Application of Wavelet Decomposition and Phase Space Reconstruction in Urban Water Consumption Forecasting: Chaotic Approach (Case Study)

Abstract

The forecasting of future value of water consumption in an urban area is highly complex and nonlinear. It often exhibits a high degree of spatial and temporal variability. It is a crucial factor for long-term sustainable management and improvement of the operation of urban water allocation system. This chapter will study the application of two preprocessing phase space reconstruction (PSR) and wavelet decomposition transform (WDT) methods to investigate the behavior of time series to forecast short-term water demand value of Kelowna City (BC, Canada). The research proposes two pre-process technique to improve the accuracy of the models. Artificial neural networks (ANNs), gene expression programming (GEP) and multilinear regression (MLR) methods are the tools that considered for forecasting the demand values. Evaluation of the tools is based on two steps with and without applying the pre-processing methods. Moreover, autocorrelation function (ACF) is used to calculate the lag time. Correlation dimension is used to study the chaotic behavior of the dataset. The models' relative performance is compared using three different fitness indexes; coefficient of determination (CD), root mean square error (RMSE) and mean absolute error (MAE). The results showed how pre-processing combination of WDT and PSR improved the performance of the models in forecasting short-term demand values.

Nonlinear Dynamic Modeling of Urban Water Consumption Using Chaotic Approach (Case Study: City of Kelowna)

“…Input variable selection challenges the effect of the number of inputs in models' performance. In other words, there are diminishing returns on performance based on the number of input variables selected [42]. The combinations were selected in a way that included daily consumption data with lag times of τ = 1 and 17 days.…”

“…to ascertain the relationship between the input and output variables. The physical-based and black box models include conventional regression models [9], artificial neural networks (ANN) [14,20,30,31], feedforward neural networks (FNN) [22,32], general regression neural networks (GRNNs) [33,34], deep belief neural network (DBNN) [35], support vector machines (SVMs) [16,18,[36][37][38], gene expression programming (GEP) [39,40], adaptive neural fuzzy inference system (ANFIS) [41], Fourier analysis [7], hybrid models (e.g., combined wavelet) [23,42,43], fuzzy regression [44], fuzzy cognitive map learning method [45], epidemiology-based forecasting framework [46], temporal disaggregation [47], harmonic analysis [48], and wavelet de-noising [49].…”

“…Moreover, GEP presents mathematical equations that clarify the relationship between input and output variables by a factor of 100-10000 [63,79,80]. The superiority of GEP and the advantages of this technique interested researchers to develop more sophisticated models with hybrid methods such as combining the extended Kalman filter [81], clustering the consumption values [82], Wavelet decomposition [39], and phase space reconstructed GEP (PSR-GEP) [42] in forecasting urban drinking water consumption. The results showed that GEP models are highly sensitive to wavelet decomposition when attempting to improve the performance of the models.…”

Estimating High Resolution Temporal Scale of Water Demand Time Series – Disaggregation Approach (Case Study)

“…The presented results (accuracy of disaggregation regarding with correlation coefficient (R) and root mean square error (RMSE) for different embedding dimensions from m=1 to 10, go following the results that are obtained from disaggregation of water demand values (See Table 3). Since the understanding of consumers' behaviour depends on the knowledge of consumption anomalies, peak-hours, usage frequencies, used devices, metrological and social information (Yousefi P. 2018), considering the mentioned factors into account to be considered as a variable to develop updated disaggregation method would be a great idea to "design targeted personalized demand management strategy, including economic incentives to upgrade inefficient appliances (e.g. (Mayer 2004)" (Cominola 2018…”

“…2013, Cominola 2018. Because, temporal high-resolution time series enable better estimation of peak demands that are very important in a short-term plan along with to develop a maintaining plan for pipeline in long-term period to overcome to probabilistic failures in the network (Beal 2016, Shabani 2016, Yousefi 2017, Yousefi P. 2018. These theories also have interpolation and extrapolation methods based on recorded values in SCADA.…”