Statistical models for on-line monitoring of cardboard quality properties
Fredrik Nordström, Torgny Lindström and Jan Holst
Centre for Mathematical Sciences
Lund Institute of Technology,
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
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
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.
On-line modelling; paper quality; partial least squares; stochastic differential
equations; tensile prediction; time dependence.