By Sears G.H
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9. Eleven separate size fractions were analyzed grades pv(gv |D) in a population of particles when the distribution of linear grades Pᐉ(gᐉ|D) has been measured or calculated from a theoretical model. 75) where K is the 12 12 transformation kernel. Pᐉ is the vector of 12 measured cumulative linear grades and pv is the desired vector of fractional volumetric grades. 76) is useless because even very small errors in the measured distribution, which must always be present, are magnified by the inversion and swamp the true solution pv.
10. The importance of transforming the data is immediately apparent from these figures. The untransformed data do not reveal the true nature of the liberation distribution and cannot be used to analyze the behavior of individual particle types in any mineral processing operation. This should be borne in mind when experimental image analysis data is to be used for model calibration purposes. 11 Liberation distributions of 11 particle size fractions of a 2-component ore measured by image analysis.
3 (upper graph). This is an essential requirement for the description of mineral liberation distributions for different particle sizes. When the particle size is distinctly larger than the sizes of the mineral grains within the ore, most particles in the population exhibit a mineral grade close to the mean value for the ore as a whole and the distribution is bell-shaped. On the other hand when the particle size is distinctly smaller than the sizes of the mineral grains, the tendency for liberated and nearly liberated particles to appear is greatly enhanced and the beta distribution function reflects this tendency by exhibiting a strong U-shape.