Comparison Study of ANFIS, ANN, and RSM and Mechanistic Modeling for Chromium(VI) Removal Using Modified Cellulose Nanocrystals–Sodium Alginate (CNC–Alg)

Abstract

The adsorption process was investigated using the ANFIS, ANN, and RSM models. The adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), and response surface methodology (RSM) were used to develop an approach for assessing the Cr(VI) adsorption from wastewater using cellulose nanocrystals and sodium alginate. The adsorbent was characterized using Fourier transform infrared spectroscopy and thermogravimetric analysis. Initial pH of 6, contact time of 100 min, initial Cr(VI) concentration of 175 mg/L, sorbent dose of 6 mg, and adsorption capacity of 350.23 mg/g were the optimal condition. The Cr(VI) adsorption mechanism was described via four mechanistic models (film diffusion, Weber and Morris, Bangham, and Dumwald-Wagner models), with correlation values of 0.997, 0.990, and 0.989 for ANFIS, ANN, and RSM, respectively, and predicted the adsorption of the Cr(VI) with incredible accuracy. Statistical error tasks were additionally applied to relate the adequacy of the models. Using the central composite design (CCD), the significance of operating factors such as time, adsorbent dose, pH, and initial Cr(VI) concentration was investigated. The same concept was used to create a training set for ANN where the Levenberg–Marquardt, variable learning rate, and Polak Ribiere conjugate algorithms were used. Further statistical indices supported ANFIS as the best prediction model for adsorption compared to ANN and RSM. The efficient algorithm was used to optimize the process, which resulted in a 350 mg/g adsorption capacity. Film diffusion was identified as the rate-limiting process via mechanistic modeling.

Optimization of adaptive neuro–fuzzy inference system (ANFIS) parameters via Box-Behnken experimental design approach: The prediction of chromium adsorption

“…It was concluded that MF numbers for each inputs can affect the predictions in different ranges, and depending on the variety and data type optimum MF number could be different. In the literature, the researchers tend to use the same MF numbers for each input [ [6] , [7] , [8] , [9] , [10] , [11] , [13] , [14] , [15] , [16] ]. As we observed that in order to make good predictions these MF numbers should be optimized for each input and for each different dataset.…”

“…As seen that ANFIS configurations vary significantly among the studies, with differences in the number and type of membership functions for different input variables. Among the predictive Cr(VI) adsorption studies, Banza et al [ 14 ] and Dubey et al [ 17 ] performed the best ANFIS prediction with the lowest RMSE (0.007 and 0.038) and high R 2 (0997 and 0.99) values, however, there is no information about the used membership function and number in their studies. The adsorption data used in the study was obtained by applying response surface methodology [ 14 ].…”

“…Among the predictive Cr(VI) adsorption studies, Banza et al [ 14 ] and Dubey et al [ 17 ] performed the best ANFIS prediction with the lowest RMSE (0.007 and 0.038) and high R 2 (0997 and 0.99) values, however, there is no information about the used membership function and number in their studies. The adsorption data used in the study was obtained by applying response surface methodology [ 14 ]. This approach may positively affect the prediction accuracy.…”

“…They indicated that the number of MFs for each input and the type of MF for each input are the structural parameters for grid partitioning ANFIS, and they tested all MFs but only with limited MF numbers (2 and 3) for each inputs [ 12 ]. There are some studies [ [13] , [14] , [15] , [16] , [17] ] related to the prediction of chromium adsorption via ANFIS, however, none of them focused on optimization of ANFIS parameters. Zafar et al [ 13 ] employed Gaussian MF for each inputs (pH, adsorbent dosage, initial concentration) on Cr(VI) adsorption data.…”

“…In the mentioned study [ 13 ], there is no examination about the MF type and number of MF for each input. Banza et al [ 14 ] indicated that compared to ANN and RSM, ANFIS is the best prediction model for Cr(VI) adsorption onto cellulose nanocrystals–sodium alginate and, however, there is no information about the chosen MF type for inputs (time, dosage, pH and concentration) and output (adsorption capacity). Cr(VI) removal in textile wastewater using activated carbon was predicted with ANFIS in another study [ 15 ], as typical, without any systematic approach all MF types with one and two input numbers were examined.…”