A Shape Prediction Model in Cold Strip Mill Integrating Principal Component Analysis and Neural Network

The efficient and reliable prediction of the strip shape in cold strip mill is a challenging problem, due to (a) too many different variables to be processed; (b) the strong intercorrelation and interaction among the process variables; (c) the time delay; (d) highly nonlinear behaviour. The conventional method to predict the strip shape in cold strip mill is difficult, so the artificial neural network with many complicated input variables was employed to simulate the complex system. To overcome the correlation effects among the process variables and the problem of dimensionality, principal component analysis (PCA) was introduced to the developed shape prediction model in cold strip mill. From the PCA, it was possible to decide the optimal dimension for the problem, to describe the dynamic behaviors of the strip shape. The calculated results are in good agreement with the measured values. The prediction model integrating principal component analysis and neural network has shown a good performance in terms of running speed and model accuracy, and it is suitable for efficient and reliable shape control in cold strip mill. Introduction The shape control has become an important issue to improve the control quality and product accuracy in cold strip mill. Previous research on the shape control showed that the shape control process is a non-linear, time-varying and time-delay system, depending on the coupled effects of many factors, such as the variations of strip materials, geometries, roll and strip temperatures etc [1,2]. Therefore, the efficient and reliable prediction of the strip shape in cold strip mill is a challenging problem, due to (a) too many different variables to be processed; (b) the strong intercorrelation and interaction among the process variables; (c) the time delay; (d) highly nonlinear behavior. The artificial neural network has the capability of establishing models according to input and output data directly. The non-linear mapping method is used to support or even to replace complex mathematical model. As the conventional method to predict the strip shape in cold strip mill is difficult, the artificial neural network with many complicated input variables is employed to simulate the complex system. Zhu et al. [3] developed a flatness prediction model in hot strip mill. Juang et al. [4] predicted the symmetric shape parameters, 2 Λ and 4 Λ , and asymmetric shape parameters, 1 Λ and 3 Λ , in cold strip mill. However, the above models cannot calculate the detailed cross-sectional shape in the rolling process, and only a few relevant parameters were introduced. In this study, the cold strip mill has five stands with a four-high configuration. The crosssectional shape is measured by a shapemeter consisting of a segmented roll with 15 rotors, so the cross-sectional shape at each measured point has up to 15 values according to the strip width. The shapemeter is assembled on the delivery side of the last stand. The strip shape is controlled by the adjustment of three factors, including the work roll bending, differential work roll bending and work roll coolant at the last stand. To calculate the detailed cross-sectional shape in cold strip mill, Key Engineering Materials Online: 2004-10-15 ISSN: 1662-9795, Vols. 274-276, pp 709-714 doi:10.4028/www.scientific.net/KEM.274-276.709 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-13/03/20,17:14:11) different measured parameters are introduced to the developed model. However, many of these measured parameters are strongly correlated with each other, and artificial neural network will need a long time for training and predicting with high dimensional input variables. Principal component analysis (PCA) is a well-known statistical processing technique that allows to study the correlations among components of multivariate data and to reduce redundancy by projecting the data over a preferred orientation basis [5]. Pearson [6] and Hotelling [7] described the theory of principal component analysis and then PCA has been applied in the wide variety of areas [8-11]. At present, there are mainly two kinds of methods to integrate principal component analysis and neural network. One is to use PCA to reduce the m-dimensional space of data to a few significant principal components, and then to follow on with the neural network to interpret the physical or chemical meaning of the principal components involved [8]. The other is an extension of traditional linear principal component analysis. The principal component analysis combined with neural network can extract features from highly non-linear data [9]. In this paper, a detailed cross-sectional shape in cold strip mill was calculated from the neural network with many complicated input variables involved. To overcome the correlation effects among the process variables and the problem of dimensionality, principal component analysis was introduced to the developed shape prediction model in cold strip mill. From the PCA, the optimal dimension for the problem was determined and the dynamic behaviors of the shape were described. The calculated results were compared with the measured values according to the testing results of the developed model. Principal Component Analysis Principal component analysis is a projection-based multivariate analysis technique. The central idea of principal component analysis is to reduce the dimension of a data set within which there are a large number of interrelated variables, while retaining the variations present in the data set. This reduction is achieved by transforming to a new set of variables, principal components (PCs), which are uncorrelated. PCA provides an approximation of an m-dimensional data matrix [ ] m x x x X , , , 2 1 L = whose variance-covariance matrix has eigenvalue-eigenvector pairs ( ) 1 1 , p λ , ( ) L , , 2 2 p λ , ( ) m m p , λ where 0 2 1 ≥ ≥ ≥ ≥ m λ λ λ L . The principal component decomposition of X can be represent as: