Using source data to aid and build variational state-space autoencoders with sparse target data for process monitoring.

In industrial processes, different operating conditions and ratios of ingredients are used to produce multi-grade products in the same production line. Yet, the production grade changes so quickly as the demand from customers varies from time to time. As a result, the process data collected in certain operating regions are often scarce. Process dynamics, nonlinearity, and process uncertainty increase the hardship in developing a reliable model to monitor the process status. In this paper, the source-aided variational state-space autoencoder (SA-VSSAE) is proposed. It integrates variational state-space autoencoder with the Gaussian mixture. With the additional information from the source grades, SA-VSSAE can be used for monitoring processes with sparse target data by performing information sharing to enhance the reliability of the target model. Unlike the past works which perform information sharing and modeling in a two-step procedure, the proposed model is designed for information sharing and modeling in a one-step procedure without causing information loss. In contrast to the traditional state-space model, which is linear and deterministic, the variational state-space autoencoder (VSSAE) extracts the dynamic and nonlinear features in the process variables using neural networks. Also, by taking process uncertainty into consideration, VSSAE describes the features in a probabilistic form. Probability density estimates of the residual and latent variables are given to design the monitoring indices for fault detection. A numerical example and an industrial polyvinyl chloride drying process are presented to show the advantages of the proposed method over the comparative methods.