Evolutionary support vector regression algorithm applied to the prediction of the thickness of the chromium layer in a hard chromium plating process.

*(English)*Zbl 1364.78040Summary: The hard chromium plating process aims at creating a coating of hard and wear-resistant chromium with a thickness of some microns directly on the metal part, without the insertion of copper or nickel layers. It is one of the most difficult electroplating processes due to the influence of the hydrogen evolution that occurs on the cathode surface simultaneously to the chromium deposition. Chromium plating is characterized by high levels of hardness and resistance to wear and it is thanks to these properties that they can be applied in a huge range of sectors. Resistance to corrosion of a hard chromium plate depends on the thickness of the coating, adherence and micro-fissures of the latter. This micro-fissured structure is what provides the optimal hardness of the layers. The electro-deposited chromium layer is not uniformly distributed: there are zones such as sharp edges or points where deposits are highly accentuated, while deposits are virtually nonexistent in holes or in the undercuts. The hard chromium plating process is one of the most effective ways of protecting the base material in a hostile environment or improving surface properties of the base material. However, in the electroplating industry, electro-platers are faced with many problems and often achieve undesirable results on chromium-plated materials. Problems such as matt deposition, milky white chromium deposition, rough or sandy chromium deposition and insufficient thickness or hardness are the most common problems faced in the electroplating industry. Finally, it must be remarked that defects in the coating locally lower the corrosion resistance of the layer and that the decomposition of chromium hydrides causes the formation of a network of cracks in the coating. This innovative research work uses an evolutionary support vector regression algorithm for the prediction of the thickness of the chromium layer in a hard chromium plating process. Evolutionary support vector machines (ESVMs) is a novel technique that assimilates the learning engine of the state-of-the-art support vector machines (SVMs) but evolves the coefficients of the decision function by means of evolutionary algorithms (EAs). In this sense, the current research is focused on the estimation of the hyper-parameters required for the support vector machines technique for regression (SVR), by means of evolutionary strategies. The results are briefly compared with those obtained by authors in a previous paper, where a model based on an artificial neural network was tuned using the design of experiments (DOE).

##### MSC:

78M32 | Neural and heuristic methods applied to problems in optics and electromagnetic theory |

68T05 | Learning and adaptive systems in artificial intelligence |

78A57 | Electrochemistry |

##### Keywords:

hard chromium plating process; support vector machines for regression (SVR); machine learning; evolutionary algorithms (EAs); evolutionary support vector machines (ESVMs)
PDF
BibTeX
XML
Cite

\textit{F. Sánchez Lasheras} et al., Appl. Math. Comput. 227, 164--170 (2014; Zbl 1364.78040)

Full Text:
DOI

##### References:

[1] | C.G. Fink, U.S. Patent 1,581,188, April 20, 1926. |

[2] | Sargent, G. J., Electrolytic chromium, Transactions of the American Electrochemical Society, 37, 479-497, (1920) |

[3] | Udy, M. J., Chromium, (1956), Reinhold Publishing Corporation New York |

[4] | Dennis, J. K.; Such, T. E., The nickel and chromium plating, (1994), Woodhead Publishing New York |

[5] | Guffie, R. K., The handbook of chromium plating, (1986), Gardner Publications Ltd New York |

[6] | Lindsay, J. H., Decorative and hard chromium plating, Plating and Surface Finishing, 90, 22-24, (2003) |

[7] | Schlesinger, M.; Paunovich, M., Modern electroplating, (2000), Wiley-Interscience New York |

[8] | Sánchez Lasheras, F.; Vilán Vilán, J. A.; García Nieto, P. J.; del Coz Díaz, J. J., The use of design of experiments to improve a neural network model in order to predict the thickness of the chromium layer in a hard chromium plating process, Mathematical and Computer Modelling, 52, 7-8, 1169-1176, (2010) |

[9] | Irvine, T. H., The chemical analysis of electroplating solutions, (2000), Chemical Publishing Company New York |

[10] | Kanani, N., Electroplating: basic principles, processes and practice, (2005), Elsevier Science Amsterdam |

[11] | Ölmez, T., The optimization of CR (VI) reduction and removal by electrocoagulation using response surface methodology, Journal of Hazardous Materials, 162, 1371-1378, (2009) |

[12] | Ortiz, M. J., Effect of a thin hard chromium coating on fatigue behavior of 4140 steel, Surface Engineering, 20, 345-352, (2004) |

[13] | Engelbrecht, A. P., Computational intelligence: an introduction, (2007), Wiley & Sons River Street, Hoboken, New Jersey |

[14] | Friedrichs, F.; Igel, C., Evolutionary tuning of multiple SVM parameters, Neurocomputing, 64, 107-117, (2005) |

[15] | Kazemian, H. B.; White, K.; Palmer-Brown, D., Applications of evolutionary SVM to prediction of membrane alpha-helices, Expert Systems with Applications, 40, 9, 3412-3420, (2013) |

[16] | Vapnik, V., Statistical learning theory, (1998), Wiley-Interscience New York · Zbl 0935.62007 |

[17] | Cortes, C.; Vapnik, V., Support vector networks, Machine Learning, 20, 3, 273-297, (1995) · Zbl 0831.68098 |

[18] | Smola, A. J.; Schölkopf, B., A tutorial on support vector regression, Statistics and Computing, 14, 3, 199-222, (1998) |

[19] | Álvarez Antón, J. C.; García Nieto, P. J.; de Cos Juez, F. J.; Sánchez Lasheras, F.; González Vega, M.; Roqueñí Gutiérrez, M. N., Battery state-of-charge estimator using the SVM technique, Applied Mathematical Modelling, 37, 9, 6244-6253, (2013) · Zbl 06948879 |

[20] | Vapnik, V., An overview of statistical learning theory, IEEE Transactions on Neural Networks, 10, 988-999, (1999) |

[21] | Shawe-Taylor, J.; Cristianini, N., Kernel methods for pattern analysis, (2004), Cambridge University Press New York |

[22] | Steinwart, I.; Christmann, A., Support vector machines, (2008), Springer New York · Zbl 1203.68171 |

[23] | Alpaydin, E., Introduction to machine learning, (2004), The MIT Press New York |

[24] | Goldberg, D. E., Genetic algorithms in search, optimization and machine learning, (1989), Addison-Wesley Reading, MA · Zbl 0721.68056 |

[25] | T. Bäck, G. Rudolph, H.P. Schwefel, Evolutionary programming and evolution strategies: similarities and differences, in: IEEE Computer Society (Eds.), Proceedings of the Second Annual Conference on Evolutionary Programming, Washington, DC, USA, 1993, pp. 11-22. |

[26] | Fogel, D. B., An introduction to simulated evolutionary optimization, IEEE Transactions on Neural Networks, 5, 1, 3-14, (1994) |

[27] | Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE Transactions on Evolutionary Computation, 3, 2, 82-102, (1999) |

[28] | Lee, C. Y.; Yao, X., Evolutionary programming using mutations based on the levy probability distribution, IEEE Transactions on Evolutionary Computation, 8, 1, 1-13, (2004) |

[29] | Salcedo-Sanz, S.; Ortiz-García, E. G.; Pérez-Bellido, A. M.; Portilla-Figueras, A., Short term wind speed prediction based on evolutionary support vector regression algorithms, Expert Systems with Applications, 38, 4052-4057, (2011) |

[30] | C.-C. Chang, C.-J. Lin, LIBSVM: a library for support vector machines, Software available at http://www.csie.ntu.edu.tw/ cjlin/libsvm, 2001. |

[31] | E. Dimitriadou, K. Hornik, F. Leisch, D. Meyer, A. Weingessel, e1071: Misc Functions of the Department of Statistics (e1071), TU Wien, R package version 1.5-24, 2010. |

[32] | R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2011. ISBN 3-900051-07-0, URL: http://www.R-project.org/. |

[33] | Chambers, J. M., Software for data analysis: programming with R, (2008), Springer New York · Zbl 1180.62002 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.