Optimal Experimental Designs in the Flow Rate of Particles

Abstract

This article focuses on analyzing the process of jam formation during the discharge by gravity of granular material stored in a two-dimensional silo. The aim of the article is two-fold. First, optimal experimental designs are computed, in which four approaches are considered: D-optimality, a combination of D-optimality and a cost/gain function, Bayesian D-optimality, and sequential designing. These results reveal that the efficiency of the design used by the experimenters can be improved dramatically. A sensitivity analysis with respect to the most important parameter is also performed. Second, estimation of the unknown parameters is done using least squares, that is, assuming normality, and also via maximum likelihood assuming the exponential distribution. Simulations for the designs considered in this article show that the variance, the mean squared error, and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares. Supplementary materials for this article are available online.

• Bayesian design
• Compound criterion
• D-optimal design
• Granular material
• Jam formation
• Sensitivity analysis
• Sequential design

ACKNOWLEDGMENTS

The authors were supported by Ministerio de Economía y Competitividad and Fondos FEDER MTM2010–20774-C03-01 and MTM2013–47879-C2-1-P and Junta de Comunidades de Castilla la Mancha PEII10–0291-1850. The authors thank the associate editor and the referees for their comments, which have contributed very much to improve the article.