A Novel CVAE-Based Sequential Monte Carlo Framework for Dynamic Soft Sensor Applications

In industrial processes, quality variables are typically sampled at a considerably lower frequency than system inputs due to technical or cost constraints. Dynamic soft sensors utilize temporal prediction to bridge these sampling gaps, thus enabling real-time closed-loop control. However, existing approaches primarily focus on one-step prediction accuracy, potentially leading to significant deviations in long-term predictions. In addition, these methods are incapable of evaluating the reliability of prediction results, subsequently increasing the potential risk of closed-loop systems. To tackle these challenges, this study presents a novel regression modeling approach based on the conditional variational autoencoder (CVAE) framework. In contrast to traditional regression approaches, this method focuses on modeling the transition probability distribution of the system, allowing the model to produce a range of credible quality variable predictions via Monte Carlo (MC) sampling. Based on the CVAEs, the sequential MC method is further employed to simulate diverse potential system state trajectories, thereby achieving multistep soft measurement prediction. Compared with traditional soft measurement techniques, the proposed method demonstrates lower prediction biases and the capacity to assess the credibility of prediction results from a probabilistic standpoint. When online quality variables are assessed by the laboratory, this method can update predictions utilizing the resampling scheme. Two case studies are offered to validate the effectiveness of the proposed scheme.