Time series forecasting is essential across diverse domains. While MLP-based methods have gained attention for achieving Transformer-comparable performance with fewer parameters and better robustness, they face critical limitations including loss of weak seasonal signals, capacity constraints in weight-sharing MLPs, and insufficient channel fusion in channel-independent strategies. To address these challenges, we propose MDMLP-EIA (Multi-domain Dynamic MLPs with Energy Invariant Attention) with three key innovations. First, we develop an adaptive fused dual-domain seasonal MLP that categorizes seasonal signals into strong and weak components. It employs an adaptive zero-initialized channel fusion strategy to minimize noise interference while effectively integrating predictions. Second, we introduce an energy invariant attention mechanism that adaptively focuses on different feature channels within trend and seasonal predictions across time steps. This mechanism maintains constant total signal energy to align with the decomposition-prediction-reconstruction framework and enhance robustness against disturbances. Third, we propose a dynamic capacity adjustment mechanism for channel-independent MLPs. This mechanism scales neuron count with the square root of channel count, ensuring sufficient capacity as channels increase. Extensive experiments across nine benchmark datasets demonstrate that MDMLP-EIA achieves state-of-the-art performance in both prediction accuracy and computational efficiency.

A common scenario in aluminum electrolysis process is that the collected dataset contains different behavioral policies and some risky policies, such industrial scenario brings new challenges for offline reinforcement learning to learn safety and feasible optimization policy. This article proposes an offline multiobjective reinforcement learning with multicategory policy constraint for operation optimization decision-making (OODM) of the aluminum electrolysis process. The learned optimization policy can surpass the behavior policy while also meet the strict safety requirements of industrial operations. To alleviate the distribution shift problem on multicategory behavioral policy, we present a multicategory policy constraint in the actor network that utilizes the mixture Gaussian variational autoencoder (GMVAE) to implement behavior cloning between the behavioral policy and the learned policy. Based on the actor-critic reinforcement learning architecture, we design two critic networks for multiobjective optimization. Except for the operational performance critic network, an additional safety critic network is introduced to guarantee that the learned policy satisfies the strict safety requirements of industrial operations. We also conduct extensive comparative experiments on the real-world aluminum electrolysis process. Experimental results demonstrate that the proposed method can achieve superior performance against the other offline reinforcement learning algorithms.

Belief rule based classification system (BRBCS) is a useful model to handle classification problems. However, there are two problems that limit its applications. On the one hand, existing non-optimization based offline generation method can not fully extract information contained in historical data. On the other hand, there is lack of non-optimization based online modification method. In some applications, optimization based online modification can be inapplicable because of its high computational expense. Non-optimization based online modification is indispensable. In this paper, the efficient data-driven methods of belief rule offline generation and online modification are proposed, which belong to non-optimization based scope. The former changes traditional one-by-one observation into batch-by-batch observation. It directly generates a belief rule from a batch of historical data without batch fusing, so that more information can be extracted from a batch of historical data. The latter is based on multi-weight extension and actual meaning of rule parameter. The multi-weight extension is to handle the drawback that single weight is easy to cause quality degeneration of belief rules during process of online modification. The actual meaning of rule parameter is used to establish a heuristic mechanism of online parameter adjustment. The related experiments have demonstrated the effectiveness and advancement of proposed methods. BRBCS equipped with proposed methods can become more useful in some industrial applications.

The industrial flotation process involves multimodal data and cross-procedural knowledge, presenting significant challenges for knowledge system management and traditional knowledge graph (KG) construction methods. This study develops a large language model (LLM)-driven framework to construct a domain-specific multimodal KG. The Flotation Knowledge Tree ontology is designed as the structural backbone of the KG to organize multi-level operations and interactions while integrating heterogeneous flotation data. To enhance the LLM's domain adaptability, adaptive prompt optimization is proposed to iteratively refine the extraction template with flotation-specific examples and performance feedback, enabling more accurate triple extraction. Additionally, a fuzzy information entropy-driven Retrieval-Augmented Generation (RAG) method is proposed, leveraging fuzzy logic to assign weights to key terms and numerical contexts to preserve causal relationships and semantic integrity under data uncertainty. Furthermore, we established a two-stage LLM-driven pipeline to generate initial triples using a LoRA fine-tuned lightweight LLM with the optimized prompt and fuzzy RAG context, followed by refinement with a large-scale LLM for precision and ontology alignment. Validated triples are mapped onto the Flotation Knowledge Tree to form a structured, high-quality KG with minimal manual intervention. This framework fuses ontology structuring, fuzzy semantic retrieval, and LLM reasoning to enable automated, domain-tailored knowledge assembly for industrial flotation processes. The constructed KG is evaluated using the Flotation Knowledge Tree-based method, achieving a score of 0.92, with a structural score of 0.97 and a semantic score of 0.88, demonstrating robustness and coherence.

Multi-task video classification is a challenging task in video understanding, which is particularly evident in industrial applications. Existing multi-task learning methods enhance task performance by sharing representations of different tasks, which lacks systematic guidance with prior knowledge. In industrial process, abundant prior knowledge is underutilized for video understanding, because the prior knowledge is usually unstructured text which is hard to be embedded for video understanding. To address this limitation, we introduce a novel fuzzy rule graph representation that systematically encodes expert knowledge derived from manual video observations, providing a highly generalized and structured knowledge representation. Correspondingly, a novel multi-channel fuzzy rule graph embedding (MC-FRGE) method is proposed to model relationships among fuzzy rules. Then, a self-supervised two-stream attention autoencoder is constructed for visual feature extraction. Combining the MC-FRGE and the two-stream attention autoencoder, a novel knowledge guided multi-task video classification (KG-MTVC) framework is developed. Finally, experimental results on both the general video understanding dataset HMDB51 and a specialized zinc flotation process video dataset demonstrate the effectiveness of the proposed method. Our implementation is available at https://github.com/Galazxhy/KG-MTVC.git

Froth flotation is a complex industrial process involving multicell cascades. During the froth flotation process, a single-cell fault not only compromises its own functionality but may also propagate to adjacent cells, ultimately affecting the entire production line. Therefore, accurate and timely recognition of fault traces in the flotation process is critical for ensuring production stability. In this article, we propose a novel fault trace recognition framework using a dynamic edge weight-based cross-cell interaction graph Transformer and joint task learning. Initially, we propose a dynamic edge weighting method to update multicell node features, enhancing the model’s adaptability to dynamic industrial scenarios. Then, we introduce a cross-cell attention mechanism to decode the fault propagation path, explicitly capturing interaction-aware state features among multiple cells. Furthermore, we employ a two-stage joint task learning scheme, progressing from fault interval prediction to fault trace recognition, thereby significantly improving efficiency and accuracy. Finally, extensive experiments conducted on both benchmark datasets and real-world froth flotation processes demonstrate the effectiveness and robustness of the proposed method.

Accurate camera calibration is essential for obtaining precise three-dimensional information of a target. However, in the froth flotation process, it is challenging to position the calibration board support surfaces correctly. This difficulty makes it hard to capture high-quality calibration images from various angles, ultimately impacting the accuracy of the calibration results. To address this issue, we propose a planar template camera calibration method based on convolutional neural networks and synthetic data augmentation. Initially, we establish a virtual imaging scene to map the relationship between the feature map and camera parameters. Then, we conduct coarse camera calibration and apply synthetic data augmentation within specific range constraints to create a comprehensive calibration dataset. After that, we develop a deep calibration network named FSC-McCNN to facilitate the correspondence between the calibration feature map and camera parameters. This network comprises feature spatial coding (FSC) and multichannel convolutional neural networks (McCNN). The proposed approach effectively compensates for changes in camera focal length and requires only a single calibration image, thereby reducing the calibration workload at flotation sites. Experiments conducted on synthetic and real flotation datasets demonstrate the effectiveness and robustness of the proposed method.

Accurately forecasting the short-term traction load of railways is of great significance for optimizing the operation and dispatching of railway departments and ensuring the safety of power grids. The strong volatility and randomness of railway load signals make it difficult for traditional short-term load forecasting models to achieve high-precision predictions. To this end, this paper proposes a hybrid deep learning model with high temporal resolution characteristics to improve the accuracy of railway load forecasting. Variational mode decomposition (VMD) is used to decompose the original load sequence to reduce its volatility and forecasting difficulty, and its parameters are optimized by the improved beluga whale optimization (IBWO) algorithm. The Kolomogorov-Arnold Network (KAN) model is used to extract intricate spatial features from load data, aiming to enhance the efficiency and precision of feature extraction. The Informer model is used to extract long-term dependencies of sequences, aiming to improve the shortcomings of traditional methods that are difficult to effectively achieve modeling of ultra long time series. The advantage of the proposed forecasting method is to improve forecasting accuracy while reducing the difficulty of model deployment. The experimental results based on a real dataset from a substation on the Longhai Railway show that the VMD algorithm optimized by IBWO effectively improves the forecasting accuracy of the proposed method. Compared to traditional methods, the KAN model enhances the operational efficiency of the hybrid model. Furthermore, the proposed method significantly outperforms some traditional baseline models and the Transformer model in terms of both forecasting accuracy and operational efficiency.

This paper presents a hierarchical decision-making framework for autonomous navigation in four-wheel independent steering and driving (4WISD) systems. The proposed approach integrates deep reinforcement learning (DRL) for high-level navigation with fuzzy logic for low-level control to ensure both task performance and physical feasibility. The DRL agent generates global motion commands, while the fuzzy logic controller enforces kinematic constraints to prevent mechanical strain and wheel slippage. Simulation experiments demonstrate that the proposed framework outperforms traditional navigation methods, offering enhanced training efficiency and stability and mitigating erratic behaviors compared to purely DRL-based solutions. Real-world validations further confirm the framework’s ability to navigate safely and effectively in dynamic industrial settings. Overall, this work provides a scalable and reliable solution for deploying 4WISD mobile robots in complex, real-world scenarios.

Reagent addition control performance of zinc first rougher significantly affects the quality of the final product. It is common to control visual features to satisfactory feature setpoints, in order to realize satisfactory reagent addition control. However, existing methods usually use the historical data under the desired production state to generate the feature setpoint, and the historical data under the undesired production state are ignored. Moreover, the number of feed grade categories for feature setpoint generation is settled, and thus the richness of corresponding query rules for presetting the reagent addition rate is limited. In this situation, a reagent addition control strategy with a dual frequent pattern tree (dual FP tree)-based feature setpoint generator and knowledge core-based reagent fine presetting is proposed for zinc first rougher. First, a dual FP tree-based feature setpoint generator with the complementary input is constructed to fully utilize the dataset, where the main tree is designed to construct the knowledge repository and the secondary tree is established for optimization. Second, the optimized knowledge rules are taken as cores to construct an optimal operational pattern base for reagent fine presetting. Then, a designed feedback controller based on a fuzzy logic system with a three-way decision mechanism is explored to adjust reagent addition rates and try to make visual features track prescribed feature setpoints. The ablation results show effectiveness of the dual FP tree-based feature setpoint generator, reagent fine presetting and feedback controller. The comparative experimental results demonstrate the potential of the proposed control strategy. Note to Practitioners—This article is motivated by the problem of reagent addition control in the zinc flotation process. This article focuses on making visual features track prescribed feature setpoints by adjusting reagent addition rates, aiming to achieve the goal of controlling the zinc concentrate grade within its acceptable range. However, two challenges exist for control: the historical data under the desired production state are usually used during feature setpoint generation, while latent process knowledge in the historical data under the undesired production state is ignored; the number of feed grade categories for feature setpoint generation is settled during reagent presetting, which means the richness of corresponding query rules for presetting the reagent addition rate is limited. Therefore, this article suggests a reagent addition control strategy with a dual FP tree-based feature setpoint generator and knowledge core-based reagent fine presetting to address those problems. A suitable feedback controller is designed for outputting reagent addition adjustment values to qualify the concentrate grade, which is based on feature setpoint generation and reagent fine presetting. The experiments are carried out for evaluation. The evaluation shows the potential and superiority of the proposed approach in terms of decision-making and automation control in froth flotation.

In order to integrate the advantages of Model Predictive Control (MPC) and artificial neural networks, this paper proposes a control framework based on sequence generation (SGCF). The main idea of SGCF is to first generate an ideal subsequent state trajectory conditioned on the current working condition, and then infer feasible control sequences accordingly. To achieve implicit optimization of the performance metric during sequence generation, different learning weights are assigned to labeled samples. A confidence score based on model interaction is further introduced to evaluate the reliability of each inference and assist training. Theoretical analysis is provided to explain how the sequence generation network learns under performance guidance, promoting better trajectories. The effectiveness of SGCF is validated through experiments on inverted pendulum control and lead-zinc rougher flotation reagent control. Multiple baseline methods are considered, including state feedback control (SFC) models and data-driven MPC approaches. Results demonstrate that SGCF achieves advantages in both control performance and cost, while maintaining favorable inference efficiency. Moreover, SGCF exhibits potential for interpretable reasoning.

Key performance indicator (KPI) reflects the quality and efficiency of manufacturing operations, and KPI forecasting enables proper operations or controls in many industrial processes. However, existing KPI forecasting methods are inadequate for managing the advance prediction of KPI across multiple cycles effectively, which impedes precise and timely control in complex industrial processes. Therefore, we propose an adaptive encoder-decoder framework with partial teacher forcing strategy (PTF-ED) to enable flexible multihorizon KPI forecasting. First, we employ an encoder that processes the input time series and an attention layer to generate the context vectors. Then, we divide the measured KPIs into delayed and current time series, and design a delayed decoder and a current decoder in series to make the delayed and current time series correspond to the input time series. Especially, we propose a partial teacher forcing strategy to utilize the measured KPI efficiently and tackle the challenge of exposure bias in the current time series between training and inference phases. Moreover, we introduce a weighted multihorizon forecasting constraint in the model training loss to constrain the input-output correspondence across different sample intervals. The effectiveness of the proposed model has been validated through both a numerical simulation study and a case study in a real-world zinc flotation process.

In high-stakes process industries, the Basic Process Control System (BPCS) relies on conventional control to enhance productivity, while the Safety Instrumented System (SIS) uses safety functions to maintain safety. Compared to the BPCS, attackers targeting the SIS can modify safety function activation conditions to trigger them prematurely or to evade the activation of the safety function. While various attack detection methods focus on the BPCS, they often overlook the SIS. This can lead to undetected safety breaches, significantly increasing the risk of catastrophic fault. Recent methods face three key limitations that hinder their practical application to SIS. First, both attackers and engineers can exploit the hot update mechanism of SIS to add or modify control logic. However, current methods lack verification for the newly added or modified logic. Second, current methods are unable to assess the rationality of dangerous value ranges. Third, these methods struggle to distinguish between faults and attacks, making it difficult to determine the appropriate time to activate the SIS’s safety function. To overcome these limitations, we propose SecureSIS, a method for securing SIS safety functions by leveraging the safety attributes of the SIS and incorporating information from the BPCS. The core of SecureSIS includes: 1) using the safety attributes of the SIS to verify automatically extracted candidate control logic detection rules; 2) utilizing information from the BPCS to verify automatically extracted candidate value range detection rules; and 3) distinguishing between safety function attacks and industrial process faults with validated rules and integration of process data from BPCS. Our scheme was evaluated using a Tricon SIS controller deployed on a gas pipeline network platform. The results indicate that SecureSIS achieved 97.3% accuracy in detecting data injection attacks and a detection accuracy of 96.0% for control logic modification attacks. Compared with the other representative detection approaches, our scheme has better detection performance.

In real-world industrial processes, it is crucial to avoid damaging faults to ensure steady operations. However, new faulty conditions can arise in variable production environments. Traditional fault diagnosis methods perform poorly with few or no fault data for training. To address this issue, we propose a graph-regularized coupled dictionary learning (GRCDL) method for zero-shot fault diagnosis in industrial processes. Our method enhances the coupled dictionary learning (CDL) framework by integrating class prototype learning, which utilizes the rich information of seen class faults in the data feature space. A feature correlation function is also designed to facilitate the transformation and reconstruction of data and semantic features in the shared space, preventing certain classes from becoming the nearest neighbors of unrelated classes in a low-dimensional semantic space. To mitigate noise interference and preserve local manifold structures, the graph-regularized constraint is developed to enhance the robustness and locality of the coupled dictionaries. Considering the different underlying distributions between unseen and seen faults, a novel domain adaptation function is proposed. This function uses the learned coupled dictionaries as mediums for knowledge transfer and update from seen to unseen classes and effectively learns the class prototypes of unseen faults. Extensive experiments in industrial processes verify the superior performance of our method for zero-shot fault diagnosis.

Accurate and stable feed-grade monitoring is essential for flotation and reagent control. Although some monitoring models for feed grade have been developed in recent years, they always use a group of time-series data with a fixed time step as input, and neglect the roles of models at different training steps. Therefore, to enhance the stability and accuracy of the feed-grade monitoring model, we propose a feature-ensemble model with an adaptive self-ensemble module. First, we use multiple groups of input vectors with different time steps as inputs to the monitoring model. Then, we introduce an adaptive self-ensemble module (ASE module) to fully use the models at different training steps with an adaptive adjustment mechanism and a self-ensemble module. After that, we construct a feature-ensemble model (FE model) embedding the ASE module to handle the multiple time series with different time steps. Effectiveness of the proposed monitoring model is validated both on a numerical example and an industrial example in froth flotation. In the numerical example, the root mean squared error (RMSE) of the three FE models with the ASE module decreases by 0.0090 to 0.0159, and the R-squared ($R^{2}$) score increases by 0.0013 to 0.0035, compared with the three single models. In industrial application, the RMSE of the three FE models with the ASE module decreases by 7.20% to 9.70%, and the$R^{2}$increases by 6.71% to 7.34%, compared with the three single models. This shows our framework can improve the feed-grade monitoring performance.

Shape shift refers to the phenomenon where by amplitude and scaling of samples of the same fault vary with the environment. How to incrementally diagnose industrial faults under shape shift samples with directly interpretability is a challenging problem. Therefore, a new convertible shapelet learning with incremental learning capability method is proposed in this study. First, incrementally learning under shape shift samples is formulated as how to learn new scaling shift and amplitude shift samples in industrial process. A shape shift detection method is proposed to detect new shape domain. Second, a new parameter initialization method for shapelet learning is proposed, which employs pretraining technology to obtain better initial shapelets. Third, the convertible shapelet-transformed representation is proposed to enhance informativeness of shapelets. An incremental convertible shapelet learning loss is proposed to alleviate catastrophic forgetting in incrementally training new shape time series. By comparing with other state-of-the-art methods, experiments on the Tennessee Eastman Process and real-world aluminum electrolysis process demonstrate the superior performance of the proposed method in accuracy, alleviating catastrophic forgetting and interpretability.

Accurate grade monitoring in froth flotation is crucial for improving process efficiency and mineral recovery. Current grade monitoring models typically use mean video features and fail to capture feature variations within individual videos. Furthermore, they usually embed the most recently available feed grade into the visual feature vector without providing a refined embedding of feed grade. Therefore, we propose a flotation grade monitoring model with feed grade refined embedding (FGRE) and nonoverlapping patch encoding (NOPE). First, we develop an FGRE module to generate fine-grained feed grade representations. This module extracts the time series of critical feed grade elements by physical topology of the flotation process, and it employs a grouped weight-sharing time-lagged-recurrent neural network (RNN) to fuse multisource temporal data. Then, we introduce an RNN with NOPE to encode video patches and extract dynamic information from each froth video. This network enables the capture of subtle visual feature variations within each individual video. After that, we implement a multivideo temporal extraction strategy to capture dynamic temporal features across multiple videos for grade monitoring. Experiments are conducted on a real-world zinc flotation process. Our proposed approach can be integrated into most existing flotation grade monitoring models, significantly enhancing their monitoring performance.

Complex imaging environments and conditions in real-world scenes pose significant challenges for stereo matching tasks. Models are susceptible to underperformance in non-Lambertian surfaces, weakly textured regions, and occluded regions, due to the difficulty in establishing accurate matching relationships between pixels. To alleviate these problems, we propose a multi-scale geometrically enhanced stereo matching model that exploits the geometric structural relationships of the objects in the scene to mitigate these problems. Firstly, a geometric structure perception module is designed to extract geometric information from the reference view. Secondly, a geometric structure-adaptive embedding module is proposed to integrate geometric information with matching similarity information. This module integrates multi-source features dynamically to predict disparity residuals in different regions. Third, a geometric-based normalized disparity correction module is proposed to improve matching robustness for pathological regions in realistic complex scenes. Extensive evaluations on popular benchmarks demonstrate that our method achieves competitive performance against leading approaches. Notably, our model provides robust and accurate predictions in challenging regions containing edges, occlusions, reflective, and non-Lambertian surfaces. Our source code will be publicly available.

Real industrial process data from various domains often exhibit divergent distributions, may occupy distinct feature spaces, and are occasionally unlabeled, which limits the effectiveness of conventional process monitoring methods. To address these challenges, we propose an adaptive discriminative transfer dictionary pair learning (ADTDPL) method with attribute embedding for generalized cross-domain industrial process monitoring. Specifically, this method aligns the feature spaces of source and target domains by the aligned transfer reconstruction, enabling the transfer of knowledge through a common synthetical dictionary. Concurrently, semantic attributes relevant to process knowledge are seamlessly fused into data information via attribute embedding, enhancing the transferability and interpretability of dictionary pairs. Considering the relative significance of marginal and conditional distributions, an adaptive distribution consistency function is designed to better reduce the distributional discrepancies. And the discriminative structure regularization is developed to ensure the discrimination of the dictionary pairs and their corresponding coding coefficients. Furthermore, in the absence of target domain labels, a novel selective pseudo-labeling strategy is advanced to adaptively update pseudo-labels. The superior performance of our method for cross-domain process monitoring is verified on the Tennessee Eastman platform and in practical aluminum electrolysis processes (AEPs).

The causal structure learning for streaming features (CSLSFs) faces the following challenges: 1) the precision of learned causal structures is limited due to the score-based learning method and 2) they fail to detect the latent confounders. To address the challenges, this article proposes a novel causal structure learning method with linear non-Gaussian acyclic models for streaming features (LiNGAM-SFs), which utilizes the causal identifiability of the data. It is the first time to utilize LiNGAMs for online causal structure learning. First, we utilize the classical SF algorithm to learn the causal skeleton. This article provides the property of this skeleton, proving that two adjacent variables on an edge is one of three possible structures. Second, we give two propositions and identify the causal directions in the presence of latent variables (ICDPLV) subalgorithm to distinguish among the three structures and precisely identify the causal directions. In addition, the subalgorithm can output a candidate set of latent confounders from a local perspective. Finally, the detecting latent confounder (DLC) subalgorithm detects the latent confounders in the candidate set with a global perspective. The precision of the proposed method is increased at least by 11% on average than those of the state-of-the-art method. Furthermore, the experiments verify that the LiNGAM-SF method is able to detect the latent confounders.

Modern industrial processes often exhibit non-Gaussian, multimodal, and time-varying behaviors due to fluctuating operating conditions, raw material variations, and external disturbances, such as sensor failures and noise. These complexities pose significant challenges for robust fault detection and identification, critical for ensuring process stability and product quality. To tackle these challenges, this article proposes an innovative robust fault identification framework that leverages a variational Bayesian student’s$t$-mixture model (VBstMM) with a lifelong learning mechanism (LLM), named VBStMM-LLM. VBStMM-LLM is particularly effective for multimodal, time-varying industrial processes due to two core innovations: first, a robust mixture modeling approach grounded in the Student’s$t$-distribution with variational Bayesian inference, which accurately captures complex process dynamics while mitigating the impact of noise and outliers; and second, the innovational integration of LLM that enables adaptive model updates, preserving historical knowledge, and preventing catastrophic forgetting. Extensive experiments on the Tennessee Eastman benchmark process and the ventilation exhaust fans utilized in a continuous casting line at a Chinese steel smelting facility demonstrate the framework’s superior performance. For the three operational modes of the TE process, VBStMM-LLM achieved fault identification accuracy of 94.5%, 93.6%, and 97.7%, respectively. Remarkably, for the fault diagnosis of VEF task, it achieved a perfect rate of 100%. These results highlight VBStMM-LLM’s exceptional robustness, accuracy, and adaptability, underscoring its potential for widespread industrial applications.

Accurate identification of multimodal Superheat Degree (SD) plays a critical decision-making role in Aluminum Electrolysis Process (AEP). Because the labeled SD data are scarce and annotation is expensive in real-world AEP, it is a challenge to develop a well-behaved SD identification model. In this paper, a Contrastive Anchors-based Label Propagation (CALP) algorithm is proposed to construct a Deep Semi-Supervised Learning (DSSL) model, called CALP-DSSL, for better identifying SD by utilizing large-scale unlabeled data and limited labeled data. Specifically, to improve the reliability of affinity graph and its affinity matrix, positive anchors and negative anchors are generated by estimating the uncertainty of label predictions, which can guide the correct direction of inferring pseudo-labels. For tackling the unsupervised domain adaptation problems existing in AEP, we propose a Variational Information Domain Adaptation (VIDA) module using the pseudo-labels generated by CALP to fine-tune the deep Variational Information Bottleneck (VIB) network. Finally, the overall CALP-DSSL model is trained by the Mini-Batch Incremental Learning (MBIL) technique in local level. It matches the nearest neighbors based on batch embedded features, which provides more distinct information flow during subsequent label propagation to construct the affinity graph. Benchmark datasets verify the superiority of CALP algorithm. Case study on a real-world AEP shows that CALP-DSSL model improves the accuracy of SD identification over other state-of-art DSSL methods. Our source code is available at https://github.com/wjiecsu/CALP-DSSL.Note to Practitioners—The focus of this paper is to develop a well-behaved SD identification model based on the improved deep semi-Supervised learning (CALP-DSSL) model. In this model, a Contrastive Anchors based-Label Propagation (CALP) algorithm is used to predict pseudo-labels to construct DSSL model for improving the reliability of the generated pseudo-labels. In this way, a Variational Information Domain Adaption (VIDA) module is constructed to solve the domain shift problems existed in the unstable working conditions. Moreover, the overall model is trained by Mini-Batch Incremental Learning (MBIL) strategy to build better underlying representation for supporting effective label propagation.

Edge preserving filter is the basis of many computational photography and image processing. This can be achieved by global optimization method or local filtering method. Generally, the filtering results of global optimization methods are better than that of local filtering methods, and local filtering methods usually run much faster than global optimization methods. In this paper, a globally optimized method called iterative self-guided image filter (isGIF) is extended based on the assumptions of the guided image filter (GIF), which can produce high-quality edge-preserving filtering results by using the input image itself as the guidance image. Some comparisons with other edge-aware filters are presented to show the advantages of our method. Extensive experiments demonstrate that our filter generates images with better visual quality, while reducing/avoiding halo artifacts in the final image, and the running time is competitive.

Early classification predicts the class of the incoming sequences before it is completely observed. How to quickly classify streaming time series without losing interpretability through early classification method is a challenging problem. A novel memory shapelet learning framework for early classification is proposed in this article. First, a memory distance matrix is introduced to store the historical characteristics of streaming time series, which can alleviate repetitive calculations caused by the growing length of time series. Second, early interpretable shapelets are extracted in the proposed method by optimizing both accuracy objective and earliness objective simultaneously. The proposed method employs end-to-end learning, which allows the model to directly learn early shapelets without the necessity of searching for numerous candidate shapelets. Third, an objective function of memory shapelet learning is proposed by overall considering accuracy and earliness, which can be optimized by gradient descent algorithm. Finally, experiments are conducted on benchmark dataset UCR, Tennessee Eastman process, and real-world aluminum electrolysis process in China. Comparable results with other state-of-the-art methods demonstrate the superior performance of the proposed method in interpretability, accuracy, earliness, and time complexity.

Virtual sample generation (VSG) is an important technology for dealing with small sample learning in some industries. Using evolutionary computation algorithms to solve virtual sample generation is a promising way. However, two issues remain unaddressed in the existing VSG approaches: estimating the distribution of original samples and ensuring the authenticity of virtual samples. Thus, this paper proposes a novel Virtual Sample Generation approach based on genetic algorithm (GA) combing with Information Gain and Acceptance-rejection Sampling, abbreviated as VSG3A2. First, this work develops the ARS-VAD subalgorithm, by integrating the acceptance rejection sampling method into the crossover and mutation operations of GA. The algorithm ensures that the distribution of offspring attribute values is close to the distribution of original samples at attribute level. Second, this work presents the IG-VSS subalgorithm, which is combined with the idea of minimizing absolute information gain, to find the optimal offspring sample as a virtual sample in each loop, ensuring the authenticity of virtual samples at the sample level. To the best of our knowledge, this is the first work that introduces the concept of information gain into VSG. Extensive experiments on four public datasets from various fields fully demonstrate that the VSG3A2 is more competitive than six state-of-the-art VSG approaches. The MAE, the RMSE and the MAPE metrics of prediction models, trained on virtual samples generated by the proposed VSG3A2, are reduced at least by 19.78%, 19.56%, 20.16% on average than that of the best compared VSG approach, respectively.

Reagent addition control level of the zinc first rougher has a significant impact on quality of the zinc concentrate. As froth visual features are important indicators of working states in froth flotation, they are usually controlled to optimal setpoints by reagent addition for the desired concentrate. Existing methods usually construct a rule base for feature setpoint generation and design an error-driven feedback controller for reagent addition. However, there are still some issues: 1) a portion of data is used for rule base establishment and knowledge in remaining data is ignored; 2) as the rule base is sparse, it may lead to match failures caused by insufficient knowledge; 3) existing controllers only consider the error at the current time, while ignore the temporal information in error sequences. Therefore, we propose a reagent addition control strategy with the dual rule-based weighted fuzzy interpolative reasoning module and temporal encoder-decoder Bayesian network. Firstly, we design a dual rule base with complementary data to fully mine knowledge. Then, we explore a weighted fuzzy interpolative reasoning module for feature setpoint generation. This module selects several nearest neighbor rules in a positive rule base as interpolative candidates and determines rule weights via the nearest neighbor rules in the negative rule base. After that, we introduce a temporal encoder-decoder network by taking temporal error sequences as the input to recognize working states, and use a Bayesian network to realize reagent adjustment. Ablations and comparative experiments on industrial data show the effectiveness of the proposed control strategy.

Online assessment of the molten iron quality of a blast furnace ironmaking process strongly depends on reliable measurement of silicon (Si) content. In this article, we propose a novel cooperative strategy to train the data-driven prediction model and estimate variable time delay (VTD) values. First, a dynamic deep network based on stacked denoising autoencoders (D-SDAE) with the ability to describe process nonlinearity and time-varying is designed for Si estimation. Then, time delay between the process variables and Si, which may disrupt the data distribution pattern (i.e., the real input–output relationship), is recovered in the modeling process. It is an overlooked data feature that occurs due to material transportation times, installation location, and the analysis period of sampling equipment. The VTD values are considered to be the parameters of the D-SDAE model and obtained in the training process by the proposed double-scale collaborative search particle swarm optimization algorithm. The effectiveness of the proposed VTD-based D-SDAE model is validated in a numerical simulation and an industrial ironmaking plant, and a marked improvement in the prediction performance is achieved when VTD information is considered.

Few-shot new faults are constantly emerging due to the dynamic environments and operations in the industrial process. It is a challenge for existing fault diagnosis methods to diagnose few-shot new faults without forgetting old faults by fine tuning the base model. This article defines this challenge as few-shot fault incremental learning problem, and proposes a multiview shapelet prototypical network to solve this problem. First, a multiview metalearning framework that simulates true incremental tasks and combines multiview information is proposed in this article to build a generalizable feature space for unseen classes. Second, a multiview shapelet prototypical classifier is proposed to enhance the generalization ability of shapelets in adapting new faults with few samples. Third, multiview metacalibration modules based on transformers are proposed to fuse multiview information and calibrate prototypes and embedded features into a distinguishable space. Finally, experiments are conducted on the benchmark Tennessee Eastman process and the real-world aluminum electrolysis process. Experimental results illustrate that the proposed method is better than the existing methods in terms of interpretability, alleviating catastrophic forgetting, and reducing time complexity.

Deep learning models are increasingly being used as effective techniques for industrial process modeling. However, decisions generated from deep learning models can hardly to interpret and cannot provide convinced results to users. To break the traditional tradeoff between accuracy and interpretability of deep neural network for industrial process modeling, we propose a deep probabilistic network-based knowledge-guided framework, which injects external knowledge into the deep neural network to guide its training process. In this framework, a deep probabilistic regression model (DPRM) is first developed to learn Gaussian latent feature representation yet establish regression relationship. Then, the external knowledge represented by fuzzy rules, which can evaluate the fitness of current network output and characterize constraints of the process, is encoded into a same structured Gaussian latent feature representation. We propose to inject the feature representation of external knowledge into DPRM using Kullback–Leibler divergence between two Gaussian distributions. The proposed knowledge-guided framework is evaluated on the Tennessee Eastman Process and the real-world aluminum electrolysis process. Experimental results highlight that our proposed approach achieves better prediction performance than the compared methods, also interprets the results.

Numerous studies on learning algorithms have been done in the neural networks community, however concerning to training strategy is limited. In this article, to enhance the performance of fuzzy neural network (FNN) in industrial process identification, an FNN based on two-stage training (TSTFNN) is proposed. First, to initialize TSTFNN, we propose a supervised clustering method. It determines the initial centers and number of neurons for TSTFNN through clustering part of samples based on their labels. Then, the gradient-based algorithm is employed to further learning the parameters of TSTFNN. To improve its generalization performance, we developed a two-stage training scheme. In the first stage, a standard 10-fold cross-validation is executed to learn parameters. The samples whose prediction errors exceed a preset threshold are utilized to train the network in the second stage. According to Lyapunov criterion, we show the convergence of TSTFNN if the learning rate is selected in an appropriate range. The effectiveness of TSTFNN is validated by simulations on two benchmark problems. The proposed TSTFNN performs better and outperforms the state-of-the-art. Compared with supervised long short-term memory, root mean square error is decreased by 17%. Then, we apply it to the industrial rougher flotation process for soft sensor modeling. The experimental results show that TSTFNN achieves a satisfactory prediction performance.

Making proper decision online in complex environment during the blast furnace (BF) operation is a key factor in achieving long-term success and profitability in the steel manufacturing industry. Regulatory lags, ore source uncertainty, and continuous decision requirement make it a challenging task. Recently, reinforcement learning (RL) has demonstrated state-of-the-art performance in various sequential decision-making problems. However, the strict safety requirements make it impossible to explore optimal decisions through online trial and error. Therefore, this article proposes a novel offline RL approach designed to ensure safety, maximize return, and address issues of partially observed states. Specifically, it utilizes an off-policy actor-critic framework to infer the optimal decision from expert operation trajectories. The "actor" in this framework is jointly trained by the supervision and evaluation signals to make decision with low risk and high return. Furthermore, we investigate a recurrent version of the actor and critic networks to better capture the complete observations, which solves the partially observed Markov decision process (POMDP) arising from sensor limitations. Verification within the BF smelting process demonstrates the improvements of the proposed algorithm in performance, i.e., safety and return.

As the profit and safety requirements become higher and higher, it is more and more necessary to realize an advanced intelligent analysis for abnormity forecast of the synthetical balance of material and energy (AF-SBME) on aluminum reduction cells (ARCs). Without loss of generality, AF-SBME belongs to classification problems. Its advanced intelligent analysis can be realized by high-performance data-driven classifiers. However, AF-SBME has some difficulties, including a high requirement for interpretability of data-driven classifiers, a small number, and decreasing-over-time correctness of training samples. In this article, based on a preferable data-driven classifier, which is called a reinforced k -nearest neighbor (R-KNN) classifier, a delicately R-KNN combined with expert knowledge (DR-KNN/CE) is proposed. It improves R-KNN in two ways, including using expert knowledge as external assistance and enhancing self-ability to mine and synthesize data knowledge. The related experiments on AF-SBME, where the relevant data are directly sampled from practical production, have demonstrated that the proposed DR-KNN/CE not only makes an effective improvement for R-KNN, but also has a more advanced performance compared with other existing high-performance data-driven classifiers.

Improving the robustness of the soft sensor model of industrial processes is an important yet challenging problem for a large amount of noise interference and missing data in practical industrial data. In this article, an adversarial training-based deep supervised variational autoencoder (Adv-DSVAE) is proposed to enhance the performance of industrial soft sensor models. Specifically, a supervised variational autoencoder (SVAE) is first designed to extract the quality-relevant feature representation. Then, a deep SVAE (DSVAE) model is constructed by stacking the hidden features extracted by SVAE, such that a high-level output-related feature representation can be captured. In this way, the missing data situation can be handled by the probabilistic latent feature representation extracted in DSVAE. To improve the robustness of a DSVAE-based soft sensor model, an adversarial training method is designed, in which adversarial examples are generated by adding perturbations to the last hidden feature of DSVAE, such that the model can perform well on both clean and perturbed feature representations. We further provide theoretical convergence analysis for the proposed Adv-DSVAE to guarantee its successful practical application. The ablation studies confirm that industrial quality prediction using the adversarial training strategy can ensure better robustness. Case studies on both the debutanizer column process and the real-world aluminum electrolysis process validate the superiority of Adv-DSVAE.

A dilemma faced by classification is that the data is not collected at the same frequency in some applications. We investigate the mixed frequency data in a new way and recognize them as a special style of multi-view data, in which each view data is collected at a different sampling frequency. This paper proposes a discriminative dictionary pair learning method constrained by ordinal locality for mixed frequency data classification (shorted by DPLOL-MF). This method integrates synthesis dictionary and analysis dictionary into a dictionary pair, which not only improves computational cost caused by the ℓ0or ℓ1-norm constraint, but also can deal with the sampling frequency inconsistency. The DPLOL-MF utilizes a synthesis dictionary to learn class-specified reconstruction information and employs an analysis dictionary to generate coding coefficients by analyzing samples. Particularly, the ordinal locality preserving term is leveraged to constrain the atoms of dictionaries pair to further facilitate the learned dictionary pair to be more discriminative. Besides, we design a specific classification scheme for the inconsistent sample size of mixed frequency data. This paper illustrates a novel idea to solve the classification task of mixed frequency data and the experimental results demonstrate the effectiveness of the proposed method.

The purpose of texture smoothing is to preserve the prominent structure in the image while smoothing the salient texture. However, the existing methods are difficult to achieve a satisfactory balance between filtering out salient textures and preserving weak edge structures and small structures. To this end, we propose a structure-preserving texture smoothing method via scale-aware bilateral total variation. First, the joint bilateral filter is introduced to construct the window bilateral variation, and combined with the window total variation, a regularizer called the bilateral total variation is formed, which accurately quantifies the characteristics of texture and structure, to finely smooth salient textures while preserving weak edge structures and small structures. Subsequently, we proposed a scale-aware scheme to make the proposed regularizer more powerful in preserving small structures and adopted an optimization scheme to convert the original non-convex optimization problem into a least squares regression problem. The effectiveness of the proposed regularizer is verified in the dataset. The experimental results demonstrate the superiority of the proposed method in texture smoothing and other applications compared to other state-of-the-art approaches.

3D froth information is a significant indicator of working condition recognition in froth flotation. To extract it accurately, the first and key step is camera calibration. Although there have been many camera calibration methods proposed in these years, they cannot handle well for binocular camera calibration in froth flotation. The main reason is that there is an open environment without support surface or special geometric shapes for camera calibration in froth flotation. Therefore, we propose a novel binocular camera calibration method based on key frame sequences and weighted normalized tilt difference. First, we extract a high-quality frame sequence by filtering out incomplete and out-of-focus images from the froth video. Then, we propose a method to measure the tilt degree of the planar plate and extract the key frame sequences of the planar plate based on the tilt difference. After that, we calculate the camera parameters by weighted normalized tilt difference under various poses. The proposed binocular camera calibration method uses the froth video to obtain accurate and robust camera parameters, and does not require auxiliary equipment. Experiments have demonstrated the effectiveness and flexibility of the proposed method in froth flotation.

This article proposes a robust end-to-end deep learning-induced fault recognition scheme by stacking multiple sparse-denoising autoencoders with a Softmax classifier, called stacked spare-denoising autoencoder (SSDAE)-Softmax, for the fault identification of complex industrial processes (CIPs). Specifically, sparse denoising autoencoder (SDAE) is established by integrating a sparse AE (SAE) with a denoising AE (DAE) for the low-dimensional but intrinsic feature representation of the CIP monitoring data (CIPMD) with possible noise contamination. SSDAE-Softmax is established by stacking multiple SDAEs with a layerwise pretraining procedure, and a Softmax classifier with a global fine-tuning strategy. Furthermore, SSDAE-Softmax hyperparameters are optimized by a relatively new global optimization algorithm, referred to as the state transition algorithm (STA). Benefiting from the deep learning-based feature representation scheme with the STA-based hyperparameter optimization, the underlying intrinsic characteristics of CIPMD can be learned automatically and adaptively for accurate fault identification. A numeric simulation system, the benchmark Tennessee Eastman process (TEP), and a real industrial process, that is, the continuous casting process (CCP) from a top steel plant of China, are used to validate the performance of the proposed method. Experimental results show that the proposed SSDAE-Softmax model can effectively identify various process faults, and has stronger robustness and adaptability against the noise interference in CIPMD for the process monitoring of CIPs.

Industrial process data have the characteristics of less label, multimode, high dimension, containing noise, and mixing with outliers, which increase the difficulty of mode identification and anomaly detection in process monitoring using limited labeled data. In this article, to address the effect of these adverse factors, a semi-supervised discriminative projective dictionary pair learning (SSDP-DPL) is proposed for industrial process monitoring. First, a semi-supervised dictionary pair learning framework with a class estimation regularization term is developed to address the problem of lacking labeled data. Based on unlabeled data and their reconstruction errors, the class estimation regularization term is designed to obtain a discriminative extended synthetical dictionary, mining the hidden discriminative information in unlabeled data and reducing the impact of incorrect class estimation. Second, a sparse constraint is added to the analytical dictionary to enhance the robustness of projective dictionary pair. Then, a class discriminative function term is designed to improve the discrimination of dictionary pair, which ensures the intraclass compactness and interclass separation of coding space. Finally, the synthetical dictionary, the analytical dictionary, and the control threshold are obtained by iterating the dictionary pair to a process monitoring model for anomaly detection and mode identification. The effectiveness of the proposed process monitoring method is verified by the continuous stirred tank heater process and Tennessee Eastman benchmark tests. The proposed method is then applied to a real-world aluminum electrolysis industrial process. Experimental results demonstrate the superiority of our SSDP-DPL in contrast to other existing methods.

The admissible consensus tracking problem of nonlinear singular multiagent systems (SMASs) with time-varying delay, uncertainties, and external disturbances under jointly connected topologies is investigated in this article. First, the sliding-mode control (SMC) is applied to effectively reduce the adverse effects of uncertainties and nonlinearities of systems. Then, by the combination of admissible analysis, the Cauchy convergence criterion, and SMC, the sufficient conditions for the admissible consensus tracking and disturbance rejection of SMASs under jointly connected topologies are provided. Furthermore, a distributed SMC law is designed such that the sliding-mode dynamics trajectories reach the sliding surface in finite time. Finally, the simulation results are utilized to indicate the effectiveness of the presented methods.

Accurate monitoring of abnormalities is of great significance to the stable operation of the blast furnace ironmaking process. This article proposes a data-driven model to accurately monitor the abnormal conditions of blast furnaces. Generally, data-driven models primarily rely on feature extraction from high-dimensional raw data. Recently, deep learning networks have been developed and considered a promising technology in extracting high-level abstract features. However, most of these networks cannot capture deep target-related features for abnormality monitoring. Thus, this article proposes a novel stacked dynamic target-driven denoising autoencoder for layer-by-layer hierarchical feature representation, and the dynamic relationship between samples and targets is described by dynamic factors. Then, we design a corresponding target-driven reconstruction loss function to pretrain the deep network successively. Experimental results in an ironmaking plant demonstrate the effectiveness and feasibility of the proposed method.

Accurate and in-time performance monitoring plays a great role in industrial processes. However, since the labeled performances are usually measured by some special devices with a relatively long-time interval, the current deep neural networks for the performance monitoring always treat them only as an output. But actually, in the industrial process like froth flotation, labeled performance at the previous moment could also offer valuable information for performance monitoring at the current moment, especially under unstable working conditions. Therefore, we propose a Siamese time series and difference network (STS-D net), which integrates input features at different time steps and labeled performance at the previous moment effectively. In this article, the proposed STS-D net includes two sub-networks. One is the Siamese time series network, which aims to extract effective and uniform feature representations for the input time series at the current and previous moments; the other is the difference network, which integrates the feature representations of the two input time series with labeled performance at the previous moment to predict the performance at the current moment in an incremental way. Effectiveness of the proposed STS-D net is validated in a real-world froth flotation process.

A dilemma faced by classification is that the data is not collected at the same frequency in some applications. We investigate the mixed frequency data in a new way and recognize them as a special style of multi-view data, in which each view data is collected at a different sampling frequency. This article proposes a discriminative dictionary pair learning method constrained by ordinal locality for mixed frequency data classification (shorted by DPLOL-MF). This method integrates synthesis dictionary and analysis dictionary into a dictionary pair, which not only improves computational cost caused by the${\ell _0}$or${\ell _1}$-norm constraint, but also can deal with the sampling frequency inconsistency. The DPLOL-MF utilizes a synthesis dictionary to learn class-specified reconstruction information and employs an analysis dictionary to generate coding coefficients by analyzing samples. Particularly, the ordinal locality preserving term is leveraged to constrain the atoms of dictionaries pair to further facilitate the learned dictionary pair to be more discriminative. Besides, we design a specific classification scheme for the inconsistent sample size of mixed frequency data. This paper illustrates a novel idea to solve the classification task of mixed frequency data and the experimental results demonstrate the effectiveness of the proposed method.

Due to technical or economic limitations, timely measuring quality-relevant key performance indicators (KPIs) of complex industrial processes (CIPs), especially the chemical composition-related indexes, is intractable. Process monitoring image sequences (PMISs) usually involve significant information about the operation states and KPIs. Thus, soft sensor-based online KPI inference by incorporating process monitoring variables (TPMVs) and PMISs is more promising. However, the extremely inconsistent sampling rates with different expression forms and concerning aspects between PMISs and TPMVs lead to a great challenge in the soft sensor modeling by combining PMISs and TPMVs. In this article, a self-attention dual-channel deep network (SADCDN)-based soft sensor model for the end-to-end online KPI detection/prediction is proposed. Specifically, one channel adopts the gated recurrent unit (GRU) network to extract intrinsic time-series features in TPMVs, and simultaneously the other channel introduces a novel frame-dilated convolution fusion neural network (FDCFNN) to extract intrinsic spatiotemporal features from PMISs to address the sampling inconsistence between PMISs and TPMVs. Successively, dual-channel network features with different concerning aspects are weighted and fused based on an introduced self-attention mechanism to bridge the gap of sampling rates and concerning aspects between PMISs and TPMVs for the soft sensor modeling. Practical application results on two real industrial processes, the bauxite flotation process and the sintering process of a cement rotary kiln, have demonstrated the effectiveness and superiority of the proposed dual-channel model, laying a foundation for the process optimization of CIPs.

The control reliability of model predictive control is largely determined by the accuracy of the process model. The Hammerstein–Wiener (HW) model is an important nonlinear process modeling technique that has obtained great success in some process industries. Disturbances result in model mismatch and steady-state deviation, but little effort has been devoted to the coupling effects and inertial information in measured disturbances. In addition, few studies try to construct a disturbance observer (DO) to alleviate unmeasured disturbances. The present work proposes prompt disturbance rejection. First, a spatial–temporal long short-term memory-based measurable disturbance encoder is devised to analyze time-series information from measured disturbances and their coupling effects. The encoder can further clarify the status of inertial interference components and the disturbance intensity. Second, a DO is designed to estimate and attenuate unmeasured disturbances. Third, to create the new HW network, which is improved by integrating the disturbance encoder and observer differential, neural networks are used as nonlinear parts. Finally, a model predictive controller based on this improved model is constructed for real-time industrial process control. Simulation comparison experiments have demonstrated the superiority of the proposed methods. Real industry application in the country’s largest lead-zinc froth flotation plant in China validated the proposed model’s effectiveness in controlling chemical reagents.

Froth color can be referred to as a direct and instant indicator to the key flotation production index, for example, concentrate grade. However, it is intractable to measure the froth color robustly due to the adverse interference of time-varying and uncontrollable multisource illuminations in the flotation process monitoring. In this article, we proposed an illumination-invariant froth color measuring method by solving a structure-preserved image-to-image color translation task via an introduced Wasserstein distance-based structure-preserving CycleGAN, called WDSPCGAN. WDSPCGAN is comprised of two generative adversarial networks (GANs), which have their own discriminators but share two generators, using an improved U-net-like full convolution network to conduct the spatial structure-preserved color translation. By an adversarial game training of the two GANs, WDSPCGAN can map the color domain of froth images under any illumination to that of the referencing illumination, while maintaining the structure and texture invariance. The proposed method is validated on two public benchmark color constancy datasets and applied to an industrial bauxite flotation process. The experimental results show that WDSPCGAN can achieve illumination-invariant color features of froth images under various unknown lighting conditions while keeping their structures and textures unchanged. In addition, WDSPCGAN can be updated online to ensure its adaptability to any operational conditions. Hence, it has the potential for being popularized to the online monitoring of the flotation concentrate grade.

Data-driven process monitoring methods have attracted many attentions and gained wide applications. However, the real industrial process data are much more complex which is characterized by multimode, high dimensional, corrupted, and less labeled data. In order to eliminate these unfavourable factors simultaneously, a semisupervised robust projective and discriminative dictionary learning method is proposed. First, a semisupervised strategy is introduced to label unsupervised training data. Then, by utilizing low-rank and sparse features of raw data and outliers, a robust decomposition method is used to obtain clean data. After that, a simultaneously projective and discriminative model is proposed to extracting the feature of the low-rank clean data. Finally, the projection matrix and global dictionary, as well as the threshold are obtained through iterative dictionary learning. This hybrid framework provides a robust model for process monitoring and mode identification, and its efficiency is demonstrated by both synthetic examples and real industrial process cases.

This article presents a simple yet powerful online flotation process working condition (FPWC) discrimination approach based on the sparse representation of froth images. It learns a local Gabor pattern-based discriminative dictionary with a linear classification model simultaneously for the FPWC identification by solving a sparsity-constrained optimization problem. The proposed method tends to achieve similar and distinct sparse codes of froth images for the same and different FPWCs, respectively, facilitating the accurate FPWC identification. To ensure the adaptability of the FPWC discrimination model, an incremental learning-based online model updating procedure is further derived to monitor the dynamically changing characteristics of FPWCs based on an introduced sparsity discrimination index. The proposed method was validated on an industrial preferential lead-flotation subcircuit process. The prototype monitoring system with extensive confirmatory and comparative experiments shows the effectiveness and superiority of the proposed method, which lays a foundation for the optimal control of industrial flotation processes.

Industrial processes often operate in the complex dynamic environment. They challenge the cost-effective and reliable operation of industrial processes. This article proposes a multiobjective optimization and control strategy for the iron removal process to be optimally operated in the dynamic environment. In the optimization layer, multiobjective optimization and local optimization problems, minimizing the process cost and maximizing economic index, are developed to obtain the optimal set-points of the outlet ferrous ion concentrations. In the control layer, model predictive control based on the system dynamic model is constructed to control the outlet ferrous ion concentrations to track the set-points. To reduce the influences from dynamic disturbances and improve the tracking performance, we use least squares support vector machine (LSSVM) to establish the correction model. Fuzzy-logic-based compensation is proposed to compensate the set-points according to the priori and posteriori information. Finally, simulations using real-world plant data are carried out to verify the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed control strategy achieves a satisfactory tracking performance with less process consumption. It improves the iron content in the goethite precipitate, which has more commercial value. The proposed control strategy can make the plant more profitable.

With the rapid development of deep neural network (DNN), many DNN-based models for performance monitoring have been developed recently. However, some challenges still exist in the industrial performance monitoring: 1) different sample rates and time delays between the inputs and labeled performance; 2) a light-weight DNN architecture. Under this circumstance, we design a DNN named feature reconstruction-regression network (FR-R net) in this article. First, we extract the feature vector series as the input feature in order to capture the dynamic temporal information of the input data. Then, we design a feature reconstruction network with a weight-shared kernel network and fixed positional encoding to generate a reconstructed feature vector. Finally, we send the reconstructed feature vector into fully connected layers as a regression network to link the labeled performance. The effectiveness of the proposed FR-R net is validated on both a simulation case and an industrial froth flotation process.

This paper addresses the admissible consensus problem for homogenous descriptor multiagent systems with undirected graphs and disturbances. First, to achieve the consensus objective and attenuate the effects of disturbances, the distributed controllers are formulated and the admissible consensus problems are formulated. Another improvement emphasizes that the proposed approach can simplify the complexity of the admissible consensus analysis by using the state transformation during the admissible analysis and disturbances suppression analysis. Moreover, based on Riccati inequalities and linear matrix inequalities, two necessary and sufficient conditions are presented to ensure the admissible consensus and disturbances suppression objectives. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approaches.

This paper presents a froth image statistical modeling-based online flotation process operation-state identification method by introducing a biologically inspired Gabor wavelet transform in accordance with the physiological findings in the biological vision system. It derived the latent probabilistic density models of these biologically inspired Gabor filtering responses (GFRs) based on a versatile intermediate probability modeling frame, Gaussian scale mixture model. It has demonstrated that both the real and the imaginary representation of GFR obey a Laplace distribution. Accordingly, the amplitude representation of GFR obeys a Gamma distribution. Whereas the phase representation of GFR is an important yet frequently ignored aspect in Gabor-based signal analysis; it is demonstrated to be a periodic distribution and can be expressed by a von Mises-like distribution model. Successively, a local spline regression (LSR)-based classifier that the maps scattered statistical feature points of froth images directly to the operation-state labels smoothly is introduced for the operation-state recognition. Extensive confirmatory and comparative experiments on an industrial-scale bauxite flotation process demonstrate the effectiveness and superiority of the proposed method. Performance effects on different parameter settings, e.g., parameters of Gabor kernel and dimensionalities of multivariate statistical models, are further discussed.

The burst bubble rate has been strongly linked to froth stability, and thus, it is always used for performance prediction or modeling in the froth flotation. Due to different bubble motions and intensity changes as the bubbles move, the current burst bubble recognition methods are ineffective. Therefore, in this article, a similarity-based method for burst bubble recognition is proposed. The proposed method uses the local motion correction to deal with the different motion cases, and it selects the chamfer distance and the weighted normalized cross correlation as the similarity to decrease the influence of the intensity changes by the convex shape. Furthermore, the weighted normalized cross correlation is flexibly integrated with the template mask matching and the partial template matching. Extensive experiments have validated the effectiveness and robustness of the proposed method, where the precision and F1-score have been increased by at least 7.41% and 4.36%, respectively, compared with the current methods.

Satisfying the process technical requirements while optimizing the control of oxygen and zinc oxide is the main task for optimal operation of the iron removal process. However, due to the complicated mechanism and varied production conditions, the process is difficult to achieve optimal operation with the simple controller. The manual control, as a result, is extensively used in practice. In this paper, we develop an optimal setting and control (OSC) system for the iron removal process to achieve its technical requirements with minimal process consumptions. The OSC system is composed of a neural network soft-sensor, an optimal setting module, an optimal controller, and a fuzzy-logic-based compensator. First, we define the oxygen reaction efficiency (ORE) to measure the difference between the theoretical oxygen amount and its actual amount. Due to the ORE cannot be measured online and it varies with the production conditions, an adaptive weight radial basis function neural network soft-sensor is designed to estimate it. The adaptive weight adjusting method contributes to improve the adaptability of the soft-sensor, and its convergence is discussed. The optimal setting module provides the set-point of outlet ferrous ion concentration for the optimal operation of every reactor. The steady-state optimal control of oxygen and zinc oxide is then established, and the compensator compensates the control inputs utilizing the feedforward and feedback information. Finally, simulations validate that the ORE is important for the optimal control of the process. Furthermore, industrial experiments are presented to verify the effectiveness and potential of the proposed strategy.

In modern process industries, many parameters or states can be acquired with sensors, and these parameters or states often have a close relationship with operation conditions. Unfortunately, the process often operates under different modes, and labels thereof are often unknown. In practice, labeling for sampled data is expensive and time-consuming, so identifying the operation conditions of the industrial process is difficult. In addition, sampled data from the industrial system are always contaminated by outliers or noise. Therefore, a robust process monitoring method for the multimode process is particularly important and challenging. In this paper, a robust dictionary learning method is proposed for processes with multiple unknown modes. Firstly, by taking the sparsity of outliers into account, a robust dictionary learning method is proposed to identify and remove the outliers and noise in the sampled training data. Secondly, an iterative minimization algorithm is designed for solving the dictionary learning optimization program. Thirdly, based on the sparsity of the sparse code, we partition the sparse code into different clusters via spectral clustering method, and then the dictionary is divided into some sub-dictionaries according to the cluster results of sparse code. Lastly, when a new sample is generated, we reconstruct it under different sub-dictionaries, and the smallest dictionary reconstruction error is calculated as a classifier for process monitoring and fault detection. To evaluate the validity and effectiveness of the proposed monitoring approach, we conduct extensive experiments on a numerical simulation, the continuous stirred tank heater (CSTH) process, and an industrial aluminum electrolysis process, in comparison with several state-of-the-art methods. The experimental results demonstrate that the proposed method is able to provide satisfying monitoring results, and it is also robust to outliers in the sampled training data. It is worth mentioning that the proposed method is an unsupervised learning method, therefore, it is more suitable for the process monitoring of real industrial systems.

In the iron removal process, which is composed of four cascaded reactors, outlet ferrous ion concentration (OFIC) is an important technical index for each reactor. The descent gradient of OFIC indicates the reduced degree of ferrous ions in each reactor. Finding the optimal descent gradient of OFIC is tightly close to the effective iron removal and the optimal operation of the process. This paper proposes a coordinated optimization strategy for setting the descent gradient of OFIC. First, an optimal setting module is established to determine the initial set-points of the descent gradient. The oxygen utilization ratio (OUR), an important parameter in this module, cannot be measured online. Therefore, a self-adjusting RBF (SARBF) neural network with an adaptive learning rate is developed to estimate the OUR. The convergence of the SARBF neural network is discussed. Then, a coordinated optimization strategy is proposed to adjust the set-points of the descent gradient when the measured OFICs drift away from their desired set-pints. If the final OFIC does not satisfy the process requirements, a compensation mechanism is developed to provide a compensation for the set-points of the descent gradient. Finally, industrial experiments in the largest zinc hydrometallurgy plant validate the effectiveness of the proposed coordinated optimization strategy. Our strategy improves the qualified ratio of the OFIC and the quality of the goethite precipitate. More profit is created to the iron removal process after our strategy is applied.

As part of the zinc hydrometallurgy plant, the iron removal process is a complex system with four cascaded reactors. Tighter process-index control is difficult to achieve due to the complicated, long, and time-varying removal process. The control performance is also affected by the quality of the ore source and external disturbances. Little research is documented in the literature to address these difficulties and manual control is widely used. An innovative hybrid control strategy is developed to control the iron removal process' indices within narrow ranges with minimum cost of additive regents, including oxygen and zinc oxide. This strategy is composed of an optimal setting model, a model-based optimal controller, an integrated prediction model, a fuzzy-logic-based feedforward compensator, and a model feedback adjustor. The optimal setting model automatically optimizes the set-points of the process indices under different production conditions. To achieve the process requirements with minimal cost, the model-based optimal controller is designed. The integrated prediction model is established to provide a more accurate on-line prediction of the process indices by integrating the mechanism prediction model and an error compensation model based on the least-square support vector machine. Based on the predicted process indices, the compensator is developed for the optimal controller. The adjustor provides a parameter adjustment mechanism. Four-week-long industrial experiments in the largest zinc hydrometallurgy plant in China show that the control strategy can not only improve the process-indexes control performance, but also save 6.55% oxygen and 4.61% zinc oxide consumptions, which translates to 222 858 m3oxygen and 1236 t zinc oxide per year (a saving of about $570 000). The hybrid control strategy can be extended to cover other similar processes in the zinc hydrometallurgy and other industries.

Vector quantization encoding requires expensive time to find the closest codeword through the codebook for each input vector. A fast search algorithm for encoding is proposed in this paper. The multilevel elimination criterion is still derived from the three features (mean, variance, and norm) inequalities constraints, but the order of the three inequalities constraints, instead of the predefined order like other conventional multilevel elimination criterion, is optimized to speed up the encoding procedure. In the proposed algorithm, the elimination criterion at the first level is set to mean inequality constraint because of its narrower search width, and the priority order at the second and/or third level of variance and norm inequalities constraints is optimized based on the codewords distribution and the location of input vector in terms of the considered features. The experimental results demonstrate the effectiveness of the proposed algorithm.