SGER/Collaborative Research: Applying Decision Theory to Machining Optimization

这个探索性研究(SGER)/合作研究项目的目标是将经典决策理论和高速铣削领域结合起来，以研究不确定性存在下的加工优化。这将使决策理论的数学严密性能够应用于铣削优化，同时结合用于描述自然包含不确定性的铣削操作的模型。该方法将扩展先前的优化研究，在基于利润的目标函数上，除了传统上考虑的刀具磨损之外，还包括由工艺稳定性和受迫振动引起的零件误差所施加的限制。控制变量之间的概率依赖关系将被纳入其中，以捕获它们之间的相关性。然后使用所有变量的联合概率分布来描述不确定性，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讨。特别是，将使用双曲绝对风险厌恶（HARA）效用函数，它概括了对数和指数效用函数。还将建立对风险厌恶的敏感性和变量分布对最优选择的方差。如果成功，该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，减少周期时间。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，研究人员将促进这种性质的未来互动。

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.