In this paper, an adaptive sensor fault-tolerant tracking control scheme is developed for state-constrained uncertain nonlinear systems. Unlike most existing methods that directly rely on fault-contaminated sensor measurements for feedback control, an adaptive fault-compensated estimator (AFCE) is developed. By embedding an adaptive compensation term into the estimator feedback channel, the AFCE dynamically counteracts sensor faults and enables the joint estimation of system states and external disturbances. To accommodate state constraints, a generalized intermittent state constraint (GISC) approach is introduced. By constructing a novel switching function and an auxiliary variable, the proposed GISC achieves smooth transitions between constrained and unconstrained phases, while eliminating the conventional requirement that the upper and lower bounds have opposite signs. Then, building upon the estimated results, a generalized barrier Lyapunov function is incorporated into the fault-tolerant controller design. Rigorous Lyapunov analysis proves that the actual system output can track the desired reference while all states remain within the prescribed bounds under the established controller. Finally, the effectiveness and superiority of the proposed approach are verified through both simulation and experimental results.

This article presents two fault-tolerant control (FTC) frameworks for high-order fully actuated systems (HOFASs) with actuator faults, sensor faults, and measurement noise. After analyzing the observable architecture corresponding to each measurement, actuator faults are compensated through fusion observers, and sensor faults are rejected through redundant observability. The first FTC framework with traditional fusion observers can merely yield an ultimately uniformly bounded (UUB) error system. To further suppress measurement noise, a dead-zone fusion observation strategy is applied to the FTC redesign. Especially in a linear HOFAS model, the noise suppression performance of the novel FTC framework is proved to be superior. In more general systems, two comparative cases experimentally illustrate trajectory tracking results and noise suppression performance.

Key-performance-indicator (KPI)-related monitoring is crucial to maintain product quality and operational efficiency of industrial processes. However, nonstationary characteristics are often encountered in modern industrial systems due to fluctuations in raw materials, external disturbances, and the change in operational modes. In this context, monitoring of KPI-related variables is hard because statistical characteristics (e.g., mean and variance) of measurement data change over time. In this article, a KPI-related orthogonal trend subspace analysis (KOTSA) is proposed for monitoring nonstationary industrial processes. The idea of KOTSA is to decrease the trend variation of KPI-related variables by means of KPI-unrelated variables. Subsequently, thanks to the well-defined principal angle between two subspaces, two new statistics are proposed for nonstationary process monitoring, which leads to a significant improvement in monitoring performance by evaluating the variation of the nonstationary subspace rather than the nonstationary sample. The monitoring performance of the proposed method is theoretically analyzed and validated on three case studies, and superior monitoring performance is achieved by the proposed method.

Stochastic process-based methods have been widely used for predicting the remaining useful life (RUL) in engineering system health management. However, real-world degradation processes often exhibit non-Markovian dynamics, nonlinear evolution patterns, and varying operating conditions, which pose significant challenges for accurate RUL prediction. To address these challenges, this study proposes an adaptive RUL prediction framework tailored for nonlinear degradation with structural variability and memory effects. The degradation process is initially modeled using fractional Brownian motion (FBM) based on a segment of historical degradation data. During operation, the model adequacy is continuously assessed through a prediction error metric. If the error exceeds a predefined threshold, a prediction error model is activated to recalibrate the model structure. Subsequently, the drift coefficient is updated using an enhanced variational Bayesian Kalman filter (VBKF). The RUL is predicted based on the first hitting time (FHT) concept, from which an approximate analytical distribution is derived. Model parameters are identified through maximum likelihood estimation (MLE). Finally, the effectiveness and adaptability of the proposed approach are demonstrated through case studies involving a blast furnace and lithium-ion batteries.

This article investigates the practical problem of the fault-tolerant tracking control for nonlinear systems subjected to dynamic uncertainties, unknown disturbances, and simultaneous actuator and sensor faults. A novel performance-enhanced intelligent fault-tolerant control (IFTC) framework is developed by integrating the predefined-time stability theory with the optimal control principle. A 1-dimensional convolutional neural network is proposed as a restorer to efficiently detect and isolate sensor faults, upon whose outputs a single radial basis function neural network is constructed to approximate two distinct components of the unknown system dynamics in real time. The proposed fault-tolerant controller ensures the boundedness of all signals within the closed-loop system and guarantees that the tracking errors converge within a user-specified time. Moreover, by incorporating a cost function related to the control effort, the developed controller avoids the excessive control input, achieving an enhanced control performance alongside the predefined-time convergence. Comprehensive simulation results validate the effectiveness and practicality of the proposed performance-enhanced IFTC scheme, highlighting its potential for real-world applications.

With the increasing complexity of industrial production systems, accurate fault diagnosis is essential to ensure safe and efficient system operation. However, due to changes in production demands, dynamic process adjustments, and complex external environmental disturbances, multiple operating conditions frequently arise during production. The multi-condition characteristics pose significant challenges to traditional fault diagnosis methods. In this context, multi-condition fault diagnosis has gradually become a key area of research, attracting extensive attention from both academia and industry. This paper aims to provide a systematic and comprehensive review of existing research in the field. Firstly, the mathematical definition of the problem is presented, followed by an overview of the current research status. Subsequently, the existing literature is reviewed and categorized from the perspectives of single-model and multi-model approaches. In addition, typical real-world application scenarios are then summarized and analyzed. Finally, the key challenges and prospects in the field are thoroughly discussed.

In this paper, the fault estimation and fault-tolerant control problems are addressed for a class of continuous-time switched affine systems with actuator faults and bounded disturbances. Two novel observer-based approaches are developed to address the fault estimation problem for switched affine systems. The first one refers to a dynamic proportional-integral observer design method, where the presented fault estimate constitute proportional and integral terms to enhance the accuracy of the fault estimation, the common assumption that the measurement output derivative needs to be measurable is eliminated. The second one is an intermediate variable observer, which relaxes the observer matching condition. The output estimation error feedback term is added to the intermediate variable observer to improve the estimation performance. Then, by introducing a switching multi-shifted-point-dependent Lyapunov functional, both a fault-tolerant controller and a new robust output-dependent switching law are jointly designed to compensate the fault effects in the closed-loop switched affine systems and to ensure the practical exponential stability of augmented system, where the convergence region consists of multiple regions and the center point is around some shifted points. The traditional switching quadratic Lyapunov function method is generalized by the designed method. A practical study of a DC-DC boost converter and a numerical example are provided to illustrate effectiveness and validity of the developed fault-tolerant control design method. Note to Practitioners—Power electronics are very common in practical systems, which are usually modeled as a class of switched affine systems. In real applications, faults inevitably occur, which may lead to undesirable behavior and damage to the system. Therefore, how to achieve better fault-tolerant control objectives to guarantee the normal operation of the system with faults is a hot topic. It is practically important to address the fault-tolerant control problem for switched affine systems, where actuator faults and bounded disturbances exist simultaneously. In addition, on account of the existence of affine terms, the controller synthesis of switched affine systems is more complicated than switched linear systems. Based on the special structure of switched affine systems, two kinds of novel fault observers are proposed, where the dynamic proportional-integral observer is proposed to improve the estimation accuracy and speed by utilizing the current output information, and the common supposition that the output derivative needs to be measurable is eliminated. Furthermore, to avoid the limitation of observer matching conditions, an improved intermediate variable observer is designed to estimate faults. Different from the conventional method, the intermediate variable parameters can be selected separately for the corresponding fault channel of each subsystem and the error feedback term of output estimation is added to the intermediate variable observer to enhance the estimation performance. In addition, it is challenging to design a fault-tolerant controller and an output-dependent switching law to guarantee that the augmented system is practically stable and robust to bounded disturbances. The results demonstrate that the designed fault-tolerant control scheme has a definitive practical value.

This article proposes a novel multicontroller-based fault tolerance method to cope with a class of high-order sub-fully actuated systems (sub-FASs) with nonlinear uncertainties and actuator faults. As a promising control-oriented theory, the FAS approach is a convenient and powerful tool for nonlinear control. However, the stabilization of sub-FASs, whose input matrix function is not globally invertible, is more sophisticated and challenging due to the issue of control singularity. To address the global fault-tolerant stabilization of uncertain sub-FASs, a high-order nonlinear system model with both multiplicative and additive actuator faults is considered. By introducing the concepts of linear singular set and singularity function, the entire state space is analytically divided into several regions. Then, according to the initial states of system, three different control strategies are developed to overcome singularity and achieve global stabilization, including a FAS-based stabilizing control law, a singularity-avoid tracking control strategy, as well as a singularity-free switching control strategy. The closed-loop response of the faulty system is proven to be ultimately uniformly bounded in all cases, and the effectiveness of proposed method is illustrated through a numerical example.

This article investigates the problem of fault-tolerant control for stochastic high-order fully actuated systems (FASs) with actuator faults. Different from the majority of existing studies focusing on deterministic high-order FASs, this work introduces stochastic disturbances into the systems. Employing the generalized martingale technique, a novel fault-tolerant equivalent controller is formulated. Additionally, an adaptive compensation law is constructed to address time-varying faults promptly. The designed preclosed-loop strategy advocates the advantage of the FAS methodology and guarantees performance by ensuring that the tracking error complies with the user-defined probabilistic ultimate bound. Finally, a numerical case and a practical example of a rotary steerable drilling platform are exploited to demonstrate the effectiveness of the proposed method.

Effective fault diagnosis is crucial for maintaining the reliability and safety of industrial systems. Incremental learning, which enables models to continuously update and adapt to new data or emerging fault classes without complete retraining, has recently gained attention as a promising solution for addressing nonstationary data streams in fault diagnosis applications. Nevertheless, most existing review articles on fault diagnosis adopt a broad perspective, primarily discussing general techniques such as deep learning and transfer learning, without providing a dedicated focus on incremental learning strategies. To the best of our knowledge, it is the first review focusing specifically on incremental learning-enabled fault diagnosis methods. In this work, state-of-the-art incremental learning-enabled fault diagnosis are systematically reviewed. These methods are categorized into distinct groups based on their incremental learning strategies and application contexts. In addition, major challenges associated with applying incremental learning to fault diagnosis, including concept drift and catastrophic forgetting, are discussed, along with emerging solutions proposed to address these issues. A novel taxonomy and perspective on incremental learning-enabled fault diagnosis approaches is presented, providing a timely and comprehensive reference for researchers and practitioners in this evolving field.

This article focuses on the fault reconstruction and bumpless transfer fault-tolerant (FT) control problems for switched linear systems with magnitude-bounded disturbances and actuator faults in continuous-time domain. A new learning-based robust unknown input observer (UIO), not requiring fault differentiability and completely decoupled disturbances, is developed to accomplish fault reconstruction and state estimation. The fault reconstruction value is updated by one iteration learning on the timeline, i.e., the fault at the current moment is reconstructed by learning historical information from the previous moment. Based on the obtained estimation information, an efficient bumpless transfer FT controller is designed to counteract the fault effects and suppress the control bumps. The bumpless transfer constraint is guaranteed via a new inequality transformation method, which improves the anti-disturbance capability of the controller and also decreases the switching bumps. The solvability conditions for the bumpless transfer controller and learning-based UIO are developed under the condition of average dwell time switching. Finally, an application of the inverted pendulum controlled by a direct current motor is presented to reveal the effectiveness and applicability of the developed methods.

This article portrays a class of local faults (LFs), whose basic characteristic is that the fault occurs only when the system state is in a certain domain. To accurately tolerate LFs for stochastic higher-order fully actuated systems, a novel active fault-tolerant control (AFTC) strategy is proposed. The indicators of entering and leaving fault domains are designed to enable the estimation of fault domains. The boundedness in probability of tracking error is guaranteed theoretically through the whole stages of AFTC. Finally, a practical example is presented to demonstrate the effectiveness of the proposed AFTC framework.

This article delves into fault-tolerant control (FTC) for stochastic fully actuated systems (SFASs) affected by component faults. Parallel to most existing studies focusing on deterministic fully actuated systems (FASs), this work considers the impact of stochastic disturbances. To stabilize the system states effectively, an adaptive state feedback FTC law is developed using a novel mixed-order backstepping technique in the sense of expectation. Under the circumstance of limited measurement, an observer-based FTC framework is also established with the necessary and sufficient condition for the distinguishableness of component faults. Both the devised fault compensation strategies ensure performance by constraining all signals within the prescribed probabilistic bounds, underscoring the advantages inherent in the FAS methodology concurrently. Finally, numerical and physical examples validate the efficacy of the proposed method.

This article studies the bumplessH∞control issue for a class of continuous-time switched linear systems with mode-dependent average dwell time (MDADT) switching. A new two-step approach is proposed to suppress the control input bumps. First, the predesigned stabilizing controller is acquired via imposing the common-matrix-based bump limitation constraints. Second, the transition bumpless transfer (BT) controller is designed to be activated at the subsystem switching instants and combined with the stabilizing controller to constitute the transition-dependent piecewise BT controller. By applying the new transition-dependent piecewise Lyapunov function and the control amplitude limitation strategy, sufficient conditions are derived for the existence of a piecewise BT controller under MDADT switching. Finally, a tunnel diode circuit system is provided to highlight the feasibility and superiority of the developed BT control method.

This article proposes an intermittent optimal learning control strategy for nonlinear discrete-time systems under time-varying pass lengths and actuator faults. The target of the problem is to minimize the timewise tracking error and the input drifts, which are combined by a time-iteration-dependent factor. By searching the nearest available pass at each time instant for the current iteration, the optimal control gain can be obtained. Theoretical analysis indicates that the tracking error converges asymptotically in spite of the actuator fault and the robustness against the shifted initial state is further proven. Numerical simulations illustrate the effectiveness and robustness of the presented method.

Active fault diagnosis (AFD) techniques can improve fault diagnosis performance by designing a set of appropriate auxiliary inputs and injecting them into the system to stimulate fault characteristics. The AFD problem for uncertain linear parameter-varying (LPV) systems with bounded external disturbances is studied based on a set-membership approach in this paper. Based on zonotopes, a set-membership observer is designed to estimate system states to reduce the influence of external disturbances, which aims to reduce conservatism. A$F_{W}$-radius-based criterion is minimized to get the optimal observer gain matrix. Because of the system uncertainties, the generator matrices of the output sets will have elements associated with the auxiliary input. A method is proposed to eliminate the relationship between the auxiliary input and the generator matrices, and a mixed-integer quadratic program (MIQP) is constructed to get the auxiliary input. By solving the optimization problem, the auxiliary input is designed for the considered finite kinds of faults to achieve fault diagnosis. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed approach.Note to Practitioners—This paper studies the AFD problem for uncertain LPV systems. Most existing AFD methods are proposed for linear time-invariant systems. The uncertainty of the LPV systems makes the existing AFD methods no longer applicable. In addition, most of the existing AFD methods for uncertain LPV systems are based on the following framework: the auxiliary input is designed at the initial time and injected directly into the system. This framework does not adjust the auxiliary input according to the real-time output of the system during the diagnosis process, which leads to the conservatism of the method. To handle these challenges, this paper proposes an AFD method based on a set-membership approach. A set-membership observer is designed to estimate the system state set based on the system output information. Then the auxiliary input is recalculated according to the estimated system state by solving a MIQP problem at each step. Simulation results suggest that the proposed method is feasible, but it has a large computational burden when the system is complex. Our future work is mainly to reduce the computational complexity and the impact of auxiliary inputs on system performance.

A novel continual learning-based probabilistic slow feature analysis algorithm is introduced for monitoring multimode nonstationary processes. Multimode slow features are extracted and an elastic weight consolidation (EWC) is adopted for sequential modes. EWC was originally introduced in the setting of machine learning of sequential multi-tasks with the aim of avoiding catastrophic forgetting issue, which equally poses as a major challenge in multimode nonstationary process monitoring. When a new mode arrives, a small set of data are collected for continual learning by the proposed algorithm. A regularization term is introduced to prevent new data from significantly interfering with the learned knowledge, where the parameter importance measures are estimated. The proposed method is referred to as PSFA–EWC, which is updated continually and is capable of achieving excellent performance. PSFA–EWC furnishes backward and forward transfer ability by a single model. The significant features of previous modes are retained while consolidating new information, which may contribute to learning new relevant modes. The effectiveness of the proposed method is demonstrated via a continuous stirred tank heater and a practical coal pulverizing system. Note to Practitioners—Since industrial systems operate in varying modes and data are nonstationary within each mode, multimode nonstationary process monitoring is increasingly important. Traditional multimode monitoring methods generally need complete data from all possible modes and may need to be retrained from scratch when a new mode arrives, which require expensive computation and storage resources. Besides, it is difficult to distinguish real faults from normal variations in multimode nonstationary processes. This paper proposes a novel continual learning-based probabilistic slow feature analysis, where elastic weight consolidation is employed to consolidate the previously learned knowledge while extracting multimode slow features. The monitoring model is updated sequentially and provides backward as well as forward transfer learning ability for successive modes. It is able to separate real faults from normal dynamics, which is beneficial to identifying a new mode for multimode nonstationary processes. In addition, the proposed approach delivers excellent model interpretability and deals with missing data as well as uncertainty. In industrial applications, such as power plants and intelligent manufacturing processes, the proposed method can provide excellent monitoring performance.

This article presents a novel self-healing fault accommodation framework for high-order fully actuated systems (HOFASs) with sensor faults. Starting from the HOFAS model with nonlinear measurements, a q -redundant observation proposition is derived from an observability normal form based on each individual measurement. On the heels of the ultimately uniformly bounded error dynamics, a definition of sensor fault accommodation is determined. After a necessary and sufficient accommodation condition is highlighted, a self-healing fault-tolerant control strategy is proposed, which can be applied in steady-state processes or transient processes. The main results are proved theoretically and illustrated experimentally.

In this article, a finite-time fault-tolerant controller based on the fully actuated system (FAS) theory is presented to realize system stabilization and trajectory tracking. Paralleling to first-order nonlinear state space theory, the high-order FAS (HOFAS) theory contains rich controller design approaches. The existing FAS approaches can only give general global asymptotic stability results. In order to enhance the applicability of FAS approaches in fast control systems, a parameterized FAS stabilization controller based on the homogeneity principle is established for global finite-time stability. Moreover, a finite-time FAS tracking controller based on a finite-time observer is proposed for a HOFAS model with process faults. The proposed observer can yield zero-value convergence of state estimation error and fault estimation error in a finite time, and the proposed fault-tolerant controller can yield zero-value convergence of tracking error in a finite time. The main results are proved theoretically and illustrated experimentally.

In recent years, high-order fully actuated (HOFA) systems, founded by Prof. GR Duan, have recorded rapid progress for deterministic systems. However, the control issue of stochastic fully actuated systems is still an open problem. This study develops a novel stochastic HOFA system model that complements the existing HOFA methodology. Notably, stochastic signals can be considered in the proposed model, different from the case in the deterministic model. By adopting a high-order operator, equivalent control and stabilization control laws are realized to guarantee the global asymptotic stability in probability of the closed-loop system. For the system with sensor gain faults, an observer-based fault-tolerant control law is designed. Finally, the simulation results validate the effectiveness of the proposed control schemes.

Effective process monitoring is both a prerequisite and a guarantee for high system reliability. In modern industrial processes, binary variables may appear together with continuous variables, making process monitoring more intractable. Recently, a model named hybrid variable monitoring (HVM) has been proposed to conduct anomaly detection with both continuous and binary variables. Although the performance of HVM has been significantly improved after using the information of binary variables, it assumes that every continuous variable obeys a single Gaussian distribution and each binary variable obeys a single Bernoulli distribution. It is difficult for practical processes to satisfy such strict assumptions. To overcome this problem, this study proposes an improved algorithm called HVM mixture model (HVMMM). The HVMMM contains multiple components with the assumption of an HVM for every component. Compared with the HVM, the HVMMM is suitable for more general situations and has a more accurate characterization of the data features. Subsequently, the expectation-maximization (EM) algorithm is adopted for parameter learning for multiple components. The mathematical expressions of the parameters are derived in detail. In addition, the improvement on the monitoring performance caused by multiple components is analyzed. Finally, a numerical example and a practical case are used to demonstrate the effectiveness and efficiency of HVMMM. After multiple components are considered, the fault detection rate increases by 5.49% in the numerical example and the false alarm rate reduces by 1.6% in the practical case.

This article is concerned with the problem of intermittent fault detection for a class of nonlinear systems through observer-based methods. Different from the permanent fault detection, this article devotes to detecting both the appearance and disappearance of intermittent faults, which has strict requirements on the convergence property of the observation error. A predefined-time observer is designed for sector-bounded nonlinear systems to guarantee that the observation error reaches stability within a preset time. Using the implicit Lyapunov function method and the homogeneity theory, some linear matrix equations and inequalities are derived to solve the observer gain such that the observation error system is input-to-state stable. Then, the residual is generated and evaluated to detect the fault. Finally, the feasibility and effectiveness of the proposed approach are verified by an experiment on the prototype of rotary steerable drilling tool system.

This paper addresses a path-guided formation-containment control problem by virtue of the aperiodic communication for networked heterogeneous multi-vehicle systems suffering from actuator faults and uncertainties. At the leader layer, a novel three-dimensional (3-D) path-following formation controller endowed with spatial-temporal decoupling and path invariance advantages is presented for multiple quadrotors to accomplish a preassigned formation pattern along implicit paths. At the follower layer, in light of neighboring transmission, a containment controller is proposed that actuates several unmanned vehicles to access the convex hull generated by the leaders. Besides, by incorporating an event-triggered criterion with a state predictor, an aperiodic transmission strategy is established to alleviate the communication burden and evade unnecessary resource wastage. Subsequently, to recognize the actuator faults and uncertainties, guided by invariant manifold principle, unknown system dynamics estimators (USDEs) are elaborated on the strength of straightforward filtering operations. Finally, the stability of entire closed-loop system is proved according to Lyapunov analysis and input-to-state stability (ISS), while the effectiveness and superiority are demonstrated by simulations.

In this article, the nonaffine high-order fully actuated system (HOFAS) structure is established, and a tracking controller and a robust fault-tolerant stabilization controller for unknown fully actuated systems are proposed. Starting from the unknown nonaffine HOFAS model, a saturated controller dynamic equation based on extended state observer is yielded, which ensures the low-power characteristics of the controller. Both the observation error and tracking error are shown to converge eventually, and the upper error bound can be adjusted to a small neighborhood near zero. Furthermore, for unknown nonaffine HOFASs with multiplicative actuator and sensor faults, a robust fault-tolerant stabilization controller is presented to guarantee the ultimately uniformly bounded stability and the convergence to zero. The main results are proved theoretically and illustrated experimentally.

In this article, the problem of fault isolation is studied for linear stochastic time-varying systems. Different from the existing results about fault isolation, the system in this article suffers from strong noise, which increases the difficulty of distinguishing different fault components since the difference in measurement distributions caused by different fault components is small. To handle this problem, a novel fault isolation scheme comprising a set of residuals, a set of evaluation functions, and a decision logic is proposed. First, based on the hypothesis testing method, two performance indices reflecting the probability of two classes of false isolation induced by noise are introduced to quantitatively evaluate the influence of strong noise on residuals. Under a given threshold, the existence of the optimal residual with two minimal performance indices is proved in this article, which minimizes the effect of noise on residuals. Subsequently, a suboptimal recursive residual whose parameter gradually tends to the parameter of the optimal residual is designed. Following this, by employing the$\chi ^{2}$test and the predesigned decision logic, fault isolation can be realized. Finally, two illustrative examples are provided to show the effectiveness of the proposed method.

This paper introduces a novel sparse dynamic inner principal component analysis (SDiPCA) based monitoring for multimode dynamic processes. Different from traditional multimode monitoring algorithms, a model is updated for sequential modes by memorizing the significant features of existing modes. By adopting the concept of intelligent synapses in continual learning, a loss of quadratic term is introduced to penalize the changes of mode–relevant parameters, where modified synaptic intelligence (MSI) is proposed to estimate the parameter importance. Thus, the proposed algorithm is referred to as SDiPCA–MSI. When a new mode arrives, a set of normal samples should be collected. The previous significant features are consolidated without explicitly storing training samples, while extracting new information from the current mode. Consequently, SDiPCA–MSI can provide outstanding performance for successive modes. Characteristics of the proposed approach are discussed, including the computational complexity, advantages and potential limitations. Compared with several state-of-the-art monitoring methods, the effectiveness and superiorities of the proposed method are demonstrated by a continuous stirred tank heater case and a practical industrial system. Note to Practitioners—Multimode process monitoring is increasingly significant as industrial systems generally operate in varying operating conditions. However, most researches focus on multiple local monitoring models for complex multimode processes and assume that data of all possible modes are available and stored before learning. When similar or new modes arrive, local models are rebuilt corresponding to each mode and the model’s capacity would increase with the continuous emergence of modes. Adaptive methods are a branch of multimode monitoring algorithms, but they strive to extract information of the current mode to ensure the monitoring performance while forgetting the previously learned knowledge gradually. This paper proposes a novel sparse dynamic inner principal component analysis with continual learning ability for multimode dynamic process monitoring, where modified synaptic intelligence is developed to measure the parameter importance accurately. It requires limited computation and storage resources for successive modes, which is convenient for practical applications. Similar to current multimode process monitoring algorithms, a set of data should be collected before learning a new mode, which may bring difficulties to real–time monitoring. For industrial systems, such as large–scale power plants and chemical systems, the proposed method has outstanding ability to monitor successive dynamic modes.

This study investigates nonstationary process monitoring under frequently varying modes, where new modes are allowed to emerge constantly. However, in current multimode process monitoring methods, generally, data are required from all possible modes and mode identification is realized by prior knowledge for multimode nonstationary processes. In contrast, recursive methods update a monitoring model based on the successive data. However, they forget the learned knowledge gracefully and fail to track drastic variations. Aimed at nonstationary data in each mode, this article proposes an adaptive cointegration analysis (CA) to distinguish real faults from normal variations, which updates a model once a normal sample is encountered and adapts to the gradual change in the cointegration relationship. Then, a modified recursive principal component analysis (RPCA) with continual learning ability is developed to deal with the remaining dynamic information, wherein elastic weight consolidation is adopted to consolidate the previously learned knowledge when a new mode appears. The preserved information is beneficial for establishing a more accurate model than traditional RPCA and avoiding drastic performance degradation for future similar modes. In addition, novel statistics are proposed with prior knowledge and thresholds are calculated by recursive kernel density estimation to enhance the performance. An in-depth comparison with recursive CA and recursive slow feature analysis is conducted to emphasize the superiority, in terms of the algorithm accuracy, memory properties, and computational complexity. Compared with state-of-the-art recursive algorithms, the effectiveness of the proposed method is shown by studying on a numerical case and a practical industrial system.

In this article, the consensus control problem is investigated for mobile train lifting jack systems (TLJSs) of electric multiple units in the context of distributed industrial systems. First, a kind of global consensus controller is dedicatedly designed to deal with the underlying actuator limitation that is a typical phenomenon in mobile TLJSs and is referred to as actuator saturation. In order to better cater for the impact from the TLJSs, we consider the asymmetric actuator saturations (rather than their symmetric counterparts) whose side effects are later attenuated by means of a novel Lyapunov-function-based method. A series of experiments are conducted on mobile TLJSs so as to illustrate the effectiveness of the proposed consensus control algorithm.

Multiple operating modes have become a key factor affecting the monitoring performance of practical industrial processes. The monitoring of multiple modes with hybrid variables (containing continuous and binary variables) is more intractable. In addition, the label information of the training data may be unavailable, and new modes may arrive or collected modes may disappear in continuous running of the system owing to the influence of production strategies, materials, loads, etc. Therefore, this article proposes an adjustable multimode monitoring with hybrid variables (AMMHV) model. In AMMHV, the expectation maximization algorithm is utilized for parameter estimation when the label information is unknown. AMMHV can not only effectively conduct the multimode process monitoring of hybrid variables without the label information of training samples, but also be updated without retraining when operation modes change. The incremental learning strategy is adopted to extend the model to give it outstanding monitoring performance for new arriving modes. If the originally collected modes no longer appear during operation, AMMHV can improve the monitoring accuracy of the remaining modes by condensing redundant irrelevant information. Finally, the superiority of AMMHV is fully demonstrated first on a numerical example and then on a process of a thermal power plant.

This article proposes a novel sparse principal component analysis algorithm with self-learning ability for multimode process monitoring, where the successive modes are learned in a sequential fashion. Different from traditional multimode monitoring methods, a small set of data are collected when a novel mode arrives. The proposed method remembers the learned knowledge by selectively slowing down the changes of parameters important for the previous modes, where the importance measure is estimated by synaptic intelligence. The sufficient condition of fault detectability is proved to provide a comprehensive understanding of the proposed method. Besides, the computation and storage resources are saved in the long run, because it is not necessary to retrain the model from scratch frequently and data are discarded once they have been learned. More importantly, the model furnishes excellent interpretability and the catastrophic forgetting problem is further alleviated owing to the sparsity of parameters. In addition, the hyperparameters are discussed to understand the proposed method comprehensively and the computational complexity is analyzed. Compared with several state-of-the-art approaches, a numerical case, and a practical pulverizing system are adopted to illustrate the effectiveness of the proposed algorithm.

This article presents a novel observer-based fault-tolerant controller framework for a class of nonideal time-varying high-order fully actuated systems (HOFASs). The HOFAS theory is an emerging nonlinear dynamical system theory, which can yield global stability. In order to improve the ability of HOFAS theory to handle parameter uncertainties, actuator faults, and measurement noises, a nonlinear extended state observer and low-power fully actuated controller framework is established in this article. Particularly, the linear framework conforms to the generalized separation principle and highlights the advantages of HOFAS parametric design. Moreover, the work takes into account fault tolerance and noise suppression in engineering applications, reducing the dependence of HOFAS theory on model accuracy. The uniformly bounded stability and noise suppression performance are also proved theoretically and illustrated experimentally.

With the increasing complexity and scale of modern industrial processes, there widely exist two-valued variables (TVs), such as status monitoring and numerical range variables. However, the traditional process monitoring approaches (such as principal component analysis and partial least square) are strongly based on continuous variables (CVs), thus they totally ignore the useful merit inherent in TVs. Recently, both CVs and TVs are used in combination for monitoring industrial processes for the first time. The mixed hidden naive Bayesian model (MHNBM) and feature-weighted mixed naive Bayes model (FWMNBM) have been proposed to enhance the monitoring performance by simultaneously and efficiently exploiting the valuable information of TVs and CVs. Nevertheless, both models are not suitable for nonstationary processes, which are consistent with the real property of many practical cases. Therefore, this article mainly proposes a novel self-learning FWMNBM (SL-FWMNBM) for nonstationary process monitoring. SL-FWMNBM constantly updates the model parameters in real time at the online detection stage to overcome the changes in the statistical characteristics of monitoring variables. It has the ability to mine process information carried by newly sampled data through self-learning, which is the main difference between SL-FWMNBM and the above two methods. The effectiveness of SL-FWMNBM is demonstrated through a simulation and an actual vibration case of the Zhoushan thermal power plant, China.

In this article, the problem of intermittent fault (IF) detection is investigated for linear stochastic systems over sensor networks, where the appearing and disappearing times, and magnitude of IF are all nondeterministic. By utilizing the moving-horizon estimator, a novel residual generator is designed to realize the distributed detection of IFs in sensor networks. Different from the traditional moving horizon estimation algorithms, weight matrices of the quadratic cost function in this article are regulated by an unreliability index of the prior estimate to suppress the smearing effect of IFs. In virtue of the matrix transformation method and statistical theory, estimator parameters are obtained and the detectability of a single IF is analyzed by using the residual. In order to avoid the collisions of detection results from different residuals, the global detectability condition is given for all IFs. A cooperative decision-making strategy is proposed such that the only detection result can be guaranteed, which includes the appearing and disappearing times of IFs, and the nodes suffering from IFs. Finally, an illustrative example is provided to show the feasibility and effectiveness of the derived results.

In this article, a robust asymptotic fault estimation (RAFE) design is proposed for discrete-time interconnected systems with sensor faults. By constructing a singular augmented system, an equivalent description of the considered interconnected systems is presented. Then, a novel RAFE observer is proposed for the singular augmented system. Furthermore, gain matrices of the RAFE observer are calculated based on multiconstrained design. Simulation results are illustrated to show the feasibility of the presented approaches.

Practical industrial processes usually have nonstationary properties, which make the monitoring more challenging because the fault information may be buried by nonstationary trends. For nonstationary processes, many methods have been proposed for fault detection based on continuous variables. However, binary variables may appear together with continuous variables in modern industrial processes. To address the issue of process monitoring with hybrid variables and nonstationarity, a model named recursive hybrid variable monitoring (RHVM) is proposed in this paper. For RHVM, recursive strategy is utilized to suppress nonstationary trend and to reveal fault information. In addition, RHVM has the ability of model self-updating with arriving samples. The closed-form updates of required parameters are derived in detail and the improvement of performance is analyzed. At last, the superiority of the proposed model is demonstrated by a simulation example and a practical nonstationary process of a power plant.

Actual industrial processes often show nonstationary characteristics, so nonstationary process monitoring is significant to ensure the safety and reliability of industrial processes. However, existing monitoring methods for nonstationary processes usually ignore process uncertainties, caused by random noises and unknown disturbances. It is worth noting that process uncertainties may degrade the monitoring performance for incipient faults, and result in over-fitting of model parameters. To address the problem of monitoring nonstationary industrial processes with uncertainty, a novel algorithm called probabilistic stationary subspace analysis (PSSA) is proposed in this article. PSSA explicitly models process uncertainties, and distinguishes actual process variations from the uncertainty. In view of the coupling between model parameters, the expectation maximization algorithm is used to estimate the parameters of PSSA, and the closed-form updates are derived in detail. Based on PSSA, two detection statistics are designed for process monitoring. Finally, the effective performance of the proposed method is demonstrated by three case studies, including a numerical example, a closed-loop continuous stirred tank reactor, and a real power plant at Zhejiang Provincial Energy Group of China.

In this article, an integrated design diagram for a stable kernel representation (SKR)-based data-driven fault detection (FD) system and performance criteria is proposed for stochastic dynamic systems in the probabilistic sense. A new distributionally robust FD system is developed using input and output data in the absence of a system model and perfect probability distributions for noises and random faults. To be specific, an SKR-based data-driven primary residual generator is first constructed. By introducing the so-called mean-covariance based ambiguity sets, families of probability distributions of the primary residual in fault-free and the concerned multiple faulty cases are characterized. The FD system design is then formulated as a distributionally robust optimization problem in the sense of minimizing the missed detection rate (MDR) with a predefined upper bound of false alarm rate (FAR). With the aid of worst-case conditional value-at-risk, a matrix-valued distribution independent solution to the targeting FD problem is derived without posing specific distribution assumptions. The developed FD system is, thus, robust against the distributional uncertainties of noises and random faults. Simultaneously, a tighter upper bound of MDR for an identical FAR criterion is achieved in comparison with the vector-valued distributionally robust FD method. An experimental study on a laboratory setup of a three-tank system shows the applicability of the proposed method.

Estimated time of arrival (ETA) is one of the most important services in intelligent transportation systems (ITS). Precise ETA ensures proper travel scheduling of passengers as well as guarantees efficient decision-making on ride-hailing platforms, which are used by an explosively growing number of people in the past few years. Recently, machine learning-based methods have been widely adopted to solve this time estimation problem and become state-of-the-art. However, they do not well explore the personalization information, as many drivers are short of personalized data and do not have sufficient trajectory data in real applications. This data sparsity problem prevents existing methods from obtaining higher prediction accuracy. In this article, we propose a novel deep learning method to solve this problem. We introduce an auxiliary task to learn an embedding of the personalized driving information under multi-task learning framework. In this task, we discriminatively learn the embedding of driving preference that preserves the historical statistics of driving speed. For this purpose, we adapt the triplet network from face recognition to learn the embedding by constructing triplets in the feature space. This simultaneously learned embedding can effectively boost the prediction accuracy of the travel time. We evaluate our method on two large-scale real-world datasets from Didi Chuxing platform. The extensive experimental results on billions of historical vehicle travel data demonstrate that the proposed method outperforms state-of-the-art algorithms.

With millions of people using ride-hailing platforms for daily travel, estimated time of arrival (ETA) has become a significant problem in intelligent transportation systems and attracted considerable attention recently. Deep learning-based ETA methods have achieved promising results using massive spatial-temporal data. However, we find that the prediction accuracy is not satisfactory in practical applications due to the prevalent data sparsity problems. Instead of focusing on the average prediction performance as many other methods, this study aims to alleviate the data sparsity problems in ETA to enhance user experience. In general, the data sparsity problems arise from two aspects. The first is the road network, where many links are only traversed by few floating cars. The second aspect is drivers, where many drivers’ trajectories are too scarce (e.g., with only 3 trip records). To alleviate the sparsity in road network, we propose a Road Network Metric Learning framework for ETA (RNML-ETA), where an auxiliary metric learning task is used to improve the link-embedding, especially for links with insufficient data. A novel triangle loss is proposed to improve metric learning effectiveness for links. Experiments on massive real-world data show that RNML-ETA outperforms competing methods by promoting the cold links with limited data. Furthermore, we propose a novel unified framework to Alleviate Data Sparsity problems in ETA (ADS-ETA) by extending RNML-ETA with an additional auxiliary task for driver ID embedding. Results with extensive experiments demonstrate that ADS-ETA can effectively alleviate the data sparsity problems caused by road network and driver sparsity.

Wheelset intermittent over-creeps (WIOs), i.e., slips or slides, can decrease the overall traction and braking performance of Electric Multiple Units (EMUs). However, they are difficult to detect and isolate due to their small magnitude and short duration. This paper presents a new index called variable-to-minimum difference (VMD) and a novel technique called weighted moving average (WMA). Their combination, i.e., the WMA-VMD index, which uses correlation information to find an optimal weight vector (OWV) for the VMD indices within a time window, is employed to detect and isolate WIOs in real time. The uniqueness of the OWV is proven, and its properties such as the symmetrical structure are revealed. WIO detectability and isolability conditions of the WMA-VMD index are provided, leading to the property analyses of two nonlinear, discontinuous operators,$\min $and VMDi. Experimental studies are conducted based on practical running data and a hardware-in-the-loop platform of an EMU, which show the effectiveness of the developed method.

This article is concerned with the problem of state estimation for continuous-time polynomial nonlinear (CTPN) systems with unknown but bounded disturbances. The Taylor polynomial expansion technique is employed to realize the conversion from polynomial nonlinear systems to linear-parameter-varying systems related to the estimate. Moreover, for the purpose of saving the communication resources, an event-triggered sampling scheme is first introduced in the state estimation for CTPN systems, where the event-triggered condition is changed dynamically and the Zeno behavior is excluded. Based on the matrix inequality approach, a sufficient condition is derived in terms of the parameter-dependent linear matrix inequality (LMI) such that the estimation error system is input-to-state stable. Then, the desired estimator parameters can be obtained by solving the parameter-dependent LMI via the sum of squares decomposition technique. Finally, two examples with one concerning the permanent magnet synchronous motor systems are provided to demonstrate the usefulness of proposed method.

Operation safety and efficiency are two main concerns in power plants. It is important to detect the anomalies in power plants, and further judge whether they affect key performance indicators (KPIs), such as the thermal efficiency. These two goals can be achieved by KPI-related nonstationary process monitoring. Although the thermal efficiency cannot be accurately measured online, it can be strongly characterized by some online measurable variables, including the exhaust gas temperature and oxygen content of flue gas. These critical variables closely related to the thermal efficiency are termed as output variables. Inspired from nonstationary common trends between input and output variables in thermal power plants, the output-relevant common trend analysis (OCTA) method is proposed, in this article, to model the input–output relationship. In OCTA, input and output variables are decomposed into nonstationary common trends and stationary residuals, and the model parameters are estimated by solving an optimization problem. It is pointed out that OCTA is a generalized form of partial least squares (PLS). The superior monitoring performance of OCTA is illustrated by case studies on a real power plant in Zhejiang Provincial Energy Group of China. Compared with the other PLS-based recursive algorithms, OCTA can effectively detect the anomalies in power plants and accurately determine whether they have an impact on the thermal efficiency or not.

The full information estimation (FIE) problem is addressed for discrete time-varying systems (TVSs) subject to the effects of a round-Robin (RR) protocol. A shared communication network is adopted for data transmissions between sensor nodes and the state estimator. In order to avoid data collisions in signal transmission, only one sensor node could have access to the network and communicate with the state estimator per time instant. The so-called RR protocol, which is also known as the token ring protocol, is employed to orchestrate the access sequence of sensor nodes, under which the chosen sensor node communicating with the state estimator could be modeled by a periodic function. A novel recursive FIE scheme is developed by defining a modified cost function and using a so-called “backward-propagation-constraints.” The modified cost function represents a special global estimation performance. The solution of the proposed FIE scheme is achieved by solving a minimization problem. Then, the recursive manner of such a solution is studied for the purpose of online applications. For the purpose of ensuring the estimation performance, sufficient conditions are obtained to derive the upper bound of the norm of the state estimation error (SEE). Finally, two illustrative examples are proposed to demonstrate the effectiveness of the developed estimation algorithm.

This paper is concerned with the moving horizon (MH) estimation issue for a type of networked nonlinear systems (NNSs) with the so-called random access (RA) protocol scheduling effects. To handle the signal transmissions between sensor nodes and the MH estimator, a constrained communication channel is employed whose channel constraints implies that at each time instant, only one sensor node is permitted to access the communication channel and then send its measurement data. The RA protocol, whose scheduling behavior is characterized by a discrete-time Markov chain (DTMC), is utilized to orchestrate the access sequence of sensor nodes. By extending the robust MH estimation method, a novel nonlinear MH estimation scheme and the corresponding approximate MH estimation scheme are developed to cope with the state estimation task. Subsequently, some sufficient conditions are established to guarantee that the estimation error is exponentially ultimately bounded in mean square. Based on that the main results are further specialized to linear systems with the RA protocol scheduling. Finally, two numerical examples and the corresponding figures are provided to verify the effectiveness/correctness of the developed MH estimation scheme and approximate MH estimation scheme.

This paper investigates the problem of quasi-synchronization for a class of discrete-time Lur'e-type switched systems with parameter mismatches and transmission channel noises. Different from the previous studies referring to the persistent dwell-time (PDT) switching signals, the average dwell-time (ADT) constraints combined with the PDT are considered simultaneously in this paper to relax the limitation of dwell-time requirements and to improve the flexibility of the PDT switching signal design. By virtue of the semi-time-varying (STV) Lyapunov function, the synchronization criteria for transmitter-receiver systems in a switched version are obtained to satisfy a prescribed synchronization error bound. An estimate of the synchronization error bound is provided via the reachable set approach and, further, an explicit description of the error bounds is given. Then, sufficient conditions on the existence of STV observers are derived with a predetermined error bound, and the corresponding observer gains are calculated via solving a group of linear matrix inequalities. Finally, the effectiveness and validness of the developed theoretical results are demonstrated via a numerical example.

Fault-tolerant cooperative control of multiagent systems has attracted ever-increasing attention in recent years due to the fact that multiple agents can provide much more redundancy than a single agent system, thereby making the fault tolerant cooperative control design more flexible. However, multiagent systems may bring severe challenges that do not exist in single-agent systems. This article aims at presenting a survey of trends and methodologies of fault tolerant cooperative control in multiagent systems. Depending on the countermeasure against the faults, the existing fault-tolerant cooperative control methodologies are first classified into four categories: Individual methodologies, cooperative methodologies, topology reconfiguration-based methodologies, and composition reconfiguration-based methodologies. Then the characteristics and implementation schemes of four categories of methodologies are discussed in detail. Furthermore, the applicability of fault tolerant cooperative control in smart grids is outlined. Finally, several challenging issues are envisioned for future research.

This article is concerned with the distributed filtering problem for a class of discrete complex networks over time-varying topology described by a sequence of variables. In the developed scalable filtering algorithm, only the local information and the information from the neighboring nodes are used. As such, the proposed filter can be implemented in a truly distributed manner at each node, and it is no longer necessary to have a certain center node collecting information from all the nodes. The aim of the addressed filtering problem is to design a time-varying filter for each node such that an upper bound of the filtering error covariance is ensured and the desired filter gain is then calculated by minimizing the obtained upper bound. The filter is established by solving two sets of recursive matrix equations, and thus, the algorithm is suitable for online application. Sufficient conditions are provided under which the filtering error is exponentially bounded in mean square. The monotonicity of the filtering error with respect to the coupling strength is discussed as well. Finally, an illustrative example is presented to demonstrate the feasibility and effectiveness of our distributed filtering strategy.

This paper studies the fault detection problem for a class of discrete-time switched linear systems under dwell-time (DT) constraints, using the parity space-based approach. The DT-dependent Lyapunov function is employed to investigate the asymptotic stability with less conservatism and to solve the constant l2-gain performance analysis problem, and its advantage is verified compared to the time-independent Lyapunov function approach. The corresponding switching residual generation is made to carry out the desired fault detection in the framework of parity space-based model. Then, by means of solving a generalized eigenvalue-eigenvector problem, the parity space matrices design is implemented. A quantitative relationship is established between the optimization performance and the choice of the parity space order. Two numerical examples are utilized to demonstrate effectiveness of the developed fault detection approach, including an application to switched RLC circuits.

In this paper, we focus our study on analysis of fault diagnosis performance for satellite attitude control systems subject to l2-norm-bounded process disturbances and measurement noises, which concerns with fault detectability and fault isolability. For an observer-based fault detection (FD), a major concern is to answer if the choice of a threshold satisfies an acceptable trade-off between fault detection rate (FDR) and false alarm rate (FAR). The smaller a threshold is, the better is the FDR, but the poorer is the FAR. In addition to this, knowledge of fault isolability is useful for answering how difficult it is to isolate a fault from another one. The main contributions of this paper are the probabilistic performance evaluation of the FD system in the context of FAR and a contribution analysis-based method of fault isolation. First, an extended Hi/H∞optimization-based FD scheme is applied to the satellite attitude control systems and a recursive algorithm is presented to the implementation of online FD. Second, regarding the uncertain statistical characteristics of the unknown inputs, randomized algorithms are developed to verify the achievable FAR for a prescribed given threshold. Especially, without knowing the l2-norm boundedness of the unknown inputs, a probabilistic estimation of worst case threshold is also obtained to guarantee an acceptable level of FAR. Third, a contribution analysis-based method of fault isolation is proposed for satellite attitude control systems. Finally, the effectiveness of the proposed algorithms is verified through a satellite attitude control system.

Due to the inner deteriorating mechanism or the mutant environmental stress, the degradation systems with multi-phase features have frequently been encountered in engineering practice. The key issue for prognostics of such systems is to account for the impact of the changing-point variability and the associated degradation state at this point on the progression of the degradation process. However, current studies usually treat the degradation state at the change point as a fixed value rather a random variable. Thus, it is still challenging to predict the lifetime of such multi-phase degrading systems. To this end, we first formulate a general degradation modeling framework based on a two-phase Wiener process. In prognostics, we take into full account the uncertainty of the degradation state at the changing point and then derive the analytical expressions of the lifetime and remaining useful life under the concept of the first passage time. The derived results are distinguished from existing results limited to the fixed state at the changing point. Furthermore, we extend our approach and results to cases with unit-to-unit variability and multiple phases. To facilitate the model implementation, we propose both offline and online methods for parameter identification, which make full use of the historical data and the in-service data. Finally, a numerical simulation and a practical case study are provided for illustration.

For some practical industrial systems or components, such as blast furnaces and Li-ion batteries, there are two important factors to model the degradation processes. One is the long-range dependence, which can reflect the non-Markovian nature of the degradation processes. The other factor is the existence of multiple modes, because the operating conditions and external environments inevitably change during the whole lifetime of these systems. In this paper, we first propose a fractional Brownian motion (FBM) based degradation model with long-range dependence and multiple modes, and then consider the prediction of remaining useful life. To identify the multiple modes in the degradation process, we propose a two-step method, including change-points detection and linear segments clustering. In each degradation mode, the degradation rate is assumed to be normally distributed. The means and variances of these distributions can be obtained by the maximum likelihood estimation. To describe the switching between different modes, the continuous-time Markov chain is applied, and its transition rate matrix can be estimated by the historical switching time. An approximation of the first passage time with a predefined threshold can be obtained by a weak convergence theorem and a time-space transformation. A numerical simulation and a practical case of a blast furnace wall are provided to demonstrate the effectiveness of the proposed method.

This study considers the decentralized maintenance of a multistate system (MSS) with low-priority components (LPCs) and high-priority components (HPCs). By introducing imperfect observations of the state, the MSS can be modeled as a partially observable Markov decision process. We propose an (m, N) maintenance policy, where it is considered that the MSS has failed when an HPC fails or when the number of failed LPCs reaches m. In contrast to a centralized maintenance mode, two maintenance teams conduct reliability evaluations and maintenance actions. One team employs the Markov method to predict the trends in the deterioration of the components. The other team estimates the status of the MSS based on the sample data, which are stochastically related to the condition of the system. The different teams may have different maintenance costs and effects, and either maintenance team can be selected based on the system's status. We discuss in detail how to arrange the maintenance teams in order to obtain the lowest expected cost rate with a guarantee of system reliability. Illustrative numerical examples are provided to show the significant cost savings under decentralized maintenance compared with centralized maintenance due to either lower expenditure or shorter time requirements.

In this paper, control performance assessment (CPA) is studied for batch processes controlled by iterative learning control (ILC). A 2-D linear quadratic Gaussian (LQG) benchmark is proposed to assess the performance of ILC in a 2-D framework. Based on the 2-D theory, an ILC-controlled batch process is first converted into a 2-D Roesser model. Subsequently, in order to assess the control performance of the converted 2-D system, the conventional LQG tradeoff curve is upgraded to the LQG performance assessment tradeoff surface. However, the complete knowledge of the system model is required to obtain the LQG tradeoff surface. For system without accurate model knowledge, a novel data-driven CPA method is further proposed. In this case, a novel 2-D closed-loop subspace identification method is proposed to identify the converted 2-D Roesser system. Based on the identified model, the LQG tradeoff surface can be obtained and utilized to assess the control performance. Overall, several simulation examples verified the feasibility and effectiveness of the proposed method.

This paper studies the stabilizability and instabilizability problems for delayed complex-valued memristive neural networks within finite-time intervals. First, more general assumptions for complex-valued activation functions are given. To check that whether the closed-loop system is stable within a finite-time interval, a novel nonlinear delayed controller with separable real-imaginary parts is designed. It includes two independent parameters different from the existing ones, which makes the controller more general but also leads to great difficulties. To overcome these difficulties, two new inequalities are proposed and proved. Then, through Lyapunov function approach, sufficient conditions are derived for the finite-time stabilizability of the closed-loop system and the settling time is estimated. Accordingly, some criteria for the finite-time instabilizability are also established by adjusting different parameters in the designed controller. Finally, several numerical simulations are given to show the effectiveness and advantages of the proposed results.

In this paper, the filtering problem is investigated for a class of discrete-time Markov jump linear parameter varying systems with packet dropouts and channel noises in the network surroundings. The partial accessibility of system modes with respect to the designed filter is described by a hidden Markov model (HMM). A typical behavior characterization mechanism is proposed in the communication channel including data losses and additive noises, which occurs in a probabilistic way based on two mutually independent Bernoulli sequences. With the aid of a class of Lyapunov function subject to parameter-dependent and mode-dependent constraints, sufficient conditions ensuring the existence of HMM-based filters are obtained such that the filtering error system is stochastically stable with a guaranteed H∞error performance. The influence of monotonicity on the performance index is explored while changing the degree of both additive noise and mode inaccessibility. The effectiveness and applicability of the obtained results are finally verified by two numerical examples.

This paper investigates distributed fault detection of wireless sensor networks with a class of faulty sensor node, fault source isolation and networked communication topology accommodation design issue considering filtering performance. The wireless sensor network in this paper is composed of spatially placed sensors which has a changeable networked communication topology, different state-space representations and different sensor gain degradations. By augmenting the state components, a set of recursive matrix equation in Riccati form is derived to calculate the distributed filter parameters and generate the residual signals for fault detection. In order to eliminate the influence of possible faulty node on distributed filtering performance, the fault source isolation is carried on by removing the communication channel between every one sensor and all other sensors according to beat isolation. The communication network topology accommodation is put forward with a framework preliminarily in view of the networked fault, distributed filtering performance and communication energy cost.

For modern industrial processes, timely detection of incipient faults is of vital importance so as to ensure safe and optimal process operation. Though recently statistical process monitoring (SPM) has been extensively studied and widely applied in practice, conventional multivariate statistics are usually not sensitive to incipient faults. In this paper, a new multivariate statistical index called augmented Mahalanobis distance (AMD) is proposed for incipient fault detection. It can be concluded from fault detectability analysis that the AMD index is more sensitive to incipient faults than the conventional Mahalanobis distance (MD) index. Besides, the idea of augmentation utilized in the AMD index can also be applied to some other SPM models. Finally, case studies on a numerical example and the continuous stirred tank heater (CSTH) process are conducted to demonstrate the effectiveness of the proposed AMD index, in comparison with the MD index, as well as the squared prediction error (SPE) and T-square indices.

Some practical systems such as blast furnaces and turbofan engines have degradation processes with memory effects. The term of memory effects implies that the future states of the degradation processes depend on both the current state and the past states because of the interaction with environments. However, most works generally used a memoryless Markovian process to model the degradation processes. To characterize the memory effects in practical systems, we develop a new type of degradation model, in which the diffusion is represented as a fractional Brownian motion (FBM). FBM is actually a special non-Markovian process with long-term dependencies. Based on the monitored data, a Monte Carlo method is used to predict the remaining useful life (RUL). The unknown parameters in the proposed model can be estimated by the maximum likelihood algorithm, and then the distribution of the RUL is predicted. The effectiveness of the proposed model is fully verified by a numerical example and a practical case study.

A prerequisite for the existing remaining useful life prediction methods based on stochastic processes is the assumption of independent increments. However, this is in sharp contrast to some practical systems including batteries and blast furnace walls, in which the degradation processes have the property of long-range dependence. Based on the fractional Brownian motion, we adopt a degradation process with long-range dependence to predict the remaining useful life of the above systems. Because the degradation process with long-range dependence is neither a Markovian process nor a semimartingale, the exact analytical first passage time is difficult to derive directly. To address this problem, a weak convergence theorem is first adopted to approximately transform a fractional Brownian motion-based degradation process into a Brownian motion-based one with a time-varying coefficient. Then, with a space-time transformation, the first passage time of the degradation process with long-range dependence can be obtained in a closed form. Unknown parameters in the degradation model can be identified using discrete dyadic wavelet transform and maximum likelihood estimation. Numerical simulations and a practical example of a blast furnace wall are given to verify the effectiveness of the proposed method.

This paper is concerned with the design and performance analysis of networked control systems with network-induced delay, packet disorder, and packet dropout. Based on the incremental form of the plant input-output model and an incremental error feedback control strategy, an incremental networked predictive control (INPC) scheme is proposed to actively compensate for the round-trip time delay resulting from the above communication constraints. The output tracking performance and closed-loop stability of the resulting INPC system are considered for two cases: 1) plant-model match case and 2) plant-model mismatch case. For the former case, the INPC system can achieve the same output tracking performance and closed-loop stability as those of the corresponding local control system. For the latter case, a sufficient condition for the stability of the closed-loop INPC system is derived using the switched system theory. Furthermore, for both cases, the INPC system can achieve a zero steady-state output tracking error for step commands. Finally, both numerical simulations and practical experiments on an Internet-based servo motor system illustrate the effectiveness of the proposed method.

A general (N, T, τ) maintenance model is developed for multicomponent systems with two types of components, namely main and auxiliary components. The main component suffers from evident failures, which are assumed to be found or detected as soon as they occur. Auxiliary components with protective or standby functions are modeled by a k-out-of-n:F subsystem, in which failures are hidden and assumed to be detected and fixed only at inspections. Although the shutdown of a subsystem may not halt the system, it could cause a potential risk to the system or financial losses. In this model, the whole system can be renewed at the Nth failure of the main component or at time T, whichever occurs first. Further, incomplete periodic inspections and the optimal number of repairs before replacement are also considered in opportunistic maintenance. Incomplete periodic inspections can efficiently overcome the drawbacks of existing maintenance based on periodic inspections and opportunistic maintenance. For the case of exponential lifetime distribution, an explicit analytical expression of the maintenance cost rate in a renewal cycle is derived by applying the Laplace transform to recursive equations. By setting parameters N, T, τ to tend to infinity, respectively, special properties are derived and a comparison with several maintenance models is performed. For a given life expectancy of the system (namely T), the existence of optimal parameters N and τ is proven. Numerical examples are presented to show the effectiveness of the proposed model.

In this paper, we investigate the distributed filtering problem over wireless sensor networks (WSNs) with bandwidth and energy constraints. To utilize the limited resources efficiently, a novel event-based mechanism is proposed for the sensor node, such that only selected valuable data are broadcasted to its neighboring sensors via the wireless channel according to whether specific events happen. By resorting to graph theory and utilizing stochastic analysis methods, the filter parameters and the event triggering rules are designed, such that the filtering error converges at an exponential rate in the mean square sense. An adaptive algorithm for determining the triggering threshold is developed, which allows the intelligent sensors to tune the boundary of a local event domain in an online manner, so as to keep the average transmission rate level off a desired value. An illustrative example is given to demonstrate the effectiveness of the proposed strategy.

Reliability estimation based on degradation model is a feasible and low-cost alternative used to estimate reliability for highly reliable systems when the failure-time data are rare. Based on reliability estimation by degradation modeling, preventive maintenance work orders need to be timely triggered to minimize unscheduled downtime. In Trans. Autom. Sci. Eng., vol. 9, no. 1, pp. 209–212, Jan. 2012, Sun et al., an approach to dynamically extract maintenance threshold is presented for maintenance scheduling, in which the reliability threshold for maintenance is determined by maximizing the expected availability and the reliability estimation is achieved by a modified two-stage degradation modeling approach. Although this approach is novel and useful, its reliability estimation is an asymptotic solution in long time scale. In this paper, we generalize the above result by considering a general degradation path model and provide the exact and explicit formulation for reliability estimation. Additionally, a maximum-likelihood estimation method for parameters in the presented model is proposed based on the historical degradation observations. Finally, an example is provided for illustration.

The problem of finding the optimal maintenance policy for partially observed systems is considered, where only a limited number of maintenance actions can be performed. The maintenance is assumed to be imperfect in that the system can be only restored to a less deteriorated level rather than to a state as good as new. In addition, the true deterioration state is known just after each replacement action, but the deterioration state at other instants during the system's operation cannot be observed, evolving as a discrete-time Markov chain with a finite state space. In this paper, the described problem can be formulated as a partially observed Markov decision process (POMDP) over the infinite time horizon. To increase the computational efficiency, several key structural properties are developed through minimizing the total expected cost per unit time. The existence of the optimal threshold-type maintenance policy is strictly proved, and the monotonicity of the threshold is obtained. The effectiveness of the optimal policy can be verified by a numerical example.

The use of the observed degradation data of a system can help to estimate its remaining useful life (RUL). However, the degradation progression of the system is typically stochastic, and thus the RUL is also a random variable, resulting in the difficulty to estimate the RUL with certainty. In general, there are three sources of variability contributing to the uncertainty of the estimated RUL: 1) temporal variability, 2) unit-to-unit variability, and 3) measurement variability. In this paper, we present a relatively general degradation model based on a Wiener process. In the presented model, the above three-source variability is simultaneously characterized to incorporate the effect of three-source variability into RUL estimation. By constructing a state-space model, the posterior distributions of the underlying degradation state and random effect parameter, which are correlated, are estimated by employing the Kalman filtering technique. Further, the analytical forms of not only the probability distribution but also the mean and variance of the estimated RUL are derived, and can be real-time updated in line with the arrivals of new degradation observations. We also investigate the issues regarding the identifiability problem in parameter estimation of the presented model, and establish the according results. For verifying the presented approach, a case study for gyros in an inertial platform is provided, and the results indicate that considering three-source variability can improve the modeling fitting and the accuracy of the estimated RUL.

In this paper, the problems of fault detection, isolation, and estimation are considered for a class of discrete time-varying networked sensing systems with incomplete measurements. A unified measurement model is utilized to simultaneously characterize both the phenomena of multiple communication delays and data missing. A least-squares filter that minimizes the estimation variance is first designed for the addressed time-varying networked sensing systems, and then a novel residual matching (RM) approach is developed to isolate and estimate the fault once it is detected. The RM strategy is implemented via a series of Kalman filters, where each filter is designed to estimate the augmented signal composed of the system state and a specific fault signal. The design scheme for each filter is proposed in a recursive way. The main idea for the fault detection and estimation is that the Kalman filter with least residual value is regarded as corresponding to the right fault signal, and its estimation is utilized to represent the actual occurred fault. The effectiveness of our proposed method is demonstrated via simulation experiments on a real Internet-based three-tank system.

For a class of multi-sensor dynamic systems subject to latent degradation, the remaining useful life prediction with anticipated performance is mainly considered in this paper. The hidden degradation process is first identified recursively by adopting distributed fusion filtering based on observations from multiple sensors. Then the remaining useful life distribution is predicted on the basis of converged degradation state and parameter updating during the operating process. The uncertainty index is aanalyzed to quantitatively evaluate the benefits of increasing multi-sensor information for predicted remaining useful life, and the sensor selection is also discussed for satisfying the anticipated performance such as variance. Our main results are verified by a numerical example, and a practical case study of the milling machine experiment.

Many works on preventive maintenance (PM) of systems only consider either a single failure mode, or statistically independent failure modes. Here, we study the maintenance policy for systems with two statistically dependent failure modes (namely maintainable, and nonmaintainable), and resource constraints. Assume (i) the nonmaintainable failures unidirectionally affect the maintainable failure rate; (ii) due to the constrained resource, only a limited number of imperfect PM actions are performed to reduce the maintainable failure; and (iii) the improvement factor due to each imperfect PM is fixed, and the maximal number before replacement is fixed. By combining a Castro model for statistically dependent failure modes with a Zhang-Jardine model for a single failure mode and imperfect PM, we propose a hybrid maintenance model for systems with statistically dependent failure modes and limited imperfect PM. To examine the maintenance policy, assume that both the nonmaintainable failures and the maintainable failures follow the same type of failure rate functions such as the increasing power law failure rate function. We discuss the relation between expected cost rate per unit-time and each decision variable, and then give a solution to a constrained optimization problem provided that the length of the interval between two successive maintenance actions cannot be too small. Numerical simulations for the increasing power law failure rate fully verify the proposed maintenance policy, which can be also extended to other increasing failure rate functions such as an exponential failure rate function.

Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) presented an interesting extended periodic imperfect preventive maintenance (EPIPM) model for a system with age-dependent failure type. Many cases studied previously are special cases of the EPIPM model. In the Errata (IEEE Trans. Rel., vol. 60, no. 2, 2011), Sheu and Chang showed that the proposed effective age and the proposed hazard rate function after the PM are incorrect. In this paper, based on the correct failure characteristics (effective age and hazard rate function after PM), the corrects-expected total cost per unit time for the EPIPM model is presented. By assigning three types of failure characteristics for the EPIPM model, we analyse and compare the correspondings-expected total costs per unit time. We find that thes-expected total cost per unit time developed by Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) is only one upper bound of the exacts-expected total cost per unit time. In addition, we also give some results on the existence of the optimal solution for the exacts-expected total cost.

Manufacturing systems run in time-varying environmental and operational conditions. For the effective manager to make a long-term preventive maintenance decision, it is necessary to integrate the time-varying environment into preventive maintenance (PM) policies. This paper considers PM for systems running in the time-varying environment, modeled as a two-state homogeneous Markov process, where one state represents a typical condition, and the other represents a severe condition. Environmental conditions affect the hazard rate function through a proportional hazard model. To avoid sudden failures in a system due to either minor failures or catastrophic failures, an extended periodic imperfect preventive maintenance model is carried out, and the maintenance effect is modeled with an age reduction factor, and a hazard improvement factor. We prove the discontinuity of the hazard rate function of the system in a time-varying environment through a Markov additive process. We also give a method to compute the probability density function of failure at any time. Further, the$s$-expected cost rate of the system in the time-varying environment is compared with the$s$-expected cost rates of the system always working in typical, and severe conditions. Finally, numerical examples fully verify our main results.

Remaining useful life estimation is central to the prognostics and health management of systems, particularly for safety-critical systems, and systems that are very expensive. We present a non-linear model to estimate the remaining useful life of a system based on monitored degradation signals. A diffusion process with a nonlinear drift coefficient with a constant threshold was transformed to a linear model with a variable threshold to characterize the dynamics and nonlinearity of the degradation process. This new diffusion process contrasts sharply with existing models that use a linear drift, and also with models that use a linear drift based on transformed data that were originally nonlinear. Both existing models are based on a constant threshold. To estimate the remaining useful life, an analytical approximation to the distribution of the first hitting time of the diffusion process crossing a threshold level is obtained in a closed form by a time-space transformation under a mild assumption. The unknown parameters in the established model are estimated using the maximum likelihood estimation approach, and goodness of fit measures are applied. The usefulness of the proposed model is demonstrated by several real-world examples. The results reveal that considering nonlinearity in the degradation process can significantly improve the accuracy of remaining useful life estimation.

In data-based monitoring field, the nonlinear iterative partial least squares procedure has been a useful tool for process data modeling, which is also the foundation of projection to latent structures (PLS) models. To describe the dynamic processes properly, a dynamic PLS algorithm is proposed in this paper for dynamic process modeling, which captures the dynamic correlation between the measurement block and quality data block. For the purpose of process monitoring, a dynamic total PLS (T-PLS) model is presented to decompose the measurement block into four subspaces. The new model is the dynamic extension of the T-PLS model, which is efficient for detecting quality-related abnormal situation. Several examples are given to show the effectiveness of dynamic T-PLS models and the corresponding fault detection methods.

Many works on condition-based maintenance of repairable systems apply to either a single failure mode, or statistically independent failure modes. Different from these works, this paper considers the problem of predictive maintenance of repairable systems with dependent failure modes, and resource constraints. Assume that (i) a repairable system is subject to two statistically dependent failure modes bidirectionally affecting each other, (ii) imperfect maintenance actions are cooperatively performed on two dependent failure modes by allocating insufficient resources spent for maintenance, and (iii) future maintenance scheduled at the current time depend on both the predicted number of future failures and the minimization of the expected maintenance cost rate defined in the long term. To resolve the above problem, a novel cooperative predictive maintenance model is proposed. Its basis is the incorporation of the hazard-rate function, and effective age. In this model, two failure modes are statistically dependent in such a way that the hazard rate of one failure mode depends on the accumulated number of failures of the other failure mode. The effect of imperfect maintenance is interpreted in terms of how the hazard rate function and the effective age are changed by maintenance actions. The age reduction factor for each failure mode due to maintenance has some deterministic relation to the degree of resources cooperatively allocated to perform maintenance. The decision variables in the maintenance policy, namely the number of maintenance actions to be performed, the interval between successive maintenance actions, and the cooperatively allocated degree of resources, can be recursively updated when new monitored information arrives. This approach relies on both the predicted number of future failures, and the minimization of the expected maintenance cost rate defined in the long term.

An error in the above titled paper (ibid., vol. 58, pp. 397-405, Jun 2009) is pointed out and a revision is presented here.

In order to determine the parameters of belief-rule-base (BRB) accurately, several optimization methods have been proposed for training BRB, on the basis of a generic rule-base inference methodology using the evidential reasoning (RIMER) approach. These optimization methods are implemented offline, and such are not suitable for training BRB in a dynamic fashion. In this paper, two recursive algorithms are proposed to update BRB online that can simulate dynamic systems. The main feature of the proposed algorithms is that only partial input and output information is required, which can be incomplete or vague, numerical or judgmental, or mixed. If the internal structure of a BRB is initially decided using expert judgments, domain-specific knowledge and/or commonsense rules, the proposed algorithms can be used to fine-tune the initial BRB online, once input and output datasets become available. Using the proposed algorithms, there is no need to collect a complete set of data before a BRB can be trained, which is necessary if the BRB is used to simulate a dynamic system. A numerical example and a case study are reported to demonstrate the potential of the algorithms for online fault diagnosis.

In this paper, a new robustHinfinfiltering problem is investigated for a class of time-varying nonlinear system with norm-bounded parameter uncertainties, bounded state delay, sector-bounded nonlinearity and probabilistic sensor gain faults. The probabilistic sensor reductions are modeled by using a random variable that obeys a specific distribution in a known interval [alpha,beta], which accounts for the following two phenomenon: 1) signal stochastic attenuation in unreliable analog channel and 2) random sensor gain reduction in severe environment. The main task is to design a robustHinfinfilter such that, for all possible uncertain measurements, system parameter uncertainties, nonlinearity as well as time-varying delays, the filtering error dynamics is asymptotically mean-square stable with a prescribedHinfinperformance level. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a certain linear matrix inequality (LMI). A numerical example is introduced to illustrate the effectiveness and applicability of the proposed methodology.

While a specific system is in use, its reliability will decrease gradually after the infant mortality period because of the components' degradation, or external attacks. Thus, reliability is a natural characteristic of a system's health, and can be used for condition monitoring & predictive maintenance. This paper introduces a new real-time reliability prediction method for dynamic systems which incorporates an on-line fault prediction algorithm. The factors that may reduce a system's reliability are modeled as an additive fault input to the system, and the fault is assumed to be varying linearly with time, approximately. The time-varying fault is roughly estimated based on a modified particle filtering algorithm at first. Then, as a time series, the fault estimate sequence is smoothed, and predicted by an exponential smoothing method. Mathematical analysis shows that the effects of the system, and measurement noises on the fault estimates are greatly reduced by exponential smoothing, which indicates that the comparatively high accuracy of the fault estimates & predictions is guaranteed. Based on the particle filtering & fault prediction results, the whole system's predictive reliability is computed through a Monte Carlo simulation strategy. The effectiveness of the proposed real-time reliability prediction method is validated by a computer simulation of a three-vessel water tank system.

This letter presents a new class of discrete-time linear stochastic systems with the statistically-constrained disturbance input, which can represent an arbitrary linear combination of dynamic, random, and deterministic disturbance inputs to generalize the complicated modeling error encountered in actual applications. An adaptive filtering scheme is proposed for such systems by recursively constructing and adaptively minimizing the upper-bounds of covariance matrices of the state predictions, innovations, and estimates. The minimum-upper-bound filter is then obtained via online scalar convex optimization. The experiment on maneuvering target tracking shows that the proposed filter can significantly reduce the peak estimation errors due to maneuvers, compared with the well-known IMM method.

This paper introduces a real-time reliability prediction method for a dynamic system which suffers from a hidden degradation process. The hidden degradation process is firstly identified by use of particle filtering based on measurable outputs of the considered dynamic system. Then the system's reliability is predicted according to the model of the degradation path. We analyze the identification algorithm mathematically, and validate the effectiveness of this method through computer simulations of a three-vessel water tank. This real-time reliability prediction method is beneficial to the dynamic system's condition monitoring, and may be further helpful to make a proper predictive maintenance policy for the system.