Predictive Model for Short-Term Water Demand Forecasting and Feature Analysis in Urban Networks ^†

Abstract

Variability in water use and user characteristics influences the operational management of water distribution systems (WDS). Types of water use and external factors including socioeconomic characteristics and weather variables can affect the normal operation of WDS. Accurate demand prediction is crucial, yet existing methods lack industry-wide comparability. This study applies a supervised learning model, IONET, that utilizes feedforward neural networks for short-term demand forecasting. IONET incorporates lagged demand, seasonal predictors, and weather variables. Tested on Italian DMA data, it swiftly produces accurate forecasts across various horizons. Feature importance analysis underscores the significance of seasonal variables and lagged demand. The IONET model offers prompt training and valuable insights for optimizing WDS management, facilitating the digital transformation of water infrastructure.

1. Introduction

Extreme weather events and population dynamics threaten the continuous supply of potable water to urban environments. As urban population grows, supply management strategies that exploit multiple water resources are no longer sustainable. Demand management methods focus on optimizing the already-low water volume with programs related to efficiency and leveraging the ongoing digital transformation of the infrastructure components. While extensive research has been applied to predict the future demand of water, population dynamics in terms of different uses bring new data sets that require swift methods to plan for water resource management.

Water demand heavily depends on the local weather conditions, including ambient temperatures, humidity, and rainfall [1]. Multiple studies have proved that consumption increases with temperature and humidity. Similarly, there are works that describe different relationships between water demand and precipitation occurrence and total precipitation values [2]. The models that incorporate external predictors use a regression approach to explain the relationship between a response variable and multiple predictors. Regression models can predict one and multiple values of water demand. However, as the models’ accuracy decreases with an increasing forecasting horizon, there is a need for an improvement in the multiple-horizon water demand forecasting models’ accuracy [3].

The rest of this paper is organized as follows. Section 2 describes the method and application data set used to develop the water demand forecasting method. Section 3 shows the Results and Discussion of the forecasting method when applied to multiple data sets. Finally, Section 4 highlights the main takeaways of our work and mentions the future directions of this research.

2. Methods and Materials

This section explains the model development to predict the one- and multiple-time steps of water demand. We implement a previously developed Artificial Neural Network model by [4] comprising a feedforward network with one hidden layer and five hidden neurons. The rest of the model parameters are discussed in [4]. Our model is considered to be an input–output neural network (IONET) in which multiple internal and external predictors (

Table 1. IONET predictors.

Predictor Name	Value/Unit
Hour of the day	1–24
Day of the week	1–7
Is it a working day?	0–1
Previous week; same hour	gph 1
Previous day; same hour	gph
Previous two days; same hour	gph

¹ gph: gallons per hour.

) are used to forecast water demand.

Prior to IONET’s implementation, we conducted an Outlier Detection Analysis (ODA) to reconstruct erroneous data sets and remove outliers. The ODA included a “fill outliers” step with the linear interpolation of neighboring data points to replace outliers. Also, a smoothing data technique using the moving mean with multiple window sizes was conducted as part of the preliminary ODA to improve the input conditions of each DMA water demand data set.

As presented in [5], we also calculated the autocorrelation and partial correlation functions to evaluate the number of lagged demand values to be used as predictors. Based on visual inspection, we determined that up to four previous steps are important predictors of the next time steps of water demand. For multiple horizon forecasting, this means that for a particular day of the week, measurements of the previous four days may positively affect the model’s performance.

IONET is applied to the data set presented by the Battle of Water Demand Forecasting (BWDF) competition. BWDF includes data sets comprising hourly water demand sampled at ten District Metered Areas (DMA) in Italy. As expected, each DMA represents different types of users. Hourly weather variables such as temperature, humidity, and precipitation were also made available by the BWDF organizing committee.

The purpose of the BWDF was to compare multiple forecasting methods’ capabilities by providing four growing-window data sets. Hourly water demand data for the first training set included demand measurements for the ten DMAs from 00H00 1 January 2021 to 23H00 24 July 2022. Finally, the metric of performance reported here includes the coefficient of determination (R²).

3. Results and Discussion

IONET was implemented to forecast one- and multiple-time steps of water demand from ten DMAs presented in the BWDF competition. This section reports the metric of performance of our forecasting methodology by comparing the available BWDF data sets with the results of the IONET forecasting values. We use the following weeks for testing:

• Week 1: 18 July 2022, at 00H00 to 24 July 2022, at 23H00.
• Week 2: 24 October 2022, at 00H00 to 30 October 2022, at 23H00.
• Week 3: 9 January 2023, at 00H00 to 15 January 2023, at 23H00.
• Week 4: 27 February 2023, at 00H00 to 5 March 2023, at 23H00.

IONET reports an average R² of 0.49 for week 1 across the ten DMAs. For week 1, IONET reports values in the range of 0.78 and 0.97, with DMA J being the only exception, which affects the overall performance (

Table 2. Mean Coefficient of Determination (R²) across the ten DMAs for each of the four test weeks.

DMA	R2 Week 1	R2 Week 2	R2 Week 3	R2 Week 4
C	0.91	0.92	0.93	0.93
B	0.92	0.90	0.88	0.90
C	0.86	0.85	0.86	0.87
D	0.94	0.94	0.94	0.94
E	0.96	0.95	0.95	0.95
F	−3.27	0.53	0.35	0.14
G	0.90	0.91	0.90	0.90
H	0.93	0.91	0.91	0.91
I	0.78	0.13	−1.44	−0.59
J	0.97	0.98	0.98	0.98

Maximum R² values are bold.

). While IONET’s performance is remarkable for well-structured, mostly residential data sets (e.g., DMA A, B, E, and J) with average R² values of up to 0.97, IONET struggles to predict the water demand of industrial/commercial and DMAs supplying office buildings and sports facilities with low and even negative R² values (Figure 1). For these types of DMAs, we opted to report the average demand of previous similar weeks as our forecasted values.

For the second week, the average R² is 0.80. In this week, there is an increment in the R² value; the two lowest values correspond to DMAs F and I with 0.53 and 0.13, respectively. The highest R² value is 0.98 for DMA J. The third testing week presents an average R² value of 0.63, with minimum and maximum R² values of −1.44 and 0.98, respectively. Finally, R² ranges from −0.59 to 0.98 for the last testing week.

The reported results included all the mentioned predictors. A sensitivity analysis was conducted to evaluate the effect of each of the thirteen predictors on the model performance, and no significant changes occurred with the R² values.

4. Conclusions

The development of an effective forecasting model that predicts one- and multiple-time steps of water demand was presented in this work. IONET is a feedforward neural network comprising one hidden layer with five hidden neurons. The model was tested on ten data sets presented in the Battle of Water Demand Forecasting competition as part of the 3rd WDSA-CCWI Joint Conference in Ferrara, Italy. IONET shows remarkable performance in terms of explaining water demand based on a set of internal and external (weather data) predictors. For well-structured data sets corresponding to mostly residential users, IONET explains up to 98% of the variability of water demand when forecasting the next week of hourly water demand (e.g., 168-time steps). However, when the input data sets represent industrial, commercial, or sports facilities, IONET’s performance is severely affected by sudden changes in the consumption trends, reporting even negative R² values.