Applicability of Factor Analysis to the Determination of Mineral Matter in Coal
Roscoe, Bradley Albert
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https://hdl.handle.net/2142/70877
Description
Title
Applicability of Factor Analysis to the Determination of Mineral Matter in Coal
Author(s)
Roscoe, Bradley Albert
Issue Date
1981
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mineralogy
Energy
Abstract
A method for determining the characteristics of the mineral matter in coal was developed based on two types of factor analysis. Classical factor analysis was shown to identify trends in data sets that are indicative of the mineral phases and data errors. If a data error was identified by classical factor analysis, appropriate corrective action produced a data set with only experimental errors present that could be used for further analysis. Target transformation factor analysis (TTFA) was then used to quantitatively identify the elemental distribution of the minerals in coal.
An iterative approach to TTFA was developed and demonstrated to identify mineral phases without prior information concerning the phases. A set of data from Borax Lake, California was used to show how one could start with unique vectors for elemental profiles and obtain physically real elemental distributions for mineral phases. Comparisons were made to show the effect of using different weighting matrices in the iteration process and hence the advantage of weighting the target transformation rotations.
Techniques to estimate the uncertainties associated with the reproduction of the data by factor analysis were also studied. The jackknife method which requires that the factor analysis be performed several times was compared to a calculational approach which requires that the factor analysis be performed only once. The two methods produced similar results with the calculational method being operationally simplier.
To evaluate the ability of TTFA to resolve sources, it was applied on four sets of data: a previously resolved set of geological data, a set of artificially prepared data, a set of coal data from the Upper Freeport coal bed, and a set of coal data from an Illinois coal mine. The results obtained from the geological data and Upper Freeport data compared favorably with results obtained by other methods while the results obtained with the artificial data compared favorably with known values. Studies on the Illinois coal samples indicated that representative elemental profiles may be obtained for an individual mine with minimum requirements for sampling and sample preparation. In addition, it was indicated that one may get local geological variation in a single coal bed sampled at various locations; thus, in general, factor analysis of samples obtained from a localized area will yield data sets that are more meaningful.
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