Uncertainty Quantification and Optimal Robust Design for Machining Operations
Uncertainty Quantification and Optimal Robust Design for Machining Operations
复制标题
机械加工操作的不确定性量化和最佳稳健设计
DOI：
10.1115/1.4055039
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发表时间：
2023
影响因子：
3.1
通讯作者：
Cheng, Changqing
中科院分区：
文献类型：
--
作者：
Wan, Jinming;Che, Yiming;Wang, Zimo;Cheng, Changqing
在这项研究中，我们进行了稳健的优化设计的加工操作，芯片制造中的晶片抛光的关键过程之一，旨在避免特有的再生颤振，并考虑到固有的材料和工艺的不确定性，最大限度地提高材料去除率（MRR）。更具体地说，我们使用延迟微分方程（DDE）的切削刀具动力学的特点，并报名的时间有限元法（TFEM），以获得其近似解和稳定性指数给定的工艺设置或设计变量。为了进一步量化固有的不确定性，在随机不可控变量的不同实现下进行了TFEM的复制，但这会带来额外的计算负担。为了避免部署这样一个原油蒙特卡洛（MC）方法在每个设计设置，我们集成了随机TFEM与随机代理模型，随机克里格，在一个主动学习框架，顺序近似的稳定边界。数值结果表明，该方法得到的名义稳定边界与原始MC方法相当，但只需要一小部分的计算开销。为了进一步确保过程稳定性的鲁棒性，我们采用了另一种替代方法，高斯过程，预测未探索的设计点的稳定性指标的方差，并确定鲁棒稳定边界的条件风险价值（CVaR）标准。由此，可以确定在鲁棒稳定区域中使MRR最大化的最优设计。
In this study, we carry out robust optimal design for the machining operations, one key process in wafer polishing in chip manufacturing, aiming to avoid the peculiar regenerative chatter and maximize the material removal rate (MRR) considering the inherent material and process uncertainty. More specifically, we characterize the cutting tool dynamics using a delay differential equation (DDE) and enlist the temporal finite element method (TFEM) to derive its approximate solution and stability index given process settings or design variables. To further quantify the inherent uncertainty, replications of TFEM under different realizations of random uncontrollable variables are performed, which however incurs extra computational burden. To eschew the deployment of such a crude Monte Carlo (MC) approach at each design setting, we integrate the stochastic TFEM with a stochastic surrogate model, stochastic kriging, in an active learning framework to sequentially approximate the stability boundary. The numerical result suggests that the nominal stability boundary attained from this method is on par with that from the crude MC, but only demands a fraction of the computational overhead. To further ensure the robustness of process stability, we adopt another surrogate, the Gaussian process, to predict the variance of the stability index at unexplored design points and identify the robust stability boundary per the conditional value at risk (CVaR) criterion. Therefrom, an optimal design in the robust stable region that maximizes the MRR can be identified.