Accurate online detection or prediction of key quality variables provides critical reference information for optimizing and controlling operating variables in industrial processes. However, frequent fluctuations in raw material properties and environmental conditions often give rise to multiple data distribution modes within the same production process. Moreover, the inherent uncertainties and the energy-material coupling characteristics of industrial processes make it particularly challenging to uncover the underlying topological relationships among process variables. To address these issues, this article proposes a novel jointly shared-specific variational graph attention autoencoder (JSS-VGATE) model for spatial topological feature extraction and key quality variable prediction in multimode industrial processes. Specifically, a variational graph attention autoencoder is first constructed, which combines graph attention mechanisms with the variational inference architecture to adaptively learn the dynamic correlation strengths between adjacent nodes, thereby capturing complex variable interactions. Subsequently, a comprehensive loss function is designed to achieve high-fidelity extraction of representative latent feature distributions. Furthermore, a cross-mode jointly shared-specific learning framework is developed to simultaneously capture global shared features across modalities and preserve local specific features of each modality, while a learnable gated fusion mechanism is introduced to balance modality invariance and heterogeneity, thereby enhancing cross-mode information integration. Finally, the effectiveness and superiority of the proposed JSS-VGATE are validated on two representative real-world industrial datasets compared to other state-of-the-art methods.

Industrial multiprocess collaborative optimization presents significant challenges due to the intricate spatiotemporal dependencies inherent in modern process industries. Traditional optimization and reinforcement learning often treat subprocesses as independent entities, neglecting the fine-grained interdependencies among operational variables across different subprocesses. To fundamentally address this limitation, we introduce, a novel spatiotemporal topology-informed multiprocess collaborative optimization (STI-MCO) framework, which pioneers action-level interdependency modeling through an innovative spatiotemporal graph architecture. Rather than treating subprocesses as monolithic entities, STI-MCO operates at the operational variable level, enabling precise representation of both interprocess relationships and intraprocess dependencies through a hierarchical two-stage decision framework. This approach enables more precise coordination through fine-grained variable interactions, better temporal consistency via dynamic graph structures, and enhanced scalability compared with conventional agent-level methods. This paradigm shift from subprocess-level to variable-level collaboration, combined with dynamic graph-based coordination, enables extensive simulations and experiments conducted across three benchmark environments with progressively complex topologies to demonstrate that STI-MCO consistently outperforms baseline methods, achieving up to 38.9% improvement over centralized methods and 171.9% improvement over existing multiagent strategies. In addition, STI-MCO exhibits superior convergence efficiency, requiring significantly fewer training steps to achieve high performance. Its practical applicability is further validated through deployment in a real-world Salt Lake chemical process. By fundamentally shifting the optimization paradigm from holistic subprocess control to fine-grained variable-level collaboration, this work establishes a new framework for more effective optimization in complex industrial processes, particularly those with strong interunit coupling.

In [1], to maintain the integrity of the publication and uphold academic standards, a correction is requested for an identified error. Fig. 12 in the article is a duplicate of Fig. 13 due to an inadvertent mistake during the final stages of manuscript preparation.

Granger causality has emerged as a valuable tool in comprehending industrial processes and facilitating data modeling by unveiling the inherent relationships within the data. However, the characteristic of causality discovery tasks results in a lack of validation sets, making hyperparameter tuning reliant solely on intuition. Existing nonlinear Granger causality discovery methods suffer from insufficient accuracy and robustness due to the significant impact of hyperparameters. Hence, this article proposes an attribution-aided nonlinear Granger causality discovery method (Attri-NGC) for accurate and robust inference of Granger causality. Attri-NGC comprises two stages. In the first stage, a novel strategy is proposed to assess whether the variability in contributions, derived from deep learning-based attribution, can significantly reflect causality. This assessment transfers the robust advantage of attribution to causal discovery. In the second stage, a sparsity-inducing penalty targeted at ambiguous causality is defined to fine-tune the deep networks used for attribution. Our method transforms the paradigm of Granger causality discovery from a challenging deep networks training problem to a fine-tuning problem, leading to a substantial enhancement in the accuracy and robustness of causality discovery. The effectiveness of the proposed method is comprehensively validated on four public datasets and two industrial process datasets. The superior performance of Attri-NGC in supporting industrial process modeling effectively promotes the integration of Granger causality into practical applications for more interpretable process modeling.

In cloud manufacturing of industrial processes, the accurate online prediction of product quality is the basis for realizing decision-making and control of the manufacturing process. However, frequent fluctuations in working conditions and data noise restrict the application of data-driven methods in industrial sites. In addition, the constrained resources on edge devices limit their ability to automatically update or deploy complex models. To address these issues, this study proposes a Koopman-constrained hierarchical deep state-space model (KHSSM) and incorporates it into the innovative cloud-edge collaboration framework for industrial quality prediction. First, KHSSM integrates a state-space model, leveraging its advantage in modeling noisy dynamic data. Second, the Koopman operator is introduced to constrain the latent variables in the measurement space, enabling it to interpretably reflect the evolution dynamics of the system. In addition, novel strategies for model mismatch detection and model simplification are designed and deployed to improve the predictive accuracy and real-time efficiency of the cloud-edge collaboration framework. Finally, the effectiveness of the proposed method is verified by extensive experiments in a numerical simulation and a real-world industrial process.

In industrial processes, frequent communication failures and information corruption may result in the loss of entire blocks of industrial process data, which is also known as blackout missing data. The imperfect data of industrial time series impede the performance of subsequent modeling and control tasks. However, traditional matrix factorization or supervised learning data imputation methods are hardly applicable to the challenging task of recovering blackout missing data. The difficulty in imputing the blackout data stems from two major factors: the imputation process lacks the reference of co- evolutionary variables, and the blackout data have strong autocorrelation and drift in distribution. To address these issues, this paper develops a novel hierarchical imputation framework for recovering blackout data based on the masked transformer network (Masked-Former). First, a reconstruction block strategy with random masked points is innovatively proposed to improve the ability of the model to recover missing values under different working conditions for incomplete datasets. Then, based on the masked incomplete data set, the proposed method utilizes the local feature capture capability of convolutional networks and the sample-level long-range dependency capture capability of the self-attention mechanism to complete coarse-grained and fine-grained missing data imputation, respectively. Finally, extensive experiments are conducted to verify the superior performance of the proposed method on two real-world industrial data sets. Note to Practitioners—Inspired by the phenomenon that industrial process data often have missing data, this paper proposes a novel hierarchical imputation Masked-Former method for blackout missing data recovery. The method combines local data features with long-term time series dependency performance to improve completion performance. Then, the obtained completed data can help practitioners monitor the status of industrial field conditions. In addition, it is helpful to perform subsequent quality prediction and process monitoring tasks, allowing practitioners to quickly take preventative measures to avoid disasters and take corrective operations to return the plant to its normal operating range.

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.

The real-time recognition of operating conditions is always critical to ensuring the efficient and stable operation of industrial flotation processes. Although the widespread use of smart devices enables the availability of multimodal data in flotation processes, recognizing operating conditions using cross-modal data information is still challenging due to the modality gap. To address this issue, this article first proposes an innovative bimodal manifold autoencoder model to predict interested quality variables from the perspective of visual modality and auditory modality. Specifically, the well-designed intra- and intermodal manifold regularization constraints are introduced to fully learn the intrinsic manifold features within each modality and the interdependencies across modalities, thereby enhancing the cross-modal data representation ability of the developed prediction models. Then, based on the prediction values of quality variables, an adaptable multimodal fuzzy decision inference module is designed to recognize the operating conditions while counteracting the influence of fluctuations in feedstock properties. Finally, extensive experiments are conducted on two industrial flotation process datasets at distinct periods to validate the superiority of the proposed methods in terms of quality prediction and operation condition recognition tasks.

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.

The occurrence of abnormal operating conditions in industrial flotation processes adversely influences flotation concentrate yields and quality. It is imperative to prioritize the maintenance of normal operating conditions within the flotation process for process optimization. Considering the influence of the operation variable adjustment of different flotation cells on the final production indicators and the difficulty of establishing an adequate mathematical model, an intelligent collaborative decision-making plan based on multiple flotation cells is proposed in this study. First, multimodal data from industrial flotation sites are collected to emulate the comprehensive perceptual capabilities exhibited by human operators. Then, based on the concept of collaborative optimization, an intelligent collaborative decision-making plan for adjusting operating parameters is proposed. Finally, a series of experiments are conducted using actual industrial data. The results demonstrate the efficacy of the proposed intelligent collaborative decision-making plan in enhancing abnormal operation conditions, thereby establishing its promising potential for practical implementation in the industrial flotation process.

Multiple modes are ubiquitous in current industrial processes, and the amount of historical data contained in different modes may vary considerably. Insufficient data can easily lead to cold start problems when building a fault detection model for a particular mode. To solve this problem, while considering the similarity and differences between multiple modes, a deep model using domain adaptation based on feature separation is proposed for nonlinear process monitoring with few samples. The model extracts common features from modes and the data deficiency is compensated by transferring the domain knowledge from the source to the common features. On the other hand, to avoid missing useful information by focusing only on common features, the model also extracts the specific features of the target domain. Thus, monitoring performance is improved with the help of domain adaptation while taking into account the specific characteristics of the target domain. Furthermore, three detection indices are designed to monitor the common feature subspace, the specific feature subspace, and the residual subspace, respectively. The benefit of this is allowing more diagnostic information to be obtained when a fault occurs. The proposed method was tested with a numerical example and a real industrial hydrocracking process to verify the detection effectiveness.

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.

Since the change of operation condition is common in industrial processes, it could cause historical process data multimodal characteristics. When the working conditions are switched, the new mode will suffer small sample problem in the initial stage of the working mode switching, which brings difficulties to the monitoring of the new mode. Different from traditional modeling method which only considers the new mode data, this paper proposes a novel multi-source transfer learning method that considers both the historical multimode and new mode data. First, the common features of historical multimode data are extracted. Then, the extracted features are transformed into the model of new mode data. In order to alleviate the problem of insufficient samples of the current working mode, the common subspace of the new mode is obtained by combining the common features of the historical multimode with the new mode data. Finally, a numerical case and a real industrial hydrocracking process are used to validate the effectiveness of the proposed method.

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.