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

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 12 years data from 2006 to 2017. The data from 2006 to 2014 (469 weeks) were considered for the training of MLR, WR, ANFIS and WANFIS models and the remaining data from 2015 to 2017 (157 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 (R2), 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: R2 = 0.92, RMSE = 34151 m3, MAE = 23908 m3 and for simulation R = 0.97, RMSE = 23486 m3, MAE = 16788 m3) and the WANFIS (for training: R2 = 0.94 RMSE = 29179 m3, MAE = 20675 m3 and for simulation: R = 0.92, RMSE = 43698 m3, MAE = 29305 m3) 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 3 via discrete wavelet transformation method.