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。

多阶段制造系统中质量传播分析的随机深度库普曼模型

Stochastic Deep Koopman Model for Quality Propagation Analysis in  Multistage Manufacturing Systems

Organisations often struggle to identify the causes of change in metrics such
as product quality and delivery duration. This task becomes increasingly
challenging when the cause lies outside of company borders in multi-echelon
supply chains that are only partially observable. Although traditional supply
chain management has advocated for data sharing to gain better insights, this
does not take place in practice due to data privacy concerns. We propose the
use of explainable artificial intelligence for decentralised computing of
estimated contributions to a metric of interest in a multi-stage production
process. This approach mitigates the need to convince supply chain actors to
share data, as all computations occur in a decentralised manner. Our method is
empirically validated using data collected from a real multi-stage
manufacturing process. The results demonstrate the effectiveness of our
approach in detecting the source of quality variations compared to a
centralised approach using Shapley additive explanations.

使用可解释的人工智能方法，通过分散计算估算多阶段生产过程中感兴趣度量的贡献来源，从而避免了数据共享的问题，并通过实证验证展示了其在检测质量变化源头方面相对于集中式方法的有效性。

在多级设置中识别对供应链结果的贡献者：一种分散化的方法

Identifying contributors to supply chain outcomes in a multi-echelon  setting: a decentralised approach

During the operation of a chemical plant, product quality must be
consistently maintained, and the production of off-specification products
should be minimized. Accordingly, process variables related to the product
quality, such as the temperature and composition of materials at various parts
of the plant must be measured, and appropriate operations (that is, control)
must be performed based on the measurements. Some process variables, such as
temperature and flow rate, can be measured continuously and instantaneously.
However, other variables, such as composition and viscosity, can only be
obtained through time-consuming analysis after sampling substances from the
plant. Soft sensors have been proposed for estimating process variables that
cannot be obtained in real time from easily measurable variables. However, the
estimation accuracy of conventional statistical soft sensors, which are
constructed from recorded measurements, can be very poor in unrecorded
situations (extrapolation). In this study, we estimate the internal state
variables of a plant by using a dynamic simulator that can estimate and predict
even unrecorded situations on the basis of chemical engineering knowledge and
an artificial intelligence (AI) technology called reinforcement learning, and
propose to use the estimated internal state variables of a plant as soft
sensors. In addition, we describe the prospects for plant operation and control
using such soft sensors and the methodology to obtain the necessary prediction
models (i.e., simulators) for the proposed system.

本文介绍使用基于化学工程知识和强化学习算法的动态模拟器进行预测并作为软传感器来估计化工厂内部状态变量的方法，并探讨了使用这种软传感器进行化工厂操作和控制的前景及其所需预测模型的方法。