SGER/Collaborative Research: Applying Decision Theory to Machining Optimization

这一小型探索性研究(SGER)/合作研究项目的目标是融合经典决策理论和高速铣削领域，以研究存在不确定性的加工优化。这将使决策理论的数学严谨性应用于铣削优化，同时纳入用于描述铣削操作的模型，这些模型自然包含不确定性。该方法将扩大先前的优化研究，以包括工艺稳定性和强迫振动造成的零件误差对基于利润的目标函数施加的限制，以及传统上认为的工具磨损。控制变量之间的概率相关性将被纳入其中，以捕捉它们之间的相关性。然后，将使用所有变量的联合概率分布来描述不确定性，并且期望效用将在控制变量上最大化。风险厌恶对这些控制的最优值的影响也将被探究。特别是，将使用双曲绝对风险厌恶(HARA)效用函数，它既包括对数效用函数，也包括指数效用函数。还将建立对风险厌恶和最优选择变量分布的方差的敏感度。如果成功，这项研究将导致在工艺规划阶段改进加工参数的选择。这将提高加工效率并缩短循环时间。这项研究的另一个好处是提高了制造业对决策理论基础的认识(反之亦然)。通过在特定学科的会议上展示这项研究，研究人员将促进未来这种性质的互动。

The objective of this Small Grant for Exploratory Research (SGER)/Collaborative Research project is to merge the fields of classical decision theory and high-speed milling in order to study machining optimization in the presence of uncertainty. This will enable the mathematical rigor of decision theory to be applied to milling optimization, while incorporating models used to describe milling operations which naturally include uncertainty. The approach will be to expand prior optimization studies to include limitations imposed by process stability and part errors due to forced vibrations, in addition to the more traditionally considered tool wear, on a profit-based objective function. Probabilistic dependence between the control variables will be incorporated to capture the correlation between them. The uncertainty will then be described using a joint probability distribution for all variables and the expected utility will be maximized over the control variables. The effects of risk aversion on the optimal values of these controls will also be explored. In particular, the hyperbolic absolute risk averse (HARA) utility function, which generalizes both the logarithmic and exponential utility functions, will be used. Sensitivity to risk aversion and variance of the variable distributions on the optimal selection will also be established. If successful, this research will lead to improved selection of machining parameters at the process planning stage. This will increase machining efficiency and reduce cycle times. Another benefit of this research will be increased awareness of decision theory fundamentals within the manufacturing community (and vice versa). By presenting this research in discipline-specific conferences, the investigators will promote future interactions of this nature.