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Soft sensor plays an increasingly important role in modern industrial processes for estimating key quality variables which are hard to measure. With the development of deep learning technologies, soft sensors based on the deep learning methods have drawn great attention. Aiming to predict key quality variables, a supervised weighted nonlinear dynamic system (WNDS) model aided by the maximal information coefficient (MIC) is proposed in this article. The variational autoencoder is employed into the system for extracting nonlinear dynamic features. The supervised WNDS model can simultaneously analyze the correlations between variables and the relationships between historical samples and present samples. Furthermore, the proposed method is extended to a semisupervised form, in order to handle the imbalanced numbers between routinely recorded process data and limited labeled quality data. The prediction performance is validated by an industrial case.

The content of free calcium oxide (f-CaO) in clinker significantly determines the quality of the final cement production. However, in practice, the value of f-CaO content in clinker is off-line sampled manually with a significant time interval and then analyzed in a laboratory with a large time delay, which could meet the needs for monitoring and control of cement quality. To tackle this problem, this article proposes a data-driven model based on deep dynamic features extracting and transferring methods to build a virtual sensor for f-CaO content prediction. First, in this model, large-scale unlabeled data collected from the process distributed control system (DCS) take a vital effect in extracting nonlinear dynamic features along with the limited labeled data samples. Then, the extracted features are transferred to a powerful regression model, the eXtreme Gradient Boosting (XGBoost), for output f-CaO prediction. Besides, an incremental model updating strategy is proposed for the augment of online data samples, which facilitates the virtual sensor to adapt the process time-variant characteristics. Finally, the proposed virtual sensor is verified by a data set acquired from a real cement production process. Comparing with traditional statistical modeling methods, the prediction accuracy of f-CaO content is significantly improved.

Dynamic data modeling has been attracting much attention from researchers and has been introduced into the probabilistic latent variable model in the process industry. It is a huge challenge to extend these dynamic probabilistic latent variable models to nonlinear forms. In this article, a supervised nonlinear dynamic system (NDS) based on variational auto-encoder (VAE) is introduced for processes with dynamic behaviors and nonlinear characteristics. Based on the framework of VAE, which has a probabilistic data representation and a high fitting ability, the supervised NDS can extract effective nonlinear features for latent variable regression. The feasibility of the proposed supervised NDS is tested on two numerical examples and an industrial case. Detailed comparisons verify the effectiveness and superiority of the proposed model.