Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 439091, 15 pages.

Modelling Laser Milling of Microcavities for the Manufacturing of DES with Ensembles

Pedro Santos, Daniel Teixidor, Jesus Maudes, and Joaquim Ciurana

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A set of designed experiments, involving the use of a pulsed Nd:YAG laser system milling 316L Stainless Steel, serve to study the laser-milling process of microcavities in the manufacture of drug-eluting stents (DES). Diameter, depth, and volume error are considered to be optimized as functions of the process parameters, which include laser intensity, pulse frequency, and scanning speed. Two different DES shapes are studied that combine semispheres and cylinders. Process inputs and outputs are defined by considering the process parameters that can be changed under industrial conditions and the industrial requirements of this manufacturing process. In total, 162 different conditions are tested in a process that is modeled with the following state-of-the-art data-mining regression techniques: Support Vector Regression, Ensembles, Artificial Neural Networks, Linear Regression, and Nearest Neighbor Regression. Ensemble regression emerged as the most suitable technique for studying this industrial problem. Specifically, Iterated Bagging ensembles with unpruned model trees outperformed the other methods in the tests. This method can predict the geometrical dimensions of the machined microcavities with relative errors related to the main average value in the range of 3 to 23%, which are considered very accurate predictions, in view of the characteristics of this innovative industrial task.

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J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 439091, 15 pages.

First available in Project Euclid: 1 October 2014

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Santos, Pedro; Teixidor, Daniel; Maudes, Jesus; Ciurana, Joaquim. Modelling Laser Milling of Microcavities for the Manufacturing of DES with Ensembles. J. Appl. Math. 2014, Special Issue (2013), Article ID 439091, 15 pages. doi:10.1155/2014/439091.

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  • K. Sugioka, M. Meunier, and A. Piqué, Laser Precision Microfabrication, vol. 135, Springer, 2010.
  • S. Garg and P. W. Serruys, “Coronary stents: current status,” Journal of the American College of Cardiology, vol. 56, no. 10, pp. S1–S42, 2010.
  • D. M. Martin and F. J. Boyle, “Drug-eluting stents for coronary artery disease: a review,” Medical Engineering and Physics, vol. 33, no. 2, pp. 148–163, 2011.
  • S. Campanelli, G. Casalino, and N. Contuzzi, “Multi-objective optimization of laser milling of 5754 aluminum alloy,” Optics & Laser Technology, vol. 52, pp. 48–56, 2013.
  • J. Ciurana, G. Arias, and T. Ozel, “Neural network modeling and particle swarm optimization (PSO) of process parameters in pulsed laser micromachining of hardened AISI H13 steel,” Materials and Manufacturing Processes, vol. 24, no. 3, pp. 358–368, 2009.
  • J. Cheng, W. Perrie, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “Effects of laser operating parameters on metals micromachining with ultrafast lasers,” Applied Surface Science, vol. 256, no. 5, pp. 1514–1520, 2009.
  • I. E. Saklakoglu and S. Kasman, “Investigation of micro-milling process parameters for surface roughness and milling depth,” The International Journal of Advanced Manufacturing Technology, vol. 54, no. 5–8, pp. 567–578, 2011.
  • D. Ashkenasi, T. Kaszemeikat, N. Mueller, R. Dietrich, H. J. Eichler, and G. Illing, “Laser trepanning for industrial applications,” Physics Procedia, vol. 12, pp. 323–331, 2011.
  • B. S. Yilbas, S. S. Akhtar, and C. Karatas, “Laser trepanning of a small diameter hole in titanium alloy: temperature and stress fields,” Journal of Materials Processing Technology, vol. 211, no. 7, pp. 1296–1304, 2011.
  • R. Biswas, A. S. Kuar, S. Sarkar, and S. Mitra, “A parametric study of pulsed Nd:YAG laser micro-drilling of gamma-titanium aluminide,” Optics & Laser Technology, vol. 42, no. 1, pp. 23–31, 2010.
  • L. Tricarico, D. Sorgente, and L. D. Scintilla, “Experimental investigation on fiber laser cutting of Ti6Al4V thin sheet,” Advanced Materials Research, vol. 264-265, pp. 1281–1286, 2011.
  • N. Muhammad, D. Whitehead, A. Boor, W. Oppenlander, Z. Liu, and L. Li, “Picosecond laser micromachining of nitinol and platinum-iridium alloy for coronary stent applications,” Applied Physics A: Materials Science and Processing, vol. 106, no. 3, pp. 607–617, 2012.
  • H. Meng, J. Liao, Y. Zhou, and Q. Zhang, “Laser micro-processing of cardiovascular stent with fiber laser cutting system,” Optics & Laser Technology, vol. 41, no. 3, pp. 300–302, 2009.
  • T.-C. Chen and R. B. Darling, “Laser micromachining of the materials using in microfluidics by high precision pulsed near and mid-ultraviolet Nd:YAG lasers,” Journal of Materials Processing Technology, vol. 198, no. 1–3, pp. 248–253, 2008.
  • D. Bruneel, G. Matras, R. le Harzic, N. Huot, K. König, and E. Audouard, “Micromachining of metals with ultra-short Ti-Sapphire lasers: prediction and optimization of the processing time,” Optics and Lasers in Engineering, vol. 48, no. 3, pp. 268–271, 2010.
  • M. Pfeiffer, A. Engel, S. Weißmantel, S. Scholze, and G. Reisse, “Microstructuring of steel and hard metal using femtosecond laser pulses,” Physics Procedia, vol. 12, pp. 60–66, 2011.
  • D. Karnakis, M. Knowles, P. Petkov, T. Dobrev, and S. Dimov, “Surface integrity optimisation in ps-laser milling of advanced engineering materials,” in Proceedings of the 4th International WLT-Conference on Lasers in Manufacturing, Munich, Germany, 2007.
  • H. Qi and H. Lai, “Micromachining of metals and thermal barrier coatings using a 532$\,$nm nanosecond ber laser,” Physics Procedia, vol. 39, pp. 603–612, 2012.
  • D. Teixidor, I. Ferrer, J. Ciurana, and T. Özel, “Optimization of process parameters for pulsed laser milling of micro-channels on AISI H13 tool steel,” Robotics and Computer-Integrated Manufacturing, vol. 29, no. 1, pp. 209–219, 2013.
  • I. Witten and E. Frank, Data Mining: Practical Machine Learning Tools and Techniques, Morgan Kaufmann, 2nd edition, 2005.
  • J. Han, M. Kamber, and J. Pei, Data Mining: Concepts and Techniques, Morgan Kaufmann, 2006.
  • A. J. Torabi, M. J. Er, L. Xiang et al., “A survey on artificial intelligence technologies in modeling of high speed end-milling processes,” in Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM '09), pp. 320–325, Singapore, July 2009.
  • M. Chandrasekaran, M. Muralidhar, C. M. Krishna, and U. S. Dixit, “Application of soft computing techniques in machining performance prediction and optimization: a literature review,” The International Journal of Advanced Manufacturing Technology, vol. 46, no. 5–8, pp. 445–464, 2010.
  • A. K. Choudhary, J. A. Harding, and M. K. Tiwari, “Data mining in manufacturing: a review based on the kind of knowledge,” Journal of Intelligent Manufacturing, vol. 20, no. 5, pp. 501–521, 2009.
  • A. K. Dubey and V. Yadava, “Laser beam machining–-a review,” International Journal of Machine Tools and Manufacture, vol. 48, no. 6, pp. 609–628, 2008.
  • B. F. Yousef, G. K. Knopf, E. V. Bordatchev, and S. K. Nikumb, “Neural network modeling and analysis of the material removal process during laser machining,” The International Journal of Advanced Manufacturing Technology, vol. 22, no. 1-2, pp. 41–53, 2003.
  • S. Campanelli, G. Casalino, A. Ludovico, and C. Bonserio, “An artificial neural network approach for the control of the laser milling process,” The International Journal of Advanced Manufacturing Technology, vol. 66, no. 9–12, pp. 1777–1784, 2012.
  • C. Jimin, Y. Jianhua, Z. Shuai, Z. Tiechuan, and G. Dixin, “Parameter optimization of non-vertical laser cutting,” The International Journal of Advanced Manufacturing Technology, vol. 33, no. 5-6, pp. 469–473, 2007.
  • D. Teixidor, M. Grzenda, A. Bustillo, and J. Ciurana, “Modeling pulsed laser micromachining of micro geometries using machine-learning techniques,” Journal of Intelligent Manufacturing, 2013.
  • N. C. Oza and K. Tumer, “Classifier ensembles: select real-world applications,” Information Fusion, vol. 9, no. 1, pp. 4–20, 2008.
  • P. Santos, L. Villa, A. Reñones, A. Bustillo, and J. Maudes, “Wind turbines fault diagnosis using ensemble classifiers,” in Advances in Data Mining. Applications and Theoretical Aspects, vol. 7377, pp. 67–76, Springer, Berlin, Germany, 2012.
  • A. Bustillo and J. J. Rodríguez, “Online breakage detection of multitooth tools using classifier ensembles for imbalanced data,” International Journal of Systems Science, pp. 1–13, 2013.
  • J.-F. Díez-Pastor, A. Bustillo, G. Quintana, and C. García-Osorio, “Boosting projections to improve surface roughness prediction in high-torque milling operations,” Soft Computing, vol. 16, no. 8, pp. 1427–1437, 2012.
  • A. Bustillo, E. Ukar, J. J. Rodriguez, and A. Lamikiz, “Modelling of process parameters in laser polishing of steel components using ensembles of regression trees,” International Journal of Computer Integrated Manufacturing, vol. 24, no. 8, pp. 735–747, 2011.
  • A. Bustillo, J.-F. Díez-Pastor, G. Quintana, and C. García-Osorio, “Avoiding neural network fine tuning by using ensemble learning: application to ball-end milling operations,” The International Journal of Advanced Manufacturing Technology, vol. 57, no. 5–8, pp. 521–532, 2011.
  • S. Ferreiro, B. Sierra, I. Irigoien, and E. Gorritxategi, “Data mining for quality control: burr detection in the drilling process,” Computers & Industrial Engineering, vol. 60, no. 4, pp. 801–810, 2011.
  • B. E. Boser, I. M. Guyon, and V. N. Vapnik, “Training algorithm for optimal margin classifiers,” in Proceedings of the 5th Annual Workshop on Computational Learning Theory, pp. 144–152, ACM, Pittsburgh, Pa, USA, July 1992.
  • R. Beale and T. Jackson, Neural Computing: An Introduction, IOP Publishing, Bristol, UK, 1990.
  • A. Sykes, An Introduction to Regression Analysis, Law School, University of Chicago, 1993.
  • X. Wu, V. Kumar, Q. J. Ross et al., “Top 10 algorithms in data mining,” Knowledge and Information Systems, vol. 14, no. 1, pp. 1–37, 2008.
  • N. Tosun and L. Özler, “A study of tool life in hot machining using artificial neural networks and regression analysis method,” Journal of Materials Processing Technology, vol. 124, no. 1-2, pp. 99–104, 2002.
  • A. Azadeh, S. F. Ghaderi, and S. Sohrabkhani, “Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors,” Energy Conversion and Management, vol. 49, no. 8, pp. 2272–2278, 2008.
  • P. Palanisamy, I. Rajendran, and S. Shanmugasundaram, “Prediction of tool wear using regression and ANN models in end-milling operation,” The International Journal of Advanced Manufacturing Technology, vol. 37, no. 1-2, pp. 29–41, 2008.
  • S. Vijayakumar and S. Schaal, “Approximate nearest neighbor regression in very high dimensions,” in Nearest-Neighbor Methods in Learning and Vision: Theory and Practice, pp. 103–142, MIT Press, Cambridge, Mass, USA, 2006.
  • L. Kuncheva, “Combining classifiers: soft computing solutions,” in Pattern Recognition: From Classical to Modern Approaches, pp. 427–451, 2001.
  • J. Yu, L. Xi, and X. Zhou, “Identifying source (s) of out-of-control signals in multivariate manufacturing processes using selective neural network ensemble,” Engineering Applications of Artificial Intelligence, vol. 22, no. 1, pp. 141–152, 2009.
  • T. W. Liao, F. Tang, J. Qu, and P. J. Blau, “Grinding wheel condition monitoring with boosted minimum distance classifiers,” Mechanical Systems and Signal Processing, vol. 22, no. 1, pp. 217–232, 2008.
  • S. Cho, S. Binsaeid, and S. Asfour, “Design of multisensor fusion-based tool condition monitoring system in end milling,” The International Journal of Advanced Manufacturing Technology, vol. 46, no. 5–8, pp. 681–694, 2010.
  • S. Binsaeid, S. Asfour, S. Cho, and A. Onar, “Machine ensemble approach for simultaneous detection of transient and gradual abnormalities in end milling using multisensor fusion,” Journal of Materials Processing Technology, vol. 209, no. 10, pp. 4728–4738, 2009.
  • H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716–723, 1974.
  • J. R. Quinlan, “Learning with continuous classes,” in Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, vol. 92, pp. 343–348, Singapore, 1992.
  • T. M. Khoshgoftaar, E. B. Allen, and J. Deng, “Using regression trees to classify fault-prone software modules,” IEEE Transactions on Reliability, vol. 51, no. 4, pp. 455–462, 2002.
  • T. K. Ho, “The random subspace method for constructing decision forests,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 8, pp. 832–844, 1998.
  • T. G. Dietterichl, “Ensemble learning,” in The Handbook of Brain Theory and Neural Networks, pp. 405–408, 2002.
  • L. Breiman, “Bagging predictors,” Machine Learning, vol. 24, no. 2, pp. 123–140, 1996.
  • Y. Freund and R. E. Schapire, “Experiments with a new boosting algorithm,” in Proceedings of the 13th International Conference on Machine Learning (ICML '96), vol. 96, pp. 148–156, Bari, Italy, 1996.
  • Y. Freund and R. E. Schapire, “A desicion-theoretic generalization of on-line learning and an application to boosting,” in Computational Learning Theory, pp. 23–37, Springer, Berlin, Germany, 1995.
  • L. Breiman, “Using iterated bagging to debias regressions,” Machine Learning, vol. 45, no. 3, pp. 261–277, 2001.
  • H. Drucker, “Improving regressors using boosting techniques,” in Proceedings of the 14th International Conference on Machine Learning (ICML '97), vol. 97, pp. 107–115, Nashville, Tenn, USA, 1997.
  • J. H. Friedman, “Stochastic gradient boosting,” Computational Statistics & Data Analysis, vol. 38, no. 4, pp. 367–378, 2002.
  • D. W. Aha, D. Kibler, and M. K. Albert, “Instance-based learning algorithms,” Machine Learning, vol. 6, no. 1, pp. 37–66, 1991.
  • A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Statistics and Computing, vol. 14, no. 3, pp. 199–222, 2004.
  • C. Cortes and V. Vapnik, “Support-vector networks,” Machine Learning, vol. 20, no. 3, pp. 273–297, 1995.
  • J. E. Dayhoff and J. M. DeLeo, “Artificial neural networks: opening the black box,” Cancer, vol. 91, supplement 8, pp. 1615–1635, 2001.
  • K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989.
  • W. H. Delashmit and M. T. Manry, “Recent developments in multilayer perceptron neural networks,” in Proceedings of the 7th Annual Memphis Area Engineering and Science Conference (MAESC '05), 2005.
  • C. Nadeau and Y. Bengio, “Inference for the generalization error,” Machine Learning, vol. 52, no. 3, pp. 239–281, 2003. \endinput