This paper presents a modeling-control synthesis to address the quality
control challenges in multistage manufacturing systems (MMSs). A new
feedforward control scheme is developed to minimize the quality variations
caused by process disturbances in MMSs. Notably, the control framework
leverages a stochastic deep Koopman (SDK) model to capture the quality
propagation mechanism in the MMSs, highlighted by its ability to transform the
nonlinear propagation dynamics into a linear one. Two roll-to-roll case studies
are presented to validate the proposed method and demonstrate its
effectiveness. The overall method is suitable for nonlinear MMSs and does not
require extensive expert knowledge.

此论文提出了一种建模控制综合方法来解决多级制造系统（MMSs）中的质量控制挑战。通过开发一种新的前馈控制方案来最小化 MMSs 中由过程干扰引起的质量变化。新的控制框架利用随机深度 Koopman（SDK）模型来捕捉 MMSs 中的质量传播机制，其突出特点是能够将非线性传播动态转化为线性动态。通过展示两个卷对卷的案例研究来验证所提出的方法，并展示其有效性。该方法适用于非线性 MMSs，并且不需要大量的专家知识。

多阶段制造系统中基于深度 Koopman 控制的质量变异

Deep Koopman-based Control of Quality Variation in Multistage  Manufacturing Systems

The modeling of multistage manufacturing systems (MMSs) has attracted
increased attention from both academia and industry. Recent advancements in
deep learning methods provide an opportunity to accomplish this task with
reduced cost and expertise. This study introduces a stochastic deep Koopman
(SDK) framework to model the complex behavior of MMSs. Specifically, we present
a novel application of Koopman operators to propagate critical quality
information extracted by variational autoencoders. Through this framework, we
can effectively capture the general nonlinear evolution of product quality
using a transferred linear representation, thus enhancing the interpretability
of the data-driven model. To evaluate the performance of the SDK framework, we
carried out a comparative study on an open-source dataset. The main findings of
this paper are as follows. Our results indicate that SDK surpasses other
popular data-driven models in accuracy when predicting stagewise product
quality within the MMS. Furthermore, the unique linear propagation property in
the stochastic latent space of SDK enables traceability for quality evolution
throughout the process, thereby facilitating the design of root cause analysis
schemes. Notably, the proposed framework requires minimal knowledge of the
underlying physics of production lines. It serves as a virtual metrology tool
that can be applied to various MMSs, contributing to the ultimate goal of Zero
Defect Manufacturing.

使用随机深度 Koopman 框架建模多级制造系统，传播质量信息并提高数据驱动模型的可解释性，从而在预测产品质量和根本原因分析方面超越其他流行的数据驱动模型，适用于各种制造系统，有助于零缺陷制造的最终目标。