Factor Analysis and Mathematical Modeling in Determining the Quality of Coal

Abstract

The separation of coal material of three types of coals originating from three various Polish hard coal mines (types 31, 34.2 and 35, according to Polish nomenclature, which were steam coal, semi-coking coal and coking coal) into particle size fractions and then into particle density fractions was done and then the following parameters were measured for each particle size-density fraction: combustion heat, ash contents, sulfur contents, volatile parts contents, analytic moisture. In this way a 7-dimensional vector of data was created. Using methods of factor analysis the important features of coal were selected, which decide about their membership to individual types. To evaluate the appropriateness of the applied method the Bartlett’s sphericity test as well coefficient of Kaiser-Mayer-Olkin (KMO) were used. To select important factors the Kaiser criterion and Cattell’s scree test were used. The obtained results were compared with the results obtained in previous works by means of observation tunnels method. The results showed which particular features are crucial to define the type of coal what is also important to select appropriate method of its enrichment. Furthermore, the construction of a mathematical model presenting the relations between these properties and particle size and density is presented. Because of the fact that particles of certain size or density may occur in neighboring fractions three sorts of relations were examined basing on regression analysis.The analysis was conducted for all three coal types. Because of the fact that the models contain various amounts of independent variables R2 coefficient, mean squared error (MSE) and Mallow’s statistics Cp were applied to evaluate and compare obtained results.