Fuzzy and neuro-fuzzy models for short-term water demand forecasting in Tehran

Water demand forecasting cannot be described by any mathematical function because it is a complicated function of a large number of interacting variables. In this paper, several fuzzy and neuro-fuzzy models are presented and their results for short-term water demand forecasting in Tehran are compared. Weather data from three Tehran weather stations is weighted with the Thissen method and effective input data parameters are selected with regression of weighted effective weather and consumption data. The effective parameters include daily average temperature, relative humidity percent and last day, last week and last year water consumption. Consumption of all days between last day and the last week were also used. For the construction of fuzzy models a fuzzy rule-based approach is applied. The working rules are formulated from a set of past observations such as the relation between the parameters and the given input/output data sets. For neuro fuzzy modeling the toolbox function of Adaptive Neuro-Fuzzy Inference System (ANFIS) constructs a Sugeno Inference System (SFIS). The membership function parameters are adjusted using a back propagation algorithm in combination with a least squares method. Outputs of the fuzzy and the neuro fuzzy models demonstrate that the results of fuzzy models do not show high accuracy, but neuro fuzzy models produce better results. Besides, outputs of the neuro fuzzy models with just water consumption inputs have high accuracy. A comparison of outputs with the results of the Artificial Neural Networks (ANN) approach shows the capability of the ANFIS model to predict Tehran water consumption.