Semi-Supervised Deep Conditional Variational Autoencoder for Soft Sensor Modeling

Variational autoencoder (VAE) as an unsupervised deep generated model has been widely applied to process modeling for industrial processes due to its excellent ability in nonlinear and uncertain feature extraction. However, soft sensor based on VAE model faces three challenges. First, the constructed supervised VAE model makes it difficult to describe the correlation between input and output based on self-network. Second, the output of the VAE may suffer from instability and uncontrollability. In addition, the limited labeled data in industries are the third challenge. To solve the above problems, a semi-supervised deep conditional VAE (SS-DCVAE) is constructed for soft sensor based on a supervised DCVAE (S-DCVAE) and an unsupervised DCVAE (U-DCVAE). The S-DCVAE model is constructed by injecting unlabeled data, the actual labels, and estimated labels as constraint conditions from the preneural network. Based on such a conditional supervised structure, the input–output correlation can be strengthened and the generated data can be controlled toward the aim direction. Furthermore, the U-DCVAE model can be built by making the latent distribution as similar as possible to S-DCVAE, as well as only using unlabeled data with corresponding estimated labels. In this way, the unlabeled data can be fully utilized and online prediction can be achieved. Finally, combining the decoder of S-DCVAE model with the encoder of U-DCVAE, the SS-DCVAE model is constructed with both advantages. The effectiveness and superiority of the SS-DCVAE model are demonstrated by comparing the prediction results of the proposed model with other deep learning methods based on industrial cases.