Electro-fused magnesium furnace (EFMF) is an important equipment for producing electric melting magnesium, and its operating performance will have a significant impact on the final product quality and economic benefits. Traditional process operating performance assessment (POPA) technologies usually establish models by mining the potential relationship between process data and performance grade labels, which heavily depend on many manually labeled samples. Inspired by transfer learning, a semi-supervised transfer adversarial domain adaptation network (STADAN) is developed for the POPA of EFMF, which is based on the challenging situation where only limited source domain (SD) data is labeled and all target domain (TD) data is unlabeled. In order to fully utilize unlabeled data and expand the labeled dataset, a pseudo-label predictor consisting of a direct predictor and an auxiliary predictor is constructed. By mining the relationship between process data and labels from the aspects of input–output mapping and data distribution, the pseudo-label predictor can ensure the accuracy and reliability of the prediction. Based on the expanded labeled dataset, a performance grade classifier is further established for the TD operating performance assessment. To narrow the data distribution discrepancy between SD and TD, a domain discriminator is simultaneously established. Through an adversarial training mechanism, the feature distribution of both TD and SD tends to be consistent, improving the accuracy of pseudo-label prediction and POPA. The simulation comparison results verify the effectiveness of the proposed method.

Complex industrial processes are influenced by various factors dur-ing operation,such as variations in operational conditions and pro-cess drift,which lead to variations in process characteristics and behaviors over time.

This paper discusses the characteristics of temporal correlations commonly found among data in complex industrial production processes. It introduces the autoencoder and attention mechanism, proposing a missing value imputation method based on a dual temporal attention autoencoder. The core idea of this method is to use the process variables at historical moments and the current moment as inputs to the network. According to the missing conditions and the state of the process variables, it learns the attention weights for each moment. Subsequently, the weighted temporal information is input into the autoencoder, which ultimately reconstructs the complete process variables at the current moment. To verify the advancement and effectiveness of the proposed method compared to other methods, this paper conducts comparative experiments using Tennessee Eastman process data under different data missing conditions.

The process operating performance assessment (POPA) plays a pivotal role in enhancing industrial production efficiency and product quality. Open-set domain adaptation (OSDA) presents a significant challenge when label space discrepancies and unknown classes exist in the target domain. However, existing OSDA methods often homogenize unknown classes, hindering fine-grained assessment and under-exploiting in-domain knowledge. To address the above open-set POPA problem, this paper proposes a novel cross-domain fine-grained unknown class separation network (CFUCS) for industrial processes. In the assessment phase for known samples, the CFUCS method leverages inter-class relationships within the source domain to obtain performance grade soft-label prototypes. By integrating Kullback-Leibler (KL) divergence, target known-unknown samples are effectively distinguished. Furthermore, maximum mean discrepancy (MMD) is employed to reduce distributional discrepancies of known samples across domains, thereby improving the classification accuracy of known performance grades. In the assessment phase for unknown samples, existing studies typically group all unknown classes into a single category to mitigate negative transfer. To achieve fine-grained partitioning, spaces are first reserved for different unknown classes. Subsequently, a performance grade similarity matrix (PGSM), which is a quantitative expression of the intrinsic relationship between performance grades, is designed to assign labels to unknown samples. Then, expert experience is combined to determine specific performance grade labels. Experiments on two industrial datasets have confirmed the feasibility of the CFCUS method in addressing the open-set POPA problem, thereby providing clear guidance for the performance optimization of subsequent production processes.

Offline reinforcement learning (RL) enables deriving optimal policies from static datasets, promising safe and efficient control in real-world applications where online interaction is costly or risky. However, a pervasive challenge in offline RL is the overestimation of Q-values for out-of-distribution (OOD) actions. Existing methods typically mitigate this via policy constraints or conservative regularization that force the policy to adhere to the dataset’s support. Such approaches, however, heavily rely on accurately estimating the behavior policy and often overlook the potential of rich representations in capturing underlying environmental dynamics. In this study, we propose the Dynamics-Aware Representation Offline Policy Optimization (DROP) algorithm, which addresses these limitations through two synergistic mechanisms. First, DROP constructs a dynamics-aware latent space by jointly predicting rewards and next-state representations, thereby extracting structural features crucial for decision-making. Second, it integrates a behavior cloning regularization directly into the value function learning objective. This effectively penalizes OOD actions without the need for explicit behavior policy modeling. Empirical evaluations on the D4RL benchmarks, including Locomotion and AntMaze tasks, demonstrate that DROP achieves superior performance over state-of-the-art algorithms, achieving a 4.9 % and 4.2 % improvement in total scores, respectively.

In risk analysis, traditional risk assessment methods cannot fully reveal the causal relationship between human factors and other complex factors. To address the above issues, this paper proposes a fault risk analysis method for Dispatching Automation Master Station Systems (DAMSS) based on an improved Human Factors Analysis and Classification Systems (HFACS) and Fuzzy Bayesian networks (BN). This method constructs Bayesian networks using the improved HFACS, and employs fuzzy set theory and Similarity Aggregation Methods (SAM) to determine the probability distribution of network nodes. Bayesian causal inference is used to calculate the probability of system functional failures, and diagnostic reasoning is employed to identify critical causal paths within standard-layer nodes. Sensitivity analysis is further applied to identify critical event nodes. Experimental results demonstrate that the proposed model can accurately identify critical causal paths and determine critical event nodes, thereby validating its superiority in DAMSS risk analysis.

Real-time perception of the operational status of the fused magnesium furnace (FMF) is the prerequisite for preventing abnormalities and timely self-healing. This paper utilizes multi-modal information, including images and current from the FMF, to propose an operational status perception method based on a working condition knowledge guided sparse self-attention mechanism (WCK-SSAM). Firstly, a feature extraction network is constructed using a depthwise separable convolutional neural network and a stacked autoencoder to extract nonlinear features from multi-modal data. Secondly, this paper extracts the working condition knowledge relevant to the present data from historical cases by calculating similarities. Subsequently, the working condition knowledge guides the self-attention mechanism to perform global fusion across multiple modalities. In addition, this paper introduces sparse matrices in self-attention. Sparse matrices map features to a low-dimensional space to calculate sparse masks. Reduce the influence of redundant features on self-attention through sparse masks. This process not only enhances the computational efficiency of self-attention but also improves the model's generalization. Finally, a Softmax classifier is utilized to achieve operational status perception. Experiments based on actual data show that the F1 score of this method is 5.6%, 4.6%, 3.73%, 4.13%, 0.73%, 0.35%, 1.79%, and 1.54% higher than those of the eight existing FMF perception methods, respectively. The ablation experiments show that the F1 score of this method increases by 7.73%, 6.51%, 5.33%, 0.91%, and 0.15% compared to each sub-algorithm, respectively. These results demonstrate the superiority and effectiveness of the method proposed in this paper.

Optimizing plant-wide industrial processes (PWIPs) under uncertain environments is challenging because uncertainties and abnormal sub-unit (SU) conditions may affect evaluation-index availability and plant-wide coordination. This article proposes a robust co-optimization (RCO) framework to support continued coordinated optimization after objective adjustment, without requiring full algorithm redesign or manual parameter reconfiguration. Specifically, the RCO problem is modeled as an infinite-horizon decision process with observable evaluation indices and measurable production conditions, and a multiobjective robust optimization (RO) model is established. A barrier function is then used to incorporate static constraints into the objective, converting the problem into an unconstrained single-objective form. To reduce conservatism, the uncertainty set is reconstructed by introducing auxiliary variables, and a tractable robust counterpart is derived through duality-based analysis. Based on this formulation, an asynchronous reinforcement learning (RL) algorithm is designed to solve the RCO problem. Simulation studies on a coal slurry flotation process under normal and abnormal SU conditions verify that the proposed framework improves the continuity, robustness, and recovery capability of plant-wide coordinated optimization under uncertain environments.

Data-driven real-time prediction of performance indicators is an essential method for monitoring production states and guiding operational decisions. In the froth flotation process, variables such as ore properties, froth image features, operating variables, and concentrate grade show complex interdependencies. Previous performance monitoring studies have rarely explored these intrinsic relationships. In particular, spatial correlations among variables at the same time step and local temporal dependencies between adjacent time steps have often been overlooked. To address this issue, this study introduces graph-based concepts into the process modeling. A graph convolutional network (GCN)-based flotation performance monitoring model is developed to capture spatiotemporal dependencies among process variables. In constructing the adjacency matrix, spatial correlations are obtained using process knowledge and mutual information. Local temporal correlations are identified through the Granger causality test. These two types of correlation are then combined to construct a final adjacency matrix. Because the receptive field of a standard GCN is fixed, it limits its feature extraction capabilities. To address this limitation, a multi-receptive field strategy is adopted to simultaneously capture both local and global relationships among variables. An attention mechanism is then applied for weighted feature fusion. The fused representations are passed into a long short-term memory network to further extract long-term dependencies. Finally, the proposed model structure incorporates self-knowledge distillation to enable self-supervised knowledge transfer and enhance the utilization of internal features. Experimental results on a real-world copper flotation dataset demonstrate the effectiveness of the proposed method, with average RMSE, R2, and MAE values of 0.8476, 0.8325, and 0.6094, respectively, outperforming other advanced methods. Ablation and comparative experiments further confirm its superior performance.

In mineral processing, the energy-intensive thickening-dewatering process requires optimized scheduling to improve energy efficiency and ensure safety. Conventional methods often struggle to cope with frequent variations in operating parameters such as feed flow rate and feed concentration during operation. To overcome these limitations, this paper proposes a human-knowledge-assisted reinforcement learning framework. The framework integrates a reinforcement learning agent, a risk identification model, and a hierarchical decision-making model to enable safe and efficient scheduling of key equipment operations. To reduce human intervention, a support vector machine model and an extreme gradient boosting model are developed to mimic human supervision and decision-making. Industrial experiments at a mineral processing plant in Shandong, which processes gold ore, showed that, compared with the conventional mixed-integer linear programming method, the human-knowledge-assisted reinforcement learning framework reduces total energy consumption by about 12.13 % and performs well in the internal pressure control of the thickener and the stability of the discharge concentration, with stronger scheduling stability and environmental adaptability, demonstrating good industrial deployability and application prospects.

This paper introduces a robust and adaptive few-shot learning framework for intelligent fault diagnosis under varying operating conditions and diverse noise interferences. The architecture integrates multi-scale signal encoding, adaptive condition modulation, prototype-driven alignment, and transformer-based decision modeling. To ensure noise robustness, raw sensor signals are first processed via parallel dilated depthwise separable convolutions and refined by a channel-spatial attention unit to enhance fault-relevant patterns. A context-aware modulation stage then recalibrates feature maps according to operating-condition indicators, promoting cross-condition generalization. For classification with limited labeled examples, prototype estimation is performed using a median-based reliable estimator, and query embeddings are aligned to these prototypes through a cross-domain attention-based alignment mechanism. A transformer encoder captures global interactions among aligned features and produces the final predictions. Training is guided by a composite loss combining classification, outlier, and dependency-aware terms, with a warm-up strategy to balance fitting and regularization. Evaluation on two industrial benchmarks, the Tennessee Eastman process and gold hydrometallurgy process, demonstrates that the framework consistently outperforms existing methods in noise resilience and domain adaptation.

During the operation of the fused magnesium furnace (FMF), failure to promptly correct non-optimal operating conditions can adversely affect production efficiency, product quality, energy consumption, and operational safety. To address this challenge, this paper proposes a dual-branch attention fusion augmented generative adversarial imitation learning with behavior cloning (DAF-GAIL-BC) method for the optimized adjustment of FMF operating variables. The proposed method is designed to address two key limitations of standard GAIL in complex industrial scenarios: insufficient feature discriminability under coupled multi-source variables and unstable adversarial training caused by random initialization. Specifically, a parallel dual-branch attention fusion structure is developed to enhance state representation quality, while a BC pre-training strategy is introduced to provide a stable initialization for subsequent adversarial optimization. Ablation and comparative experiments show that the proposed method outperforms the benchmark methods across multiple evaluation metrics. Furthermore, semi-physical validation based on historical industrial data indicates that the generated adjustment actions can improve the operating condition level in the offline evaluation environment. These results demonstrate the effectiveness and application potential of DAF-GAIL-BC for FMF self-optimization.

Time-varying characteristics are widely prevalent in industrial processes, and traditional reinforcement learning methods often lose the effectiveness due to the non-stationary Markov decision processes (MDPs). In this paper, an incremental control-based deep reinforcement learning approach is proposed for the optimization control of time-varying systems. The core of this approach is to utilize the incremental control strategy to address the optimization difficulty caused by time variation, thereby improving the learning efficiency and control robustness of deep reinforcement learning (DRL) in time-varying systems. Initially, aiming at the problem that the action-value function (Q-function) of time-varying systems changes dynamically with time, the approximation problem of the Q-function and policy function in traditional DRL is transformed into the approximation problem of increments $\Delta Q$ and $\Delta a$. Subsequently, based on the incremental transformation strategy, two neural networks are constructed to approximate $\Delta a$ and $\Delta Q$ respectively, which replaces the complex Q-function and policy function approximation process in traditional DRL algorithms for time-varying systems. Finally, the set-point tracking control of a specific time-varying system is employed to verify the effectiveness of the proposed method. Simulation experiments demonstrate that, in contrast to the traditional TD3 algorithm, the proposed method boasts a faster convergence speed in the early training stage while attaining superior control performance.

Fault diagnosis in multi-condition environments is challenging, especially with limited labeled data. This paper proposes a federated meta-learning framework with transformer-based feature fusion and adversarial training to address the few-shot multi-condition fault diagnosis problem. The framework enhances the extraction of discriminative fault features across different operating conditions by employing cross-attention mechanisms and feature fusion, thereby improving adaptability and generalization. Federated meta-learning enables decentralized learning while preserving data privacy, making it suitable for real-world industrial applications. Adversarial training further enhances robustness by promoting the learning of condition-invariant fault representations. A memory-augmented neural network classifier enables rapid adaptation to new fault types with minimal labeled data. The proposed framework is evaluated on the Tennessee Eastman process and gold hydrometallurgy process datasets. On the gold hydrometallurgy dataset, the proposed approach achieves 99.33% and 98.00% Accuracy for the 5-way 5-shot and 5-way 1-shot tasks, surpassing the strongest competing method among those evaluated by 7.00 and 10.33 percentage points, respectively. On the Tennessee Eastman dataset, it attains 77.33% and 70.00% Accuracy under the same experimental settings, outperforming the best comparative method in our experiments by 14.00 and 10.67 percentage points, respectively. These results indicate the consistent and significant superiority of the present solution in multi-condition few-shot fault diagnosis scenarios.

Coordinated optimization of the thickening-dewatering process is crucial for reducing energy consumption in hydrometallurgy. Reinforcement Learning (RL) offers a promising solution to this complex sequential decision-making problem, but its high cost of online exploration limits its application in real-world industrial environments. A viable approach to enhance RL efficiency is to leverage existing historical operational data from the plant to guide the learning process. However, such data are often imperfect, exhibiting sub-optimality and sparsity. In this paper, we refer to this imperfect data as historical experience. To address this challenge, this paper proposes the experience-guided RL (EGRL) framework. EGRL effectively utilizes imperfect historical experience through two core components. The first is a value-regularized actor-critic architecture that balances leverag ing sub-optimal experience with autonomous exploration through a regularized value function. The second is a non-parametric guidance algorithm based on nearest neighbors that smoothly generalizes sparse experiential knowledge to unseen states, thereby maintaining effective state-dependent guidance when the agent encounters operating conditions not covered by historical data. We validate our framework in a high-fidelity simulation envi ronment. Experimental results demonstrate that, compared with mainstream RL baselines and the domain-specific state-of-the-art algorithm, EGRL improves learning efficiency and achieves lower total energy consumption, vali dating its effectiveness under imperfect historical experience. This demonstrates the potential of EGRL in handling the flawed data characteristic of real-world applications.

Modern industrial processes have intricate operating mechanisms and dynamically coupled spatiotemporal relationships. Efficiently capturing dynamic spatiotemporal dependencies is crucial for improving the performance of process operating performance assessment (POPA). Graph neural networks (GNNs) are capable of deeply exploiting structural characteristics inherent in data and industrial processes, thereby facilitating the learning of complex relationships and latent patterns in industrial systems. Nevertheless, due to inherent constraints imposed by network architectures on the receptive field, conventional GNNs exhibit limited capability in perceiving global spatiotemporal information, which directly undermines the stability and reliability of POPA. To address this issue, we propose a global spatiotemporal information-aware operating performance assessment method for complex industrial processes based on dynamic cluster-guided graph Transformer. Specifically, to effectively model the complex and dynamic interaction relationships in industrial process data, the self-attention mechanism is employed to adaptively learn dynamically varying edge relationships among nodes. Subsequently, dynamic clustering analysis is performed on hidden-layer node features of the graph convolutional network in the high-dimensional feature space, and enhanced connections are deliberately established among the core nodes of local clusters to dynamically reconstruct the topological structure between clusters. In addition, the topology-aware bias term is introduced into the self-attention layers of the Transformer to capture the dynamic spatial relationships of nodes along the temporal dimension, thereby enabling effective modeling of global spatiotemporal dependencies. The proposed method is applied to the coal slurry flotation process and the dense medium coal preparation process. Experimental results demonstrate the feasibility and effectiveness of the proposed approach.

Abstract Multiscale fusion-based fault diagnosis methods can exploit complementary fault information across different scales and are therefore effective in improving diagnostic accuracy. However, when noisy multiscale information is represented or fused, noise components from different scales tend to interfere with one another, which may obscure critical fault-related features and consequently degrade diagnostic performance. To address this issue, we propose a Multi-Channel Noise-Resistant Transformer (MNRformer) for fault diagnosis under noisy conditions, with the aim of reducing noise interference among multiscale information. Specifically, a channel-independent modeling strategy is adopted to construct Transformer subchannels with shared embedding representations and parameter weights, where features from different scales are modeled independently to mitigate mutual noise interference across scales. In addition, we design a dynamic weighting algorithm based on inverse information entropy to guide the feedforward network to adaptively enhance the response to channels with higher feature representation stability, thereby improving the discriminant robustness and overall reliability in the fault diagnosis process. Experimental results on four public rotating machinery datasets and one laboratory-built natural-noise dataset show that MNRformer maintains smaller performance degradation under different noise conditions, verifying its noise robustness in rotating machinery fault diagnosis.

The process operating performance assessment (POPA) of electro-fused magnesium furnace (EFMF) is very important to ensure product quality and pursue the maximum comprehensive economic benefit. However, the data at the beginning of the new production processes do not have performance grade labels and often includes new performance grades. Traditional multi-source domain open-set domain adaptation (OSDA) method categorizes all unknown classes into one class without further subdivision. To address this issue, a method based on multi-source domain open-set deep transfer adversarial network (MDODTAN) is studied to solve the POPA problem of the EFMF, which focuses on subdividing multiple unknown classes into different unknown performance grades. This network designs a task classifier for each source domain, and the assessment accuracy of known performance grades is further enhanced. Then, the domain gap between the known performance grades in each source-target domain is reduced through multi-source domain adversarial training. By constructing a similarity matrix between the known and unknown performance grades, pseudo-labels are assigned to the target domain data, and the assessment accuracy of performance grade of the new smelting process is improved through iterative training. The experimental results indicate that our method achieves higher performance assessment accuracy in open-set scenarios compared to existing methods, while also accurately classifying and subdividing multiple unknown performance grades.

Constrained multimodal multiobjective optimization problems (CMMOPs) frequently arise in practical applications, where multiple constrained Pareto sets (CPSs) correspond to a single constrained Pareto front (CPF). The presence of constraints and multimodal characteristics poses significant challenges for simultaneously achieving convergence and maintaining diversity in both the decision and objective spaces. To address these challenges, this paper proposes a novel two-stage constrained multimodal multiobjective coevolutionary algorithm, termed TSCEA. In the first stage, two growing neural gas (GNG) networks are employed to learn the topological characteristics of the CPSs and the unconstrained Pareto sets, respectively, thereby facilitating effective exploration of the decision space. In the second stage, the learned GNG-based structural information is utilized to adaptively guide the optimization process, avoiding unnecessary collaborative search and conserving computational resources. In addition, an adaptive archive updating strategy is introduced to support elite retention and balanced diversity in both decision and objective spaces. The proposed TSCEA is evaluated against six state-of-the-art algorithms on two benchmark sets and a real-world location-selection problem. Experimental results demonstrate that TSCEA exhibits competitive and robust performance in solving CMMOPs.

Process operating performance assessment (POPA) enables enterprises to comprehensively monitor production process states in real time, ensuring optimal operational conditions. Traditional POPA methods either lack real-time analysis capabilities due to post-event assessment or struggle to distinguish performance grades in process data with subtle differences due to shallow learning architectures. To address these limitations, this study proposes a broad learning system combined with inter-layer mutual attention-based stacked performance-relevant autoencoder (IMASPAE-BLS) for online POPA applications. First, to extract highly discriminative deep features from high-dimensional data with weak inter-grade differences, IMASPAE is employed to perform multi-layer feature extraction on raw modelling data. By introducing performance grade labels into the stacked autoencoder framework and integrating an inter-layer mutual attention mechanism, the model effectively fuses feature information across different hidden layers. This design not only mitigates the limitations of traditional BLS in deep feature extraction due to its flat structure but also fully captures performance-related features from various layers, thereby reducing information loss and enhancing classification capability. Second, two distinct enhancement node generation and cascading strategies are designed to improve the adaptability of the model to various data types and to strengthen its data mining capacity. Furthermore, an adaptive algorithm is proposed to determine the optimal number of enhancement nodes, ensuring high model performance while addressing the uncertainty in node quantity in BLS. Finally, three industrial case studies demonstrate the effectiveness of the proposed model, showing its superiority over existing methods.