Deep Koopman-VAE Based Process Monitoring for Industrial Biosystems

Industrial biosystem (IBS) applies biological principles and technologies to the industrial sector, encompassing bioreactors, fermenters, and biosensors. It is extensively employed in the pharmaceutical, food, and chemical industries. Ensuring the stability of IBS is crucial to maintaining production quality, and thus, real-time and accurate monitoring is necessary. Generally, monitoring involves detecting changes in the quantity of molecules to determine whether the system is relatively stable. However, due to the complexity, non-linearity and remarkable intrinsic uncertainties of IBS, process monitoring can be challenging. To tackle this issue, we propose an innovative, entirely data-driven detecting and monitoring technology that combines Koopman theory and deep neural networks to effectively analyze the nonlinear dynamical system. We use the spectral decomposition of the Koopman operator, often through Dynamic Mode Decomposition (DMD), for state prediction. Additionally, we employ a neural network to identify nonlinear observation basis functions. The optimal residual sequence is analyzed using probability graphs to enable real-time monitoring. The effectiveness of our approach is demonstrated through testing on two canonical gene expression systems, characterized by intrinsic stochastic dynamics, providing a unique benchmark for comparing performance across diverse process monitoring algorithms, thereby extending the contributions of this paper.