Statistical models for on-line monitoring of cardboard quality properties

Fredrik Nordström, Torgny Lindström and Jan Holst

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
A statistical study of data containing observations of process and quality variables from the SCA paper mill in Munksund, Sweden, is presented. The emphasis in this analysis has been on modelling the laboratory collected paper quality variables by means of the data available on-line, during production.
The primary tool for prediction, or estimation at non observed time instants, of variables was partial least squares (PLS). In this analysis, good prediction results were obtained for the laboratory measured paper quality variables. Thus by these results, process and quality variables obtained during production can be used on-line to achieve good estimates of the important quality variables that otherwise only can be obtained off-line. Another important result obtained from the PLS analysis was the relative importance of the variables used for estimation. From these results the most important variables for quality control, with respect to the paper quality variables, could be identified.
It was shown that the temporal correlations within the variables were generally quite strong. In order to model this dependency in time, stochastic differential equations were utilized. These models were found to successfully explain the correlations in the data such that the resulting residuals were nearly independent.
Further, the possibility for on-line modelling of the paper tensile properties were investigated. More precisely, using on-line predictions of the tensile strength, the tensile stiffness and the elongation, on-line prediction of the stress vs strain curves were conducted. No data for verification of these results were available from the Munksund paper mill, therefore another set of laboratory data were utilized for this purpose. Good results were achieved by fitting a parametric model to the tensile variables, in that the estimated stress vs strain curves showed good agreement with the measured values.
Key words:
On-line modelling; paper quality; partial least squares; stochastic differential equations; tensile prediction; time dependence.