Multidimensional statistical and visualization methods in description of grained materials

Abstract

Abstract.As far as coal is concerned, the data are usually considered to be independent variables, and such an approach is not always appropriate. Therefore, the paper focuses on the multidimensional analysis, which allows to conduct the comparisons of the coal types and to determine the relationship between their specific characteristics. The paper presents an analysis of variance and an observational tunnels method, which enabled to examine the differences between three types of coals: 31, 34.2 and 35. In order to achieve the experimental aim, a number of laboratory analyses of coal were carried out. Such parameters as combustion heat, ash contents, sulfur contents, volatile parts contents and analytical moisture were determined for samples, including the mass and density of these fractions, so seven various features were specified for each coal. The results of the observational tunnels method and the ANOVA application confirmed that the accepted parameters were sufficient for the proper identification of the coal sample origin and their size fractions. As a result of ANOVA, the volatile matter content was determined as the feature on which identification of the coal types can be based, regardless of size fraction. However, the remaining parameters affect the study groups randomly. While applying the methods of multidimensional analysis, some limitations were encountered that indicated the complex structure of the grained material.

A multidimensional analysis and modelling of flotation process for selected Polish lithological copper ore types

“…In this case, the multivariate vector of dependent variables Yi (5) is characterized by the following variables:Y1 = βCu, Y2 = ϑCu Y3 = εCu, Y4 = ηCu. However, in the analysis, the vectors of mean values of the variables i (6), where i=1, 2, …, N for different systems of factors and their levels (6) were compared [Stanisz, 2007;Niedoba, 2013;Niedoba et al, 2016a, Niedoba et al, 2016b. The relevance of the main effects among the investigated factors was considered for significance level equalled to 95%, which means that the model with a P-value lower than 0.05 could be considered.…”

A multidimensional analysis and modelling of flotation process for selected Polish lithological copper ore types

“…In this case, the multivariate vector of dependent variables Yi (5) is characterized by the following variables:Y1 = βCu, Y2 = ϑCu Y3 = εCu, Y4 = ηCu. However, in the analysis, the vectors of mean values of the variables i (6), where i=1, 2, …, N for different systems of factors and their levels (6) were compared [Stanisz, 2007;Niedoba, 2013;Niedoba et al, 2016a, Niedoba et al, 2016b. The relevance of the main effects among the investigated factors was considered for significance level equalled to 95%, which means that the model with a P-value lower than 0.05 could be considered.…”

Gospodarka Surowcami Mineralnymi - Mineral Resources Management

“…During the presentation of results of beneficiation conducted especially in laboratory conditions, three types of upgrading curves have been used so far: Henry curves (the only ones allowing direct reading of the parameters values), Halbich curves and Fuerstenau curves (Ding et al 2015;Drzymala 2007;Drzymala and Ahmed 2005;Drzymala et al 2013;Foszcz et al 2010;2016;Kelly and Spottiswood 1982;Madej 1978;Mayer and Craig 2010;Niedoba 2013;Yang et al 2015). Henry's curves are usually used (for technical reasons -the possibility to partition into density fractions) for coal.…”