Recursive Dynamic Inner Partial Least Squares for Virtual Metrology of Time-Varying Dynamic Processes

Virtual metrology plays a vital role in dynamic industrial processes by improving decision-making, enabling real-time monitoring of process states, and supporting adaptive control strategies. However, existing virtual metrology approches often struggle to address persistent time-varying dynamics inherent in real-world industrial systems. To overcome this limitation, we propose the Recursive Dynamic Inner PLS (RDIPLS) algorithm, a novel approach that dynamically updates virtual metrology models using real-time process data. More precisely, we propose a novel framework where model updates can be efficiently achieved through the incremental updates of several covariance matrices and the implementation of a parameter initialization preservation strategy. This framework ensures continuous adaptation to evolving process conditions while maintaining computational efficiency. The algorithm's performance is rigorously validated through experiments on both simulated datasets and real industrial applications, demonstrating its effectiveness in addressing time-varying challenges.