Stochastic Deep Koopman Model for Quality Propagation Analysis 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.