Estimation of Post Milling Particle Size Distribution Using Linear Transformation in Parameter Space
by Jesang Yim
Abstract – The research attempts to predict the change in the size distribution of the particles after the milling process. The data for the research was sourced from https://www.innocentive.com/. It consisted of pre and post-milling data of the size distributions of the particles. This research made two assumptions: the distribution of particle sizes can be described by combining several individual normal distribution graphs with different parameters. Curve fitting was used to find out the best fitting parameters of the component normal distribution functions. We also assumed that the formula for predicting post-milling distribution from pre-milling distribution is linear, i.e., a matrix operation on the pre-milling parameters will predict the post-milling one. A single matrix should be able to convert all 26 datasets. However, only 25 of the datasets were used in order to test the remaining one for cross-validation. Four normal distributions were determined to be optimal for describing the particle size distribution in the data. The prediction had a sum of squared errors ratio ranging from 4.95% to 31.2%, with the average value of 18.7%, which shows the potential of this approach. With more data, or with an ability to conduct the experiment, higher and more consistent particle size predictions should be within reach.
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