Rotating machinery fault diagnosis is essential for ensuring the reliability of industrial assets in IIoT-enabled manufacturing environments, where the high variability of operating conditions has driven the widespread adoption of multi-sensor fusion (MSF) to extract discriminative fault features. However, harsh IIoT environments frequently cause partial sensor failures or communication interruptions, under which conventional multi-sensor fusion systems often suffer significant performance degradation or even complete fusion failure. To address this issue, a Multi-task Multi-input Multi-scale Mixture-of-Experts (M4oE) framework is proposed, in which an independent diagnosis task is constructed for each sensor signal, ensuring that any individual sensor stream, representing the most extreme case of single-sensor availability, can independently perform diagnostic inference. First, a multi-scale mixture-of-experts feature extraction scheme is proposed, in which both the task-specific experts and each shared expert are implemented using the proposed Omni-scale Dilated Convolution Neural Network (OSD-CNN) architecture. Subsequently, task-specific features and shared features are integrated through multi-level feature fusion and fed into task-specific decoders to generate diagnostic results. Since the diagnostic outputs obtained from each sensor have the same identification framework and independent evidence sources, M4oE further employs Dempster-Shafer (D-S) decision-level fusion to enhance the reliability of the overall diagnostic system. Finally, comprehensive evaluations are conducted on three different types of rotating machinery datasets, including pumps, rolling mills, and bogies, to verify the accuracy, robustness, and scalability of the proposed M4oE framework.

This work proposes an encrypted controller framework for closed-loop control systems with nonlinear dynamics over fully homomorphic encryption (FHE). Unlike differential privacy and output masking, FHE is a cryptographic primitive that provides assumption-based confidentiality guarantees under standard hardness assumptions. We observe that existing encrypted control frameworks remain largely limited to linear open-loop systems, primarily due to two key challenges: rapid ciphertext noise accumulation in feedback loops and the substantial computational overhead of nonlinear operations. In control systems, feedback is essential for real-time error correction, while nonlinear characteristics are critical for accurately modelling complex system behaviours. To address these challenges, we propose ENClose, a novel encrypted control framework that enables low-latency execution of both feedback control and nonlinear function evaluation. Specifically, ENClose introduces a low-latency homomorphic nonlinear computation framework that accelerates functional bootstrapping (FBS) by combining function segmentation with tree-based encrypted selection. This framework not only mitigates noise accumulation in encrypted feedback loops but also significantly improves the efficiency of FBS under high-precision settings, meeting the computational demands of dynamic control systems. Experimental results show that ENClose achieves a 3× to 20× speedup over state-of-the-art encrypted controllers. We validate ENClose through realworld applications, including multi-vehicle formation, spring–mass–damper control, and anomaly recovery, where the results demonstrate high-precision tracking and successful reconvergence after anomalies.

Practically inaccessible precise probability distribution for disturbance poses significant challenges to stochastic active fault detection (AFD) in achieving satisfactory detection accuracy. In this paper, without making specific distribution assumption on disturbance, a distributionally robust data-driven approach is proposed to AFD for stochastic linear dynamic systems. On the basis of constructing a data-driven stable kernel representation-based residual generator, the distributional uncertainty of disturbance is characterized by the mean-covariance-based ambiguity set of residual both for the fault-free and faulty cases. To minimize the energy of input while guarantee tolerable false alarm rate (FAR) and missed detection rate (MDR), the design of AFD system is formulated as an optimization problem subject to distributionally robust chance constraints (DRCCs). By bridging the DRCCs with deterministic constraints in the probabilistic context, the targeting optimization problem is then converted into a generalized eigenvalue-eigenvector problem, by solving which analytical solutions of the input and separating hyperplane for online detection are derived. Hence, the developed AFD system can not only ensure the FAR and MDR criteria not exceeding predefined levels, but also improve the robustness of the system against distributional uncertainties of disturbance. Besides, a batch-wise realization algorithm is developed for continuous online fault detection. A simulation study based on a four-tank system is demonstrated to validate the effectiveness of the proposed approach.

This article focuses on the formation reconfiguration mechanism for an aerial cable towed system (ACTS), which is composed of three quadrotors manipulating a point-mass payload. The system dynamics are analyzed in depth, which yields a refined decoupled model under actuator faults by utilizing the variation linearization technique and coordinate transformations. Based on this model, a fixed-time sliding mode observer is applied to estimate the degree of thrust degradation. The estimates are used for analyzing and optimizing the capacity margin under thrust loss fault, which reconfigures the desired formation. Leader-follower controllers are then designed to track the planned trajectory with the desired formation. Finally, simulation results demonstrate the effectiveness of the proposed method.

This paper presents a point-to-point encryption framework for nonlinear cyber-physical systems, integrating data protection, resilient control, and attack detection. A long short-term memory autoencoder (LSTM-AE) is employed to protect control signals against cyber attacks. The LSTM-AE model is trained offline and deployed online. When system dynamic models are unknown, adversarial training is adopted to preserve reconstruction accuracy and reduce the impact of attacks for control. When model knowledge is available, it is embedded into the training process. For attack detection, a dual-decoder architecture is proposed, where the discrepancy between decoder outputs serves as the detection residual. The proposed approach is more lightweight than conventional encryption schemes, works for secure control and anomaly detection simultaneously, and is well applicable for nonlinear systems. Simulation results on a three-tank system demonstrate the effectiveness of the proposed scheme.

This article addresses issues of covert attacks detection and resilient control of quadcopters. In the presence of generalized covert attacks characterized by strong stealth, passive detection techniques prove to be insufficient. Active detection methods are common solutions to this problem, but the balance between the detection capability and the stability of quadcopters still remains as a challenge. Different from the existing active attack detection methods, a coding and channel switching approach and its matched resilient controller for quadcopters are proposed. First, the design and detectability analysis of the coding-based attack detection method are given. Once covert attacks revealed, a secure channel is activated to replace the attacked channel. Second, to enhance quadcopter resilience against covert attacks, a resilient control framework is proposed. It incorporates attack effect estimation and compensation via a fixed-time observer. This framework maintains the stability of the quadcopter's control system under covert attacks. Finally, the numerical simulation and real-world experiments are conducted to evaluate the effectiveness and feasibility of the proposed scheme.

In this article, the deception attack detection problem is studied in scenarios involving multisecurity level transmission channels. Powerful attackers can construct stealthy deception attacks by exploiting data from reliable and unreliable channels. From the perspective of data correlation, we develop three detection schemes with different resource consumption. First, a fully security channel is utilized to establish innovation-based time-varying data correlation, which triggers residual covariance variation under attacks. Second, a noise-encryption mechanism is introduced without requiring the fully security channel. For the initial two methods, we propose a targeted optimization method to improve the detection performance by exploiting the quantified residual covariance variation. Third, we propose a time-shift coding method from the perspective of dynamic system stability, which is rigorously proved to be sensitive to attack behavior. For these proposed methods, we quantify the residual covariance variation induced by attacks and achieve detection by the$\chi ^{2}$test and generalized likelihood ratio test. Finally, the efficiency and reliability of these detection schemes are validated by examples.

American fuzzy lop (AFL), as a representative tool for fuzzing, is capable of uncovering security vulnerabilities in industrial systems. It suffers from consuming a large amount of computational resources during the mutation. To improve the performance of AFL, researchers adopt algorithms, such as particle swarm optimization and long short-term memory, to optimize mutation operator selection. However, challenges persist in these approaches integrated with AFL, including optimization model complexity, insufficient accuracy, and poor generalization scalability. To address these issues, the article proposes a new fuzzer calledDPRFuzzto optimize AFL’s mutation phases. First, in the deterministic mutation strategy mutation phase, deep Q network and trust region policy optimization are leveraged to precisely generate effective mutated samples through perceiving mutation process in a relatively short time. Then, to boost the efficiency of the Havoc random mutation phase, we improve the Thompson sampling algorithm based on a multiagent strategy to generate an overall optimal mutation strategy chain. Finally, the approach is tested on eight programs, such asreadelf,tcpdump,andnm, and the advantages ofDPRFuzzare analyzed. Most importantly, the experiment reveals results thatDPRFuzzachieves better fuzzing performance compared to the traditional and other AFL-based fuzzers, such as AFL, AFL++, AFLSmart, etc. On average,DPRFuzzachieves an improvement in code coverage of over 10%, along with a significant increase in the number of crashes.

This paper aims to deal with the fault monitoring problems for chillers considering the key performance indicator (KPI). To reach this objective, the coefficient of performance (COP), which measures the energy utilization performance in the chiller, is first selected as the KPI. Then, the fuzzy clustering method is used to establish the prediction model of the COP of the chiller. On this basis, considering the membership matrix difference between the normal and faulty data of COP after clustering, the chiller fault monitoring is realized via the changes of membership functions. Also, with the COP prediction data of the chiller, the$T^{2}$statistic is used to design the evaluation function, and the kernel density estimation method is employed for the threshold design. Thus, an additional COP-related fault monitoring algorithm for chillers is proposed. Finally, an experimental study is carried out on the chiller dataset for method demonstration.

Group-sparse mode decomposition (GSMD) is an efficient signal decomposition algorithm for separating harmonic signals, but fails to split modes for periodic pulse signals. In order to address the limitations of the GSMD algorithm in dealing with periodic pulse signals, this study proposes two improved GSMD methods, namely adaptive adjusted bandwidth sparse mode decomposition (AABSMD) and adaptive Gaussian window sparse mode decomposition (AGWSMD). The AABSMD method utilizes an iterative least-squares curve fitting approach to plot the energy spectrum and adjusts the filter using a –3 dB bandwidth, which avoids unreasonable bandwidth estimation. The AGWSMD method employs a segmented quantile regression method to fit the energy spectrum and utilizes a Gaussian window as a filter to extract the signal, which selects energy entropy as the parameter to optimize the Gaussian function. Both methods overcome the defects of splitting periodic pulse signals in GSMD and provide more accurate determination of the number of modes, resulting in a well-performed decomposition. In addition, the AGWSMD method exhibits outstanding reconstructive performance and high efficiency. Numerical and experimental results indicate the effectiveness and superiority of the proposed methods, which can be successfully applied to fault diagnosis of rotating machineries.

The current mainstream time series prediction methods exhibit commendable accuracy in prediction, but they often lack interpretability. One approach to address this issue is through the utilization of fuzzy cognitive maps for prediction. The multimodal fuzzy cognitive maps method stands out for its superior interpretability and adeptness in handling nonlinear and uncertain problems. However, the traditional modal segmentation method makes it difficult to effectively identify the modal information, affecting the method's effectiveness and accuracy. In this article, we proposed a novel multimodal fuzzy temporal cognitive maps time series prediction method based on complex dynamic slow independent symbol aggregation approximation. First, we constructed complex dynamic slow independent symbol aggregation approximation, which integrates slow features to obtain the modal information of the model. Then, the multimodal model parameters were determined by an optimization algorithm. Finally, a multimodal online matching mechanism based on slow feature tracking was proposed to address transitional states between modals. The validation based on two examples shows that the proposed method can effectively improve the prediction accuracy.

In this article, a distributed learning-based fault accommodation scheme is proposed for a class of nonlinear interconnected systems under event-triggered communication of control and measurement signals. Process faults occurring in the local dynamics and/or propagated from interconnected neighboring subsystems are considered. An event-triggered nominal control law is used for each subsystem before detecting any fault occurrence in its dynamics. After fault detection, the corresponding event-triggered fault accommodation law is utilized to reconfigure the nominal control law with a neural-network-based adaptive learning scheme employed to estimate an ideal fault-tolerant control function online. Under the asynchronous controller reconfiguration mechanism for each subsystem, the closed-loop stability of the interconnected systems in different operating modes with the proposed event-triggered learning-based fault accommodation scheme is rigorously analyzed with the explicit stabilization condition and state upper bound derived in terms of event-triggering parameters, and the Zeno behavior is shown to be excluded. An interconnected inverted pendulum system is used to illustrate the proposed fault accommodation scheme.

The correlation of control system data is characterized by its intrinsic dynamics, which is pretty hard to forge by the attacker. In this paper, false data injection detection problem for linear time-invariant systems is studied from a perspective of correlation analysis. Two detection methods are proposed based on targeted data correction construction and analysis. First, a noise encryption-based correlation enhancement mechanism and the optimization-based attack detection method are proposed. Second, a coding-based data correlation construction mechanism is designed and analyzed, and the corresponding detection scheme is proposed. The effectiveness and performance are illustrated by simulation. The proposed correlation-based detection schemes require no control performance sacrifice and can be implemented easily.

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the$L_{2}$input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi–Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.

Fault diagnosability evaluation is important for monitoring and control system design. The evaluation results provide knowledge of the achievable performance of concerned systems from the fault diagnosis perspective. In this article, the diagnosability analysis of Markov jump systems with multiple time delays is addressed by using statistics. Specifically, cases with both completely and partially known transition probabilities are considered. First, the characteristics of the multiple time delays and the Markov process are extracted based on a constructed system dynamic. This step is followed by defining the fault detectability and isolability of the considered system. On this basis, Kullback–Leibler divergence-based fault diagnosability measures for different fault cases are given, and the relations between these measures are investigated. For cases with completely known transition probabilities, due to random variation in the structure, a quantitative fault diagnosability method is proposed by simultaneously considering the fault diagnosis performance and the importance of different system structures. For cases with partially known or even completely unknown transition probabilities, instead of a scalar measure, an interval measure and the corresponding evaluation method are developed to take advantage of as much available information as possible. Finally, the effectiveness of the developed measures is verified via simulation.

In this paper, the distributed fault accommodation problem is studied for a class of interconnected nonlinear systems with event-triggered control and inter-subsystem communications. Each subsystem is subject to potential faults resulting from the local dynamics and/or transmitted from neighboring subsystems. The time periods before and after the fault detection in each subsystem are considered and corresponding event-triggered controllers are proposed, where the neural network based adaptive approximation technique is used to estimate the fault effect online. The closed-loop stability of the interconnected system with the proposed event-triggered fault accommodation controllers is rigorously analyzed.

This paper addresses the finite horizon H∞fault estimation problem for 2-D linear discrete time-varying systems with bounded unknown input and measurement noise. The main contribution of this paper is the H∞fault estimator for 2-D systems with a necessary and sufficient existence condition. By introducing a partially equivalent stochastic dynamic system in Krein space, the necessary and sufficient condition for the existence of the H∞fault estimator is derived based on innovation analysis and projection formula in Krein space. Then, the solution of the estimator is achieved by means of a Riccati-like difference equation for 2-D systems. Finally, a thermal process example is given to demonstrate the effectiveness of the proposed method.