UBC Theses and Dissertations

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UBC Theses and Dissertations

Estimating paper sheet process variations from scanned data using compressive sensing Towfighi, Parisa


During paper fabrication, system actuators are used to control paper properties over the entire sheet on the basis of a restricted set of measurements taken from the moving sheet. From these measurements it is necessary to estimate the properties of the full paper sheet. The axis perpendicular to the direction of motion of the paper through the machine is referred to as the cross direction (CD), and the axis of the sheet motion itself is the machine direction (MD). Low pass filtering is commonly used in industrial practice to separate the slow vibrations in the cross direction from the typically faster variations in machine direction. Exponential low pass filtering can reconstruct the actual variations if uniform sampling has been carried out at a sampling rate that is at least twice the bandwidth of the original signal. Such conditions are almost never met in practice. To overcome this limitation, we propose here a novel algorithm based on the well-established theory of compressive sensing. The bandwidth constraints of conventional sampling can be avoided if certain general characteristics of the unknown signal are assumed to be known, and if a few computational conditions are satisfied. Compressive sensing can then estimate the signal with impressive accuracy from a minimal number of samples. This new technique requires that samples are collected in a random fashion. In this thesis, compressive sampling is applied to paper machine data. The data representation is optimized in an l1 basis and its resulting performance is evaluated using both industrial and simulated data. It should be noted that this approach has broad potential industrial application in situations where process constraints dictate the timing and location of available process data that is to be used for control and monitoring purposes.

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