Optimization of wavelet-ANFIS and wavelet-ANN hybrid models by taguchi method for groundwater level forecasting

In the recent years, artificial intelligence tech- niques have been widely developed formodeling 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 struc- ture of these models that should be optimized. Selecting the best model structure by testing all of the possible combina- tions of factors is very time consuming and labor intensive. Using the optimization Taguchi method, this study assessed different factors affecting the performance ofWavelet-ANN and Wavelet-ANFIS hybrid models each of which has sev- eral levels. A L18 orthogonal array was selected according to the selected factors and levels and experimental testswere 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, amodel having 14 neurons in the hidden layer and trained with 1,000 epochs using Tangent Sigmoid (Tan- Sig) transfer function in both hidden and output layers, and trained with Levenberg–Marquardt (LM) algorithm, whose input datawere decomposed usingReverse 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, whoseinput dataweredecomposedusingDaubechies4(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 bestWavelet-ANFIS model outperforms the bestWavelet-ANN model.