In the maritime Internet of Things (MIoT), automatic identification system (AIS) devices serve as mobile sensing nodes at sea and rely on satellite-based reception and relaying for global ship situational awareness. However, their signals are susceptible to spoofing and deception, posing a potential threat to maritime security. Satellite constellation design enables the effective detection and localization of non-cooperative AIS signals by optimizing satellite orbits in targeted regions. Nevertheless, balancing positioning performance with deployment cost remains a central challenge in constellation design. This paper proposes an average positioning error (APE)-driven satellite constellation design scheme. First, a global AIS signal distribution model is constructed using real-world AIS data. The probabilities of different coverage multiplicities under dynamic network topologies are analyzed, and benchmark localization errors for various positioning regimes are established. Based on these insights, an analytical APE formula is derived to quantitatively evaluate the positioning performance of satellite constellations. Then, we model the constellation design as a multi-objective continuous optimization problem and propose a balanced adaptive constrained genetic algorithm (BACGA) to optimize the constellation configuration parameters. Simulation results show that under the minimum positioning error constraint, the proposed algorithm generates the optimal low-Earth orbit constellation configuration that meets accuracy requirements and achieves good coverage of key areas at low cost.

In industrial soft-sensor modeling, the scarcity and imbalance of process data often lead to overfitting and poor generalization of predictive models. To address these challenges, this article proposes a transformation-aware diffusion model (TA-DM) that integrates transformed-domain supervision for data-augmented soft sensing. We explore transformation-aware designs and introduce a novel structure-breaking loss framework that enhances the denoising objectives of denoising diffusion implicit model and TimeDDIM by encouraging the model to disrupt redundant patterns and capture richer structural variations. In implementation, our proposed approach formulates loss functions across multiple transformation domains—including discrete Fourier transform, wavelet transform, and principal component analysis (PCA)—to explicitly guide the model in learning complementary and diverse structural features beyond the original time domain, significantly advancing the representational quality and diversity of generated time-series data. To further bridge the discrepancy between the data generated by TA-DM and the real data, we propose a just-in-time learning-based sample selection strategy. This strategy leverages the representation space of the diffusion model to adaptively select local samples relevant to the current operating condition through similarity matching. These samples are then fused with limited real data to improve soft-sensor modeling. This targeted augmentation effectively narrows the synthetic-real domain gap and enhances model robustness under complex conditions. Experimental results on a numerical example and real-world industrial datasets demonstrate that TA-DM significantly outperforms existing augmentation baselines under data-scarce and distribution-shifting scenarios.

Integrating graph neural networks (GNNs) with variational inference (VI) provides a promising direction for blending structured prior knowledge with observational empirical data for data-driven industrial process modeling. However, this task requires inference of the normalized adjacency matrix (NAM), where each row is normalized to be non-negative and to sum to one, matching the support of Dirichlet distribution. This requirement presents two main technical challenges: 1) intractable Kullback-Leibler (KL) divergence optimization between Dirichlet distributions, and 2) constrained optimization for standard- gradient-descent-based neural network parameter optimization. To handle issue 1), we first formulate the inference of the NAM as a differential equation simulation problem and derive an easy-to-implement expression to iteratively improve the KL divergence without explicitly computing it. Based on this, to alleviate issue 2), we involve Riemannian optimization to precondition this simulation procedure, which ensures that the inferred NAM conforms to the row-normalization constraint. After that, we collectively designate these approaches for NAM inference as Preconditioned-Simulation-Induced Variational Inference ($\psi$-VI), and provide theoretical guarantees of convergence. On this foundation, we propose a new graph neural network architecture, the Preconditioned-Simulation-Induced-based Variational Graph Neural Network ($\psi$-VGNN) for industrial process modeling. Finally, we validate the efficacy of$\psi$-VGNN through comprehensive experiments on industrial modeling tasks.

Nowadays, the application of federated learning in the industry has received a lot of attention and research. It achieves joint modeling across factories by sharing models or gradients and breaks factory-level data silos. However, due to the existence of reverse attacks, attackers can still infer the original data from the shared model parameters or gradients, which poses a serious threat to the privacy of industrial data and the practical deployment of industrial federated learning. Nevertheless, the model vulnerability, evaluation mechanism, and privacy protection methods against reverse attacks have not been thoroughly studied. Therefore, data privacy leakage of industrial federated learning is systematically discussed and thoroughly investigated in two specific scenarios in this article. The results show that the reverse attack against gradient aggregation achieves excellent recovery for all variables of industrial data, and gradient compression can limit this attack well. The inverse attack against model aggregation threatens privacy for some variables with poor robustness, but differential privacy (DP) is ineffective in protecting against such attacks. Consequently, when federated learning cooperation between factories is performed, privacy protection methods of gradient compression are needed if gradient aggregation is used. If model aggregation is used, variables that are less robust to model reversal attacks can be prevented by first finding them through experiments.

For soft sensor modeling of multimode chemical processes, a common method is to build an individual model corresponding to each mode. However, certain individual mode models may not be reliable due to the imbalanced data across different modes. The soft sensor built for one mode with sufficient data exhibits suboptimal performance for other modes with insufficient data. To address this issue, a deep transfer learning method is introduced for soft sensor and a deep transfer spatial–temporal slow feature regression framework (STSFE) is proposed. In the framework, a Siamese network is employed for slow feature extraction. In addition, the encoder–decoder structure is embedded for input reconstruction verifying the effectiveness of slow features. However, the Siamese network fails to consider correlation of variables in quality prediction. To address this limitation, the Siamese network is designed with an embedded spatial–temporal attention mechanism to construct the STSFE model, and the spatial–temporal slow features are augmented with the historical quality variable for current quality prediction. The STSFE model is initially trained for the mode with sufficient data (source domain), and then transfer learning is employed to facilitate knowledge transfer from the source domain to the target domain (the mode with insufficient data) by reusing the lower level extraction part of STSFE. The effectiveness of the proposed method is validated through a benchmark sewage treatment case and a real chemical process.

The prediction of key quality variables plays an important role in industrial status identification and monitoring. Due to process disturbance and hard device limitation, data collection in modern industries often exhibits high noise and irregular data sampling. To solve the above problems, this article proposes a stacked supervised and reconstructed input denoising autoencoder integrated with internal attention long short-term memory (SSRDAE-IALSTM) network for soft sensing modeling. First, a stacked supervised and reconstructed input denoising autoencoder (SSRDAE) is designed. Compared with the original DAE, each supervised and reconstructed input DAE (SRDAE) can simultaneously reconstruct the process data and quality data at the output layer, aiming to reduce information loss and extract quality-related features. Second, the denoised features are fed into the interval attention LSTM (IALSTM) to adjust the influence of different historical samples on the current sample in irregular sampling data to capture long-term temporal features. Finally, performance validations are carried out on an industrial debutanizer column and a penicillin fermentation process. The experimental results show that the proposed model can enhance the learning ability of process features and obtain better prediction performance than other comparison methods.

Modern industrial data is commonly dynamic and contains outliers, which challenges the accurate isolation of faulty variables in abnormal situations. To deal with process dynamics, a robust stacked probabilistic latent variable model is proposed, which is formed by stacking a series of static probabilistic latent variable models. A fault indicator matrix with the Bernoulli-Gaussian prior is constructed to indicate which process variables are faulty. The Bernoulli-Gaussian prior neatly accommodates the stacked structure of the indicator matrix so that rows corresponding to normal variables will shrink to zero. The stacked probabilistic latent variable model is further extended to deal with outliers by introducing an outlier indicator vector with the Beta-Bernoulli prior. The location and magnitude of the outliers can be successfully identified. Based on the robust stacked model, a variational Bayesian inference algorithm is developed to estimate unknown parameters. By using the piecewise affine approximation, the proposed fault isolation method can be extended to deal with nonlinear processes. The effectiveness and superiority of the method are illustrated by application studies to a simulation case and an industrial boiler case.Note to Practitioners—Data-driven fault isolation methods are critical to helping find the accurate root causes of industrial faults. While designing the fault isolation procedures, traditional data-based methods seldom consider autocorrelation and outliers characteristics in the collected process data simultaneously. This paper proposes an accurate and robust fault isolation method based on the stacked probabilistic latent variable model. For the full implementation of the model, it is necessary to: 1) construct the stacked structure of the fault indicator matrix based on the Bernoulli-Gaussian prior; 2) establish the outlier indicator vector with the Beta-Bernoulli prior to determine the location and magnitude of the outliers; 3) optimize the robust stacked model through the variational Bayesian inference algorithm with appropriately selected priors; 4) extract the faulty information of the industrial data to further enhance the faulty isolation performance. The two case studies have shown satisfactory fault-locating accuracy with the proposed model.

Nonlinear dynamical probabilistic latent variable model (NDPLVM) and its variants, essential in industrial inferential sensors, face challenges in latent space inference and deep learning (DL) backend implementation. The first issue arises from the assumption that covariates directly infer the latent variable, potentially leading to inaccuracies. The second issue involves the discrepancy between the probabilistic distribution function form of NDPLVMs and data sample-based operation of DL backends. Addressing these, this study introduces the optimal control-NDPLVM (OC-NDPLVM), a model designed to enhance performance by analyzing NDPLVMs learning and tackling these issues. For the first problem, NDPLVMs' learning is reinterpreted as an optimization problem, solved by alternating direction method of multipliers, and selecting the inference network's input via studying optimal solution's structure. To address the second issue, OC-NDPLVM adapts mean and covariance equations for compatibility with DL backends. This model's effectiveness is validated through experiments on inferential sensor datasets.

Chemical processes involve complex physical and chemical mechanisms that exhibit slow and fast-varying features and nonstationary characteristics, making it difficult for single model-based methods to satisfactorily extract both slow and nonstationary fast-varying features for soft sensing. To address this issue, we propose a two-stream slow and nonstationary fast feature (TS-SNFF) model. This model includes a slow feature stream (SF-stream) and a nonstationary fast feature stream (NFF-streama). In the SF-stream, an encoder-decoder based Siamese network and a linear mapping layer are used for slow feature extraction. It employs long-short term memory (LSTM) networks as encoder and decoder units. Meanwhile, the NFF-stream utilizes the LSTM, differential LSTM (D-LSTM), and linear mapping layers for nonstationary fast feature extraction. The D-LSTM unit is established by embedding differential operations into the LSTM cell to obtain the nonstationary information. Then, the obtained features are fused using the merging layer, followed by a multilayer perceptron as the regressor. The proposed TS-SNFF model is utilized to address the slow and fast-varying dynamics in nonstationary conditions and nonlinearity problem in chemical processes. The effectiveness and superiority of the proposed method are demonstrated in a numerical example and an industrial process case

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.

Due to the complex reaction mechanisms of industrial process units, causality and correlations exist between industrial process variables. Causal discovery algorithms have been utilized to discover the knowledge on variable relationships and guide process modeling and control optimization. However, most of them are limited by strict assumptions, such as linear relationships, additive noise, steady-state process, etc. Therefore, these methods cannot gain good performance for most practical industrial processes. To solve these problems, a novel weight comparison causal mining (WCCM) algorithm is proposed in this article for industrial causal graph discovery. It first trains a group of hidden layer neural networks with process data, then mines an undirected skeleton of the process variables according to the comparison of the network weights, and further determines the causal directions of the undirected edges in the skeleton to get a directed causal graph. The effectiveness of WCCM is verified on a benchmark and a practical industrial case from the urea synthesis process. The undirected and direct edges mined by WCCM show high consistency with the ground truths. Moreover, the causal discovery results of WCCM are utilized to guide the feature selection of soft sensor modeling, resulting in improved prediction accuracy and enhanced model interpretability.

For most modern industrial processes with strong nonlinear and multimodal characteristics, the traditional linear PLS-based soft sensor may not work well. Meanwhile, the traditional global modeling approach has a high demand for data representation capability in the face of complex data distribution, which poses a challenge to soft sensing. In addition, the unbalanced nature of data distribution exacerbates the model's neglect of local information to some extent, which enhances the overall prediction difficulty of the model. To this end, based on the PLS, a novel quality-relevant feature clustering (QRFC) model is proposed for the first time in this article from the view of local modeling of probabilistic fusion. In the QRFC, the PLS can give reasonable and explanatory guidance on the initial feature space for the modeling. Besides, the different data distributions are modeled using a unified perspective through a balanced grouping of the data. Further, a regulation variable is introduced to learn the feature space and complete the output-relevant clustering by iterative approach, to implicitly construct the correlation with the quality variable, forming a local approximation of the overall prediction capability. In general, the benefits of this framework, including better consistency of correlation and stronger abilities to deal with process nonlinearities and multimodality, lead to superior performance. To evaluate the feasibility and efficiency of the developed soft sensor, a real industrial case is taken as a demonstration. The experimental results demonstrate that the proposed method outperforms several other soft sensing approaches.

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.

The widely used Internet of Things (IoT) mobile devices (MDs) require fast processing capability to handle a large volume of computing tasks. Mobile-edge computing (MEC) can augment the capability of IoT MDs through offloading their computing tasks to the MEC-enabled base station (MEC-BS) that covers them. Most of the existing research works only focus on the computation offloading problems for a single MEC-BS. However, the load of a MEC-BS will rise as the increase of the scale of the offloaded tasks, especially during rush hours, and further it will result in deterioration of system performance. In this article, we propose a game-based multitype task offloading scheme among MEC-BSs. The tasks offloaded from IoT MDs can be further offloaded among MEC-BSs to alleviate high-load MEC-BSs. Aiming at balancing the computing delays of the tasks on each MEC-BS, a noncooperative game is formulated to model the computation offloading for the tasks with different types, indicated by computation amount, data size, and delay tolerance. The existence and convergence of the Nash equilibrium of the game are first proved using the variational inequality and regularization techniques. Then, we design a distributed iterative algorithm to efficiently solve the game problem. Simulation results show the fast convergence of our algorithm. The reduction of total computing delay optimized by our scheme can reach 45%–50% on average in multiple scenarios, and the superiority of our scheme is also demonstrated in comparisons with reference schemes.

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.

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.

For large-scale industrial plants, quality-related process monitoring is challenging because of the complex features of multiunit, multimode, high-dimension data. Hence, a hierarchical quality monitoring (HQM) algorithm based on the distributed parallel semisupervised Gaussian mixture model (dp-S2GMM) is proposed in this article. In HQM, a large-scale process is first decomposed into a group of unit blocks according to the process structure. Subsequently, in each block, a quality regression model with multimode big process data is built using the dp-S2GMM, which is derived from a scalable stochastic variational inference semisupervised GMM (SVI-S2GMM). With the regression model, a hierarchical fault detection and diagnosis scheme in both quality-related and quality-unrelated subspaces is proposed from the variable level, block level to plant-wide level. Finally, an industrial case study on the Tennessee Eastman process demonstrates the feasibility and effectiveness of the proposed HQM algorithm.

Virtual sensors have established themselves as effective tools in process industries for online estimating variables that are crucial but difficult to measure. However, multimode industrial processes render developing high-accuracy virtual sensors quite challenging. The main difficulties lie in that, in multimode processes, the distributions of process data are strongly non-Gaussian and the mathematical relationships between the explanatory and primary variables are highly nonlinear. Even within one operating mode, the primary variables could depend on the explanatory variables in nonlinear ways. In order to address these issues, this article proposes a virtual sensing approach named Bayesian nonlinear Gaussian mixture regression (BNGMR) with the aid of single-hidden layer feedforward neural networks (SLFNs). In the BNGMR, a fully Bayesian model structure that absorbs the merits of SLFNs and the mixture models is designed. In addition, we develop a training algorithm for the BNGMR to realize predictive virtual sensor development based on variational inference. Extensive assessments of the performance of the BNGMR are carried out using both artificial example and real-world industrial processes. The experiments have demonstrated the predictive advantage of the BNGMR over several benchmark methods and also have provided practitioners with good illustrations.

An enhanced nonlinear Gaussian mixture regression (NLGMR) algorithm is proposed for quality prediction of a nonlinear multimode process. The traditional Gaussian mixture regression (GMR) model has been utilized for quality prediction with a linear model in each local mode, which will not suit for many cases that nonlinear relationships exist between input and output variables. Besides, large scales of process data that can be used for modeling are partially labeled on account of the low sampling rate of quality variables. Most of the unlabeled samples are discarded while building the GMR model, which leads to the loss of information and limits the improvement of prediction accuracy. To tackle these two problems, a locally weighted semisupervised factor analysis model is developed in each mode of GMR. The locally weighted model divides the nonlinear process into pieces of linear model and the semisupervised factor analysis model can effectively take advantage of the massive unlabeled data. Moreover, the variational inference (VI) algorithm is conducted on the GMR model to determine the amount of process modes automatically. The proposed method is first verified by a numerical example and then applied in a multimode primary reformer to predict the oxygen content, where prominent improvements are obtained, compared with traditional methods.

Through calculating the similarity between the historical and the new query data samples, a probabilistic locally weighted prediction method based on supervised latent factor analysis (SLFA) model is proposed. In this method, the contributions of different historical samples are expressed through incorporating the similarity index into the noise variance of the process variables, which renders strong adaptability of the method for describing nonlinear relationships and abrupt changes of the process. Additionally, the proposed locally weighted method is extended to the semisupervised form, which is apparently more practical in real industrial processes, since the sampling rates of quality variables are much lower than those of ordinary process variables. Efficient expectation maximization algorithms are designed for parameter learning in both SLFA and semisupervised locally weighted LFA methods. Two real industrial processes are provided to evaluate the feasibility and the effectiveness of the newly developed soft sensors.