A comparative study using response surface methodology and artificial neural network for modeling the bio-reduction of hexavalent chromium (Cr⁶⁺) by immobilized cells of Paenibacillus taichungensis strain MAHA in an alginate-gellan gum matrix

Chromium (Cr⁶⁺) waste poses a hazard as it leads to imbalanced ecosystems and severe health issues. Although, it is widely associated with many industries. Chromium (Cr⁶⁺) reduction by the immobilized cells of Paenibacillus taitungensis strain MAHA-MIE was optimized using response surface methodology (RSM) and artificial neural networks (ANN). The RSM-Box-Behnken Design (BBD) was selected to investigate the effects of chromium (Cr⁶⁺) concentration, alginate concentration, gellan gum concentration, bead size, and the number of beads on chromium (Cr⁶⁺) reduction rate. Experimental data from the BBD was used to train a feed-forward, multilayer artificial neural network (ANN). Results show that the ANN model outperformed the response surface methodology (RSM) based on actual and predicted data, with lower errors and a higher R² value. The ANN model predicted the optimum points as follows: 155 ppm chromium (Cr⁶⁺), 0.32% alginate, 0.65% gellan gum, 0.5 cm beads, and 27 beads. The validation confirmed a high agreement of chromium (Cr⁶⁺) reduction rate between the validation value (99.00%) and the predicted value (99.99%), with the lowest deviation at 0.1%. Modeling abilities were compared using statistical criteria, including Root Mean Square Error (RMSE), Standard Error of Prediction (SEP), Relative Percent Deviation (RPD), and regression coefficients (R²). The ANN analysis showed the high predictive performance, with high R² (0.9911), low SEP (0.45%), RPD (1.88), and RMSE (1.37%). The results of this study approved that alginate-gellan gum immobilized cells of Paenibacillus taitungensis strain MAHA-MIE could be effectively used for the handling of chromium (Cr⁶⁺).