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M. Kellomäki, J.J. Pawlak, Y.-J. Sung and D.S. Keller. Characterization of Non-stationary Structural Non-uniformities in Paper. In The science of papermaking, Trans. of the XIIth Fund. Res. Symp. Oxford, 2001, (C.F. Baker, ed.), pp 1313–1342, FRC, Manchester, 2018.


In this investigation, a novel approach to separating the static and stochastic components of paper variability data, such as mass formation or apparent density, was developed. Based on a discrete implementation of the continuous wavelet transform, the method provides information about the scale of features, e. g. flocs or streaks, as function of position within the data array in one direction. A non-rigorous, yet self-contained theoretical development of the method was given. The main discovery in this work was to mathematically show that, under conditions applying to a typical paper variability data, the distribution of energy among wavelets of different scale and at different positions, or simply, the local energy map, can be decomposed into two different parts that contain all the energy related to the static mean grammage profile or the local stochastic variability.

In order to validate the approach and to justify its value, a set of simulated basis weight maps with different types of streaks were generated and analyzed successfully. This method was evenable to decompose overlapping grammage and formation streaks, which would have been impossible using traditional methods. As a final demonstration, data measured from real papers made in the laboratory and with a pilot machine were analyzed. Apparent density maps were determined using β-radiographic transmission imaging for mass formation and two-sided laser profilometry for local thickness maps. The method was able to reveal floc size variations buried into strong grammage streaks. The periodicity and the scale of the grammage streaks were also characterized by the decomposition of the wavelet map.

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