Predictive Uncertainty Estimation in Water Demand Forecasting Using the Model Conditional Processor

Abstract

In a previous paper, a number of potential models for short-term water demand (STWD) prediction have been analysed to find the ones with the best fit. The results obtained in Anele et al. (2017) showed that hybrid models may be considered as the accurate and appropriate forecasting models for STWD prediction. However, such best single valued forecast does not guarantee reliable and robust decisions, which can be properly obtained via model uncertainty processors (MUPs). MUPs provide an estimate of the full predictive densities and not only the single valued expected prediction. Amongst other MUPs, the purpose of this paper is to use the multi-variate version of the model conditional processor (MCP), proposed by Todini (2008), to demonstrate how the estimation of the predictive probability conditional to a number of relatively good predictive models may improve our knowledge, thus reducing the predictive uncertainty (PU) when forecasting into the unknown future. Through the MCP approach, the probability distribution of the future water demand can be assessed depending on the forecast provided by one or more deterministic forecasting models. Based on an average weekly data of 168 h, the probability density of the future demand is built conditional on three models' predictions, namely the autoregressive-moving average (ARMA), feed-forward back propagation neural network (FFBP-NN) and hybrid model (i.e., combined forecast from ARMA and FFBP-NN). The results obtained show that MCP may be effectively used for real-time STWD prediction since it brings out the PU connected to its forecast, and such information could help water utilities estimate the risk connected to a decision.

Solving Management Problems in Water Distribution Networks: A Survey of Approaches and Mathematical Models

“…It is based upon the past water use, and socio-economic and climate parameters associated with the past water use. These parameters are precipitation (rain), temperature, seasonality, and evapotranspiration, water price, income, family size and other related factors [113][114][115][116]. Short-term water demand forecasting is essential for operation and management of networks whereas long-term forecasting is required by utility managers for planning and design of WDNs.…”

Real-Time Dynamic Hydraulic Model of Water Distribution Networks

“…In this work, the predictive uncertainty is estimated based on a set of predictions by an autoregressive-moving average (ARMA) model and a feed-forward neural network (FFBP-NN) model [32]. The algorithm starts by selecting the training datasets that include subsets of the real observed values and subsets for the forecasted values of ARMA and FFBP-NN.…”

“…Therefore, upper and lower tail models are developed to eliminate such values. For further details, we refer the reader to [32].…”

A Short-Term Data Based Water Consumption Prediction Approach

“…The MCP technique was used by Anele et al [34] to evaluate the knowledge improvement obtained by the utilization of several predictive models and, thus, being able to estimate Predictive Uncertainty (PU) in future water demand predictions. The authors observed that MCP is suitable for water short-term predictions due to the extraction of the PU connected to the MCP forecast obtained.…”