Reconstructing Paper Machine Sheet Process Data Variation Using Compressive Sensing

During paper manufacture, system actuators need to control the properties of the entire sheet based on a restricted set of data measured by a scanning sensor that traverses the moving sheet. Cross direction variations (CD) are those along an axis perpendicular to the motion of the sheet, while machine direction (MD) variations are those along the axis of motion, and are assumed uniform in CD. Current industrial practice is to separate the relatively slow variations of the CD profile from the higher bandwidth MD variations using low pass filtering, although the spacing and timing of the scanned data measurements makes it inevitable that some process variations will be distorted or lost to aliasing in the filtered data. In this paper, a novel approach to estimation of MD and CD variations is proposed – compressive sensing. In this approach, knowledge of the process is used to help characterize the expected process variations, allowing accurate reconstruction of the true process variations from far fewer measurements than would be indicated by simple bandwidth-based uniform sampling theory. Instead, a random sampling protocol is used to accurately reconstruct the sheet properties. The approach is found to be effective, using simulated and actual industrial process data.