This article proposes a data-driven distributed Kalman filter (DKF)-based sensor fault isolation and estimation scheme for large-scale interconnected dynamic systems, composed of heterogeneous subsystems coupled through a directed topological graph. A local diagnosis unit (LDU) is established for each subsystem, where the data-driven DKF-based residual generator is constructed using local and neighboring process data, effectively decoupling the totally unknown interaction component. Subsequently, fully distributed sensor fault isolation is realized at the subsystem and element levels in simultaneous-fault cases. Both local and neighboring sensor fault isolation can be realized in the LDU, allowing the global system sensor fault isolation with only several key LDUs. Then, the data-driven DKF-based estimator is built in each LDU to estimate sensor faults occurring in multiple subsystems. The distributed Kalman gain is computed in a fully distributed manner, with stability analysis performed locally without overall system knowledge. Finally, the effectiveness and performance of the proposed scheme are validated through case studies on the power network system.

Considering the influence of subsystem state interconnection in large-scale systems, the existing integrated design methods of data-driven fault detection (FD) and fault-tolerant control (FTC) that follow centralized architecture cannot be applied in distributed scenarios. To address this problem, this article proposes a subspace predictor-assisted framework to perform the data-driven integrated design of FD and FTC for large-scale systems. FD and FTC are organically combined through a subspace predictor framework. For the subspace predictor designed for each subsystem, no global input and output (I/O) data information is required but only the I/O data of the local and neighboring subsystems is used, thus realizing a distributed design. In addition, the integrated architecture of FD and FTC does not need any large-scale system mechanism information, and is completely driven by process I/O data. Two case studies including a numerical simulation example and cascaded continuously stirred-tank reactor verify the feasibility and effectiveness of the proposed data-driven distributed FD and FTC method.

This article presents a data-driven distributed Kalman filter (DKF)-based fault diagnosis scheme, which can successfully detect actuator and sensor faults in large-scale dynamic systems, with heterogeneous subsystems interconnected through the directed topological graph. In the developed distributed framework, a local computing model (LCM) is formulated for each individual subsystem. In each LCM, based on the subspace identification method, the data-driven distributed Luenberger observer-based residual generator is constructed for each subsystem using local and neighboring process data. This offers an alternative expression of subsystem dynamics, supporting the design of more practical functions, for example, integrated monitoring and control design. The totally unknown interaction term is decoupled in the local residual, preventing the effect of actuator faults from propagating through the diagnostic network, so that the actuator fault isolation can be realized in each LCM. Then, the local noise covariance matrices are identified, and thus the data-driven DKF-based residual generator is formed, attaining improved detection performance by attenuating the effect of strong noises. Moreover, the adaptive configuration is developed for each subsystem, where the detector does not require retraining for changes in operating points or interconnection parameters, ensuring the continuity of the diagnostic process. Finally, case studies on the hot strip mill process verify the effectiveness and performance of the proposed method.

This paper is concerned with distributed fault estimation and fault-tolerant control for interconnected systems. Based on the local and interconnected information relevant to neighbors, a distributed fault estimation observer (DFEO) is constructed in a fully distributed fashion for each subsystem. The generated estimation errors are decoupled with external disturbances such that the DFEO has an asymptotical estimation feature. Then, using the estimated state and fault, a fault compensation based distributed fault-tolerant control (DFTC) law is designed for each subsystem. Sufficient conditions in the form of linear matrix inequalities (LMIs) are presented to guarantee the closed-loop system’s properties of stability and disturbance attenuation. Moreover, the proposed DFEOs and DFTC laws allow subsystems to be added or removed in a plug-and-play (PnP) fashion, which enhances the scalability of interconnected systems. Finally, the effectiveness and performance of the proposed method are demonstrated through simulations conducted on the power network system (PNS).

This paper presents a novel approach for passivity analysis and hierarchical fault detection of passive systems employing model-free reinforcement learning (RL). The proposed method can analyze the passivity of a system without knowing or identifying the system model and furthermore construct a fault detection logic grounded on energy indicators from the analysis result. Initially, the data-driven Bellman optimality equation is formulated, which is equivalent to the system’s passivity condition. Subsequently, the RL algorithm is delineated, and its time efficient advantage is elucidated in terms of both convergence and computational complexity. Simultaneously, the Bellman optimality equation in RL is clarified to be equivalent to the energy conservation constraint in the system. Based on this revelation, a hierarchical detection method based on the energy performance indicator is introduced. This approach can effectively detect faults within passive systems online and assess the severity of their consequences. The effectiveness of the proposed method is validated through simulation.

In this article, an issue of data-driven optimal strictly stealthy attack design for the stochastic linear invariant systems is investigated, with the aim of maximizing the system performance degradation under an energy bounded constraint and bypassing the parity-space-based attack detector. Importantly, the proposed attack policy refrains from the assumption that the system knowledge is known to attackers. A novel strictly stealthy attack sequence (SSAS), coordinating the sensor and actuator signals simultaneously, is proposed with a sufficient and necessary condition for the existence of such an attack presented. Specifically, the SSAS is parameterized as a vector in the null space of a specific matrix which is constructed by a parity matrix and the system Markov parameters. For the purpose of data-driven attack realization, modified subspace identification methods are utilized to achieve an unbiased estimation of the required parameters via the closed-loop data. On this basis, the attack design is formulated as a constrained optimization problem, an explicit solution to which is given to characterize the optimal strictly stealthy attack. Finally, the vulnerability of the cyber-physical systems is analysed from the perspective of the parameter selection for the parity space-based detector. A case study on a three-tank model verifies the efficiency of the proposed approach.

Fault-tolerant control (FTC) is vital for the safety and reliability of automatic systems. Most of the existing FTC methods are developed for open-loop systems subject to additive faults, regardless of the widely present control loops and multiplicative faults within systems. In this article, a performance-based FTC strategy is proposed for the closed-loop systems with multiplicative faults. Considering the high efforts in modeling complex systems, the proposed FTC strategy is realized in the data-driven context. Specifically, a nominal feedback-feedforward controller is first established for the fault-free systems. By selecting the system stability and reference tracking behavior as the key performance indices, two performance evaluators are constructed to detect and classify the occurred multiplicative faults based on the fault-induced effects on the system performance. Then, with the aid of the coprime factorization technique, the multiplicative faults, in the form of additive perturbations to the system coprime factors, are estimated utilizing the closed-loop process data. Furthermore, based on the fault knowledge, a hierarchical fault-tolerant tracking controller is developed according to the levels of system performance degradations, where the functional controller parameters are reconfigured with different priorities. Finally, case studies are provided to validate the effectiveness of the proposed method.

This article investigates the problem of data-driven distributed optimal fault detection for large-scale interconnected systems with the unmeasurable interaction term of neighboring system information. For large-scale systems, the computational and storage burdens hinder the application of centralized fault detection methods, while the existence of the unknown interaction term in residual generators brings challenges to distributed fault detection problems. To solve the above problems, the unknown interaction term is implicitly included in each subsystem through an algebraic equivalent transformation, so that the residual generator constructed by the distributed method will not lose the fault information propagated along the network topology. Furthermore, an optimization scheme is designed to measure the effect of the residual signal on noise and faults in all dimensions of the parity space, making the residual generator sufficiently sensitive to even weak faults. Numerical examples and a real hot strip rolling case verify the effectiveness and superiority of the proposed method.

Traditional data-driven fault detection methods based on subspace identification encounter difficulties when performing distributed fault detection on large-scale systems, mainly due to the presence of the unknown interaction term in the residual generator constructed for each subsystem. To tackle these problems, this article proposes a robust distributed fault detection method based on subspace identification for large-scale systems. First, the initial identification error of the residual generator constructed by each subsystem is obtained by using the input and output data information of the local and neighbors, and then a one-step correction theorem is introduced to minimize the error further. In addition, a robust residual generator that is sensitive to faults and robust to noise is constructed by studying all dimensions of the parity space. The effectiveness and superiority of the proposed method are illustrated by comparing the existing methods in two case studies of numerical simulation and real finishing mill system in hot strip rolling.

Unknown interaction items in the construction of distributed residual generators for large-scale systems will lead to the failure of existing data-driven fault detection (FD) methods based on subspace identification. To solve this problem, a subspace-assisted distributed FD scheme under the cloud-edge-end collaboration framework is proposed. For the residual generator constructed for each subsystem, the unknown input item is proved to be represented by the global system's input and output (I/O) data. In addition, based on the represented unknown input term, a data-driven form of the residual generator required for each subsystem is designed. Meanwhile, to eliminate the computing and storage burden caused by the global I/O data required by the represented unknown input item, a cloud-edge-end collaboration architecture is proposed and the corresponding tasks are deployed on the three sides of the cloud-edge-end, respectively. The effectiveness of the proposed method is analyzed and verified by numerical simulation and a real hot rolling case.

Considering that the interaction information between neighbor subsystems is unmeasurable, this article investigates the problem of distributed fault detection (FD) for individual subsystems in a large-scale system. Unmeasurable interaction terms as unknown inputs to subsystems pose a challenge for distributed FD. To cope with this problem, in this article, a distributed FD scheme for large-scale systems is proposed, which utilizes only local and neighbor input and output data information to achieve the estimation of the unknown input term by subspace intersection. In addition, a data-driven distributed residual generator construction method is designed based on the estimated unknown input term. Meanwhile, the rank conditions that need to be satisfied by the distributed method are provided. Finally, the effectiveness of the proposed method is verified and discussed in a simulation example and a real manufacturing case.

The canonical correlation analysis (CCA) has attracted wide attention in fault detection (FD). To improve the detection performance, we propose a new joint sparse constrained CCA (JSCCCA) model that integrates the$\ell _{2,0}$-norm joint sparse constraints into classical CCA. The key idea is that JSCCCA can fully exploit the joint sparse structure to determine the number of extracted variables. We then develop an efficient alternating minimization algorithm using the improved iterative hard thresholding and manifold constrained gradient descent method. More importantly, we establish the convergence guarantee with detailed analysis. Finally, we provide extensive numerical studies on the simulated dataset, the benchmark Tennessee Eastman process, and a practical cylinder-piston process. In some cases, the computing time is reduced by 600 times, and the FD rate is increased by 12.62% compared with classical CCA. The results suggest that the proposed approach is efficient and fast.

This article mainly studies the performance-driven fault detection for general uncertain Takagi–Sugeno fuzzy feedback control systems, where the infinite-horizon quadratic index is introduced to describe the concerned system performance. Different from the existing output-driven fault detection methods, the proposed approach aims to detect the performance degradations induced by faults. For this purpose, the performance index embedded with the information of system dynamics is reformulated for linear feedback control systems with reference inputs. The performance residual, which is adopted as the evaluation function, is derived based on the Bellman equation and further represented into an explainable form. Then, for uncertain linear feedback control systems, the boundaries of the performance residual are analyzed via the linear matrix inequality technique, and an advantaged threshold setting scheme is proposed with the aid of randomized algorithm. Concerning the main objective, a novel approximation method that combines the fuzzy blend of local performance indexes and the radial basis function neural network is developed to approximate the global performance index for Takagi–Sugeno fuzzy systems. Based on the result in the linear case, the performance residual is constructed along the closed-loop system trajectory, and the threshold is determined for the fuzzy control systems with reference inputs and model uncertainties. Finally, simulation studies are provided to show the effectiveness of the proposed theoretical results.

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 studies the performance-oriented fault detection (FD) for nonlinear control systems in the data-driven framework. Unlike the traditional residual- or test statistic-based FD methods, the proposed approach focuses on evaluating the system performance changes/degradations caused by the faults. Specifically, the regulation performance described by an infinite-time cost function is first introduced as a control performance index of the feedback system. Using only the process input and output (I/O) data, a Takagi–Sugeno fuzzy dynamic model is constructed with the aid of subspace identification method. Then, the internal system state variables are expressed in terms of the I/O data and a fuzzy cost function is proposed to approximate the performance index. On this basis, the temporal difference error induced by the Bellman equation is adopted as the process evaluation indicator, whose threshold is determined through the randomized algorithm. To demonstrate the effectiveness of the proposed FD approach, case studies are performed in the end on a ship propulsion system and a three-tank system.

This article proposes an efficient nonlinear process monitoring method (DCCA-SCO) by integrating canonical correlation analysis (CCA), deep autoencoder neural networks (DAENNs), and sparsity-constrained optimization (SCO). Specifically, DAENNs are first used to learn a nonlinear function automatically, which characterizes intrinsic features of the original process data. Then, the CCA is performed in that low-dimensional representation space to extract the most correlated variables. In addition, the SCO is imposed to reduce the redundancy of the hidden representation. Unlike other deep CCA methods, the DCCA-SCO provides a new nonlinear method that is able to learn a nonlinear mapping with a sparse prior. The validity of the proposed DCCA-SCO is extensively demonstrated on the benchmark Tennessee Eastman (TE) process and the diesel generator process. In particular, compared with the classical CCA, the fault detection rate is increased by 8.00% for the fault IDV(11) in the TE process.

This article proposes a novel modeling method for the stochastic nonlinear degradation process by using the relevance vector machine (RVM), which can describe the nonlinearity of degradation process more flexibly and accurately. Compared with the existing methods, where degradation processes are modeled as the Wiener process with a nonlinear drift function formulized as the power law or exponential law, this kind of modeling method can characterize degradation processes with more nonlinear behavior. Instead of modeling the drift coefficient of the Wiener process directly, the weighted combination of basis functions is utilized to express the increment of the Wiener process and the parameters are calculated by a sparse Bayesian learning algorithm. Based on the proposed model, a numerical approximation formula for the probability density function (PDF) of the remaining useful life (RUL) is derived. Finally, comparison studies, including a numerical simulation and a practical case, are provided to demonstrate the effectiveness and the accuracy of the proposed methods for RUL estimation.

This article addresses the performance-based fault detection (FD) and fault-tolerant control (FTC) issues for nonlinear systems. For this purpose, in the first part of this article, the performance-based FD and FTC scheme is investigated with the aid of the nonlinear factorization technique. To be specific, the controller parameterization for nonlinear systems is first discussed. The so-called fault-tolerant margin is introduced as an indicator of the system fault-tolerant ability. Then, the FD scheme aiming at estimating and detecting the stability performance degradation of the closed-loop system caused by the system faults is developed. Furthermore, to recover the system performance, the performance-based FTC strategy is presented. In the second part of this article, the design approach of the performance-based FD and FTC scheme is studied by applying the Takagi-Sugeno fuzzy dynamic modeling technique. The achieved results are demonstrated in the end by a case study on the three-tank system.

This article investigates the problem of fault estimation and fault-tolerant control for a class of Takagi–Sugeno fuzzy stochastic singular systems. An integral-type sliding-surface-based augmented singular sliding-mode observer, which is applicable to both dual-normalized and nondual-normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then, a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated, and the open-loop system can be stabilized. Moreover, a new adaptive sliding-mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.

The approach of feedback iteration in control theory is considered for solving the problem of control allocation algorithm for the case of three moments in this paper. The core of our novel idea is to introduce a closed-loop feedback iteration for obtaining an available solution to control allocation, which is referred to as control theoretic control allocation (CTCA). Two types of CTCA are investigated in this paper: linear case and nonlinear case, where, in the former, the control Lyapunov function (Lyapunov optimizing) and conjugate gradient are introduced, and in the latter, a nonlinear feedback theory is utilized. Thus, the control Lyapunov function and Lyapunov optimizing control allocation (CLF/LOCA), conjugate gradient control allocation (CGCA), and nonlinear CTCA (NCTCA) are proposed in this paper. The performance of each algorithm is evaluated for computational efficiency and accuracy by use of linear or nonlinear aircraft models, respectively. The simulation results show that the proposed CTCA algorithm will terminate in finite steps.

This article discusses the problem of sliding-mode observer (SMO)-based fault reconstruction for T-S fuzzy descriptor systems by using the RBF neural network. First, a descriptor learning SMO, without the observability condition of fast subsystem, is developed such that the reconstruction of fault and states is achieved, simultaneously. Then, a sufficient linear matrix inequality (LMI) condition is presented to guarantee the admissibility of the sliding motion. Meanwhile, the LMI condition ensures the boundedness of the state and fault estimation errors. By utilizing robust H∞strategy, the impact of disturbance on the system can be reduced. Moreover, an RBF neural network-based sliding-mode control (SMC) strategy is adopted to estimate the nonlinearity, unknown positive constants, and ensure the reachability condition, simultaneously. Finally, an example is presented to verify the efficacy of our approach.

This article is concerned with the problem of sliding-mode observer (SMO) design for Takagi-Sugeno (T-S) fuzzy descriptor systems with time-varying delay. First, based on the restricted equivalent transformation, a new restricted equivalent form (REF) of descriptor systems is proposed. Under the new REF, an integral-type sliding surface is constructed for the error system. Then, a sufficient condition is established in terms of linear matrix inequality, which guarantees the admissibility of the sliding-mode dynamics. Furthermore, an radial basis function (RBF) neural network based adaptive sliding-mode control (SMC) strategy is adopted such that the reachability condition can be ensured. By utilizing the RBF neural network to approximate the unknown nonlinearity, many restricted conditions, which are required in most existing results about SMC for T-S fuzzy systems, can be removed. Finally, simulation examples are presented to show the effectiveness of our results.

In this article, two performance-based fault-tolerant control strategies are investigated for multiplicative faults in industrial processes. This is motivated by the fact that the changes in the system parameters caused by malfunctions generally lead to multiplicative faults, which may cause remarkable changes in system dynamics and performance. To be specific, the representation forms of the faulty plants are first given in terms of the so-called stable image and kernel representations, respectively. Then, by measuring the fault-induced system performance degradation, two performance-based fault-tolerant control strategies are formulated. Specifically, a residual-driven dynamic controller, which is also called plug-and-play control, is implemented to achieve control performance recovery in the context of stability margin. Finally, a benchmark study is demonstrated to show the efficiency of the proposed methods.

This paper is concerned with a control performance-based fault-tolerant control strategy for singular systems in presence of multiplicative faults. To be specific, the observer-based realization of Youla parameterization is first addressed for singular systems. Then the fault-tolerant margin for closed-loop systems is studied and further modified to bring forth the stability margin degradation, which serves as an indicator for the performance change caused by the faults in the closed-loop. Based on it, a control performance-based fault detection scheme is realized, aiming at detecting those faults that may affect the system stability. Controller reconstruction rule is given afterwards to ensure the system performance when fault occurs. A circuit system model is finally provided to illustrate the validness of the derived control scheme.

This paper addresses fault-tolerant control (FTC) issues for linear systems with model uncertainty and multiplicative faults. The left and right coprime factorization techniques are first adopted for system modeling. Then, the fault detection (FD) approaches are investigated in the coprime factorization context. Based on the information provided by the FD systems, the corresponding FTC architectures and design schemes are presented. Moreover, the gap metric techniques are applied to fault detectability analysis, including the fault detectability indicators to quantify the detection performance in the presence of model uncertainty. The effectiveness of the developed methods for industrial application is illustrated by a case study on a dc motor.

This paper deals with a real-time-weighted observer-based fault-detection (FD) scheme for Takagi-Sugeno (T-S) fuzzy systems. The essential idea is to develop a weighted diagnostic observer-based FD system to optimize the worst case robustness and fault sensitivity simultaneously by using the information provided by each local system. To achieve an early detection of potential fault, the robustness issue is investigated in the L∞/L2observer-based FD context. Meanwhile, the L-fault sensitivity condition is addressed to optimize the fault detectability. Using fuzzy Lyapunov functions, sufficient conditions on the FD system design are studied. Two examples are given in the end to show the efficiency of the proposed results.

This paper is devoted to the data-driven fault detection of nonlinear systems. For our purpose, the definition of Takagi-Sugeno fuzzy data-driven forms of kernel representations for nonlinear systems is introduced first, which builds the basis of our work. The major contributions consist of two parts. In the first part, a data-driven method for fuzzy process modeling is proposed, and associated with it, some modeling issues are addressed with the aid of the so-called randomized algorithm technique in the probabilistic framework. It is followed by a data-driven realization of fuzzy kernel representation and its implementation in the fault detection system design. To link the data-driven methods to the well-established observer-based fault detection approaches, the recursive form of the fuzzy kernel representation is proposed. In the second part, the fuzzy-observer-based fault detection design scheme is investigated based on the recursive fuzzy kernel representation. The main results of our study are illustrated by an experimental study on the laboratory setup of a three-tank system.

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an £∞/£2type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the £∞/£2observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

This paper is concerned with the analysis and integrated design of a type of observer-based fault detection (FD) system for general nonlinear processes. To this end, the existence and design condition for this type of nonlinear observer-based FD systems is first introduced. In this context, the integrated design scheme is investigated by dealing with the design condition with the aid of Takagi-Sugeno (T-S) fuzzy dynamic modeling technique. To be specific, the universal T-S fuzzy observer-based residual generator is developed via fuzzy Lyapunov functions. Subsequently, an integrated observer-based FD scheme is proposed with an embedded dynamic threshold, which is generated to meet the real-time FD requirements from industrial processes. In the end, a numerical example and case simulation study on a continuous stirred tank heater process are performed to show the application of the proposed method.

The main focus of this paper is on the analysis and integrated design of $\mathcal {L}_2$ observer-based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a deeper insight into this FD framework, the existence condition is introduced first. Then, an integrated design of $\mathcal {L}_2$ observer-based FD approach is realized by solving the proposed existence condition with the aid of Takagi-Sugeno fuzzy dynamic modeling technique and piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems. The core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors. In comparison with the standard norm-based fuzzy observer-based FD methods, the proposed scheme may lead to a significant improvement of the FD performance. In the end, the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant.

A stabilizing regulator designed by any technique whatsoever can be viewed as the combination of a state estimate feedback controller and additional feedback from a dynamic compensator driven by the residual signal (difference between actual and estimated system outputs). Motivated by such an observation, this paper presents the controller design from the premise that system stability is first guaranteed. Control performance can then be enhanced by the optimal design of a residual-driven dynamic compensator subject to some quadratic performance index. The resulting compensator design methods are carried out using both offline and online iterative algorithms with guaranteed convergence. Moreover, the final iterative realization strategy can be implemented online with observed state variables and input updates in case of unknown system dynamics or parameter changes. Simulation results are presented to illustrate design procedures as well as the feasibility of our proposed scheme.