Nonlinear and multimode characteristics commonly appear in modern industrial process data with increasing complexity and dynamics, which have brought challenges to soft sensor modeling. To solve these issues, in this article, a dynamic mixture variational autoencoder regression model is first proposed to handle the multimode industrial process modeling with dynamic features. Furthermore, to deal with the partially labeled process data with rare quality values and large-scale unlabeled samples, a semi-supervised mixture variational autoencoder regression model is proposed, where a corresponding semi-supervised data sequence division scheme is introduced to make full use of the information in both labeled and unlabeled data. Finally, to verify the feasibility and effectiveness of the proposed methods, the models are applied to a numerical case and a methanation furnace case. The results show that the proposed methods have superior soft sensing performance, compared with the state-of-the-art methods.

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

In industrial processes, the sampling rates of process variables are discrepant because of the nature of instruments and measuring demands, which forms the challenging issue, that is, the multirate modeling in the data-driven soft sensor development. In this work, a multiresolution pyramid variational autoencoder (MR-PVAE) predictive model is proposed to solve this problem based on the deep feature extraction and feature pyramid augmentation. First, a multirate data filter is designed through a resolution searching strategy to turn the original process data into a multiresolution dataset. Then, the pyramid variational autoencoder (PVAE) is proposed to extract deep nonlinear features from the data with different resolutions. In PVAE, the augmented feature pyramid is constructed layer by layer to fuse extracted features from low resolution to the high. As a consequence, the extracted features with various resolutions are gathered to form the regression model, where the process information contained in data with discrepant sampling rates can be fully utilized. Due to the layer-by-layer enhanced features, the prediction accuracy of the soft sensing model are gradually improved. Meanwhile, an optimized training strategy is established to select the optimal feature pyramid for prediction. A numerical experiment and an industrial soft sensing case are given to validate the effectiveness and superiority of the proposed MR-PVAE model.

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.

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.

This letter studies the identification of a typical nonlinear time-series model, i.e., the exponential autoregressive model with unknown time-delay and colored noise. To deal with the identification difficulties caused by the time-delay, the identification model is transformed into an augmented one according to the redundant rule. Then, by means of the data filtering technique and the hierarchical principle, a novel three-stage filtering identification frame is presented to decrease the effect of the colored noise and complex nonlinearity. Moreover, a multi-innovation identification algorithm is proposed to improve the data utilization and estimation accuracy, and to jointly estimate the unknown model parameters and time-delay. The effectiveness of the proposed algorithm is evaluated by a numerical example.