Modern industrial systems are typically characterized by closed-loop control, massive data volumes, and high dimensionality, posing significant challenges for root cause analysis. This paper presents a prior-informed differentiable graph learning approach designed for large-scale industrial processes. Specifically, a masked generalized structural equation model is developed for causal modeling. The framework leverages a differentiable learning schema to generate an adjacency matrix constrained by prior knowledge. This matrix acts as a mask on the input data, ensuring that the causal sub-model for each variable is exclusively conditioned on its parent nodes. To enhance robustness against process uncertainties, a probability-based objective function is employed during optimization. Furthermore, incorporating prior knowledge into the regularization term enhances the interpretability of the discovered causal structures. Finally, the paper introduces a root node identification technique specifically tailored for handling cyclic causal graphs. The effectiveness of the proposed method is validated through a numerical study and two industrial cases.

This article addresses the fault detection and isolation problem for discrete-time Lipschitz nonlinear systems represented by Takagi-Sugeno fuzzy models. A zonotopic set-membership estimation framework is proposed to robustly handle system uncertainties and bounded disturbances. First, an $H_\infty$ observer is designed based on linear matrix inequality conditions to ensure robust performance. The estimation error is bounded within a recursively propagated zonotope, where generator growth is controlled via zonotope order reduction. Second, a fault detection scheme is developed by constructing residual zonotopes and checking whether the residual lies within the associated bounding boxes. Third, to achieve fault isolation, two augmented observers are designed, respectively, addressing actuator fault isolation and sensor fault isolation. For actuator fault isolation, a state-augmented observer is proposed to eliminate the influence of sensor faults in the residual. For sensor fault isolation, a disturbance-augmented observer is constructed to decouple the actuator fault effect. In both cases, zonotopic residual bounds are derived to detect and isolate the fault source. Finally, simulation results on a fuzzy nonlinear system illustrate the effectiveness and robustness of the proposed fault detection and isolation approach.

Boolean network provides an efficient and qualitative insight into gene regulatory networks in that it can unveil the causal relationships between different genes and excavate their dynamics. Numerous approaches have been investigated to infer Boolean networks from the observed gene expression time-series data. Nevertheless, existing algorithms fail to precisely infer large-scale Boolean networks owing to the complex state transitions and the noisy data. Moreover, these algorithms suffer performance deterioration when encountering novel Boolean network architectures. To address these problems, this study proposes a novel knowledge-guided hyper-heuristic genetic programming combined with the mutual information theory called KMHHGP. Firstly, a novel hyper-heuristic genetic programming with the dual-domain encoding scheme is proposed to enhance generalization capability for inferring large-scale Boolean networks. Secondly, six novel operators are developed to compose a set of knowledge-guided low-level heuristics. Thirdly, a novel mutual information scheme is introduced to evaluate the correlation among target nodes and their regulatory nodes. In addition, a parsimony pressure mechanism is introduced to mitigate the overfitting phenomenon. Comprehensive experiments demonstrate that the proposed method robustly outperforms state-of-the-art methods in accurately inferring various large-scale networks.

This paper investigates a fault detection method for Boolean control networks (BCNs) with self-triggered strategies. First, the concepts of strong active fault detection, active fault detection, and weak active fault detection are redefined, with their theoretical validity established through the construction of an auxiliary system. Based on this investigation, the concept of partial fault detectability for BCNs is proposed, enhancing the applicability of the detection method under various contexts. Subsequently, a model-free method using XGBoost is developed to achieve closed-loop control that guides the system toward fault-detectable states. Furthermore, reachability-based state partitions are constructed, and a scaling function is incorporated. Together, these components establish automatic triggering conditions, enabling the detection strategy to adapt autonomously to system dynamics. Without the need to track individual state trajectories precisely, the proposed method reduces controller updates and lowers computational cost. Finally, extensive validation across gene regulatory networks and a high-dimensional multi-motor industrial coordination system confirms the effectiveness and generalizability of the proposed method.

In practical applications, the degradation behavior of lithium-ion batteries exhibits significant differences due to variations in operating conditions. Meanwhile, the scarcity of labeled data poses considerable challenges for capacity prediction in terms of both accuracy and generalization. To address these issues, this article proposes a cross-domain semisupervised capacity prediction framework that integrates multigranularity feature modeling with a confidence controlled pseudolabel selection mechanism. Specifically, the proposed method enhances the model's ability to capture the granularity of nonlinear degradation trends in battery capacity, thereby improving prediction accuracy and stability. In addition, a pseudolabel learning strategy based on confidence filtering and stagewise regulation is designed to dynamically guide high-quality pseudolabels in the target domain into training, effectively reducing the risk of noisy label propagation. Experiments conducted on eight tasks across two heterogeneous battery datasets demonstrate R-2 improvements of 1.3%-8.7% and Mean Absolute Error (MAE) reductions of 38%-80%, validating the practical potential of the proposed method under complex degradation scenarios.

With the rapid proliferation of the Internet of Things (IoT), Li-ion batteries have become the primary energy source for massive interconnected devices, making precise State of Charge (SOC) estimation a pivotal function for IoT-enabled battery management systems (BMS). The proposed methodology integrates a RC equivalent circuit model, a Dual-scale TCN-SE-GRU (DTSG) network, and an adaptive zonotopic filter to estimate the SOC. First, the equivalent circuit model is employed to separate the transient voltage fluctuations from the terminal voltage. The resulting equivalent open-circuit voltage is then used as the network input to reduce estimation fluctuation. Then, the DTSG network is developed to facilitate the extraction of multiple time-scale temporal features and generate a preliminary SOC estimate through dual-scale temporal convolution, squeeze-and-excitation-based adaptive fusion, and GRU-based sequential modeling. Finally, the network output is incorporated into the adaptive zonotopic filter as a pseudo-measurement to realize closed-loop SOC estimation under unknown-but-bounded noise. Moreover, this approach offers a reliable prediction interval for SOC, providing additional decision support to the BMS under bounded but uncertain noise conditions.Empirical evidence confirms that the proposed approach can achieve higher accuracy and greater stability under various operating conditions and temperatures, and can also provide a reliable range for the estimation of SOC.

Focusing on state estimation in nonlinear time-delay systems, this article proposes a novel particle-based zonotopic hybrid filtering algorithm. First, linearization errors are bounded using zonotopes, and the overall search space is constructed via the Minkowski sum of state, noise, delay, and linearization uncertainties. This zonotopic space is then optimized using the $F$-norm to yield a compact prediction domain, completing the prefiltering stage. A particle swarm is subsequently introduced to search for the optimal estimate. To address particle degeneracy and computational cost, a boundary reflection strategy is employed to resample outliers. The optimal particle set is then transformed into a recursively updated ellipsoidal representation, providing tight bounds on the estimated states. The proposed algorithm is validated on a nonlinear bounded-noise state estimation task using experimental data from a representative battery case, demonstrating its general effectiveness and applicability.

Modern industries exhibit irregular characteristics due to factors such as mode transitions, incomplete data and outliers. Accurate monitoring of key performance indicators (KPIs) in irregular processes is essential for improving product quality and reducing scrap rates. This paper proposes a novel KPI-related process monitoring method that leverages the multiple kernel learning (MKL) technique, designed specifically for irregular scenarios with incomplete data. First, a novel MKL-based nonlinear matrix completion is proposed that utilizes a hierarchical strategy-based algorithm to estimate the missing values in incomplete data and the linear coefficients of multiple kernels. In addition, the corresponding convergence analysis is given. Based on the estimated completed data matrix, a novel MKL-based feature correlation analysis is proposed for indirect prediction of KPIs. Two statistics are established for detecting KPI-related and KPI-unrelated faults, respectively. A numerical case and an industrial example demonstrate that the proposed method not only accurately identifies the missing data, but also effectively detects the KPI-related faults.

This paper investigates the dynamic maintenance problem of the multi-unit k-out-of-n: G system. First, the real-time dynamic maintenance decision problem is modeled by a sequential decision-making framework aimed at a k-out-of-n: G system subject to stochastic failures. Second, a maintenance decision agent is established by efficiently integrating a customized deep reinforcement learning (DRL) method, in which there are several important improvements: (i) the dueling deep neural network is established to optimize the maintenance decision process by independently learning the state-value function and action-advantage function; (ii) the non-uniform prioritized experience replay technique is adopted to enhance the training efficiency of the decision-making agent; (iii) the weighted double Q network technique is developed to alleviate the estimation error of the maintenance decision agent, and enhance the system reliability through the weighted combination of dueling neural network estimators. Finally, the effectiveness is validated by carrying out numerical experiments, and the superiority is demonstrated by comparing the proposed method with several popular DRL algorithms.

Fault detection (process monitoring) for dynamic and nonlinear industrial processes, which can be viewed as complex systems, has become increasingly important in recent years. Under complex and dynamic operating conditions, traditional multivariate statistical process monitoring (MSPM) methods struggle to effectively capture the evolving behaviors of quality indicators at the system level. In this article, a novel variable selection-based adaptive MSPM method is proposed for quality-related process monitoring. First, an improved part mutual information (PMI) method is proposed for variable selection, categorizing process variables into quality-related and quality-unrelated groups, addressing the shortcomings of the original PMI being able to measure the correlation between only two variables. Second, a novel recursive kernel principal component regression (RKPCR) incorporating the hierarchical model order-reduction strategy is proposed to effectively track quality indicators. This method screens high-quality data for model updates based on distance-based classification and linear approximation, which mitigates model degradation caused by faulty data. In addition, a recursive kernel principal component analysis (RKPCA) method similar to RKPCR is proposed to monitor quality-unrelated faults. Finally, a numerical example and two industrial processes are used to demonstrate the performance of the proposed method.

Battery energy storage systems (BESSs) require reliable fault diagnosis to ensure long-term safe operation. However, most deep learning (DL)-based diagnostic methods assume a fixed set of fault types and static training data. This assumption is inconsistent with practical BESS deployments, where new fault modes emerge sequentially, and historical data cannot be fully retained. To address this challenge, we propose a three-phase continual learning (CL) framework designed for class-incremental BESS fault diagnosis from long-term time-series data. The proposed framework is designed to maintain stable fault representations while remaining adaptive to newly emerging fault types over long-term operation. Compared with existing DL-based fault diagnosis and CL methods, the proposed framework enhances representation stability through a self-supervised data twin objective, mitigates catastrophic forgetting via lightweight class-balanced stochastic replay, and maintains model plasticity using a utility-guided neuron aging mechanism. Experimental results on a real-world BESS test platform demonstrate that the proposed method achieves a superior stability-plasticity balance and consistently outperforms state-of-the-art baselines in terms of accuracy, robustness, and adaptability under evolving fault distributions.

Accurate multivariate time-series forecasting is a critical task that directly affects both product quality and energy consumption in the modern industry. However, existing methods fail to adaptively capture dynamic couplings under vague operating states and inevitably suffer from over-smoothing that erases critical high-frequency physical details. To address these challenges, this paper proposes a novel multi-view collaborative deep learning framework named Perceptual Fuzzy-Gated Convolutional Network (PFGCNet). Guided by the multi-view collaborative principle, we introduce a triple-stream parallel embedding architecture to jointly extract nonlinear semantic features and local spatiotemporal patterns. Crucially, we propose a fuzzy-gated convolutional mechanism that modulates local feature extraction using fuzzy membership signals, enabling the adaptive capture of physically meaningful inter-variable couplings. To grasp high-frequency disturbances, we design a Large Language Model empowered spectral supervisor to guide frequency-domain perceptual loss, enforcing structural consistency between predictions and ground truth in the frequency domain. Extensive experiments on real-world honeysuckle triple-effect concentration process and the public steel energy consumption dataset demonstrate that PFGCNet achieves state-of-the-art performance in terms of accuracy and robustness, effectively capturing complex dynamic variations and local abrupt changes.

This paper introduces Robust $k$ -Maintained Multi-Agent Path Replanning (R $k$ M-MAPR) algorithm, designed to address robustness in Multi-Agent Path Replanning (MAPR) when agents encounter faults. First, we introduce the temporary destination assignment strategy, which dynamically reassigns goals to agents when the primary destinations are inaccessible due to the failure of other agents. Then, we propose the R $k$ M-MAPR algorithm which replans paths and ensures safety while considering $k$ delays in MAPR under fault conditions. We delineate the replanned paths by giving the initial $k$ steps special consideration, using the Action Dependency Graph (ADG) to simulate and establish the simulated paths as the initial $k$ steps of the paths. Beyond this critical phase, the Multi-Agent Path Finding (MAPF) algorithm takes over, ensuring collision avoidance for the subsequent paths. Furthermore, we prove the collision-free nature and the $k$ -step robustness of the replanned paths. This analysis underpins the practical applicability of the R $k$ M-MAPR algorithm, demonstrating its effectiveness through both simulations and real-world experiments.

This work proposes a novel method for minor-fault diagnosis based on reduced-dimensional zonotopic filtering (RDZF). First, the zonotope space that contains the fault-state prediction is constructed using zero missed alarm rate (MAR) of fault diagnosis as the design index of the minor-fault amplifier to achieve optimal amplification. Subsequently, the zonotope order is reduced without increasing the conservative properties of the algorithm. The Euclidean distance is used to achieve the lowest dimension of the zonotope, and the upper and lower bounds of the fault state are obtained from the box space. Then, the estimation interval of the minimal fault is solved in reverse. Finally, an experimental platform based on the buck-boost circuit is constructed to verify the effectiveness and practicability of the proposed algorithm in a practical scenario.

To address the challenges of state estimation in switching time-varying systems with unknown but bounded noises, we first construct a feasible set from the particle distribution. This allows for a more effective representation of system uncertainty. The feasible set is then iteratively contracted to enhance compactness and tightly bound particle state deviations. Besides, the proposed algorithm combines the contracted zonotope with zonotopic Kalman filter to update the initial zonotope, refining the state estimate. The proposed set-valued based particle filter (SV-PF) can improve both the accuracy of state estimation and the representation of uncertainty in dynamic systems. Finally, the SV-PF algorithm is demonstrated to outperform other related methods in terms of robustness and precision, offering a reliable solution for real-time state estimation of switching time-varying systems.

Accurate extraction tank temperature prediction is essential for ensuring product quality and process reliability in pharmaceutical manufacturing. This task remains challenging due to concealed temporal patterns, long-range dependencies, and heterogeneous dynamics arising from coexisting continuous process variables and binary valve-state signals. To address these problems, this study develops an ensemble model integrating a pre-trained large language model (LLM) with a multi-scale fusion attention network by leveraging the sequence modeling capability of LLMs. Firstly, a multi-perspective refiner attention module is introduced to capture critical spatial and channel features, while a multi-scale feature fusion module is presented to extract heterogeneous characteristics across different temporal resolutions. Secondly, the pre-trained LLM module is designed to capture intricate temporal dynamics and long-term dependencies in industrial time series. Finally, an improved Adaboost ensemble strategy further enhances prediction accuracy and stability. Experiments on six real-world extraction tank datasets show that the proposed model outperforms state-of-the-art baselines, demonstrating its effectiveness for industrial temperature prediction.

In this paper, for the Lipschitz nonlinear discrete system with unknown distributed and interference inputs characterized by bounded amplitudes, based on the reformulation of Lipschitz properties, the H_/LOC fault observer is meticulously crafted to render the residual robust to disturbances and noise while maintaining sensitivity to faults. This design is transformed into a solution based on linear matrix inequalities. The feasible set of fault-free system residuals is obtained, and the fault detection is realized by comparing the residuals and feasible sets. Ultimately, the simulation is conducted using a single-link flexible robotic arm as an example to validate the effectiveness of the presented method. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In industrial production processes, fault propagation analysis is essential for performing targeted maintenance on malfunctions. Fault propagation analysis for nonlinear and dynamic industrial processes is challenging due to a lack of prior knowledge and the complex correlations between variables. This paper proposes a novel fault propagation analysis method based on a deep learning architecture, which includes two steps: fault localization and causal inference. Firstly, a window-level reconstruction-based contribution method is proposed for fault localization. Specifically, a GRU autoencoder is established to identify and extract sliding data windows containing fault points. Subsequently, the framework of GRU autoencoder is integrated into window-level reconstruction-based contribution analysis to achieve fault localization through aggregate analysis of all faulty windows. When conducting causal inference for fault variables, this paper proposes an adversarial learning-based method for dynamic Bayesian network (DBN) structure learning, which adopts a bi-level optimization framework. This adversarial optimization not only enables accurate modeling of DBNs but also allows for a keen perception of acyclicity in the DBN network. Case studies demonstrate the superiority of the proposed method in both fault localization and causal inference for fault variables within nonlinear and dynamic processes.

To address the problem of state estimation for a linear time-invariant discrete system with time delay, an adaptive momentum zonotopic filter with self-evolving noise bounds (AMZF-SENBs) is proposed based on the Frobenius radius. First, a parameterized zonotope is used to wrap the system state. Subsequently, a scalar cost function and its first-order gradient are introduced to measure the distance between the real and predicted measurements. Then, an adaptive momentum (Adm) gradient descent algorithm is studied to optimize the cost function. By adjusting the momentum terms, an effective optimization process is achieved by adjusting the number and step sizes of the iterations. Furthermore, with the aim of being more accurate in modeling measurement noise, a forgetting factor is added to the iterations. The current and estimated noise bounds are combined to form a new zonotope, which is then optimized using the Frobenius radius to be more conservative. Finally, the performance of the proposed AMZF-SENB algorithm is validated using an experimental buck-boost circuit platform. Experimental results demonstrate that, compared to the traditional $P$ -radius method, the interval observer (IO), and the robust zonotopic Kalman filter (R-ZKF), AMZF-SENB achieves faster convergence, wider adaptability, and reduces the average interval width of the state feasible region, thereby enabling faster and more accurate state estimation while maintaining robustness.

Scheduling optimization and bottleneck identification have long been prominent research areas in intelligent manufacturing, yielding numerous effective methodologies. However, the rapid advancement of Industrial Internet has intensified the demand for highly efficient bottleneck prediction methods and greater explainability in practical applications. Focusing on flexible manufacturing systems, this study proposes an integrated hyper-heuristic scheduling framework that incorporates an advanced explainable algorithm to facilitate customized prediction of global composite bottlenecks based on predefined job orders and scheduling schemes. The framework integrates bottleneck prediction into the scheduling process and consists of three principal submodules: the first submodule is responsible for generating a heterogeneous set of preliminarily feasible schemes; the second constructs the solution space and implements a pre-screening strategy to filter candidate bottleneck machines; and the third refines a hyper-heuristic algorithm to derive explainable heuristic rules for bottleneck prediction. Simulation results demonstrate the effectiveness of the proposed approach, showing that bottleneck prediction yields substantial improvements in efficiency and markedly enhanced explainability.