Models of Surface Roughness with Applications in Paper Industry
(2002) 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 microstructure 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... (More)  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 microstructure 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 onedimensional 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 twodimensional kurtosis, which reflect the spatial homogeneity by using a single number. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/464499
 author
 Johansson, JanOlof ^{LU}
 opponent

 Penttinen, Antti, Prof., University of Jyväskylä, Finland
 organization
 publishing date
 2002
 type
 Thesis
 publication status
 published
 subject
 keywords
 Statistik, actuarial mathematics, operations research, programming, Matematik, Statistics, Mathematics, estimation., Surface roughness, parametric models, operationsanalys, programmering, aktuariematematik, Wood, pulp and paper technology, Pappers och massateknik
 pages
 138 pages
 publisher
 Halmstad University
 defense location
 Matimatikcentrum, Sölvegatan 18, sal MH:C
 defense date
 20020405 13:15
 ISSN
 14040034
 ISBN
 9162851497
 language
 English
 LU publication?
 yes
 id
 f8ab636d40ea4a128907f6d6f5ccdfcd (old id 464499)
 date added to LUP
 20070927 15:43:50
 date last changed
 20160919 08:44:52
@phdthesis{f8ab636d40ea4a128907f6d6f5ccdfcd, 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 microstructure 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.<br/><br> <br/><br> 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.<br/><br> <br/><br> 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 onedimensional orthogonal measurement, we estimate these parameters and show that they can distinguish different paper qualities.<br/><br> <br/><br> 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.<br/><br> <br/><br> Finally, we propose a measure of homogeneity in the last paper in the theses. We suggest here the twodimensional kurtosis, which reflect the spatial homogeneity by using a single number.}, author = {Johansson, JanOlof}, isbn = {9162851497}, issn = {14040034}, keyword = {Statistik,actuarial mathematics,operations research,programming,Matematik,Statistics,Mathematics,estimation.,Surface roughness,parametric models,operationsanalys,programmering,aktuariematematik,Wood,pulp and paper technology,Pappers och massateknik}, language = {eng}, pages = {138}, publisher = {Halmstad University}, school = {Lund University}, title = {Models of Surface Roughness with Applications in Paper Industry}, year = {2002}, }