Optimization of Wavelet-ANFIS and Wavelet-ANN Hybrid Models by Taguchi Method for Groundwater Level Forecasting

In the recent years, artificial intelligence techniques have been widely developed for modeling hydrologic processes. Determining the best structures of these models such as Wavelet-ANN and Wavelet-ANFIS still remains a difficult task. In fact, there are several factors in the structure of these models that should be optimized. Selecting the best model structure by testing all of the possible combinations of factors is very time consuming and labor intensive. Using the optimization Taguchi method, this study assessed different factors affecting the performance of Wavelet-ANN and Wavelet-ANFIS hybrid models each of which has several levels. A L18 orthogonal array was selected according to the selected factors and levels and experimental tests were performed accordingly. Analysis of the signal-to-noise (S/N) ratio was used to evaluate the models performance. The optimum structures for both models were determined. For Wavelet-ANN, a model having 14 neurons in the hidden layer and trained with 1,000 epochs using Tangent Sigmoid (TanSig) transfer function in both hidden and output layers, and trained with Levenberg–Marquardt (LM) algorithm, whose input data were decomposed using Reverse Bior 1.5 (rbio1.5) wavelet in level 2, is the optimal Wavelet-ANN model. For Wavelet-ANFIS, a model with 700 iterations, using bell-shaped membership function and 5 membership functions, whose input data were decomposed using Daubechies 4 (db4) wavelet in level 2, is the optimal Wavelet-ANFIS model. Confirmation tests were then conducted using the optimum structures. It is also concluded that the best Wavelet-ANFIS model outperforms the best Wavelet-ANN model.