Soft Measurement Modeling Method Based on Quality-Related Mixed Variational Autoencoder Regression

In recent years, the Mixture Variational Autoencoder (MVAE) model has been widely applied in industrial process monitoring and soft sensor modeling due to its strong feature extraction capabilities for multimodal data. However, the traditional MVAE, as an unsupervised generative model, often contains a large amount of irrelevant information during feature extraction, which is not conducive to predicting quality variables. To address this issue, a soft sensor modeling method based on quality-related Mixture Variational Autoencoder Regression (MVAE-R) is proposed and applied to complex multimodal industrial processes. This method first maps the process variables into two subspaces through nonlinear mapping: a quality-independent subspace and a quality-related subspace. It then extracts the prior information on these two subspaces from both process and quality variables, which better separates the latent variables related and unrelated to quality, effectively capturing the nonlinear features that are highly correlated with the target quality variable. Subsequently, the latent variables under each modality are learned to obtain an effective feature representation of the process variables while predicting the quality variables. Finally, the performance of the proposed model is evaluated through a numerical example and a real industrial case, demonstrating the model's effectiveness and superiority.