An ensemble wavelet bootstrap machine learning approach to water demand forecasting: a case study in the city of Calgary,Canada

This paper explores a hybrid wavelet, bootstrap and neural network (WBNN) modeling approach for daily (1, 3 and 5 day) urban water demand forecasting in situations with limited data availability. This method was tested using 3 years of daily water demand and meteorological data for the city of Calgary, Alberta, Canada. The performance of the WBNN method was compared to that of three other methods: traditional neural networks (NN), wavelet NNs (WNN), and bootstrap-based NN (BNN) models. While the hybrid WBNN and WNN models equally provided 1-day lead-time forecasts of greater accuracy than those obtained with other methods, for longer lead-time (3- or 5-day) forecasts the WBNN model alone outperformed the other models. The confidence bands generated using the WBNN model displayed the uncertainty associated with the forecasts.     

Large metropolitan water demand forecasting using DAN2, FTDNN,and KNN models: A case study of the city of Tehran,Iran

Efficient operation of urban water systems necessitates accurate water demand forecasting. We present daily, weekly, and monthly water demand forecasting using dynamic artificial neural network (DAN2), focused time-delay neural network (FTDNN), and K-nearest neighbor (KNN) models for the city of Tehran. The daily model investigates whether partitioning weekdays into weekends and non-weekends can improve forecast results; it did not. The weekly model yielded good results by using the summation of the daily forecast values into their corresponding weeks. The monthly results showed that partitioning the year into high and low seasons can improve forecast accuracy. All three models offer very good results for water demand forecasting. DAN2, the best model, yielded forecasting accuracies of 96%, 99%, and 98%, for daily, weekly, and monthly models respectively.     

Wavelet and ANN combination model for prediction of daily suspended sediment load in rivers

In this research, a new wavelet artificial neural network (WANN) model was proposed for daily suspended sediment load (SSL) prediction in rivers. In the developed model, wavelet analysis was linked to an artificial neural network (ANN). For this purpose, daily observed time series of river discharge (Q) and SSL in Yadkin River at Yadkin College, NC station in the USA were decomposed to some sub-time series at different levels by wavelet analysis. Then, these sub-time series were imposed to the ANN technique for SSL time series modeling. To evaluate the model accuracy, the proposed model was compared with ANN, multi linear regression (MLR), and conventional sediment rating curve (SRC) models. The comparison of prediction accuracy of the models illustrated that the WANN was the most accurate model in SSL prediction. Results presented that the WANN model could satisfactorily simulate hysteresis phenomenon, acceptably estimate cumulative SSL, and reasonably predict high SSL values.     

人工神经网络模型在应对城市内涝中的应用

现在城市排水系统的规划和运营管理一般不考虑城市下游受纳水体变化的影响,这也是国内城市内涝频发的原因之一。目前,越来越多的城市应用模型来应对城市内涝,模型中受纳水体的水位一直以来都是利用经验设定一个恒定值。本文利用ANN(人工神经网络)技术,以城市上游观测站的实测水位为输入,以城市未来某时段的水位为目标选择合理的参数,建立了预测河流水位模型。利用更准确的动态预测值代替恒定值,可以提高城市排水系统水力模型的精度。选择某地区水位站的资料,对预报模型进行了检验,结果表明,在合理选择输入层数据和预测时间段的条件下,可以取得很好的预报结果。     

改进单指数平滑法预测某市日用水量

为实现供水管网经济、可靠、科学的优化调配用水量,给出一种基于改进单指数平滑预测方法,该预测方法引进"追踪信号"来反应时间序列的变化,通过重新修正平滑常数a以建立改进单指数预测模型。以东北某城市日用水量为原始数据进行了实际预测,模型精度检验的结果满足Y市用水量要求,该预测模型应用于Y市的日用水量预测,为Y市供水优化调配提供有效依据。     

Evaluation of a multiple regression model for the forecasting of the concentrations of NOx and PM10 in Athens and Helsinki

Forecasting models based on stepwise multiple linear regression (MLR) have been developed for Athens and Helsinki. The predictor variables were the hourly concentrations of pollutants (NO, NO₂, NO_x, CO, O₃, PM_2.5 and PM₁₀) and the meteorological variables (ambient temperature, wind speed/direction, and relative humidity) and in case of Helsinki also Monin-Obukhov length and mixing height of the present day. The variables to be forecasted are the maximum hourly concentrations of PM₁₀ and NO_x, and the daily average PM₁₀ concentrations of the next day. The meteorological pre-processing model MPP-FMI was used for computing the Monin-Obukhov length and the mixing height. The limitations of such statistical models include the persistence of both the meteorological and air quality situation; the model cannot account for rapid changes (on a temporal scale of hours or less than a day) that are commonly associated, e.g., with meteorological fronts, or episodes of a long-range transport origin. We have selected the input data for the model from one urban background and one urban traffic station both in Athens and Helsinki, in 2005. We have used various statistical evaluation parameters to analyze the performance of the models, and inter-compared the performance of the predictions for both cities. Forecasts from the MLR model were also compared to those from an Artificial Neural Network model (ANN) to investigate, if there are substantial gains that might justify the additional computational effort. The best predictor variables for both cities were the concentrations of NO_x and PM₁₀ during the evening hours as well as wind speed, and the Monin-Obukhov length. In Athens, the index of agreement (IA) for NO_x ranged from 0.77 to 0.84 and from 0.69 to 0.72, in the warm and cold periods of the year. In Helsinki, the corresponding values of IA ranged from 0.32 to 0.82 and from 0.67 to 0.86 for the warm and cold periods. In case of Helsinki the model accuracy was expectedly better on the average, when Monin-Obukhov length and mixing height were included as predictor variables. The models provide better forecasts of the daily average concentration, compared with the maximum hourly concentration for PM₁₀. The results derived by the ANN model where only slightly better than the ones derived by the MLR methodology. The results therefore suggest that the MLR methodology is a useful and fairly accurate tool for regulatory purposes.     

Daily suspended sediment concentration simulation using ANN and neuro-fuzzy models

In the present study, artificial neural networks (ANNs), neuro-fuzzy (NF), multi linear regression (MLR) and conventional sediment rating curve (SRC) models are considered for time series modeling of suspended sediment concentration (SSC) in rivers. As for the artificial intelligence systems, feed forward back propagation (FFBP) method and Sugeno inference system are used for ANNs and NF models, respectively. The models are trained using daily river discharge and SSC data belonging to Little Black River and Salt River gauging stations in the USA.Obtained results demonstrate that ANN and NF models are in good agreement with the observed SSC values; while they depict better results than MLR and SRC methods. For example, in Little Black River station, the determination coefficient is 0.697 for NF model, while it is 0.457, 0.257 and 0.225 for ANN, MLR and SRC models, respectively. The values of cumulative suspended sediment load estimated by ANN and NF models are closer to the observed data than the other models. In general, the results illustrate that NF model presents better performance in SSC prediction in compression to other models.     

Assessment of predictive uncertainty within the framework of water demand forecasting using the Model Conditional Processor (MCP)

This paper presents an application of the Model Conditional Processor (MCP), originally proposed by Todini (2008) within the hydrological framework, to assess the predictive uncertainty in water demand forecasting related to water distribution systems. The MCP enables us to assess the probability distribution of the future water demand conditional on the forecasts provided by two or more deterministic forecasting models. In the numerical application described here, where two years of hourly water demand data for a town in northern Italy are considered, two forecasting models are applied in order to forecast hourly water demands from 1 to 24 hours ahead: the first model has a modular structure comprising a periodic component which reflects the long-term effects and a persistence component which represents the short-term memory of the process; the latter is based on neural networks. The results highlight the effectiveness of the approach, provided that the data set used for the MCP parameterization is properly selected so as to be actually representative of the accuracy of the real-time water demand forecasting models.     

Development of a neural-based forecasting tool to classify recreational water quality using fecal indicator organisms

Users of recreational waters may be exposed to elevated pathogen levels through various point/non-point sources. Typical daily notifications rely on microbial analysis of indicator organisms (e.g., Escherichia coli) that require 18, or more, hours to provide an adequate response. Modeling approaches, such as multivariate linear regression (MLR) and artificial neural networks (ANN), have been utilized to provide quick predictions of microbial concentrations for classification purposes, but generally suffer from high false negative rates. This study introduces the use of learning vector quantization (LVQ) - a direct classification approach - for comparison with MLR and ANN approaches and integrates input selection for model development with respect to primary and secondary water quality standards within the Charles River Basin (Massachusetts, USA) using meteorologic, hydrologic, and microbial explanatory variables. Integrating input selection into model development showed that discharge variables were the most important explanatory variables while antecedent rainfall and time since previous events were also important. With respect to classification, all three models adequately represented the non-violated samples (>90%). The MLR approach had the highest false negative rates associated with classifying violated samples (41-62% vs 13-43% (ANN) and <16% (LVQ)) when using five or more explanatory variables. The ANN performance was more similar to LVQ when a larger number of explanatory variables were utilized, but the ANN performance degraded toward MLR performance as explanatory variables were removed. Overall, the use of LVQ as a direct classifier provided the best overall classification ability with respect to violated/non-violated samples for both standards.     

Daily urban water supply modeling and forecasting based on the elliptic orbit model with weekly quasi-periodic extension

ABSTRACT

Modeling and forecasting for various time horizons of urban water supply are important for different operations within a utility company. This study proposes the ‘elliptic orbit model’ for daily urban water supply prediction from the viewpoint of time-series analysis. As additional efforts and costs are required to acquire and predict more different forecast variables, it is argued that many studies failed to carefully check whether such efforts and costs were deserved and to what degree they might ameliorate the prediction accuracy. Thus predictive modeling based on available water supply data has its own advantages. Only the water-supply time-sequence data is used and mapped into the polar coordinates to design the proposed ‘elliptic orbit model’, so the purpose of this study is to present one vivid approach for forecasting daily urban water supply in an intuitive and concise way. The proposed model archives satisfying experimental results and may inspire other applications.     

Online sequential extreme learning machine in river water quality (turbidity) prediction: a comparative study on different data mining approaches

As a measure of water quality, water turbidity might be a source of water pollution in drinking water resources. Henceforth, having a reliable tool for predicting turbidity values based on common water quantity/quality measured parameters is of great importance. In the present paper, the performance of the online sequential extreme learning machine (OS‐ELM) in predicting daily values of turbidity in Brandywine Creek, Pennsylvania, is evaluated. For this purpose, in addition to the developed OS‐ELM, several data‐driven models, that is, multilayer perceptron neural network (MLPANN), the classification and regression tree (CART), the group method of data handling (GMDH) and the response surface method (RSM) have been applied. The general findings of the study confirm the superiority of the OS‐ELM model over the other applied models so that the OS‐ELM improved the averaged RMSE of the predicted values 9.1, 11.7, 20.5 and 29.3% over the MLPANN, GMDH, RSM and CART models, respectively.     

An evaluation of the accuracy of the multiple regression approach in forecasting sectoral construction demand in Singapore

In the current state of research in construction demand modelling and forecasting there is a predominant use of the multiple regression approach, particularly the linear technique. Because of the popularity, it may be useful at this stage to gain an insight into the accuracy of the approach by comparing the forecasting performance of different forms of regression analysis. It is only through such formal means that the relative accuracy of different regression techniques can be assessed. In a case-study of modelling Singapore's residential, industrial and commercial construction demand, both linear and nonlinear regression techniques are applied. The techniques used include multiple linear regression (MLR), multiple log-linear regression (MLGR) and autoregressive nonlinear regression (ANLR). Quarterly time-series data over the period 1975–1994 are used. The objective is to evaluate the reliability of these techniques in modelling sectoral demand based on ex-post forecasting accuracy. Relative measures of forecasting accuracy dealing with percentage errors are used. It is found that the MLGR outperforms the other two methods in two of the three sectors examined by achieving the lowest mean absolute percentage error. The general conclusion is that nonlinear techniques are more accurate in representing the complex relationship between demand for construction and its various associated indicators. In addition to improved accuracy, the use of nonlinear forms also expands the scope of regression analysis.     

混沌局域法与神经网络组合供水量预测

城市供水量是非线性、非平稳时间序列,组合预测模型能获得更高精度预测结果。通过深入分析混沌局域法与神经网络预测模型特点,提出了一种新的组合预测模型。首先,应用混沌局域法对城市日供水量进行初预测,然后,应用神经网络对预测结果进行修正。由于所提出的组合模型利用了混沌局域法及神经网络进行优势互补,能同时提高预测精度与计算效率。为验证所提出组合预测模型的可行性,采用某市7a实测供水量数据,对混沌局域法、BPNN、RBF及GRNN神经网络4种单一预测模型及相应的3种组合模型预测精度进行定量分析,结果表明,组合预测模型精度都高于对应单一预测模型,混沌局域法与GRNN神经网络组合模型预测精度最高,且运算时间远低于单一神经网络模型运算时间。     

Probabilistic prediction of urban water consumption using the SCEM-UA algorithm

Prediction of urban water consumption can help to improve the performance of water distribution systems. Despite the obvious presence of uncertainty in measurements and in assumed model types/structures, most of the existing water consumption prediction models are developed and used in a deterministic context. Methods for more realistic assessment of parameter and model prediction uncertainties have begun to appear in literature only recently. A novel application of the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) for the calibration of a water consumption prediction model is proposed here. The model is applied to a case study of the city of Catania (Italy) with the aim to predict daily water consumption. The SCEM-UA algorithm is used to calibrate the parameters of the artificial neural network based prediction model and in turn to determine the associated parameter and model prediction uncertainties. The results obtained using the SCEM-UA ANN approach were compared to the corresponding results obtained using other predictive models developed recently by the authors of the paper. When compared to the these models, the SCEM-UA ANN based water consumption prediction model shows similar predictive capability but also the ability to identify simultaneously the prediction uncertainty bounds associated with the posterior distribution of the parameter estimates.     

An ARIMA-NARX hybrid model for forecasting urban water consumption (case study: Tehran metropolis)

ABSTRACT

In this research, an ARIMA-NARX (Autoregressive Integrated Moving Average-Nonlinear Auto-Regressive eXogenous) hybrid model is proposed to forecast daily Urban Water Consumption (UWC) for Tehran Metropolis. The linear and nonlinear component of the UWC was forecast by ARIMA as a linear forecasting model and the artificial neural network as a nonlinear forecasting model, respectively. An alternative hybrid model including sunshine hour in addition to the previous studies’ predictors (the minimum, maximum and average temperature, relative humidity and precipitation) was selected as the superior alternative model. Then, the performance of proposed model was compared with ARIMA and NARX models. The results showed that the hybrid model, which benefits from capability of both linear and nonlinear models, has a higher accuracy than the other two models in forecasting UWC. Therefore, the proposed hybrid model has better results in UWC forecasting and, as a consequence, better urban water reservoir management will be provided.     

Determination of the optimal parameters in regression models for the prediction of chlorophyll-a: A case study of the Yeongsan Reservoir, Korea

Statistical regression models involve linear equations, which often lead to significant prediction errors due to poor statistical stability and accuracy. This concern arises from multicollinearity in the models, which may drastically affect model performance in terms of a trade-off scenario for effective water resource management logistics. In this paper, we propose a new methodology for improving the statistical stability and accuracy of regression models, and then show how to cope with pitfalls in the models and determine optimal parameters with a decreased number of predictive variables. Here, a comparison of the predictive performance was made using four types of multiple linear regression (MLR) and principal component regression (PCR) models in the prediction of chlorophyll-a (chl-a) concentration in the Yeongsan (YS) Reservoir, Korea, an estuarine reservoir that historically suffers from high levels of nutrient input. During a 3-year water quality monitoring period, results showed that PCRs could be a compact solution for improving the accuracy of the models, as in each case MLR could not accurately produce reliable predictions due to a persistent collinearity problem. Furthermore, based on R² (goodness of fit) and F-overall number (confidence of regression), and the number of explanatory variables (R-F-N) curve, it was revealed that PCR-F(7) was the best model among the four regression models in predicting chl-a, having the fewest explanatory variables (seven) and the lowest uncertainty. Seven PCs were identified as significant variables, related to eight water quality parameters: pH, 5-day biochemical oxygen demand, total coliform, fecal indicator bacteria, chemical oxygen demand, ammonia-nitrogen, total nitrogen, and dissolved oxygen. Overall, the results not only demonstrated that the models employed successfully simulated chl-a in a reservoir in both the test and validation periods, but also suggested that the optimal parameters should cautiously be considered in the design of regression models.     

基于小波分解的城市供水管网短期水量负荷预测

利用小波分解和人工神经网络相结合的方法建立了城市供水管网短期水量负荷的组合预测模型。该方法首先利用小波分解技术将时负荷水量分解为相对简单的带通分量信号，然后根据各分量信号的特点分别建立独立的神经网络预测模型，最后将预报结果集成。由于小波分解后各分量的频率相对单一，因而可有效缩短网络训练时间，提高计算速度。仿真计算结果表明，该方法建模合理、计算量适中，可准确预测管网水量。     

Forecasting short-term electricity load using hybrid support vector regression with grey catastrophe and random forest modeling

This paper develops a novel short-term load forecasting model that hybridizes several machine learning methods, such as support vector regression (SVR), grey catastrophe (GC (1,1)), and random forest (RF) modeling. The modeling process is based on the minimization of both SVR and risk. GC is used to process and extract catastrophe points in the long term to reduce randomness. RF is used to optimize forecasting performance by exploiting its superior optimization capability. The proposed SVR-GC-RF model has higher forecasting accuracy (MAPE values are 6.35% and 6.21%, respectively) using electric loads from Australian-Energy-Market-Operator; it can provide analytical support to forecast electricity consumption accurately.     

Predicting a water infrastructure leakage index via machine learning

In this study, the infrastructure leakage index (ILI) indicator that is preferred frequently by the water utilities with sufficient data to determine the performances of water distribution systems is modeled for the first time through the three different methodologies using different input data. In addition to the variables in the literature used for the classical ILI calculations, the age parameter is also included in the models. In the first step, the ILI values have been estimated via multiple linear regression (MLR) using water supply quantity, water accrual quantity, network length, service connection length, number of service connections, and pressure variables. Secondly, the Artificial Neural Network (ANN) approach has been applied with raw data to improve the ILI prediction performance. Finally, the data set has been standardized with the Z-Score method for increasing the learning power of the ANN models, and then the ANN predictions have been made by converting the data through the principal component analysis (PCA) method to minimize complexity by reducing the data set size. The model predictions have been evaluated via mean square error, G-value, mean absolute error, mean bias error, and adjusted-R² model performance scale. When the model outputs obtained at the end of the study are evaluated together with the classical ILI calculations, it is seen that the successful ILI predictions with three and four variables, including the age parameter, rather than six variables, have been made through the PC-ANN method. Water utilities with insufficient physical and operational data for ILI indicator calculation can make network performance evaluations by predicting the ILI through the models suggested in this study with high accuracy in a reliable way.     

局域法邻近点选取对供水量预测精度的影响

混沌局域法预测模型适用于非线性、非平稳的城市日供水量预测,而邻近相点个数的选取对该模型预测精度有直接影响。传统方法通常以嵌入维m作为参考值,凭经验选取m+1个邻近相点,且仅使用欧式距离法计算当前相点距离,无法反映相点的运动趋势,易引入伪邻近相点,导致预测精度的降低。鉴于此,将演化追踪法引入城市日供水量预测,通过挖掘邻近相点的历史演化规律对参考样本进行优选,以提高预测精度。最后,采用实际日供水量数据验证所提出方法,结果表明,运用演化追踪法优选邻近相点能显著提高日供水量预测精度,预测平均绝对误差由2.501%降低到1.683%。