Urban Water Demand Forecasting Research Articles

Combining wavelet-enhanced feature selection and deep learning techniques for multi-step forecasting of urban water demand

Abstract Urban water demand (UWD) forecasting is essential for water supply network optimization and management, both in business-as-usual scenarios, as well as under external climate and socio-economic stressors. Different machine learning and deep learning models have shown promising forecasting skills in various areas of application. However, their potential to forecast multi-step ahead UWD has not been fully explored. Modelling uncertain UWD patterns and accounting for variations in water demand behaviors require techniques that can extract time-varying information and multi-scale changes. In this research, we comparatively investigate different state-of-the-art machine learning- and deep learning-based predictive models on 1-day- and 7-day-ahead UWD forecasting, using daily demand data from the city of Milan, Italy. The contribution of this paper is two-fold. First, we compare the forecasting performance of different machine learning and deep learning models on single- and multi-step daily UWD forecasting. These models include Artificial Neural Network (ANN), Support Vector Regression (SVR), Light Gradient Boosting Machine (LightGBM), and Long Short-Term Memory network with and without an attention mechanism (LSTM and AM-LSTM). We benchmark their prediction accuracy against autoregressive time series models. Second, we investigate the potential enhancement in predictive accuracy by incorporating the wavelet transform and feature selection performed by LightGBM into these models. Results show that, overall, wavelet-enhanced feature selection improves the model predictive performance. The hybrid model combining wavelet-enhanced feature selection via LightGBM with LSTM (WT-LightGBM-(AM)-LSTM) can achieve high levels of accuracy with Nash-Sutcliffe Efficiency larger than 0.95 and Kling–Gupta Efficiency higher than 0.93 for both 1-day- and 7-day-ahead UWD forecasts. Furthermore, performance is shown to be robust under the influence of external stressors causing sudden changes in UWD.

Knowledge-based Bi-correction model for achieving effective lag-free characteristic on daily urban water demand forecasting

Accurate demand forecasting is crucial for the efficient management of smart cities. However, the non-stationary and nonlinear characteristics of daily water demand series present significant challenges, leading to the lag forecasting problem and unreliable predictions. To address these challenges, this paper introduces a novel bi-correction model based on knowledge extraction, named the knowledge-based bi-correction model (KbBcM). The KbBcM leverages prior and posterior knowledge to achieve effective lag-free forecasting. The prior knowledge, in the form of sequence and feature information, is extracted using an autoregressive long short-term memory (AR-LSTM) network and a newly proposed lag penalty attention (LPA) module. Furthermore, a hybrid stacked LSTM network is employed to obtain primary forecasting results, which are then corrected with a masked weighted Markov chain (MWMC) based on posterior knowledge. Addressing the limitations of current metrics focused on absolute error, we also introduce the novel mean prediction trend effectiveness (MPTE) to comprehensively evaluate the effectiveness of lag-free forecasting performance. Comparation experiments performed on the urban water demand dataset of a megacity demonstrate the superiority of the KbBcM over baseline models. Additionally, ablation studies are performed to examine the effectiveness of the proposed sub-modules, further validating the robustness and reliability of the KbBcM in addressing the complexities of urban water demand forecasting.

Forecasting Water Demand With the Long Short-Term Memory Deep Learning Mode

Traditional methods often fall short in modeling the nonlinear, seasonally variable nature of urban water demand. This proposed solution is an integrated ARIMA-LSTM deep learning model, combining ARIMA's proficiency in linear trend and seasonal modeling with LSTM's strength in capturing nonlinear time dependencies. In these experiments, the authors trained and evaluated using daily water demand data from 2015 to 2020, with its performance validated for the year 2021. The ARIMA-LSTM model demonstrates promising results, outperforming individual models in terms of accuracy. In validation, it achieves a high coefficient of determination (R2) of 0.98 and a significantly low root mean square error (RMSE) of 2.94. These metrics indicate an excellent fit to the data and a high level of precision in its predictions. The significance of this research lies in its potential to advance the field of urban water demand forecasting, ultimately contributing to better water resource management and sustainability in urban areas.

Performance of TANN, NARX, and GMDHT Models for Urban Water Demand Forecasting: A Case Study in a Residential Complex in Qom, Iran

To keep the balance between demand and supply, methods based on the average per capita consumption were usually applied to predict water demand. More complicated models such as linear regression and time series models were developed for this purpose. However, after the introduction of artificial neural networks (ANNs), different applications of this method were used in the field of water supply management, especially for urban water demand prediction. In this study, multiple types of ANNs were studied to understand their suitability for a residential complex water demand prediction in the city of Qom, Iran. The results indicated that time series ANN (TANN), nonlinear autoregressive network with exogenous inputs (NARX), group method of data handling time series (GMDHT), and their wavelet counterparts (i.e., w-TANN and w-NARX) exhibited varying degrees of performance. Among the aforementioned models, w-NARX performed the best (based on the average overall error) with the test set root mean squared error (MSE) of 49.5 (m3 /h) and R of 0.93, followed by the GMDHT model with the test set MSE of 104 (m3 /h) and R of 0.97 and w-TANN with the test set MSE of 68.8 (m3 /h) and R of 0.91. In addition, the feedback connection in NARX compared to TANN demonstrated overall performance improvement.

Correction: Short-term urban water demand forecasting; application of 1D convolutional neural network (1D CNN) in comparison with different deep learning schemes

Correction: Short-term urban water demand forecasting; application of 1D convolutional neural network (1D CNN) in comparison with different deep learning schemes

Short-term urban water demand forecasting; application of 1D convolutional neural network (1D CNN) in comparison with different deep learning schemes

Short-term urban water demand forecasting; application of 1D convolutional neural network (1D CNN) in comparison with different deep learning schemes

Dynamic Graph Convolution-Based Spatio-Temporal Feature Network for Urban Water Demand Forecasting

Urban water demand forecasting is the key component of smart water, which plays an important role in building a smart city. Although various methods have been proposed to improve forecast accuracy, most of these methods lack the ability to model spatio-temporal correlations. When dealing with the rich water demand monitoring data currently, it is difficult to achieve the desired prediction results. To address this issue from the perspective of improving the ability to extract temporal and spatial features, we propose a dynamic graph convolution-based spatio-temporal feature network (DG-STFN) model. Our model contains two major components, one is the dynamic graph generation module, which builds the dynamic graph structure based on the attention mechanism, and the other is the spatio-temporal feature block, which extracts the spatial and temporal features through graph convolution and conventional convolution. Based on the Shenzhen urban water supply dataset, five models SARIMAX, LSTM, STGCN, DCRNN, and ASTGCN are used to compare with DG-STFN proposed. The results show that DG-STFN outperforms the other models.

A Hybrid Framework for Multivariate Time Series Forecasting of Daily Urban Water Demand Using Attention-Based Convolutional Neural Network and Long Short-Term Memory Network

Urban water demand forecasting is beneficial for reducing the waste of water resources and enhancing environmental protection in sustainable water management. However, it is a challenging task to accurately predict water demand affected by a range of factors with nonlinear and uncertainty temporal patterns. This paper proposes a new hybrid framework for urban daily water demand with multiple variables, called the attention-based CNN-LSTM model, which combines convolutional neural network (CNN), long short-term memory (LSTM), attention mechanism (AM), and encoder-decoder network. CNN layers are used to learn the representation and correlation between multivariate variables. LSTM layers are utilized as the building blocks of the encoder-decoder network to capture temporal characteristics from the input sequence, while AM is introduced to the encoder-decoder network to assign corresponding attention according to the importance of water demand multivariable time series at different times. The new hybrid framework considers correlation between multiple variables and neglects irrelevant data points, which helps to improve the prediction accuracy of multivariable time series. The proposed model is contrasted with the LSTM model, the CNN-LSTM model, and the attention-based LSTM to predict the daily water demand time series in Suzhou, China. The results show that the hybrid model achieves higher prediction performance with the smallest mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), and largest correlation coefficient (R2).

Probabilistic Water Demand Forecasting Using Quantile Regression Algorithms

AbstractMachine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we fill this gap, thereby proposing a new family of probabilistic urban water demand forecasting algorithms. We further extensively compare seven algorithms from this family in practical one‐day ahead urban water demand forecasting settings. More precisely, we compare five individual quantile regression algorithms (i.e., the quantile regression, linear boosting, generalized random forest, gradient boosting machine and quantile regression neural network algorithms), their mean combiner and their median combiner. The comparison is conducted by exploiting a large urban water flow data set, as well as several types of hydrometeorological time series (which are considered as exogenous predictor variables in the forecasting setting). The results mostly favor the linear boosting algorithm, probably due to the presence of shifts (and perhaps trends) in the urban water flow time series. The forecasts of the mean and median combiners are also found to be skillful.

Multivariate monthly water demand prediction using ensemble and gradient boosting machine learning techniques

Water management planning requires reliable and accurate water demand forecasting. Water demand prediction is affected by variables, such as climate, socio-economic, and demographic data. This paper investigates urban monthly average water demand prediction, using classical, ensemble, and gradient boosting-based machine learning models, using the available monthly water demand, climatic, economic, and demographic data. Three train-test data split schemes on water demand timeseries were considered to determine the effect of data size on water demand prediction. Sensitivity analysis was employed to reduce input feature dimensionality while maintaining model accuracy. A univariate timeseries (water demand only) produced R2 scores up to 0.91, which increased to 0.94 with the addition of calendar and climatic features. Increasing the training data size from 70% to 90% improved the RMSE and MAE scores by ensemble and gradient boosting methods, with the random forest and the AdaBoost models showing improvements of up to 69%. The sensitivity analysis revealed a successful input reduction scheme from a potential 17 input attributes to seven inputs. Gradient boosting models showed robust and faster execution time, especially with the increase in training data, which is attractive for medium-term urban water demand forecasting.

Comparing Predictive Machine Learning Models for Short- and Long-Term Urban Water Demand Forecasting in Milan, Italy

Urban water demand forecasting is essential for water supply network optimization and management. In this case study, we comparatively investigate different state-of-the-art predictive models on short- (1 day-ahead) and long-term (7 day-ahead) urban water demand (UWD) forecasting for the city of Milan, Italy. The contribution of this paper is two-fold. First, we compare the forecasting performance of different time series and machine learning models on daily UWD. The tested models include Autoregressive Integrated Moving Average (ARIMA) models, Artificial Neural Networks (ANN), Support Vector Regression (SVR), Light Gradient Boosting Machine (LightGBM), and Long Short-Term Memory (LSTM) networks. Second, we investigate whether coupling a Wavelet Data-Driven Forecasting Framework (WDDFF) with these models further improves predictive capacity. Results show that, in general, WDDFF can improve model predictive performance. LSTM coupled wavelet decomposition technique can achieve high levels of accuracy with R2 larger than 0.9 for both short- and long-term UWD forecasts. LightGBM can efficiently reduce the number of predictors and show the potential to forecast and select important features in the hydrology and water resources field.

Hourly and Daily Urban Water Demand Predictions Using a Long Short-Term Memory Based Model

This case study uses a long short-term memory (LSTM)-based model to predict short-term urban water demands for the Hefei City of China. The performance of the LSTM-based model is compared with the autoregressive integrated moving average (ARIMA) model, the support vector regression (SVR) model, and the random forests (RF) model based on data with time resolutions ranging from 15 min to 24 h. Additionally, this paper investigates the performance of the LSTM-based model in predicting multiple successive data points. Results show that the LSTM-based model can offer predictions with improved accuracy than the other models when dealing with data with high time resolutions, data points with abrupt changes, and data with a relatively high uncertainty level. It is also observed that the LSTM-based model exhibits the best performance in predicting multiple successive water demands with high time resolutions. In addition, the inclusion of external parameters (e.g., temperature) cannot enhance the performance of the LSTM-based model, but it can improve ARIMAX's prediction ability (ARIMAX is the ARIMA with variables). These observations provide additional and improved evaluations regarding the LSTM-based models used for short-term urban water demand forecasting, thereby enabling their wider adoption in practical applications.

Integrated nonlinear daily water demand forecast model (case study: City of Guelph, Canada)

Urban water demand forecasting is a significant issue in the design, maintenance, and operation of a reliable and economical water supply system. The large variations in daily water demand are the leading source of health risks due to water pressure drops within the distribution network, increasing the likelihood of contamination leaking into the system and/or excessive retention time. This study presents an explicit mathematical equation, based on the air temperature and precipitation effects on the outdoors water uses and the seasonal and weekly trends in the domestic/industrial water demands that can accurately forecast the daily water demand fluctuations for a municipality. Recent time series prediction methods are based on linear, non-linear and hybrid methods that can be effectively applied to solve time series problems. However, due to the presence of the high-frequency values in the data, these methods show some limitations for practical applications. To solve these limitations, this study introduced a non-linear model through a grouping method of data handling for water demand management and tested for the case study City of Guelph, Ontario, Canada. The coefficient of determination and mean absolute percent error of the new water demand forecast model was 71.03 and 2.93, respectively, compared to 56.12 and 3.49 for the popular linear model, 58.91 and 3.37 for the non-linear model, 61.37 and 3.28 for the hybrid model (respectively). The proposed new model will allow optimizing the water storage costs versus pumping capacity costs of the water supply system to maximize the usage of the lower electricity costs for the production/pumping at the off-peak hours. Further, to assist the City with water demand management and reduce its peaking factors.

Urban Water Demand Forecasting: A Comparative Evaluation of Conventional and Soft Computing Techniques

Previous studies have shown that soft computing models are excellent predictive models for demand management problems. However, their applications in solving water demand forecasting problems have been scantily reported. In this study, feedforward artificial neural networks (ANNs) and a support vector machine (SVM) were used to forecast water consumption. Two ANN models were trained using different algorithms: differential evolution (DE) and conjugate gradient (CG). The performance of these soft computing models was investigated with real-world data sets from the City of Ekurhuleni, South Africa, and compared with conventionally used exponential smoothing (ES) and multiple linear regression (MLR). The results obtained showed that the ANN model that was trained with DE performed better than the CG-trained ANN and other predictive models (SVM, ES and MLR). This observation further demonstrates the robustness of evolutionary computation techniques amongst soft computing techniques.

Daily Urban Water Demand Forecasting Based on Chaotic Theory and Continuous Deep Belief Neural Network

The prediction of daily water demands is a crucial part of the effective functioning of the water supply system. This work proposed that a continuous deep belief neural network (CDBNN) model based on the chaotic theory should be implemented to predict the daily water demand time series in Zhuzhou, China. CDBNN should initially be used to predict the urban water demand time series. First, the power spectrum and the largest Lyapunov exponent is used to determine the chaotic characteristic of the daily water demand time series. Second, C–C method is utilized to reconstruct the water demand time series’ phase space. Lastly, the forecasting model should be produced with the continuous deep belief network and neural network algorithms implemented for feature learning and regression, respectively, and the CDBNN input established by the best embedding dimension of the reconstructed phase space. The proposed method is contrasted with the support vector regression, generalized regression neural networks and feed forward neural networks, and they are accepted with the identical dataset. The predictive performance of the models is examined using normalized root-mean-square error (NRMSE), correlation coefficient (COR), and mean absolute percentage error (MAPE). The results suggest that the hybrid model has the smallest NRMSE and MAPE values, and the largest COR.

A Novel Dual-Scale Deep Belief Network Method for Daily Urban Water Demand Forecasting

Water demand forecasting applies data supports for the scheduling and decision-making of urban water supply systems. In this study, a new dual-scale deep belief network (DSDBN) approach for daily urban water demand forecasting was proposed. Original daily water demand time series was decomposed into several intrinsic mode functions (IMFs) and one residue component with ensemble empirical mode decomposition (EEMD) technique. Stochastic and deterministic terms were reconstructed through analyzing the frequency characteristics of IMFs and residue using generalized Fourier transform. The deep belief network (DBN) model was used for prediction using the two feature terms. The outputs of the double DBNs are summed as the final forecasting results. Historical daily water demand datasets from an urban waterworks in Zhuzhou, China, were investigated by the proposed DSDBN model. The mean absolute percentage error (MAPE), normalized root-mean-square error (NRMSE), correlation coefficient (CC) and determination coefficient (DC) were used as evaluation criteria. The results were compared with the autoregressive integrated moving average (ARIMA) model, feed forward neural network (FFNN) model, support vector regression (SVR) model, EEMD and their combinations, and single DBN model. The results obtained in the test period indicate that the proposed model has the smallest MAPE and NRMSE values of 1.291099 and 0.016625, respectively, and the largest CC and DC values of 0.976528 and 0.953512, respectively. Therefore, the proposed DSDBN method is a useful tool for daily urban water demand forecasting and outperforms other models in common use.

A Comparative Assessment of Variable Selection Methods in Urban Water Demand Forecasting

Urban water demand is influenced by a variety of factors such as climate change, population growth, socio-economic conditions and policy issues. These variables are often correlated with each other, which may create a problem in building appropriate water demand forecasting model. Therefore, selection of the appropriate predictor variables is important for accurate prediction of future water demand. In this study, seven variable selection methods in the context of multiple linear regression analysis were examined in selecting the optimal predictor variable set for long-term residential water demand forecasting model development. These methods were (i) stepwise selection, (ii) backward elimination, (iii) forward selection, (iv) best model with residual mean square error criteria, (v) best model with the Akaike information criterion, (vi) best model with Mallow’s Cp criterion and (vii) principal component analysis (PCA). The results showed that different variable selection methods produced different multiple linear regression models with different sets of predictor variables. Moreover, the selection methods (i)–(vi) showed some irrational relationships between the water demand and the predictor variables due to the presence of a high degree of correlations among the predictor variables, whereas PCA showed promising results in avoiding these irrational behaviours and minimising multicollinearity problems.

A geospatially-enabled web tool for urban water demand forecasting and assessment of alternative urban water management strategies

This study develops and demonstrates the Integrated Urban Water Model (IUWM) for forecasting urban water demand with options to assess effects of water conservation and reuse. While water and energy balance drive hydrologic, storage and recycling simulations on a daily timestep, social and infrastructural processes are resolved by spatially distributed parameters. IUWM is deployed as an online tool with geographical information system (GIS) interfaces, enhancing its ease of use and applicability at building to municipal scales. The performance of the model at varying spatial scales was evaluated with extensive water metering data for the City of Fort Collins, Colorado. The calibrated model provided very good estimates of demands at individual block group as well as the municipal service area. The capacity of IUWM for the assessment of the spatiotemporal variability of water consumption and effects of water demand management strategies under climate and urban growth scenarios is discussed.

Support Vector Machines in Urban Water Demand Forecasting Using Phase Space Reconstruction

High complexity of water distribution systems’ (WDS) dynamics has convinced researchers to look for more sophisticated statistical approaches in urban water demand forecasting. Given the huge threat to major water reserves and ongoing draughts, water authorities are concerned with long term analysis of water demand to deal with uncertain future of this dynamic infrastructure. Researchers have tried a wide range of modelling techniques to propose an accurate model. However, applications of machine learning techniques are yet to be explored in detail. This research proposes a support vector machine (SVM) model, using polynomial kernel function to forecast monthly water demand of City of Kelowna (CKD), Canada. The prime objective of this research is to assess the use of phase space reconstruction prior to design of models’ input variables combinations. Results of this study proved optimum lag time of the input variables can significantly improve the performance of SVM models.

Water Demand Modelling Using Independent Component Regression Technique

Water demand modelling is an active field of research. The modelling and forecasting tools are useful to get the estimation of forecasted water demand for different forecast horizons (e.g. 1 h to 10 years) in order to achieve more efficient and sustainable water resources management systems. However, modelling and forecasting of accurate water demand are challenging and difficult tasks. Several issues make the demand forecasting challenging such as the nature and quality of available data, numerous water demand variables, diversity in forecast horizons and geographical differences in modelling catchments. These issues have motivated a number of studies to be conducted to produce better water demand modelling and forecasting tools in order to improve forecast reliability. A variety of techniques have been adopted in water demand forecasting, however, application of independent component regression (ICR) technique has not been investigated yet. Hence, this study explores, for the first time, the use of the ICR technique in medium term urban water demand forecasting. This uses data from the city of Aquidauana, Brazil. It also compares the performance of the developed ICR model with two other commonly modeling methods, principal component regression and multiple linear regression models. It has been found that ICR model perform better than the other two models in modelling water demand with a higher performance indices (i.e. R 2 , RMSE, NSE and MARE) for the independent validation period. The results indicate that the ICR technique has the potential to develop water demand models successfully. The methodology adopted in this paper can be applied to other countries to develop water demand forecasting model.