Supervised Variational Autoencoders for Soft Sensor Modeling With Missing Data

Autoencoder (AE) is a deep neural network that has been widely utilized in process industry owing to its superior abilities of feature extraction and data reconstruction. Recently, assuming the latent variables to be random variables, a probabilistic variant of it called variational autoencoder (VAE) has achieved a major success in different applications. In this article, we develop two novel submodels based on deep VAEs (DVAE), which are further utilized to establish a soft sensor framework. By the use of our first submodel known as supervised DVAE (SDVAE), the distribution information of latent features can be obtained. This is used as a prior of the second submodel known as the modified unsupervised DVAE (MUDVAE). Then, a new soft sensor framework can be constructed by combing the encoder of SDVAE with the decoder of MUDVAE. Since our designed VAE has superior ability in data reconstruction, it also works well under the missing data situation which is common in process industries due to sensor failures. Thus, we extend the proposed soft sensor framework to handle the missing data situation. The effectiveness of our proposed soft sensor frameworks is finally demonstrated via an industrial polymerization dataset.