Enhancing monitoring performance of data sparse nonlinear processes through information sharing among different grades using Gaussian mixture prior variational autoencoders

In the chemical industry, manufacturers produce multiple products with different grades constantly by changing the operating conditions and raw materials in the same production line to meet the customers' needs and market demands. Thus, establishing a model for monitoring such a process is inadequate because the data available in an operating region is often scarce. To deal with the hardship in monitoring the process that produces various products with multi-grades, the data sparsity problem in the target grade is addressed by simultaneously extracting and sharing common knowledge of the available grades with the target grade. In fact, multi-grade processes have similar operating conditions but they may have different ratios of ingredients. In this paper, the Gaussian mixture prior variational autoencoder (GMPVAE) is proposed to perform information sharing to enhance the target model. Complementary encoder and decoder networks represent the mapping of the source and target input data to extract the common features among the grades from the same production line. In contrast with an ordinary variational autoencoder, a Gaussian mixture model instead of a unit Gaussian distribution is set as the prior distribution of GMPVAE so that the unique characteristics of the target and source grades can be obtained. In addition, the objective function is designed on the basis of the goals to increase the reliability of the target model and to do information sharing and modeling in one step to reduce information loss during the information transferring procedure. Accordingly, the probability density estimates of latent variables and residuals rather than point estimates are then given so that distribution-based monitoring indices of the target grade can be designed and the fault detection decisions can be made opportunely. A numerical example and an industrial ammonia synthesis example are presented to show the effectiveness of the proposed method.

Automated summary

In the chemical industry, the GMPVAE method is proposed to address the monitoring difficulties in producing multiple products with different grades, by extracting and sharing common knowledge of available grades to overcome data sparsity in the target grade.