Abstract
Data-driven soft sensors play an important role in practical processes and have been widely applied. They provide real-time prediction of quality variables and then guide production and improve product quality. In practical chemical production processes, nonlinear dynamic multirate data is widespread and challenging to model. This paper innovatively proposes a temporal-spatial pyramid variational autoencoder (TS-PVAE) model for the nonlinear temporal-spatial feature pyramid extraction from multirate data. This structure not only selectively utilizes multirate data but also handles complex nonlinear time-series data. Based on this, integrated with just-in-time (JIT) learning, an adaptive TS-PVAE (ATS-PVAE) model is developed. In this model, historical data are used for real-time fine-tuning of the model, leading to the development of an adaptive model. Finally, the proposed models are validated by an industrial case of a methanation furnace, demonstrating a superior estimation performance.