Abstract
An artificial neural network (ANN) hybrid structure was proposed that, unlike the standard ANN structure optimization, allows the fit of several adsorption curves simultaneously by indirectly minimizing the real output error. To model a case study of 3-aminophenol adsorption phenomena onto avocado seed activated carbon, a hybrid ANN was applied to fit the parameters of the Langmuir and Sips isotherm models. Network weights and biases were optimized with two different methods: particle swarm optimization (PSO) and genetic algorithm (GA), due to their good convergence in large-scale problems. In addition, the data were also fitted with the Levenberg-Marquardt feedforward optimization method to compare the performance between a standard ANN model and the hybrid model proposed. Results showed that the ANN-isotherm hybrid models with both PSO and GA were able to accurately fit the experimental equilibrium adsorption capacity data using the Sips isotherm model, obtaining Pearson’s correlation coefficient (R) of the order of 0.9999 and mean squared error (MSE) around 0.5, very similar to the performance of standard ANN using Levenberg-Marquardt optimization. On the other hand, the results with Langmuir isotherm models were quite inferior in the ANN-isotherm hybrid models with both PSO and GA, with R and MSE of around 0.944 and 4.04 × 102, respectively. The proposed ANN-isotherm hybrid structure was successfully applied to estimate the parameters of adsorption isotherms, reducing the computational demand and the exhausting task of estimating the parameters of each adsorption curve individually.
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Abbreviations
- AC:
-
Activated carbon
- ANN:
-
Artificial neural network
- C 0 :
-
Solution initial concentration mg/L
- C e :
-
Equilibrium concentration mg/L
- F obj :
-
Objective function value Variable
- GA:
-
Genetic algorithm
- K S :
-
Sips affinity constant L/mg
- MSE:
-
Mean squared error
- N S :
-
Sips heterogeneity factor
- PSO:
-
Particle swarm optimization
- q e :
-
Equilibrium adsorption capacity mg/g
- q e,t :
-
Measured equilibrium adsorption capacity mg/g
- q e,o :
-
Predicted equilibrium adsorption capacity mg/g
- q S :
-
Sips theoretical saturation capacity mg/g
- R :
-
Pearson’s coefficient of correlation
- R 2 :
-
Coefficient of determination
- RMSE :
-
Root mean squared error
- T :
-
Adsorption temperature K
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Acknowledgements
The authors would like to thank the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) and the Research Support Foundation of Rio Grande do Sul (FAPERGS) for the financial support of this work.
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This work was supported by the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) and the Research Support Foundation of Rio Grande do Sul (FAPERGS).
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Jean Lucca Souza Fagundez: Conceptualization; Investigation; Resources; Writing, original draft; Methodology; Formal analysis.
Nina Paula Gonçalves Salau: Supervision; Project administration; Funding acquisition; Conceptualization; Writing, review and editing.
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Fagundez, J.L.S., Salau, N.P.G. Optimization-based artificial neural networks to fit the isotherm models parameters of aqueous-phase adsorption systems. Environ Sci Pollut Res 29, 79798–79807 (2022). https://doi.org/10.1007/s11356-021-17244-5
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DOI: https://doi.org/10.1007/s11356-021-17244-5