Models of Surface Roughness with Applications in Paper Industry
Abstract: This thesis comprises general parametric models for surface roughness. The models can be used in several technical and natural applications but are here only applied to the micro-structure of paper. In that application, earlier models are generalized and new models introduced. The different models are related to the scale of the roughness and by using different approaches, different roughness properties are captured and put in a context, which is closely related to their practical use. The thesis consists of five papers. The first paper in the thesis treats a small scale roughness, which depends on the geometric properties of the cellulose fibers. In that paper, we formulate a parametric model whos parameters are connected to the fiber geomerty. We also introduce an estimator of the model parameters based on measurements in two orthogonal directions on the surface. The next paper aims to find a concise and, with repect to scale, generally applicable characterization of the surface roughness. We have found that the fractal dimension and the topothesy well meet these demands. Also based upon one-dimensional orthogonal measurement, we estimate these parameters and show that they can distinguish different paper qualities. Paper three describes a hierarchical model of the surface irregularities based on assumptions of Markov properties. In this model, two kind of scales are considered. A relative large scale comprising large clusters and a small scale close to the separate fibers. Descriptions and methods rely much on digital images analysis. Also this model distinguish different paper qualities but uses 8 parameters. In connection to this model, an investigation of different methods for finding global extremes is performed and reported in paper four. Newton's method and simulating annealing are compared and we found that simulated annealing sometimes can be used when Newton's method fails. However, Newton's method is generally the fastest one. Finally, we propose a measure of homogeneity in the last paper in the theses. We suggest here the two-dimensional kurtosis, which reflect the spatial homogeneity by using a single number.
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