Adaptive neuro-fuzzy inference system (ANFIS) and multiple linear regression (MLR) modelling of Cu, Cd, and Pb...

Soils interact in many ways with metal ions thereby modifying their mobility, phase distribution, plant availability, speciation, and so on. The most prominent of such interactions is sorption. In this study, we investigated the sorption of Pb, Cd, and Cu in five natural soils of Nigerian origin. A relatively sparsely used method of modelling soil-metal ion adsorption, i.e. adaptive neuro-fuzzy inference system (ANFIS), was applied comparatively with multiple linear regression (MLR) models. The isotherms were well described by Freundlich and Langmuir equations (R² ≥ 0.95) and the kinetics by nonlinear two-stage kinetic model, TSKM (R² ≥ 0.81). Based on the values delivered by the Langmuir equation, the maximum adsorption capacities (Q_m*) were found to be in the ranges 10,000-20,000, 12,500-50,000, and 4929-35,037 µmol kg^-1 for Cd, Cu, and Pb, respectively. The study revealed significant correlations between Q_m* and routinely determined soil parameters such as soil organic carbon (C_org), cation exchange capacity (CEC), amorphous Fe and Mn oxides, and percentage clay content. These soil parameters, combined with operational variables (i.e. solution/soil pH, initial metal concentration (C_o), and temperature), were used as input vectors in ANFIS and MLR models to predict the adsorption capacities (Q_e) of the soil-metal ion systems. A total of 255 different ANFIS and 255 different MLR architectures/models were developed and compared based on three performance metrics: MAE (mean absolute error), RMSE (root mean square errors), and R² (coefficient of determination). The best ANFIS returned MAE_test 0.134, RMSE_test 0.164, and R²_test 0.76, while the best MLR returned MAE_test 0.158, RMSE_test 0.199, and R²_test 0.66, indicating the predictive advantage of ANFIS over MLR. Thus, ANFIS can fairly accurately predict the adsorption capacity and/or distribution coefficient of a soil-metal ion system a priori. Nevertheless, more investigation is required to further confirm the robustness/generalisation of the proposed ANFIS.