Comparative Study of Artificial Neural Networks and Wavelet Artificial Neural Networks for Groundwater Depth Data Forecasting with Various Curve Fractal Dimensions

The objective of this study was comparative study of artificial neural networks (ANN) and wavelet artificial neural networks (WANN) for time-series groundwater depth data (GWD) forecasting with various curve fractal dimensions. The paper offered a better method of revealing the change characteristics of GWD. Time series prediction based on ANN algorithms is fundamentally difficult to capture the data change details, when the time-series GWD data changes are more complex. For this purpose, Wavelet analysis and fractal theory methods are proposed to link to ANN models in predicting GWD and analysis the change characteristics. The trend and random components were separated from the original time-series GWD using wavelet methods. The fractal dimension is convenient for quantitatively describing the irregularity or randomness of time series data. Three types of training algorithms for ANN and WANN models using a Mallat decomposition algorithm were investigated as case study at three sites in the Ganzhou region of northwest China to find an optimal model that is suitable for certain characteristics of time-series GWD data. The simulation results indicate that both WANN and ANN models with the Bayesian regularization algorithm are accurate in reproducing GWD at sites with smaller fractal dimensions. However, WANN models alone are suitable for sites at which the fractal dimension of the wavelet decomposition detail components is larger. Prediction error is also greater when the fractal dimension is larger.