Due to the existence of complex disturbances and frequent switching of operational conditions characteristics in the real industrial processes, the process data under different operational conditions subject to different distributions, which means there exist different manifold structures under broad operations. Globally, the entire process data are distributed in a multimanifold structure. Nevertheless, the existing data-driven quality prediction methods do not consider the relationships among different manifolds of data and just treats the process data as a single manifold. How to extract effective multimanifold structure feature representation from complex process data and enhance online prediction ability are still challenging in the field of real industrial processes. To this end, in this article, a novel stacked multimanifold autoencoder (S-MMAE) is proposed for feature extraction and quality prediction. Especially, by introducing a new multimanifold regularization into the original loss function of stacked autoencoder at each layer, the intrinsic multimanifold structure information of data is utilized to guide the feature learning procedure. In this way, the learned features can offer a more comprehensive representation of original data and help enhance the prediction performance. At last, the application results in a practical hydrocracking process demonstrate that the proposed S-MMAE can achieve excellent prediction accuracy, which outperforms other state-of-the-art methods.

Accurate prediction of quality variables that are difficult to measure is crucial for industrial process control and optimization. However, the fluctuations in raw material quality and production conditions may cause industrial process data to be distributed in multiple working conditions. The data under the same working condition show similar characteristics, which are often defined as one data mode. Hence, the overall process data exhibit multimode characteristics, which brings great challenges in developing a uniform prediction model. Besides, the noninterpretability of the existing data-driven prediction models brings great resistance to their practical application. To address these issues, this article proposes a novel data mode related interpretable transformer network (DMRI-Former) for predictive modeling and key sample analysis in industrial processes. In DMRI-Former, a novel data mode related interpretable self-attention mechanism is designed to enhance the homomode perceptual ability of each individual mode while also capturing cross-mode features of different modes. Moreover, the key samples under different modes can be discovered using DMRI-Former, which further improves the interpretability of the modeling process. Finally, the superiority of the proposed DMRI-Former is verified in two real-world industrial processes compared to other state-of-the-art methods.

This article studies the performance monitoring problem for the potassium chloride flotation process, which is a critical component of potassium fertilizer processing. To address its froth image segmentation problem, this article proposes a multiscale feature extraction and fusion network (MsFEFNet) to overcome the multiscale and weak edge characteristics of potassium chloride flotation froth images. MsFEFNet performs simultaneous feature extraction at multiple image scales and automatically learns spatial information of interest at each scale to achieve efficient multiscale information fusion. In addition, the potassium chloride flotation process is a multistage dynamic process with massive unlabeled data. To overcome its dynamic time-varying and working condition spatial similarity characteristics, a semi-supervised froth-grade prediction model based on a temporal-spatial neighborhood learning network combined with Mean Teacher (MT-TSNLNet) is proposed. MT-TSNLNet designs a new objective function for learning the temporal-spatial neighborhood structure of data. The introduction of Mean Teacher can further utilize unlabeled data to promote the proposed prediction model to better track the concentrate grade. To verify the effectiveness of the proposed MsFEFNet and MT-TSNLNet, froth image segmentation and grade prediction experiments are performed on a real-world potassium chloride flotation process dataset.

Real-time prediction of key quality variables based on data-driven soft sensor modeling is an important way to monitor flotation status and product quality in the froth flotation process. However, the existing data-driven methods have limitations in terms of nonlinear feature extraction and interpretability. In addition, the prevalent correlations between process variables can help improve the model interpretability and feature extraction of the model, but there are still challenges in exploring the potential correlations between process variables due to the complexity of the industrial process mechanism and the presence of high noise in process data. These relationships can be abstracted as edges between nodes in a graph representation. To fully explore the deep process-related structural features of data, a novel stacked graph convolutional network (S-GCN) is proposed. First, S-GCN aggregates the features of neighboring nodes by an adaptive adjacency matrix to achieve the extraction of structural features among process variables. Then, the labeled quality variable data detected by laboratory assay analysis are utilized to pre-train the network layer by layer to obtain better initial parameters and adjacency matrices for quality prediction. Finally, the prediction model is constructed based on the learned parameters to explore the interpretability of model and perform prediction tasks. Experimental results on real industrial potassium chloride froth flotation process data show a significant improvement in the prediction accuracy and interpretability of the proposed method.

Missing data is a common phenomenon in the industrial field. The recovery of missing data is crucial to enhance the reliability of subsequent data-driven monitoring and control of industrial processes. Most existing methods are limited by the confined scope of feature extraction, which makes it impossible to rely on global information to impute missing data. In addition, they usually assume that industrial data is a uniform distribution across all working conditions, ignoring the differences in data evolution patterns across different conditions. To address these issues, this paper proposes an innovative scope-free global multi-condition-aware imputation framework based on diffusion transformer (SGMCAI-DiT). First, it extends the diffusion model by introducing conditional probability to capture the condition distribution of the entire data. Then, a noise prediction model is designed based on a novel double-weighted attention mechanism (DW-SA) to broaden the horizons of feature extraction. By discerning the inter-conditional interactions and the intra-conditional local information, the missing data imputation performance can be improved. Finally, the effectiveness and suitability of the proposed SGMCAI-DiT are verified on four real datasets sourced from industrial processes and two public non-industrial datasets. Extensive experimental results demonstrate that the proposed method outperforms several state-of-the-art methods in different missing data scenarios.