و فاضلاب. 21(1): 84-95.

روشنگر ک. ضرغامی م. و طرلانی آذر م. 1393. پیش­بینی مصرف روانه آب شهری با استفاده از ترکیب الگوریتم­های تکاملی و آنالیز تبدیل موجک، مطالعه موردی: شهر همدان. مجله آب و فاضلاب. 26(4): 110-120

کیا م. 1390. منطق فازی در MATLAB. انتشارات کیان رایانه سبز تهران. 304 ص.

صادقی ح. آخوند علی ع. م. حداد م. و گلابی م. 1394. الگوبندی و پیش­بینی تقاضای آب شهر اصفهان با روند ضمنی و سری زمانی. فصلنامه آب و خاک. 29(2): 251-262.


  •  No announces available