Reconstruction of the Taguchi Orthogonal Arrays with the Support Vector Machines Method

Year 2021, Volume: 9 Issue: 2, 129 - 137, 30.04.2021

Selçuk Yazar

https://doi.org/10.17694/bajece.839449

Abstract

Design of Experiment (DOE) is a widely used method for examining experiments especially in industrial production and robust design processes. This method is a set of statistical approaches in which mathematical models are developed through experimental testing to estimate possible outputs and given input values or parameters. The method aims to determine the main factors that affect the results with the smallest number of experimental studies. In this study, L16 (2^15) orthogonal array, which was used in the Taguchi parameter design was reconstructed with the Support Vector Machines learning model and the Pearson VII kernel function. With this model, array elements were successfully classified in 87.04%. The new and original array were compared and 3.8% difference was measured between their Signal to Noise (S / N) ratios in an exemplary experiment.

Keywords

Machine Learning, Support Vector Machine, Taguchi Design, Design of Experiment, Robust Design

References

• G. Taguchi and S. Konishi, Taguchi Methods: Orthogonal Arrays and Linear Graphs. Tools for Quality Engineering. Dearborn: MI: American Supplier Institute, 1987.
• L. E. Katz and M. S. Phadke, "Macro-Quality with Micro-Money," in Quality Control, Robust Design, and the Taguchi Method, K. Dehnad, Ed. Boston, MA: Springer US, 1989, pp. 23-30.
• P. T. Dhorabe, D. H. Lataye, A. R. Tenpe, and R. S. Ingole, "Adsorption of p-nitrophenol onto acacia glauca saw dust and waste orange peels activated carbon: application of Taguchi’s design of experiment," SN Applied Sciences, journal article vol. 1, no. 3, p. 250, February 20 2019.
• M. Rahmani, M. Kaykhaii, and M. Sasani, "Application of Taguchi L16 design method for comparative study of ability of 3A zeolite in removal of Rhodamine B and Malachite green from environmental water samples," Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 188, pp. 164-169, 2018/01/05/ 2018.
• S. Sadr, V. Mozafari, H. Shirani, H. Alaei, A. Tajabadi Pour, and A. Rajabi Behjat, "Control of pistachio endocarp lesion by optimizing the concentration of some nutrients using taguchi method," Scientia Horticulturae, vol. 256, p. 108575, 2019/10/15/ 2019.
• H.-A. Mehedi et al., "Synthesis of graphene by cobalt-catalyzed decomposition of methane in plasma-enhanced CVD: Optimization of experimental parameters with Taguchi method," Journal of Applied Physics, vol. 120, no. 6, p. 065304, 2016.
• L. Zhang et al., "Taguchi method assisted multiple effects optimization on optical and luminescence performance of Ce: YAG transparent ceramics for high power white LEDs," Journal of Materials Chemistry C, 10.1039/C9TC03916C 2019
• R. Romero-Villafranca, L. Zúnica, and R. Romero-Zúnica, "Ds-optimal experimental plans for robust parameter design," Journal of Statistical Planning and Inference, vol. 137, no. 4, pp. 1488-1495, 2007/04/01/ 2007.
• E. Y. Ng and W. K. Ng, "Parametric study of the biopotential equation for breast tumour identification using ANOVA and Taguchi method," (in eng), no. 0140-0118 (Print).
• R. N. Kacker, E. S. Lagergren, and J. J. Filliben, "Taguchi's Orthogonal Arrays Are Classical Designs of Experiments," Journal of research of the National Institute of Standards and Technology, vol. 96, no. 5, pp. 577-591, Sep-Oct 1991.
• P. J. Rahul Davis, "Application of Taguchi-Based Design of Experiments for Industrial Chemical Processes," in Statistical Approaches With Emphasis on Design of Experiments Applied to Chemical Processes, 2017.
• C. R. Rao, "Hypercube of Strength "d‟ leading to Confounded Designs in Factorial Experiments," Bull. Calcutta Math. Soc., vol. 38, pp. 67-68, 1946.
• B. E. Boser, I. M. Guyon, and V. N. Vapnik, "A training algorithm for optimal margin classifiers," presented at the Proceedings of the fifth annual workshop on Computational learning theory, Pittsburgh, Pennsylvania, USA, 1992.
• B. Scholkop and A. Smola., Learning with kernels. M.I.T. Press, 2001.
• B. Üstün, W. J. Melssen, and L. M. C. Buydens, "Facilitating the application of Support Vector Regression by using a universal Pearson VII function based kernel," Chemometrics and Intelligent Laboratory Systems, vol. 81, no. 1, pp. 29-40, 2006/03/01/ 2006.
• J. Mercer, "Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations," Philosophical Transactions of the Royal Society of London Series A, vol. 209, p. 415, January 01, 1909 1909
• J. Platt, "Sequential minimal optimization: A fast algorithm for training support vector machines," 1998.
• Catalogue of Taguchi designs. Available: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/doe/supporting-topics/taguchi-designs/catalogue-of-taguchi-designs/ K. Q. Ye, D. Park, W. Li, and A. M. Dean, "Construction and classification of orthogonal arrays with small numbers of runs," Statistics and Applications, vol. 6, no. 1, pp. 5-15, 2008.
• S. D. Bolboacă and L. Jäntschi, "Design of experiments: Useful orthogonal arrays for number of experiments from 4 to 16," Entropy, vol. 9, no. 4, pp. 198-232, 2007.
• H. Bayrak and A. Alhan, "On the construction of orthogonal arrays," Hacettepe Journal of Mathematics and Statistics, vol. 31, pp. 45-51, 2002.
• J. Kunert, "A note on optimal designs with a non-orthogonal row—column-structure," Journal of Statistical Planning and Inference, vol. 37, no. 2, pp. 265-270, 1993/11/01/ 1993.
• I. H. Kurt, M. Oduncuoglu, F. N. Yilmaz, E. Ergul, and R. Asmatulu, "A Comparative Study on the Effect of Welding Parameters of Austenitic Stainless Steels Using Artificial Neural Network and Taguchi Approaches with ANOVA Analysis," Metals, vol. 8, no. 5, 2018.
• A. Alizadeh and H. Omrani, "An integrated multi response Taguchi- neural network- robust data envelopment analysis model for CO2 laser cutting," Measurement, vol. 131, pp. 69-78, 2019/01/01/ 2019.