Virtual sensing for dynamic industrial process based on localized linear dynamical system models with time-delay optimization

Virtual sensors play an important role in real-time sensing of key quality-related variables in industrial processes. Linear dynamical system (LDS) paradigm has established itself as a powerful tool for developing dynamic virtual sensors. However, there are still some practically pivotal issues unresolved, such as how to improve the generalization reliability and accuracy when accounting for the time delays and how to broaden the application sphere by breaking their limitations to linear processes. Motivated by dealing with these challenging issues this paper proposes a virtual sensing framework called 'localized LDS (LoLDS)'. In the LoLDS framework, the process dynamics and nonlinearities are taken into consideration from different scales without increasing the model complexity, and the time delays are intelligently optimized which triggers the model inconsistency by a designed diversified localization scheme at the offline stage. Moreover, an adaptive online model switch scheme is developed to enable the real-timely best LDS models to be responsible to predict the quality variables. The offline and online operations together enable the LoLDS to improve the generalization performance of the dynamic virtual sensor. The LoLDS framework is highly automated, and its performance has been extensively evaluated by two real-life industrial processes, showing very promising application foregrounds.