A hybrid approach combining the multi-dimensional time series k-means algorithm and long short-term memory networks to predict the monthly water demand according to the uncertainty in the dataset

An authentic water consumption forecast is an auxiliary tool to support the management of the water supply and demand in urban areas. Providing a highly accurate forecasting model depends a lot on the quality of the input data. Despite the advancement of technology, water consumption in some places is still recorded by operators, so its database usually has some approximate and incomplete data. For this reason, the methods used to predict the water demand should be able to handle the drawbacks caused by the uncertainty in the dataset. In this regard, a structured hybrid approach was designed to cluster the customers and predict their water demand according to the uncertainty in the dataset. First, a fuzzy-based algorithm consisting of Forward-Filling, Backward-Filling, and Mean methods was innovatively proposed to impute the missing data. Then, a multi-dimensional time series k-means clustering technique was developed to group the consumers based on their consumption behavior, for which the missing data were estimated with fuzzy numbers. Finally, one forecasting model inspired by Long Short-Term Memory (LSTM) networks was adjusted for each cluster to predict the monthly water demand using the lagged demand and the temperature. This approach was implemented on the water time series of the residential consumers in Yazd, Iran, from January 2011 to November 2020. Based on the performance evaluation in terms of the Root Mean Squared Error (RMSE), the proposed approach had an acceptable level of confidence to predict the water demand of all the clusters.