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 paper, we develop two novel sub-models based on deep VAEs (DVAE), which are furtherly utilized to establish a soft sensor framework. By the use of our first sub-model known as supervised DVAE (SDVAE), the distribution information of latent features can be obtained. This is used as a prior of the second sub-model known as 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.

Data-driven soft sensors, estimating the pivotal quality variables, have been widely employed in industrial process. This paper proposes a novel soft sensor modeling approach based on a two-stream $\lambda$ gated recurrent unit (TS- $\lambda$ GRU) network. First, factors $\lambda_1$ and $\lambda_2$ are implemented to alter the linear constraint existing in the original GRU unit, enriching the information passing through. Then a two-stream network structure is designed, equipped with some advanced network parameter adjustment techniques such as batch normalization and dropout rate, to learn diverse features of the various process data. Last, the learned features from the two streams are fused and a supervised learning regression layer is employed to decrease the error between the output and label. The application in melt viscosity index estimation for a real polymerization industrial process has demonstrated that the proposed TS- $\lambda$ GRUs algorithm for soft sensor modeling is more accurate and promising than other existing methods.