Water Demand Forecasting with Multi-Objective Computational Intelligence †
1
Programa de Pós-Graduação em Engenharia de Produção e Sistemas (PPGEPS), Pontifícia Universidade Católica do Paraná (PUCPR), Curitiba 80215-901, Brazil
2
Laboratório de Otimização de Sistemas (LOSC), Pontifícia Universidade Católica do Paraná (PUCPR), Curitiba 80215-901, Brazil
3
Programa de Pós-graduação em Engenharia de Recursos Hídricos e Ambiental (PPGERHA), Universidade Federal do Paraná (UFPR), Curitiba 82590-300, Brazil
*
Author to whom correspondence should be addressed.
†
Presented at the 3rd International Joint Conference on Water Distribution Systems Analysis & Computing and Control for the Water Industry (WDSA/CCWI 2024), Ferrara, Italy, 1–4 July 2024.
Eng. Proc. 2024, 69(1), 79; https://doi.org/10.3390/engproc2024069079
Published: 6 September 2024
(This article belongs to the Proceedings of The 3rd International Joint Conference on Water Distribution Systems Analysis & Computing and Control for the Water Industry (WDSA/CCWI 2024))
Abstract
:With increasing pressures from population growth, urbanization, and climate change, effective water resource management is crucial. This paper presents a computational intelligence framework employing machine learning and multi-objective optimization for the short-term forecasting battle of urban water demand within District Metered Areas (DMAs). Our methodology utilizes historical data from DMAs in North-East Italy, focusing on daily and weekly forecasts to optimize water utility operations and energy purchasing. By integrating environmental variables, the proposed models aim to improve forecasting accuracy, model interpretability, and structural complexity, thus meeting the practical needs of water utilities.
1. Introduction
Population growth, urbanization, and climate change make water resource management imperative, with an emphasis on the need to be extremely judicious. Within this context, the accurate short-term forecasting of urban water demand is identified as a critical challenge, particularly within the intricate water net of District Metered Areas (DMAs). The problem is rooted in the pivotal role of water demand forecasts in the operational decisions of drinking water utilities. Therefore, an acute need arises for forecasting models that capture the complexities of DMA time series and incorporate relevant environmental variables. Within this context, the battle of water demand forecasting (BWDF) is organized by the third International WDSA-CCWI Joint Conference. Real DMAs in the North-East of Italy will serve as the experimental backdrop to test different approaches for demand forecasting with environmental variables. This proposal presents a computational intelligence framework that fuses machine learning and multi-objective optimization techniques to address the challenge. Our proposal uses a multi-objective computational intelligence approach, wherein machine learning models are trained to catch non-linear patterns within DMA time series via multi-objective optimization during the training phase. Previous works [1,2,3,4] employing similar strategies have shown improved performance using compact and classical machine learning techniques. Our methodology aims to balance predictive accuracy (forecasting performance), model interpretability (explainability for decision making), and complexity (learner structure). Therefore, our approach aligns with the pragmatic needs of water utilities.
2. Materials and Methods
2.1. Benchmark
The dataset for the BWDF competition focuses on forecasting water demands for a water distribution network (WDN) in North-East Italy. This network includes ten District Metered Areas (DMAs), each with distinct characteristics, user populations, and average water demands. These areas vary from hospital and residential districts to commercial and industrial zones near the city center and port areas. Key dataset features include the following:
- DMA descriptions: Each DMA is defined by its location type (hospital, residential, suburban, etc.), the number of users it serves, and the average net inflow rates measured in liters per second for 2021 and 2022.
- Net inflow calculation: The dataset provides hourly net inflow time series for each DMA from 1 January 2021 to 31 March 2023. Net inflow represents water consumed and leakage within each DMA and is calculated using a water balance equation. This includes inflows from inlet points and outflows to outlet points, all monitored by the water utility’s SCADA system.
- Data quality: The net inflow data are raw and unprocessed, potentially including gaps due to SCADA system malfunctions or other data transmission issues.
The aim of this dataset is to aid in creating forecasting models to optimize system operations and energy purchasing decisions for the immediate future, covering daily and weekly forecasts. The provided data span initially from the beginning of 2021 to the middle of 2022 to facilitate the development of these models.
2.2. Machine Learning Pipeline
A classical machine learning pipeline is used to build the model based on the time series information. Such a pipeline consists of the following steps: data cleaning, data inputting, data pre-processing, training, and validation.
- Data cleaning: Missing data, repeated entries, and missing entries were identified in the DMA time series as well as in the weather time series.
- Data Inputting: In the event of missing data, the median value on the historical record for a given day and time was used.
- Data Preprocessing: For each DMA, a recursive artificial neural network (RNN) was selected and a time window of 336 samples (2 weeks) was used.
- Training stage: For each DMA, the RNN used 13,000 samples.
- Test stage: The performance of each RNN was evaluated for the recursive prediction of 168 samples (1 week).
2.3. Multi-Objective Optimization Pipeline
The second part of the prediction model consists of a multi-objective optimization approach to build a linear compensator model using the weather time series. The advantage of this is that the information from the time series as well as the compensator is available for decision making. A linear regression learner model is selected, using RNN prediction, time weather, and past week information as features, including the day-by-day difference of each feature. As fitting objectives, the positive and negative error are used, with a regularization index (weighting sum). For such a purpose, the sp-MODEx toolbox is used, with default parameters. Tests were performed on a Desktop DELL precision 3561, Intel(R) 11th generation i7-11800H, 2.30 GHz, with 16GB RAM, running Matlab R2021b. The model with the lower negative error (that is, error of not attending a given demand) is selected.
3. Results
A comparison of the results obtained with the baseline solution and the proposed model is presented in Table 1. As can be noticed, the proposed model achieves a better performance.
4. Conclusions
A two-stage prediction model was proposed for water demand forecasting. In the first part, an RNN is trained to predict the demand one week ahead. After that, a linear compensator adjusted via multi-objective optimization considering weather information, positive error, negative error, and regularization is implemented. The proposed model improves the prediction of the baseline results as presented in the previous section. It is true that the proposal should be evaluated against more elaborated approaches, which will be tackled in future work.
Author Contributions
Conceptualization, G.R.-M. and E.P.C.-A.; methodology, G.R.-M.; software, G.R.-M.; validation, G.R.-M.; formal analysis, G.R.-M. and E.P.C.-A.; investigation, G.R.-M. and E.P.C.-A.; resources, G.R.-M.; data curation, G.R.-M.; writing—original draft preparation, G.R.-M. and E.P.C.-A.; writing—review and editing, G.R.-M. and E.P.C.-A.; visualization, G.R.-M.; supervision, G.R.-M.; project administration, G.R.-M.; funding acquisition, G.R.-M. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by CNPq-Brazil, grant numbers PQ-2/310195/2022-5 and Universal/408164/2021-2.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
spMODEx toolbox available at https://www.mathworks.com/matlabcentral/fileexchange/65145 (accessed on 20 January 2024).
Conflicts of Interest
The authors declare no conflicts of interest.
References
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Table 1.
Performance comparison. Cumulative absolute value of the prediction error for one week.
| DMA | Baseline | Proposed Model |
|---|---|---|
| 1 | 5.3054 × 102 | 2.2511 × 102 |
| 2 | 3.8373 × 102 | 3.4705 × 102 |
| 3 | 3.1774 × 102 | 1.0094 × 102 |
| 4 | 5.7028 × 102 | 3.9824 × 102 |
| 5 | 9.1191 × 102 | 4.7079 × 102 |
| 6 | 1.4864 × 102 | 1.4592 × 102 |
| 7 | 1.0672 × 102 | 2.7704 × 102 |
| 8 | 3.4202 × 102 | 2.8915 × 102 |
| 9 | 5.3224 × 102 | 1.5698 × 102 |
| 10 | 6.4595 × 102 | 1.9904 × 102 |
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MDPI and ACS Style
Reynoso-Meza, G.; Carreño-Alvarado, E.P. Water Demand Forecasting with Multi-Objective Computational Intelligence. Eng. Proc. 2024, 69, 79. https://doi.org/10.3390/engproc2024069079
AMA Style
Reynoso-Meza G, Carreño-Alvarado EP. Water Demand Forecasting with Multi-Objective Computational Intelligence. Engineering Proceedings. 2024; 69(1):79. https://doi.org/10.3390/engproc2024069079
Chicago/Turabian StyleReynoso-Meza, Gilberto, and Elizabeth Pauline Carreño-Alvarado. 2024. "Water Demand Forecasting with Multi-Objective Computational Intelligence" Engineering Proceedings 69, no. 1: 79. https://doi.org/10.3390/engproc2024069079
APA StyleReynoso-Meza, G., & Carreño-Alvarado, E. P. (2024). Water Demand Forecasting with Multi-Objective Computational Intelligence. Engineering Proceedings, 69(1), 79. https://doi.org/10.3390/engproc2024069079