Research And Application On Water Supplies Forecasting Based On Feature-Driven Of The Time Series

Recently, water consumptions have increased dramatically with high-speeddeveloped economy, increased urbanization and improved living standards, causing thecomplexities of the water supply system increased gradually. It makes traditionalscheduling methods of the water supply system facing unprecedented challenges. Watersupplies forecasting is the basis and prerequisite for the water supplies scheduling,hence the water supplies forecating have been one of the most concern issues in watersupply enterprises and operation management departments. By water suppliesforecasting, it can provide data basis for the water supplies scheduling, improveutilization efficiencies of water resources, and promote social harmony and healthydevelopment.Daily water supplies forecasting can ensure the users’ requirements of waterquantity and water pressure in different time, at the same time also can increaseproductivity of the water supply companies with low costs, so as to improve the qualityof water supplies services. Monthly water supplies forecasting can balance watersources and water supplies of different water supply companies, improving the ability ofregional scheduling, and reducing the waste of water resources. Therefore, this paperfocuses on the issues of the daily and monthly water supplies forecasting, taking thetimes series of three scales water supply companies under the normal workingconditions in Chongqing as the research objects. The main research contents are asfollows:①This paper studies the predictability of the water supplies series (five timeseries collected from three scales water supply companies). The results of qualitativeanalysis (power spectrum analysis) and quantitative analysis (maximum Lyapunovindex) show that the daily and monthly water supplies series both exist chaoscharacteristic, indicating that the water supplies series involved are predictable based onthe chaos theroy.②Four common-used methods (classified two categories, traditional model anddata mining model), i.e. autoregressive integrated moving average (ARIMA), backpropagation neutral network (BPNN), adaptive neuro fuzzy inference system (ANFIS),and least square support vector regression (LSSVR), are applied to forecast the dailyand monthly water supplies respectively These algorithms are all programmed by Matlab2011. Among these models, the structures of the BPNN, ANFIS, and LSSVR aredetermined by phase space restructure based on their chaos features. The forecastingresults show that the data mining model has better performances than the traditionalmodel. Especially, the LSSVR model exhibits the best fitting performance in the dailyforecasting and poor performance in the monthly forecasting. Therefore, the LSSVRmodel is employed as the core method for forecasting the daily water supplies in thenext contents.③Due to diversities of the daily water supplies in local, low modeling speed andhigh computational cost in the global modeling, a local modeling method based onmulti-scale least square support vector regression (MS-LSSVR) is proposed to forecastthe daily water supplies. The non-stationary time series of the daily water supplies aredecomposed by stationary wavelet transform into different scales stationary time series.In each scale, establish the least square support vector machine for regression model.Then the forecast results of the LSSVR outputs at all the scales are employed toreconstruct the forecasting result of the original daily water supplies time series throughthe inverse wavelet transform. The case study results demonstrate that the proposedmodel is beneficial to the improvement of the forecasting accuracy and stability.Compared with the LSSVR model, three assessment criteria (i.e., mean absolute error(MAE), mean absolute percentage error (MAPE), and normalized root mean squareerror (NRMSE)) have significant developments respectively. Specific improvingindexes are as follows: MAE1889.838m3/d,827.722m3/d,153.729m3/d; MAPE0.919%,1.262%,1.576%; NRMSE0.0116,0.0162,0.0174.④In view of the time-varying characteristic of the daily water supplies, leading tothe model structures degraded and the forecasting accuracy reduced, a dynamicforecasting model based on variable structure least square support vector regression(VS-LSSVR) is proposed. Train LSSVR model using the historical data of the dailywater supplies, and get the historical data series of forecasting model structureparameters. According to the historical series of model structure parameters, estimatethe next-day model structure parameters using data assimilation technology--extendedkalman filter. Then the estimated structure parameters are used to update the LSSVRstructure. Finally forecast the next-day water supplies with new structure LSSVR model.In this way, the structure of forecasting model has been updated dynamically. The casestudy results show that the proposed model overcomes the forecasting accuracydegraded over time, and improves the dynamic forecasting performance on the basis of lossing time. Compared with the LSSVR, MAE improves1966.866m3/d,1379.634m3/d,177.905m3/d, respectively; MAPE improves1.462%,2.173%,1.780%, respectively;NRMSE improves0.0197,0.0253,0.0189, respectively.⑤Considering the characteristics of the monthly water supplies (trend,seasonality, and randomness) and the performance of the different modelzzs fordifferent time series features, an additive model is proposed to forecast the monthlywater supplies. Because different features are represented by different frequency bandsof the time series, historical time series of the monthly water supplies are decomposedby ensemble empirical mode decomposition into several intrinsic mode functions and aresidue. According to frequency signatures analyzed by Fourier spectral representation,all intrinsic mode functions and residue are grouped into three terms: trend term,periodic term, and stochastic term. To accommodate the different characteristics of thethree terms, ARIMA, LSSVR, and ANFIS are adopted for the three subforecasts,respectively. The sub-models are determined by the introducetion and case study resultsof Chapter1and Chaper3(ARIMA is good at tracking the linear and stationarytendency, LSSVR has good fitting capacity for the nonlinear time series, and ANFIS isgoode at forecasting complex time series). The additive model is subsequently used tointegrate the three subforecasts representing different characteristics to achieve the finalforecasting results. The case study results indicate that the proposed model, consideringthe different adaptability and traceability of the different models for the different changerules of the different character items, can improve the overall prediction accuracy.Compared with four single models in Chapter3, MAE improves6388.546m3/d~8759.052m3/d, MAPE improves1.929%~2.525%, and NRMSEimproves0.0195~0.0307, respectively.