Virtual Sensing Techniques for Nonstationary Processes Based on a Multirate Probabilistic Dual-Latent-Variable Supervised Slow Feature Analysis

Quality prediction of multirate nonstationary processes has always been a challenging task in the past decades. In this article, a novel multirate probabilistic dual-latent-variable supervised slow feature analysis (MR-PDSSFA) method is proposed to give a full explanation for multirate nonstationary process soft sensing technique. A dual-latent variable structure is proposed to extract long-term latent information for incomplete data collection. The first latent variable is designed to describe the quality-related long-term trend and will be employed for key quality variable prediction while the second latent variable can provide extra information for quality-related latent variable construction in an incomplete data collection. The constraint between these two latent variables is discussed in details. In addition, a multirate parameter learning algorithm is introduced to adaptively capture necessary long-term information and improve the soft sensing performance of the proposed method in multirate process. Finally, the superiority of the proposed method is demonstrated by two industrial cases where MR-PDSSFA outperforms several state-of-the-art methods on quality prediction accuracy in multirate nonstationary processes.