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.

The uneven distribution of process industrial data poses a significant challenge for soft sensor modeling. Hence, it is necessary to employ generative models to generate some new data used for augmenting the distribution fitting ability of the model by the full utilization of sparse regions. Existing generative models are mostly applied in the image and text generation fields, which are more suitable for discrete data where each variable only consists of integers. To enhance the applicability of generative models in industrial data modeling, a novel vector-quantized weighted-Wasserstein variational autoencoder based soft sensor is developed in this article to solve uneven distribution data. The proposed model further enhances the advantages of present generative models in generating qualified data by redesigning the model structure for clustering and training the data, thereby greatly alleviating poor generative performance caused by sparse regions. Specifically, first, the vector quantization strategy is designed to address the problem of sparse regions. After that, the sparse regions are transferred into the boundary of each group to generate more well-proportioned points. Then, the weighted and continuous variation distance mixture strategy is introduced to better evaluate the divergence between the real and learned distribution without mutation in the training part. Finally, a soft sensor model with the above data augmentation strategies is developed. By comparing it with three state-of-the-art augmentation strategies on a real polyester polymerization dataset, the superiority of the proposed soft sensor model with the novel data augmentation strategies is unequivocally verified.

1. All along, polyester fibers are the most widely used and the most popular synthetic fibers. In the past few decades, research on polyester fibers has mainly focused on fiber differential develop...