Operating condition recognition is crucial for equipment health monitoring and production optimization in smart manufacturing. However, industrial data annotation relies heavily on experts and incurs high costs, leading to scarce annotated samples. Traditional unimodal models also struggle to effectively fuse heterogeneous information. Existing approaches still fall short in balancing annotation costs and cross-modal feature representation, limiting industrial practical applications. To address this, we propose MMFformer—a condition recognition network integrating semi-supervised learning with cross-modal Transformers to reduce annotation dependency and enhance feature fusion capabilities. The model comprises a tokenization module, cross-modal encoder, and task decoder. The tokenization module extracts 3D image blocks from the visual modality and 1D vectors from the electrical current modality through multi-scale processing, converting them into unified dimensional representations. The encoder captures intra-modal features via self-attention and cross-modal correlations via cross-attention. The decoder transforms the fused features into operational condition predictions. Training integrates three semi-supervised methods—Mean Teacher, MixMatch, and FixMatch—while employing a majority voting strategy to select high-confidence pseudo labels, enhancing model robustness. Experiments demonstrate that MMFformer achieves accuracy rates of $\text{9 1. 1 5 \%, ~} \text{8 6. 8 6 \%}$, and 83.91 % when unlabeled data constitutes $20 \%, 50 \%$, and 80 % of the dataset, respectively.

Time series data collected from real-world frequently exhibit intricate multi-scale dynamics, which hinder accurate long-term forecasting. To address them, we propose MSSTMixer, a novel Multi-Scale Spatiotemporal Dual-Stream Fusion Model. Specifically, the framework first employs a multi-scale patching strategy to decompose the input sequence into sub-sequences of varying scales. It then adopts a dual-stream architecture: (i) a spatial stream that uncovers dependencies among variables, and (ii) a temporal stream that extracts short-term fluctuations and long-term trends. To effectively integrate these representations, we devise a two-stage fusion mechanism: (i) features at same-scale are concatenated to obtain preliminary fused embeddings; (ii) multiplicative and differential interaction pathways are designed to exploit complementary patterns across scales. Finally, a rolling-window strategy is employed for long-term forecasting. Experiments on six public benchmarks demonstrate that MSSTMixer consistently outperforms state-of-the-art baselines and achieves superior performance on molten iron quality prediction in an operational blast furnace, highlighting its industrial potential.

This paper proposes an adaptive control approach integrating the extended state observer (ESO) with the model-free adaptive control (MFAC) algorithm, tailored for the blast furnace ironmaking process subject to unknown uncertainties and external disturbances. First, the original twoinput two-output blast furnace system is transformed into two single-input single-output virtual linear data models using compact-form dynamic linearization techniques. Next, the unknown pseudo partial derivatives and the lumped disturbance terms in the model are estimated in real time using an improved projection algorithm and the ESO, respectively. Finally, an improved MFAC algorithm is designed based on the ESO estimates, and the corresponding stability analysis is carried out, as well as data experimental verification under the conditions of no external disturbances, step disturbances, and sinusoidal disturbances, respectively. The results indicate that, compared with the conventional MFAC algorithm, the proposed ESO-based MFAC algorithm exhibits better control performance.

The blast furnace ironmaking process (BFIP) requires rational dynamic operation optimization to achieve multiple production objectives. However, the changes in raw materials and working environment lead to multiple operating conditions with time-varying operation variables. This characteristic induces the BFIP operation optimization problems into dynamic multi-objective optimization problems (DMOPs) with changing decision variables (CDV-DMOPs). Focusing on such practical challenges, this paper proposes a heterogeneous knowledge transfer-based dynamic multi-objective evolutionary algorithm (HKT-DMOEA). Specifically, when the environment changes, HKT-DMOEA extracts distributions knowledge of historical Pareto-optimal sets (POSs), and then modifies distributions to sample candidate solutions by two variation schemes, differential variation for dynamic trends tracking and polynomial variation for diversity enhancement. Subsequently, the decision variable adjustment strategy is employed to revise candidate solutions, adapting them to the new environments. On this basis, heterogeneous transfer learning technique aligns decision spaces, and transfers historical POSs knowledge to assist in selecting the high-quality initial population from candidate solutions, thereby guiding the evolutionary search. The benchmarks and BFIP experiment results demonstrate the effectiveness and practicability of the proposed algorithm, which can meet the production requirements of BFIP.

Hydrocyclone feed solids concentration is a key process variable in grinding–classification circuits. Its fluctuations reduce classification efficiency and destabilize product particle size. Because the process is strongly nonlinear and subject to parameter drift and input delay, conventional control methods struggle to balance tracking performance with operating constraints. This paper proposes a mechanistic physical neural network-based model predictive control (MPNN-MPC) method for regulating hydrocyclone feed concentration. First, a conservation-based dynamic model of sump solids inventory and slurry volume is established. A lightweight temporal convolutional memory compensation network is then introduced to capture unmodelled dynamics and delay effects while preserving the physical structure of the process. On this basis, a multi-objective MPC formulation with explicit delay-horizon predictive compensation, multi-stage weight switching, and adaptive-gradient optimization is developed. A bounded residual-error analysis is further introduced to quantify the effect of the learned compensation error on output prediction and recursive feasibility. Comparative closed-loop simulations show that MPNN-MPC achieves the best overall tracking performance, yielding the best control effect among the controllers considered.

With the increasing application of machine learning in industrial production, model uncertainty quantification has become a critical tool to evaluate the prediction reliability and guide decision-making. The Conformal Predictive System (CPS), which generates Cumulative Distribution Functions (CDFs), provides valuable support for uncertainty quantification. However, CPS faces limitations when addressing heteroskedasticity. This paper proposes a Mondrian Conformal Predictive System (LWT-MCPS) based on an enhanced Decision Tree. The proposed approach constructs decision trees using splitting criteria derived from Levene's test and Welch's t-test, ensuring that the variance and mean within each partition remain as homogeneous as possible. Furthermore, it incorporates predicted values and prediction variances estimated using the k-Nearest Neighbors (KNN) as splitting features, effectively mitigating the impact of high-dimensional data on tree partitioning and enhancing the model's ability to identify heterogeneous regions. Experiments conducted on simulated data, public datasets, and blast furnace ironmaking data demonstrate that LWT-MCPS generates CDFs with lower Continuous Ranked Probability Scores (CRPS) than traditional CPS. These results validate its significant advantages in addressing heteroskedasticity challenges.

Optimal operation control (OOC) for complex industrial processes (such as mineral flotation) is often constrained by multi-timescale dynamics and model-plant mismatch. From an artificial intelligence perspective, this paper proposes a novel data-driven hierarchical reinforcement learning (HRL) architecture. Through a state-dependent adaptive switching mechanism and a dual-scale integral compensation strategy, it effectively decouples the complex control task into two time-scale independent loops—solving the stability and plasticity dilemma in policy optimization. In engineering applications, the proposed framework is specifically tailored to the high-precision requirements of mineral flotation processes. At the upper layer, a proximal policy optimization (PPO) agent optimizes slow-scale economies of scale, while the lower layer employs a twin delayed deep deterministic policy gradient (TD3) controller, achieving robust and fast setpoint tracking under strict actuator constraints. Simulation results in a coarser flotation process validate the effectiveness of the proposed architecture, demonstrating significant improvements in tracking accuracy and operational robustness.

Optimization problems in real-world applications often involve dynamic environmental changes, requiring algorithms to adapt quickly, track optimal solutions, and maintain efficiency. Existing dynamic multiobjective optimization evolutionary algorithms (DMOEAs) typically rely on fixed or limited dynamic response mechanisms, which are often insufficient to handle complex and varied dynamic environments. To overcome these limitations, this article proposes an adaptive dynamic response-based DMOEA (ADR-DMOEA), which employs a subpopulation-level adaptive mechanism to coordinate diversity-driven, prediction-driven, and memory-driven strategies. The strategy weights are dynamically adjusted according to the static optimization distance of each subpopulation, ensuring that appropriate strategies are adaptively deployed in different environments. This design overcomes the inefficiency of fixed assignments and the instability of individual-level perturbations, enabling coordinated and stable evolution. Extensive experiments on DF benchmark functions and a blast furnace (BF) ironmaking case study demonstrate that ADR-DMOEA achieves superior convergence, diversity, and robustness compared to state-of-the-art algorithms, effectively supporting real-world decision-making under dynamic conditions.

Randomization-based learning offers an efficient alternative to fully iterative training by fixing part of a model’s internal transformation and estimating only a small set of trainable parameters. This paradigm can substantially reduce training time and computational demand while retaining competitive predictive performance. It also provides a distinctive scientific lens through which the architectural bias and representational capacity of neural systems can be investigated in the absence of iterative learning. This editorial introduces the Special Issue on Randomization-Based Deep and Shallow Learning Algorithms, which brings together twelve contributions covering theoretical and architectural developments, systematic benchmarking, hybrid deep-randomized models, uncertainty quantification, and applications in computer vision, neuroimaging, renewable energy forecasting, industrial process modeling, intelligent transportation, maritime safety, and network science. Collectively, the papers demonstrate that randomization-based learning is evolving from a family of shallow, computationally efficient learners into a broader design principle for deep, ensemble, and uncertainty-aware systems. The Special Issue also exposes open challenges concerning principled random-feature design, reproducible benchmarking, scalable linear solvers, robustness, calibration, interpretability, and deployment under streaming and resource-constrained conditions.

During the sintering process, real-time measurement of FeO content is crucial for the subsequent operation of blast furnace smelting. However, the traditional chemical analysis methods suffer from significant time delays (3-6 h). Although intelligent recognition methods offer good timeliness, the high cost of data labelling limits their practical application in industrial settings. In order to address the problem of practical engineering, a new deep active learning method integrated with conformal prediction is proposed for the rapid classification of FeO content in sintered ore. This method leverages the ConvNeXt network as the base model and quantifies model uncertainty through the statistical confidence intervals of conformal prediction. The number of samples selected for each training round is dynamically adjusted: when prediction uncertainty is high in the early stages of training, the sample size is automatically increased; as the model performance improves in the later stages, the sample size is reduced. This approach achieves a balance between labelling cost and model performance. Furthermore, the strict confidence intervals ensure the reliability of the predictions, and the method uses the generated prediction set to adaptively select the most informative samples for model refinement. To validate the effectiveness of the proposed method, benchmark tests are initially conducted on a public dataset consisting of 4,752 images across nine categories. Subsequently, the proposed approach is applied to the practical task of detecting FeO content in industrial sintered ore. On a dataset of infrared images capturing three types of sinter tail ends, the model trained with 1,674 samples achieves a recognition accuracy of 97.93%, surpassing the performance of baseline methods.

For the output probability density function (PDF) control problem of singularly perturbed systems, a new neural networks-based output PDF shape identification and control is proposed to address the impact of fast and slow time scales. First, an identification scheme for the output probability density function of singularly perturbed systems based on multi-time scale neural networks is proposed, by designing a new weight adaptive update algorithm through the optimal bounded ellipsoid constraint. Second, two control methods are proposed under different uncertainty conditions. By uncertainty approximation assumption, a direct optimization method based on derivation is proposed. Then, to enhance the applicability, a control strategy based on convergence domain and the gradient descent optimization method is proposed to update the control parameters. The closed-loop stability is analyzed by constraining the convergence domain under Lyapunov stability, ensuring the tracking effect of the system state. Simulation results and grinding process confirm the effectiveness of the proposed method.

Real time and precise recognition of industrial process working conditions is essential for control and optimization, playing a crucial role in ensuring production safety and efficiency. Nevertheless, the substantial costs associated with labeled samples result in the underutilization of unlabeled data in production. Additionally, leveraging the complementary characteristics of heterogeneous data can enhance recognition accuracy. Therefore, this article proposes a novel intelligent working conditions recognition method that integrates semi-supervised learning and multilevel information fusion, effectively increasing information capacity and enhancing modeling accuracy. Initially, a multiscale feature fusion network (MSFFNet) is established to accommodate the fine-grained feature requirements of image modeling. Subsequently, samples are evaluated for uncertainty both before and after semi-supervised recognition, using an aggregation strategy to refine the quality of pseudolabels. Ultimately, the features of heterogeneous data are fused using a bilinear attention network, and a consistent description of working conditions is achieved through decision-level fusion, culminating in the final working conditions recognition results. The effectiveness of the proposed method is validated with actual industrial multimodal data, achieving a remarkable recognition accuracy of 98.91%.

To address the critical challenges of premature convergence, insufficient diversity, and constrained boundary search difficulties in constrained multi-objective optimization problems (CMOPs), this paper proposes a novel adaptive auxiliary phase switching multi-task (AAPSMT) optimization algorithm. By evaluating the population state in real time, the algorithm achieves adaptive bidirectional switching between global exploration and local exploitation. It also employs phase-differentiated migration and processing to leverage their complementary strengths, improving population diversity and convergence efficiency. To strengthen search performance near complex constraint boundaries, a local exploitation strategy with adaptive constraint relaxation anchored to the main population’s feasibility is introduced. Additionally, an archive update mechanism guided by reference vectors is developed to enhance the quality and uniformity of the solution distribution. Experimental studies on classical benchmark problems and real-world blast furnace ironmaking processes demonstrate that AAPSMT achieves notable performance advantages and shows strong potential for practical applications.

In the complex environments of modern process industries, timely and accurate anomaly detection is paramount for maintaining smooth, efficient, and safe production processes. Traditional anomaly detection techniques typically rely on unimodal data. However, with the advent of smart factories and advanced sensor technologies, multimodal information such as video data and time-series data has emerged as critical enablers for improving anomaly detection efficiency. To address this evolving challenge, this paper introduces a novel two-stage multimodal anomaly detection framework, termed MoBiM2, which leverages both video and time-series data. The proposed method adopts a bidirectional Mamba structure with linear complexity, effectively integrating multisource information through a shared matrix that bridges the two modalities. First, a 3D Tokenization technique is introduced to efficiently extract spatiotemporal features from video data. The initial stage of the framework, called the MBi-Mamba module, which extracts and integrates crucial information from video and time-series data via the shared matrix in the bidirectional Mamba structure. To further refine feature extraction, the second stage incorporates the EBi-Mamba module, which intensifies the interaction and fusion of multimodal information. To accommodate the diverse demands of real-world industrial applications, three model configurations of varying scales are presented. Experimental validation on a publicly available multimodal industrial smelting furnace dataset, demonstrates that the proposed method achieves accuracies of 95.71%, 94.91%, and 93.03% at different scales, respectively. Moreover, this approach surpasses existing Transformer-based and CNNbased methods, highlighting superior performance.

In this letter, a prescribed performance function-based data-driven virtual setpoint P-type controller (PPF-DDVSPC) is proposed for single-input single-output (SISO) systems with nonlinear nonaffine dynamics. First, the original model with error constraint is converted into an unconstrained form using the prescribed performance function and error transformation technique. A virtual setpoint updating law, nested within the outer layer of the traditional P-type controller, is developed based on the newly defined unconstrained variable to limit the tracking error. Then, the unconstrained model and virtual setpoint law are converted into the available equivalent linear data models through dynamic linearization technology. The unknown pseudo-partial derivatives in the two models are estimated utilizing the modified projection algorithm. Finally, the P-type controller with prescribed performance is obtained by replacing the actual setpoint signal with the resulting virtual setpoint law. The bounded input and bounded output (BIBO) stability of the system is demonstrated by the contraction mapping principle, which ensures that the constraint conditions are satisfied. The effectiveness and robustness of the PPF-DDVSPC method are validated through a data-driven simulation of the blast furnace ironmaking process.

For a class of non-Gaussian stochastic system with measurable probability density function (PDF) of output, an event-triggered PDF shape control algorithm is proposed to solve network congestion and calculation pressure caused by high frequency transmission of PDF data. The square root B-Spline model is used to learn the relationship between the output PDF and the control input of the stochastic system, and under the event-triggered mechanism, the output PDF tracking problem is transformed into a weight vector dynamic tracking control problem with time delay and constraints. Then, the level of model uncertainty and external disturbance is described by L 1 performance index, then the stability and robustness of the proposed control algorithm is analyzed. To reduce the calculation pressure and facilitate the performance analysis of the closed-loop control system, the Pseudo-PID controller is adopted. Finally, the problem of solving the controller and trigger parameter is transformed into the LMI convex optimization under the framework of stochastic system analysis and synthesis, which avoids the reduction of the control effect caused by the two-coupling parameter. The performance of the proposed method is theoretically analyzed and also verified by numerical simulation. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In the realm of industrial applications for machine learning, multiple challenges are frequently encountered, such as concept drift (CD) and the prohibitive costs associated with data labeling. CD refers to the scenario where the underlying data distribution of the model shifts over time, potentially deteriorating model performance. Addressing these challenges, this paper proposes an innovative semi-supervised CD detection method, specifically designed to tackle both CD and the high costs of data labeling in regression tasks. Initially, considering the high expense of acquiring labeled data in industrial application scenarios, a semi-supervised learning strategy based on self-training is utilized. In this strategy, prediction intervals generated by Conformal Prediction (CP) are used to select high-reliability pseudo-labels. Furthermore, to effectively address CD in real-world industrial settings, the Conformal Martingale (CM) is employed for real-time detection. This framework detects changes by identifying increases in martingale values when CD occurs. Upon detection, the model is promptly retrained using the most recent data following the drift. Finally, the proposed method is validated through experiments conducted on three datasets: the UCI dataset, the alumina evaporation process dataset, and the blast furnace ironmaking dataset. Experimental results demonstrate that the proposed semi-supervised method significantly enhances the performance of the original training model. The detection method accurately identifies CD and notably reduces test errors through model retraining, thereby improving the effectiveness of the model in realworld industrial applications.

Conformal prediction (CP) is known to theoretically guarantee prediction interval coverage under the exchangeability assumption. However, industrial time series collected from real-world industrial processes often violates this assumption due to temporal dependencies and distribution drift. Therefore, an uncertainty quantification framework is proposed for industrial time series, with the prediction interval composed of two one-sided intervals. Specifically, it adopts CP as the basic framework and integrates entire and local nonconformity score information to adjust the confidence levels of two one-tailed intervals over time. This enables the proposed method can adapt quickly to distribution shifts and provides effective prediction intervals. Two experiments show that the proposed method improves the efficiency of prediction intervals while guaranteeing coverage. Specifically, under a nominal confidence level 95%, the proposed method achieves an average empirical coverage of 95.0% with a 6.29% reduction in prediction interval width in the wastewater dataset. While in the actual sintering production dataset, it achieves a similar improvement, with a 95.6% coverage and a 15.70% reduction in width, compared to the best-performing benchmark model.

In this paper, a P-type adaptive predictive control (PAPC) method is presented for a category of unknown multi-input multi-output (MIMO) discrete-time systems with nonaffine nonlinear dynamics. First, the unknown nonlinear model is altered to a linear form containing an unknown pseudo-partial derivative (PPD) matrix utilizing the partial-form dynamic linearization (PFDL). A predictive model is then established by employing the modified projection algorithm, an auto-regressive model, and an output estimation technique. Based on the predictive model, an adaptive learning law that incorporates estimated tracking error information is used to generate the virtual error. Then, a data-driven PFDL-PAPC algorithm is constructed by replacing the actual tracking error in the P-type controller with the virtual one. The bounded convergence properties of the output estimation and tracking error dynamics are theoretically analyzed using the contraction mapping principle. The effectiveness of the PFDL-PAPC method is demonstrated through coupled tanks and actual data-based blast furnace ironmaking experiments. Note to Practitioners-Model-based control strategies are highly dependent on the model of the controlled plant, which makes it challenging to apply them in complicated industrial processes. In this paper, a P-type adaptive predictive control algorithm is presented. It is directly driven by the virtual error generated through the multi-layer prediction mechanism without requiring any modeling procedure. The operators can flexibly adjust the linearization length according to the system's dynamic complexity. Furthermore, the proposed algorithm can effectively resist the negative influence of input disturbances. The coupled tanks and actual blast furnace ironmaking data-based experiments are provided to verify the effectiveness of the proposed algorithm.

For real-world industrial system modeling, dynamic stochastic errors inevitably exist in data- driven deterministic predictions (i.e., point predictions). The uncertainty of such prediction results directly affects various prediction-based operations for work condition identification and production decision-making. Therefore, a novel interval prediction method quantifying multi-output uncertainty is proposed by combining conformal prediction with random vector functional link networks (RVFLNs), which has fast learning speed and high accuracy performance. The proposed algorithm is used for the reliable prediction of molten iron quality in blast furnace ironmaking process. Firstly, to address the issue that shallow learning models have limited expression capabilities to describe complex nonlinear relationships, the dynamic attention mechanism and semi-supervised autoencoder are utilized to reveal and represent the correlations between different input variables and multi-output variables. Subsequently, the Elastic Net regularization technique is adopted to improve the multicollinearity and overfitting problems of traditional RVFLNs. Further, considering the deterioration of prediction accuracy and credibility caused by uncertain system dynamics, an Empirical Copula function-based Copula prediction uncertainty quantification method is introduced to realize multi-output variables reliable prediction with a given confidence level. Finally, actual blast furnace industrial data is applied to demonstrate the validity, utility, and sophistication of model.