Polimer içerikli membran verimi tahmininde yapay sinir ağları öğrenme algoritmalarının değerlendirilmesi

Abstract

Bu çalışmanın amacı, polimer içerikli membranlar (PIMs) ile Cr (VI) giderimi için geliştirilecek yapay sinir ağı (YSA) modelinde optimum YSA mimarisi için en uygun öğrenme algoritmasının belirlenmesidir.  Bu amaçla, geliştirilen yapay sinir ağı modelinde Levenberg-Marquardt, Bayesian Regularization, Ölçeklenmiş Konjuge Gradyan olmak üzere 3 faklı öğrenme algoritması uygulanmıştır. Ağ mimarisinin ve kullanılan öğrenme algoritmasının ağın tahmin performansına etkisinin belirlenmesinde Regresyon katsayısı (R²) ve ortalama karesel hata (OKH) teknikleri kullanılmıştır.  Sonuç olarak geliştirilen bir YSA modelinde doğru öğrenme algoritması seçiminin ağın tahmin kabiliyeti açısından önemli olduğu sonucuna varılmıştır.  

Keywords

• yapay sinir ağları,öğrenme algoritması,levenberg-marquardt,bayesian regularization,ölçeklenmiş konjuge gradyen.

Assessment of neural network training algorithms for the prediction of polymeric inclusion membranes efficiency

Abstract

The aim of this study is to introduce, through an appropriate selection of the training algorithm, a better and optimum artificial neural network (ANN) that will capable to predict Polymeric Inclusion Membranes (PIMs) Cr(VI) removal efficiency from aqueous solutions. To accomplish that, three training algorithms including Levenberg-Marquardt (LM), Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG) have been assessed by training different ANN. The performances of developed models are evaluated by Coefficient of Regression (R²) and Root Mean Square Error (RMSE) to find the best ANN training algorithms. This study clears that right choice of the training algorithm grants maximizing the predictive capability of the ANN models.

Keywords

• Neural Network,Training Algorithm,Levenberg-Marquardt,Bayesian Regularization,Scaled Conjugate Gradient.

References

1. B. Volesky and Z. R. Holan, “Biosorption of heavy metals.,” Biotechnol. Prog., vol. 11, no. 3, pp. 235–50, 1995.
2. F. Veglio’ and F. Beolchini, “Removal of metals by biosorption: a review,” Hydrometallurgy, vol. 44, no. 3, pp. 301–316, 1997.
3. Z. Kowalski, “Treatment of chromic tannery wastes,” in Journal of Hazardous Materials, 1994, vol. 37, no. 1, pp. 137–141.
4. V. Gomez and M. P. Callao, “Chromium determination and speciation since 2000,” TrAC - Trends Anal. Chem., vol. 25, no. 10, pp. 1006–1015, 2006.
5. A. Leusch and B. Volesky, “The influence of film diffusion on cadmium biosorption by marine biomass,” J. Biotechnol., vol. 43, no. 1, pp. 1–10, 1995.
6. A. Dabrowski, Z. Hubicki, P. Podkoscielny, and E. Robens, “Selective removal of the heavy metal ions from waters and industrial wastewaters by ion-exchange method,” Chemosphere, vol. 56, no. 2, pp. 91–106, 2004.
7. E. S. Z. El-Ashtoukhy, N. K. Amin, and O. Abdelwahab, “Removal of lead (II) and copper (II) from aqueous solution using pomegranate peel as a new adsorbent,” Desalination, vol. 223, no. 1–3, pp. 162–173, 2008.
8. A. K. Pabby, S. S. H. Rizvi, and A. M. Sastre, Handbook of Membrane Separations Chemical, Pharmaceutical, Food, and Biotechnological Applications, vol. 1. 2008.

9. N. Sipocz, F. A. Tobiesen, and M. Assadi, “The use of Artificial Neural Network models for CO2 capture plants,” Appl. Energy, vol. 88, no. 7, pp. 2368–2376, 2011.
10. Y.-S. Park, T.-S. Chon, I.-S. Kwak, and S. Lek, “Hierarchical community classification and assessment of aquatic ecosystems using artificial neural networks.,” Sci. Total Environ., vol. 327, no. 1–3, pp. 105–122, 2004.
11. L. Belanche, J. J. Valdes, J. Comas, I. R. Roda, and M. Poch, “Prediction of the bulking phenomenon in wastewater treatment plants,” Artif. Intell. Eng., vol. 14, no. 4, pp. 307–317, 2000.
12. G. R. Shetty and S. Chellam, “Predicting membrane fouling during municipal drinking water nanofiltration using artificial neural networks,” J. Memb. Sci., vol. 217, no. 1–2, pp. 69–86, 2003.
13. W. S. Sarle, “Neural Network FAQ, Part 3 of 7: Generalization, periodic posting to the Usenet newsgroup comp. ai. neural-nets,” Retrieved August, vol. 12, p. 2011, 2002.
14. A. P. Plumb, R. C. Rowe, P. York, and M. Brown, “Optimisation of the predictive ability of artificial neural network (ANN) models: A comparison of three ANN programs and four classes of training algorithm,” Eur. J. Pharm. Sci., vol. 25, no. 4–5, pp. 395–405, 2005.
15. “Ağır Metallerin Seçici Ekstraksiyonu için İmidazolyum Tuzları İçeren Polimer İçerikli Membranların Üretimi Karakterizasyonu ve Taşınım Verimlerinin Yapay Sinir Ağları ile Modellenmesi, proje no: 112T806, Türkiye Bilimsel ve Teknolojik Araştirma Kurumu,” 2015.
16. C. Sgarlata, G. Arena, E. Longo, D. Zhang, Y. Yang, and R. A. Bartsch, “Heavy metal separation with polymer inclusion membranes,” J. Memb. Sci., vol. 323, no. 2, pp. 444–451, 2008.
17. L. M. and M. B. O. Kebiche-Senhadji, “Consideration of Polymer Inclusion Membranes Containing D2EHPA for Toxic Metallic Ion (Pb2+) Extraction Recovery,” 2015 5th Int. Conf. Environ. Sci. Eng., vol. 83, no. 26, p. 30, 2015.
18. V. Eyupoglu, “Alkyl chain structure-dependent separation of Cr(VI) from acidic solutions containing various metal ions using liquid–liquid solvent extraction by butyl-based imidazolium bromide salts,” Desalin. Water Treat., vol. 3994, no. April 2016, pp. 1–16, 2015.
19. J. S. Torrecilla, L. Otero, and P. D. Sanz, “Optimization of an artificial neural network for thermal/pressure food processing: Evaluation of training algorithms,” Comput. Electron. Agric., vol. 56, no. 2, pp. 101–110, 2007.
20. H. Demuth and M. Beale, “Neural network toolbox for use with MATLAB,” Citeseer, 1993.
21. V. Vacic, “Summary of the training functions in Matlab’s NN toolbox,” Matlab, 2005.
22. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math., vol. 2, pp. 196–168, 1944.
23. D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” Journal of the Society for Industrial and Applied Mathematics, vol. 11, no. 2. pp. 431–441, 1963.
24. D. S. Watkins, “The Least Squares Problem,” Fundam. Matrix Comput., no. 1989, pp. 181–259, 2005.
25. S. Geman, E. Bienenstock, and R. Doursat, “Neural Networks and the Bias/Variance Dilemma,” Neural Computation, vol. 4, no. 1. pp. 1–58, 1992.
26. D. J. C. MacKay, “Bayesian Interpolation,” Neural Comput., vol. 4, no. 3, pp. 415–447, 1992.
27. D. J. C. MacKay, “A Practical Bayesian Framework for Backpropagation Networks,” Neural Comput., vol. 4, no. 3, pp. 448–472, 1992.
28. G. E. Hinton, “Connectionist learning procedures,” Artif. Intell., vol. 40, no. 1–3, pp. 185–234, 1989.
29. M. Møller, “A scaled conjugate gradient algorithm for fast supervised learning,” Neural networks, vol. 6. pp. 525–533, 1993.
30. E. M. Johansson, F. U. Dowla, and D. M. Goodman, “Backpropagation learning for multilayer feed-forward neural networks using the conjugate gradient method,” Int. J. Neural Syst. J. Neural Syst., vol. 2, no. 4, pp. 291–301, 1991.
31. K. K. Abbo and H. H. Mohamed, “New Scaled Conjugate Gradient Algorithm for Training Artificial Neural Networks Based on Pure Conjugacy Condition,” vol. 10, no. 3, 2015.
32. R. ~L. Watrous, “Learning Algorithms for Connectionist Networks : Applied Gradient Methods of Non-Linear Optimization,” Tech. Reports, no. MS-CIS-87–51, p. 597, 1987.
33. E. Dogan, A. Ates, E. C. Yilmaz, and B. Eren, “Application of Artificial Neural Networks to Estimate Wastewater Treatment Plant Inlet Biochemical Oxygen Demand,” Environ. Prog., vol. 27, no. 4, pp. 439–446, 2008.