Data Reconstruction Method for CD Basis Weight Analysis of Paper by using Compressed Sensing Technology

Abstract

The control of the cross-directional (CD) basis weight of paper is very challenging. The actuator of the system needs to control the properties of the entire sheet according to a set of restricted data measured by a scanning sensor. The scanning sensor measures the sheet in the cross direction of the paper. For the moving sheet, CD variations were those along an axis perpendicular to the motion of the sheet, while MD (machine direction) variations were those along the axis of motion. One of the problems that make the CD control difficult is data sampling, which is obtained by continuously measuring the CD basis weight of paper through multiple scanning sensors. As the paper moves vertically, the scanning sensor can only measure the “Z” shape area on the paper. When the scanning frequency was not at least twice the maximum frequency of the paper variation, it was difficult to estimate the sheet profile. According to the sparse characteristics of paper signal, a novel approach to accurately reconstruct the sheet properties by a random sampling protocol was proposed by using compressed sensing technology. Compared with the simple bandwidth based uniform sampling theory, it could accurately reconstruct the real process variations from less measurement data. Based on the reconstructed data and actual industrial process data, the CD response model was identified and the reconstruction effect was verified. The CD and MD basis weight data were separated by the predictive separation algorithm, which ensured the basis for CD control. The approach of the compressed sensing technology was found to be effective.