Optimal Experimental Designs in the Flow Rate of Particles

This paper focuses on analysing the process of jam formation during the discharge by gravity of granular material stored in a 2D silo. The aim of the paper is twofold. Firstly, 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. Secondly, estimation of the unknown parameters is done using least squares, i.e. assuming normality, and also via maximum likelihood assuming the exponential distribution. Simulations for the designs considered in this paper show that the variance, the mean square error and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares.本研究聚焦于分析二维料仓（2D silo）内储存的散粒物料在重力卸料过程中的堵塞形成过程。本研究兼具双重研究目标：其一，开展最优试验设计的计算工作，共考量四类方法：D最优性（D-optimality）、D最优性与成本/收益函数的组合方案、贝叶斯D最优性（Bayesian D-optimality）以及序贯设计。研究结果表明，当前实验人员所采用的设计方案的效率可得到大幅提升；此外，本研究还针对核心参数开展了敏感性分析。其二，针对未知参数的估计，本研究采用了两种方法：一是假设误差服从正态分布的最小二乘法，二是假设服从指数分布的极大似然估计法。针对本文所涉及的各类设计方案开展的仿真实验显示，在绝大多数场景下，极大似然估计法得到的估计量的方差、均方误差与偏差均低于最小二乘法的对应结果。