Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach

Active fault detection and isolation (AFDI) is used for detection and isolation of faults that are hidden in the normal operation because of a low excitation signal or due to the regulatory actions of the controller. In this paper, a new AFDI method based on set-membership approaches is proposed. In set-membership approaches, instead of a point-wise estimation of the states, a set-valued estimation of them is computed. If this set becomes empty the given model of the system is not consistent with the measurements. Therefore, the model is falsified. When more than one model of the system remains un-falsified, the AFDI method is used to generate an auxiliary signal that is injected into the system for detection and isolation of faults that remain otherwise hidden or non-isolated using passive FDI (PFDI) methods. Having the set-valued estimation of the states for each model, the proposed AFDI method finds an optimal input signal that guarantees FDI in a finite time horizon. The input signal is updated at each iteration in a decreasing receding horizon manner based on the set-valued estimation of the current states and un-falsified models at the current sample time. The problem is solved by a number of linear and quadratic programming problems, which result in a computationally efficient algorithm. The method is tested on a numerical example as well as on the pitch actuator of a benchmark wind turbine.     

Observer-based fault detection and isolation filter design for linear time-invariant systems

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault detection and isolation filter such that the ?_∞-norm of the transfer matrix function from disturbances to the residual is minimised (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for isolation of possibly simultaneous occurring faults). Our solution is given in the form of linear matrix inequalities using state-space techniques, as well as a model matching problem using matrix factorisation techniques. A numerical example is given to illustrate the efficiency of the fault detection and isolation filter.     

A geometric approach to nonlinear fault detection and isolation in a hybrid three-cell converter

In this paper, the problem of fault detection and isolation in a three-cell converter is investigated using a nonlinear geometric approach. This powerful method based on the unobservability distribution is used to detect and isolate the faulty cell in the three-cell converter. First, a model describing the faults in the cells is presented. The geometric approach is then applied on this faulty model to generate residual signals based on a sliding-mode observer that allows the detection of faults in the three-cell converter. Numerical results show the effectiveness of the proposed sliding-mode residual generators for fault detection and isolation in the three-cell converter.     

A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach

Optimal H_∞ deconvolution filter theory is exploited for the design of robust fault detection and isolation (FDI) units for uncertain polytopic linear systems. Such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation, residual decoupling and deconvolution performance in prescribed frequency ranges. By means of the Projection Lemma, a quasi-convex formulation of the problem is obtained via LMIs. A FDI logic based on adaptive thresholds is also proposed for reducing the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.     

Structured residual vector-based approach to sensor fault detection and isolation

This paper proposes a novel approach to detection and isolation of faulty sensors in multivariate dynamic systems. After formulating the problem of sensor fault detection and isolation in a dynamic system represented by a state space model, we develop the optimal design of a primary residual vector for fault detection and a set of structured residual vectors for fault isolation using an extended observability matrix and a lower triangular block Toeplitz matrix of the system. This work is, therefore, a vector extension to the earlier scalar-based approach to fault detection and isolation. Besides proposing a new algorithm for consistent identification of the Toeplitz matrix from noisy input and output observations without identifying the state space matrices {A, B, C, D} of the system, the main contributions of this newly proposed fault detection and isolation scheme are: (1) a set of structured residual vectors is employed for fault isolation; (2) after determination of the maximum number of multiple sensors that are most likely to fail simultaneously, a unified scheme for isolation of single and multiple faulty sensors is proposed; and (3) the optimality of the primary residual vector and the structured residual vectors is proven. We prove the advantage of our newly proposed vector-based scheme over the existing scalar element-based approach for fault isolation and illustrate its practicality by simulated and experimental evaluation on a multivariate pilot scale, computer interfaced system.     

Robust fault detection and isolation of time-delay systems using a geometric approach

This paper investigates the development of Fault Detection and Isolation (FDI) filters for both retarded and neutral time-delay systems with unknown time-varying delays. Using a geometric framework, the notion of a finite unobservability subspace is introduced for time-delay systems and an algorithm for its construction is presented. A bank of residual generators is then designed so that each residual is affected by one fault and is partially decoupled from the others while the H_∞ norm of the transfer function between the disturbances and the uncertainties in delays and the residuals are guaranteed to remain less than a prescribed value. Furthermore, it is shown that in the case of known delays it is possible to generate residuals that enjoy perfect decoupling properties among faults. Simulation results presented demonstrate the effectiveness of our proposed FDI algorithms.     

A discrete event systems approach to network fault management: detection and diagnosis of faults

An important aspect of network management is fault management, which involves, detecting, locating, isolating, correcting and adapting to faults in the network. We study modeling of communication network protocol and fault detection, identification and localization in the discrete event system diagnosis framework. As an illustration of the approach, normal and faulty behavior of the X.25 network protocol is modeled as a finite state machine. This modeling formalism allows the utilization of discrete event system analysis for the detection and diagnosis of faults. Our approach provides a systematic way of performing fault diagnosis for network fault management. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A robust fault detection and isolation filter design under sensitivity constraint: An LMI approach

This paper deals with the design of a residual generator (RG) for linear time‐invariant systems subject to simultaneous different faults, disturbances and measurement noises. The objective is to design an RG filter that maximizes the transmission from a potential fault to a related residual, while minimizing the ones from nuisances (disturbances, measurement noises and other faults). The isolation of each fault is carried out by designing a bank of RG filters, each one insensitive, as much as possible, to nuisances and capable of detecting the occurrence of its related fault. The design is carried out through ℋ︁_∞ filtering techniques under an eigenstructure assignment constraint. Under mild assumptions, the RG filter can be obtained by solving a λ‐parameterized linear matrix inequality optimization problem. A comparison with existing fault detection and isolation (FDI) methods is considered in order to exhibit the relative merits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

设计高阶PI观测器对线性系统故障作鲁棒检测

针对具有干扰的线性定常系统,研究了基于高阶PI观测器的鲁棒故障检测设计问题.基于Sylvester矩阵方程的参数化解,给出了干扰与残差解耦的充要条件,并提出了基于高阶PI观测器的线性系统鲁棒故障检测参数化设计方法.数值算例及仿真分析表明所提鲁棒故障检测参数化设计方法是有效的.     

A geometric approach to nonlinear fault detection and isolation

We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an “observable” quotient subsystem unaffected by all fault signals but one. For this subsystem, a fault detection filter is designed     

Set‐based fault detection and isolation for detectable linear parameter‐varying systems

In the context of fault detection and isolation of linear parameter‐varying systems, a challenging task appears when the dynamics and the available measurements render the model unobservable, which invalidates the use of standard set‐valued observers. Two results are obtained in this paper, namely, using a left‐coprime factorization, one can achieve set‐valued estimates with ultimately bounded hyper‐volume and convergence dependent on the slowest unobservable mode; and by rewriting the set‐valued observer equations and taking advantage of a coprime factorization, it is possible to have a low‐complexity fault detection and isolation method. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults. Copyright © 2017 John Wiley & Sons, Ltd.     

Current-sensor fault detection and isolation for induction-motor drives using a geometric approach

This work presents the design of a current-sensor fault detection and isolation system for induction-motor drives. A differential geometric approach is addressed to determine if faults can be detected and isolated in drives with two line current sensors by using a model based strategy. A set of subsystems is obtained based on the observability co-distribution, whose outputs are decoupled from the load torque (detectability) and only affected by one of the sensors (isolability). A bank of observers is designed for these subsystems in order to obtain residuals for the fault detection and isolation. It is demonstrated that the proposed strategy allows detecting single and multiple sensor faults, including disconnection, offset and gain faults. Experimental results validate the proposal.     

具有自适应调节律的非线性系统执行器故障检测和隔离方法

针对受到外部干扰的非线性系统,讨论了基于观测器的执行器故障检测和隔离方法.首先,通过引入一个对Lipschitz非线性项Lipschitz常数自适应调节的微分调节项,使得观测器具有自适应性,从而使观测器设计具有无须知道Lipschitz常数大小的优点;然后,通过一滑模控制项来抑制干扰,使观测器具有鲁棒性,并在此基础上,结合多观测器故障隔离的思想,提出了执行器故障检测和隔离方法;最后,通过对一个七阶飞行器实际模型的仿真,表明了该方法的实用性.     

采样数据系统故障检测的H∞方法

提出一种对采样数据系统进行故障检测的H_∞方法. 首先构造离散时间故障检测系统, 分析残差产生器的动态特性. 然后从故障检测的角度引入算子, 定量考察连续时间未知输入信号和故障信号对离散时间残差信号的影响. 最后优化残差产生器的参数, 使得故障检测系统对未知输入具有较强的鲁棒性, 同时对故障具有较高的灵敏度.     

基于故障映射向量和结构化残差的主元分析(PCA)故障隔离

在基于主元分析(PCA)的多变量统计过程监控中, 现有方法很难直观有效地完全实现故障的隔离与诊断. 本文通过分析各类故障的数学模型, 提出一种基于结构化残差和故障映射向量的隔离方法, 并推导出PCA模型下过程故障映射向量方向的提取算法, 进而实现了传感器/执行器故障和过程故障的故障隔离, 在CSTR仿真上的研究进一步验证了该法的有效性.     

Data‐driven fault detection for linear systems: A q‐step residual iteration approach

This article studies the problem of data‐driven (DD) fault detection (FD) for linear systems. First, based on the DD realization of kernel representation, new residual generators are designed via a q‐step residual iteration method. Then, it is proved that the proposed residual generators guarantee the stability and L₁ performance of the FD error systems, and the presented residual design method is more sensitive to faults than the existing ones constructed directly from available process data. Finally, two simulation examples are provided to verify the effectiveness and advantages of the designed method.     

Active fault detection based on set‐membership approach for uncertain discrete‐time systems

Active fault detection facilitates determination of the fault characteristics by injecting proper auxiliary input signals into the system. This article proposes an observer‐based on‐line active fault detection method for discrete‐time systems with bounded uncertainties. First, the output including disturbances, measurement noise and interval uncertainties at each sample time is enclosed in a zonotope. In order to reduce the conservativeness in the fault detection process, a zonotopic observer is designed to estimate the system states allowing to generate the output zonotopes. Then, a proper auxiliary input signal is designed to separate the output zonotopes of the faulty model from the healthy model that is injected into the system to facilitate the detection of small fault . Since the auxiliary input signal generation leads to a nonconvex optimization problem, it is transformed into a mixed integer quadratic programming problem. Finally, a case study based on a DC motor is used to show the effectiveness of the proposed method.     

Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach

Fault detection and isolation(FDI) problems for linear parameter-varying(LPV) systems with state time-delays are studied in this paper. By defining the concept of unobservability subspace and designing its calculation algorithm, the geometric approach is introduced to the time-delay LPV systems. Utilizing Wirtinger-based integral inequality, we obtain a sufficient condition to solve the so-called H∞-based residual generation problem for the LPV systems. In this paper, we consider two cases: the ...     

Robust fault detection and isolation in stochastic systems

This article outlines the formulation of a robust fault detection and isolation (FDI) scheme that can precisely detect and isolate simultaneous actuator and sensor faults for uncertain linear stochastic systems. The given robust fault detection scheme based on the discontinuous robust observer approach would be able to distinguish between model uncertainties and actuator failures and therefore eliminate the problem of false alarms. Since the proposed approach involves estimating sensor faults, it can also be used for sensor fault identification and the reconstruction of true outputs from faulty sensor outputs. Simulation results presented here validate the effectiveness of the proposed robust FDI system.