Title: Relevance vector machine-based defect modelling and optimisation – an application

Authors: Moutushi Chatterjee, Sujit K. Majumdar

Addresses: Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India. ' SQC-Operations Research Division, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India

Abstract: In presence of many correlated and autocorrelated process variables, initially the support vector machine (SVM) and later the relevance vector machine (RVM) were used for modelling the bonding defect in Hi-Cr rolls as function of explanatory variables by mapping the original input data space to high-dimensional feature space using appropriate kernels. The RVM-Bessel kernel, which turned out to be the best-fit regression model with minimum error (MSE) from among the competing kernels, was developed when the best-fit SVM-RBF kernel regression model was found associated with high absolute value of MSE and a large number of support vectors. The final sparse defect model was developed with the relevance vectors (RVs) generated while fitting the RVM-Bessel kernel model by taking recourse to hierarchical regression. Constrained optimisation treatment of the sparse defect model helped identifying the factor-setting corresponding to minimum length (0) of bonding defect. Confirmatory trial runs showed encouraging trends.

Keywords: defect modelling; SVM-RBF kernel; RVM-Bessel kernel; relevance vectors; hierarchical regression; sparse models; constrained optimisation; optimum factor setting; relevance vector machines; support vector machines; SVM; RVM; bonding defects; subsurface defects; Hi-Cr rolls; steel rolling mills; high chromium.

DOI: 10.1504/IJOR.2011.041859

International Journal of Operational Research, 2011 Vol.12 No.1, pp.56 - 78

Published online: 08 Aug 2011 *

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