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.

In this paper, a novel variational inference semi-supervised GMM (VI-S2GMM) model is firstly pro-posed for semi-supervised predictive modeling in multi-mode processes. Parameters of Gaussian components are identified more accurately with extra unlabeled sam-ples, which improves the prediction performance of the regression model. Since all labeled and unlabeled data samples are involved in each iteration of parameter up-dating, intractable computing problems occur when fac-ing high-dimension datasets. To tackle this problem, a scalable Stochastic VI-S2GMM (SVI-S2GMM) is further proposed. Through taking advantage of stochastic gradi-ent optimization algorithm to maximize the Evidence of Lower Bound (ELBO), the VI-based algorithm becomes scalable. In SVI-S2GMM, only one or a mini-batch of sam-ples are randomly selected to update parameters in each iteration, which is more efficient than VI-S2GMM. Since the whole dataset is divided and transferred to iterations batch by batch, the scalable SVI-S2GMM algorithm can easily handle the big data modeling issue. In this way, a large number of unlabeled data can be useful in the mod-eling, which will further benefit the prediction perfor-mance. The SVI-S2GMM is then exploited for the predic-tion of quality-related key performance index (KPI). Two examples demonstrate the feasibility and effectiveness of the proposed algorithms.

In this article, a novel data-driven industrial quality predictor is proposed based on the cooperative deep dynamic feature extraction and variable time-delay (VTD) estimation. A semisupervised dynamic feature extracting (SSDFE) network is first proposed to extract nonlinear dynamic features to build a regression model for output quality prediction. Due to the inherent process structure and different positions of sampling instruments, time-delays commonly exist between process variables and quality variables, which may distort the original distribution and relationship in collected data. To recover the original process data pattern, the VTDs are regarded as model parameters and cooperatively obtained in the training process of the SSDFE network through an integer differential evolution algorithm. With the estimated VTD values, the reconstructed dataset further helps improve the prediction performance of the proposed SSDFE network. Two case studies are presented to demonstrate the superiority of the proposed method with VTD estimation.

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.

This article proposes a distributed parallel modeling and monitoring framework for plant-wide processes with big data. The “distributed” contains two layers of meaning. One is the spatially distributed modeling and hierarchical monitoring for the plant-wide process with multiple operating units. The other represents the distributed parallel modeling for big process data with various features. Under the framework, the distributed parallel mixture probabilistic latent variable model is proposed based on the stochastic variational inference algorithm and the parameter server architecture to cope with the big process data. Then, the model is utilized to develop the plant-wide hierarchical and distributed process monitoring algorithms, where the multilevel monitoring indexes and fault contribution indexes are established based on the Bayesian fusion algorithm for process fault detection and diagnosis. The performance comparison and visualization for the industrial plant-wide process case has demonstrated the reliability and superiority of the proposed algorithm and framework.