Solution of the breakage matrix reverse problem

• The reverse problem in the breakage matrix context is considered.
• Solving procedures for the overdetermined case are given.
• Best-fit solution of the problem in the least square sense is obtained.
• Applicability of the proposed model was confirmed by some examples.

This paper is a complete overview of the reverse problem in the breakage matrix context. The procedure for calculating the input particle size distribution to a milling operation in order to obtain the desired output particle size distribution is given. The reverse problem was solved by the “precision” and “approximation” approaches. For the precision case, a detailed algorithm is presented, where in every step a precise range for the current output is provided. This approach is limited with a number of output size fractions that can be freely chosen. On the other hand, the approximation approach gives the best-fit solution which corresponds to the desired output particle size distribution. In this case the problem is solved by the orthogonal decomposition and non-negative least squares method and by semilogarithmic loss function. Applicability of the proposed methods was confirmed by examples related to wheat milling.

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