Optimization of ANFIS model using wavelet transform for simulating groundwater level variations

In this study, for the first time, groundwater level (GWL) variations of the Sarab-e Qanbar well located in the city of Kermanshah, are simulated over a 13-year period by a hybrid model named WANFIS (wavelet-adaptive neuro fuzzy inference system). In order to develop the hybrid model, the wavelet transform and the adaptive neuro fuzzy inference system (ANFIS) model are utilized. Furthermore, the 9 and 4 year data are used for training and testing the artificial intelligence models, respectively. Moreover, the effective lags are detected by the autocorrelation function (ACF) and then eight different models are developed for each of the ANFIS and WANFIS models using them. After that, all mother wavelets are evaluated and Dmey mother wavelet is chosen as the most optimal. For this mother wavelet, the values of scatter index (SI), variance account for (VAF) and Root mean square error (RMSE) are obtained 0.192, 94.951 and 3.117, respectively. Next, the superior model is detected through the analysis of the results obtained by all ANFIS and WANFIS models. The superior model estimates the objective function values with reasonable accuracy. For example, the correlation coefficient (R), Scatter Index (SI) and variance account for (VAF) for this model are obtained 0.974, 0.192 and 94.951, respectively. The modeling results indicate that the wavelet transform noticeably enhances the ANFIS model accuracy. Finally, the lags of the time series data for the Sarab-e Qanbar well including (t-1), (t-2), (t-3) and (t-4) are introduced as the most effective lags.