Application neural network approach for the estimation of heavy metal concentrations in the Inaouen watershed
Abstract
This paper describes how the multilayer perceptron neural network (MLPNN) trained by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-newton back-propagation approach was used to estimate heavy metal concentrations: Aluminum (Al), Lead (Pb), Copper (Cu), and Iron (Fe), in the province of Taza using sixteen physicochemical factors measured from 100 samples collected from surface water sources by our team, according to the protocol of the national water office (ONE). We chose a network with only one hidden layer to identify the network architecture to employ. The number of neurons in the hidden layer was varied, as were the types of transfer and activation functions, and the BFGS learning method was used. The following statistical metrics were used to evaluate the performance of the neural network’s stochastic models: Examining the adjustment graphs and residue, as well as the Error Sum of Squares (SSE); the mean bias error (MBE) and determination coefficient (R²). The results reveal that the predictive models created using the artificial neural network method (ANN) are quite efficient, thanks to the BFGS algorithm’s efficiency and speed of convergence. An architectural network [16-8-1] (16: number of variables in input layer, 8: number of hidden layer, 1: number of variables in output layer) produced the best results,{R²: Al(0.954), Pb(0.942), Cu(0.921), Fe(0.968)}, {SSE: Al(0.396), Pb(0.0059), Cu(0.252), Fe(4.29)} and {MBE: Al(–0.033), Pb(0.008), Cu(–0.004), Fe(0.091)}, which is developed so that each model is responsible for estimating the concentration of a single heavy metal. This result demonstrates that there is a non-linear relationship between the physical-chemical properties evaluated and the heavy metal content of surface water in the Taza province.
Keyword : algorithm BFGS, neural networks, heavy metals, environmental processes modelling, prediction
How to Cite
El Chaal, R., & Aboutafail, M. O. (2022). Application neural network approach for the estimation of heavy metal concentrations in the Inaouen watershed. Journal of Environmental Engineering and Landscape Management, 30(4), 515–526. https://doi.org/10.3846/jeelm.2022.18059
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Coulibaly, P., Anctil, F., & Bobée, B. (1999). Prévision hydrologique par réseaux de neurones artificiels: État de l’art. Canadian Journal of Civil Engineering, 26(3), 293–304. https://doi.org/10.1139/l98-069
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Dreyfus, G. (2006). Les réseaux de neurones. Revue de l’Electricité et de l’Electronique, 8, 37.
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El Chaal, R., & Aboutafail, M. O. (2022). A comparative study of back-propagation algorithms: Levenberg-Marquart and BFGS for the formation of multilayer neural networks for estimation of fluoride. Communications in Mathematical Biology and Neuroscience, 1–17.
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El Hmaidi, A., El Badaoui, H., Abdallaoui, A., & El Moumni, B. (2013). Application des réseaux de neurones artificiels de type PMC pour la prédiction des teneurs en carbone organique dans les dépôts du quaternaire terminal de la mer d’alboran. European Journal of Scientific Research, 107(3), 400–413.
Fletcher, R. (1981). Constrained optimization. In Practical methods of optimization (Vol. 2). John Wiley & Sons Ltd.
Funahashi, K.-I. (1989). On the approximate realization of continuous mappings by neural networks. Neural Networks, 2(3), 183–192. https://doi.org/10.1016/0893-6080(89)90003-8
Graupe, D. (2007). Principles of artificial neural networks (2nd ed.). World Scientific. https://doi.org/10.1142/6429
Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural Networks, 4(2), 251–257. https://doi.org/10.1016/0893-6080(91)90009-T
Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2(5), 359–366. https://doi.org/10.1016/0893-6080(89)90020-8
Ibrahim, M. A. H. Bin, Mamat, M., & June, L. W. (2014). BFGS method: A new search direction. Sains Malaysiana, 43(10), 1591–1597.
Jacobs, R. A. (1988). Increased rates of convergence through learning rate adaptation. Neural Networks, 1(4), 295–307. https://doi.org/10.1016/0893-6080(88)90003-2
Jiang, Y., Zhang, G., Wang, J., & Vaferi, B. (2021). Hydrogen solubility in aromatic/cyclic compounds: Prediction by different machine learning techniques. International Journal of Hydrogen Energy, 46(46), 23591–23602. https://doi.org/10.1016/j.ijhydene.2021.04.148
Karimi, M., Vaferi, B., Hosseini, S. H., Olazar, M., & Rashidi, S. (2021). Smart computing approach for design and scale-up of conical spouted beds with open-sided draft tubes. Particuology, 55, 179–190. https://doi.org/10.1016/j.partic.2020.09.003
Kharroubi, O., Blanpain, O., Masson, E., & Lallahem, S. (2016). Application du réseau des neurones artificiels à la prévision des débits horaires: Cas du bassin versant de l’Eure, France. Hydrological Sciences Journal, 61(3), 541–550. https://doi.org/10.1080/02626667.2014.933225
Mottelet, S. (2003). RO04/TI07 – Optimisation non-linéaire. Université de Technologie de Compiègne.
Parizeau, M. (2004). Reseaux De Neurones GIF-21140 et GIF-64326. Universite LAVAL.
Patro, S. G. K., & sahu, K. K. (2015). Normalization: A preprocessing stage. International Advanced Research Journal in Science, Engineering and Technology, 2(3), 20–22. https://doi.org/10.17148/IARJSET.2015.2305
Rahnama, E., Bazrafshan, O., & Asadollahfardi, G. (2020). Application of data-driven methods to predict the sodium adsorption rate (SAR) in different climates in Iran. Arabian Journal of Geosciences, 13(21), 1160. https://doi.org/10.1007/s12517-020-06146-4
Shouyu, C., & Honglan, J. (2005). Fuzzy optimization neural network approach for ice forecast in the inner Mongolia reach of the Yellow River. Hydrological Sciences Journal, 50(2), 37–41. https://doi.org/10.1623/hysj.50.2.319.61793
Skansi, S. (2018). Introduction to deep learning. From logical calculus to artificial intelligence. Springer International Publishing AG. https://doi.org/10.1007/978-3-319-73004-2
Snyman, J. A., & Wilke, D. N. (2018). Springer optimization and its applications: Vol. 133. Practical mathematical optimization (2nd ed.). Springer Cham. https://doi.org/10.1007/978-3-319-77586-9
STATISTICA. (2014, June 4). Logiciel STATISTICA (version 12.5.192.5). http://www.statsoft.fr/logiciels/reseaux-de-neurones-automatises.php
Touzet, C. (2016). Les reseaux de neurones artificiels, introduction au connexionnisme. HAL Open Science.
Vaferi, B., Eslamloueyan, R., & Ayatollahi, S. (2011). Automatic recognition of oil reservoir models from well testing data by using multilayer perceptron networks. Journal of Petroleum Science and Engineering, 77(3), 254–262. https://doi.org/10.1016/j.petrol.2011.03.002
Verma, A. K., & Singh, T. N. (2013). Prediction of water quality from simple field parameters. Environmental Earth Sciences, 69(3), 821–829. https://doi.org/10.1007/s12665-012-1967-6
Zhou, Z., Davoudi, E., & Vaferi, B. (2021). Monitoring the effect of surface functionalization on the CO2 capture by graphene oxide/methyl diethanolamine nanofluids. Journal of Environmental Chemical Engineering, 9(5), 106202. https://doi.org/10.1016/j.jece.2021.106202
Anagu, I., Ingwersen, J., Utermann, J., & Streck, T. (2009). Estimation of heavy metal sorption in German soils using artificial neural networks. Geoderma, 152(1–2), 104–112. https://doi.org/10.1016/j.geoderma.2009.06.004
Antoine, X., Dreyfuss, P., & Privat, Y. (2007). Introduction à l,optimisation: aspects théoriques, numériques et algorithmes. https://math.unice.fr/~dreyfuss/D4.pdf
Asadollahfardi, G., Taklify, A., & Ghanbari, A. (2012). Application of artificial neural network to predict TDS in Talkheh Rud River. Journal of Irrigation and Drainage Engineering, 138(4), 363–370. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000402
Asadollahfardi, G., Zangooi, H., Asadi, M., Jebeli, M. T., Meshkat-Dini, M., & Roohani, N. (2018). Comparison of box-jenkins time series and ANN in predicting total dissolved solid at the Zāyandé-Rūd River, Iran. Journal of Water Supply: Research and Technology – AQUA, 67(7), 673–684. https://doi.org/10.2166/aqua.2018.108
Bayatzadeh Fard, Z., Ghadimi, F., & Fattahi, H. (2017). Use of artificial intelligence techniques to predict distribution of heavy metals in groundwater of Lakan lead-zinc mine in Iran. Journal of Mining and Environment, 8(1), 35–48. https://doi.org/10.22044/jme.2016.592
Ben Abbou, M., El Haji, M., Zemzami, M., & Fadil, F. (2013). Determination de la qualite des eaux souterraines des nappes de la province De Taza (Maroc). Larhyss Journal, 16, 77–90.
Berhail, A. (2016). Optimisation sans contraintes. https://dspace.univ-guelma.dz/jspui/bitstream/123456789/640/1/Cours%20Optimisation%20%282017%29-5.pdf
Boudad, B., Sahbi, H., & Boudebbouz, B. (2015). Prédiction de la sécheresse dans le bassin d’Inaouène en utilisant les réseaux de neurones et la régression linéaire multiple. Journal of Scientific Association for Water Information Systems, 1, 13–18.
Boudebbouz, B., Manssouri, I., Mouchtachi, A., & Manssouri, T. (2016). Utilisation d,un modèle hybride basé sur les réseaux de neurones artificiels-PMC couplés à la décomposition en ondelettes pour la modélisation du régime normale à point de fonctionnement variable. Cas d,une installation industrielle. HAL Open Science.
Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems, 2, 303–314. https://doi.org/10.1007/BF02551274
Chamekh, A. (2007). Optimisation des procédés de mise en forme par les réseaux de neurones artificiels. https://tel.archives-ouvertes.fr/tel-00445341/document
Coulibaly, P., Anctil, F., & Bobée, B. (1999). Prévision hydrologique par réseaux de neurones artificiels: État de l’art. Canadian Journal of Civil Engineering, 26(3), 293–304. https://doi.org/10.1139/l98-069
Davoudi, E., & Vaferi, B. (2018). Applying artificial neural networks for systematic estimation of degree of fouling in heat exchangers. Chemical Engineering Research and Design, 130, 138–153. https://doi.org/10.1016/j.cherd.2017.12.017
Dreyfus, G. (2006). Les réseaux de neurones. Revue de l’Electricité et de l’Electronique, 8, 37.
El Badaoui, H., Abdallaoui, A., Manssouri, I., & Lancelot, L. (2012). Elaboration de modèles mathématiques stochastiques pour la prédiction des teneurs en métaux lourds des eaux superficielles en utilisant les réseaux de neurones artificiels et la régression linéaire multiple. Journal of Hydrocarbons Mines and Environmental Research, 3(2), 31–36.
El Chaal, R., & Aboutafail, M. O. (2022). A comparative study of back-propagation algorithms: Levenberg-Marquart and BFGS for the formation of multilayer neural networks for estimation of fluoride. Communications in Mathematical Biology and Neuroscience, 1–17.
El Haji, M., Boutaleb, S., Laamarti, R., & Laarej, L. (2012). Qualité des eaux de surface et souterraine de la région de Taza (Maroc): bilan et situation des eaux. Afrique Science: Revue Internationale Des Sciences et Technologie, 8(1), 67–78.
El Hmaidi, A., El Badaoui, H., Abdallaoui, A., & El Moumni, B. (2013). Application des réseaux de neurones artificiels de type PMC pour la prédiction des teneurs en carbone organique dans les dépôts du quaternaire terminal de la mer d’alboran. European Journal of Scientific Research, 107(3), 400–413.
Fletcher, R. (1981). Constrained optimization. In Practical methods of optimization (Vol. 2). John Wiley & Sons Ltd.
Funahashi, K.-I. (1989). On the approximate realization of continuous mappings by neural networks. Neural Networks, 2(3), 183–192. https://doi.org/10.1016/0893-6080(89)90003-8
Graupe, D. (2007). Principles of artificial neural networks (2nd ed.). World Scientific. https://doi.org/10.1142/6429
Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural Networks, 4(2), 251–257. https://doi.org/10.1016/0893-6080(91)90009-T
Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2(5), 359–366. https://doi.org/10.1016/0893-6080(89)90020-8
Ibrahim, M. A. H. Bin, Mamat, M., & June, L. W. (2014). BFGS method: A new search direction. Sains Malaysiana, 43(10), 1591–1597.
Jacobs, R. A. (1988). Increased rates of convergence through learning rate adaptation. Neural Networks, 1(4), 295–307. https://doi.org/10.1016/0893-6080(88)90003-2
Jiang, Y., Zhang, G., Wang, J., & Vaferi, B. (2021). Hydrogen solubility in aromatic/cyclic compounds: Prediction by different machine learning techniques. International Journal of Hydrogen Energy, 46(46), 23591–23602. https://doi.org/10.1016/j.ijhydene.2021.04.148
Karimi, M., Vaferi, B., Hosseini, S. H., Olazar, M., & Rashidi, S. (2021). Smart computing approach for design and scale-up of conical spouted beds with open-sided draft tubes. Particuology, 55, 179–190. https://doi.org/10.1016/j.partic.2020.09.003
Kharroubi, O., Blanpain, O., Masson, E., & Lallahem, S. (2016). Application du réseau des neurones artificiels à la prévision des débits horaires: Cas du bassin versant de l’Eure, France. Hydrological Sciences Journal, 61(3), 541–550. https://doi.org/10.1080/02626667.2014.933225
Mottelet, S. (2003). RO04/TI07 – Optimisation non-linéaire. Université de Technologie de Compiègne.
Parizeau, M. (2004). Reseaux De Neurones GIF-21140 et GIF-64326. Universite LAVAL.
Patro, S. G. K., & sahu, K. K. (2015). Normalization: A preprocessing stage. International Advanced Research Journal in Science, Engineering and Technology, 2(3), 20–22. https://doi.org/10.17148/IARJSET.2015.2305
Rahnama, E., Bazrafshan, O., & Asadollahfardi, G. (2020). Application of data-driven methods to predict the sodium adsorption rate (SAR) in different climates in Iran. Arabian Journal of Geosciences, 13(21), 1160. https://doi.org/10.1007/s12517-020-06146-4
Shouyu, C., & Honglan, J. (2005). Fuzzy optimization neural network approach for ice forecast in the inner Mongolia reach of the Yellow River. Hydrological Sciences Journal, 50(2), 37–41. https://doi.org/10.1623/hysj.50.2.319.61793
Skansi, S. (2018). Introduction to deep learning. From logical calculus to artificial intelligence. Springer International Publishing AG. https://doi.org/10.1007/978-3-319-73004-2
Snyman, J. A., & Wilke, D. N. (2018). Springer optimization and its applications: Vol. 133. Practical mathematical optimization (2nd ed.). Springer Cham. https://doi.org/10.1007/978-3-319-77586-9
STATISTICA. (2014, June 4). Logiciel STATISTICA (version 12.5.192.5). http://www.statsoft.fr/logiciels/reseaux-de-neurones-automatises.php
Touzet, C. (2016). Les reseaux de neurones artificiels, introduction au connexionnisme. HAL Open Science.
Vaferi, B., Eslamloueyan, R., & Ayatollahi, S. (2011). Automatic recognition of oil reservoir models from well testing data by using multilayer perceptron networks. Journal of Petroleum Science and Engineering, 77(3), 254–262. https://doi.org/10.1016/j.petrol.2011.03.002
Verma, A. K., & Singh, T. N. (2013). Prediction of water quality from simple field parameters. Environmental Earth Sciences, 69(3), 821–829. https://doi.org/10.1007/s12665-012-1967-6
Zhou, Z., Davoudi, E., & Vaferi, B. (2021). Monitoring the effect of surface functionalization on the CO2 capture by graphene oxide/methyl diethanolamine nanofluids. Journal of Environmental Chemical Engineering, 9(5), 106202. https://doi.org/10.1016/j.jece.2021.106202