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.     

A sliding mode observer-based strategy for fault detection,isolation, and estimation in a class of Lipschitz nonlinear systems

This article investigates the design and application of a sliding mode observer (SMO) strategy for actuator as well as sensor fault detection, isolation, and estimation (FDIE) problem for a class of uncertain Lipschitz nonlinear systems. Actuator FDIE is addressed by regrouping the system's inputs into a structure suitable for SMO design. Similarly, by filtering the regrouped outputs, a similar system structure can be developed for sensor FDIE problem. Once in the suitable form and under certain assumptions, nonlinear SMOs are proposed for actuator and sensor FDIE. A systematic LMI-based design approach for the proposed SMO is presented. Additionally, the article addresses four problems, namely: (P1) What are the conditions for isolating single and/or multiple faults? (P2) What is the maximum number of faults that can be isolated simultaneously? (P3) How should one design SMO-based FDI approach in order to achieve multiple fault isolation using as few observers as possible? (P4) How can one estimate the shape of the faults? To solve the above problems, a new concept called fault isolation index (FIX) is proposed for actuator and sensor FDIE. It is proved that fault isolation can only be achieved if FIX?≠?0, and also that the maximum number of faults that can be isolated is equal to FIX. Using the proposed fault isolation strategy and by treating some healthy inputs or outputs as unknown inputs, a systematic FDIE design scheme using a bank of nonlinear SMOs, which provides a solution for the four problems is provided. An example is used to illustrate the proposed ideas. The simulation results show that the proposed FDIE scheme can successfully detect and isolate both slowly and fast-changing actuator faults. It is also shown that accurate estimation of actuator faults can be achieved.     

不确定时滞系统增益型故障的检测与估计

针对一类不确定连续线性定常时滞系统,提出了一种执行器、传感器增益故障的鲁棒检测与估计策略。该类系统含有多状态与输出时滞,状态和输出方程上同时作用有非结构有界未知扰动。在Trunov和Polycarpou方法的基础上,设计了一种新的时滞系统自适应观测器用于检测并估计突变或缓变的增益故障。与Wang等针对线性无时滞不合输出扰动系统的工作相比,该结论更具一般性。理论分析表明,该方法对于未知扰动鲁棒,能够保证故障的估计,状态与输出估计偏差一致有界。数值仿真验证了方法的有效性。     

Actuator fault detection and isolation: An optimised parity space approach

The use of an optimised parity space approach for actuator fault detection and isolation (FDI) is explored. The parity space spans all the parity relations that quantify the analytical redundancies available between the sensor outputs and the actuator inputs of a system. A transformation matrix is then optimised to transform these parity relations into residuals that are especially sensitive to specific actuator faults. Actuator faults cause the variance of parity space residuals to increase. A cumulative summation procedure is used to determine when residual variance has changed sufficiently to indicate a locked-in-place actuator fault. A pseudoinverse actuator estimation scheme is used to extract the actuator deflections from the parity relations. It is found that the optimisation of the parity space approach introduces the advantage of added design freedom to the fault detection algorithm. The approach is applied to the identification of faulty aircraft control surface actuators that remain locked-in-place during flight and is successfully tested both in simulation and practical flight.     

Diagnosis of timed automata: Theory and application to the DAMADICS actuator benchmark problem

This paper concerns the problem of fault diagnosis in discrete-event systems which are represented by timed automata. The diagnostic algorithm for timed automata detects and identifies faults in the system based on the investigation whether the measured input and output sequences are consistent with the timed automaton. This diagnostic approach can be applied spontaneously to the discrete-event system since no a priori information about the initial state of the system is required. It is shown in the paper how the timed automaton which represents the DAMADICS actuator can be obtained and how the diagnostic algorithm based on the timed automaton is applied to detect and identify actuator faults. A representative diagnostic result is presented and discussed to illustrate the effectiveness of the method.     

A Recurrent Neural-Network-Based Sensor and Actuator Fault Detection and Isolation for Nonlinear Systems With Application to the Satellite's Attitude Control Subsystem

This paper presents a robust fault detection and isolation (FDI) scheme for a general class of nonlinear systems using a neural-network-based observer strategy. Both actuator and sensor faults are considered. The nonlinear system considered is subject to both state and sensor uncertainties and disturbances. Two recurrent neural networks are employed to identify general unknown actuator and sensor faults, respectively. The neural network weights are updated according to a modified backpropagation scheme. Unlike many previous methods developed in the literature, our proposed FDI scheme does not rely on availability of full state measurements. The stability of the overall FDI scheme in presence of unknown sensor and actuator faults as well as plant and sensor noise and uncertainties is shown by using the Lyapunov's direct method. The stability analysis developed requires no restrictive assumptions on the system and/or the FDI algorithm. Magnetorquer-type actuators and magnetometer-type sensors that are commonly employed in the attitude control subsystem (ACS) of low-Earth orbit (LEO) satellites for attitude determination and control are considered in our case studies. The effectiveness and capabilities of our proposed fault diagnosis strategy are demonstrated and validated through extensive simulation studies.     

一种滑模观测器的多故障诊断方法

针对非线性系统的执行器故障及传感器故障,提出一种鲁棒多故障检测方法．首先,对可能发生的每种执行器故障分别构造模型,并设计相应的滑模观测器用于残差生成,从而实现执行器故障检测．然后,设计一种算法,利用简单滤波器将传感器故障转换为执行器故障,从而直接利用执行器故障检测的方法实现传感器故障的检测,将执行器故障的检测方法推广到执行器、传感器故障同时存在的情况．最后,通过在单关节机械手中的仿真应用验证了所提方法的有效性．     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

ROBUST FAULT DETECTION AND ISOLATION FOR UNCERTAIN LINEAR RETARDED SYSTEMS

A robust fault detection and isolation scheme is proposed for uncertain continuous linear systems with discrete state delays for both additive and multiplicative faults. Model uncertainties, disturbances and noises are represented as unstructured unknown inputs. The proposed scheme consists of a Luenberger observer for fault detection and a group of adaptive observers, one for each class of faults, for fault isolation. The threshold determination and fault isolation are based on a multi‐observer strategy. Robustness to model uncertainties and disturbances can be guaranteed for the scheme by selecting proper thresholds. All the signals, i.e., the fault estimate and the state and output estimation errors of each isolation observer can be shown to be uniformly bounded, and the estimate of the fault by the matched observer is shown to be satisfactory in the sense of extended H₂ norm. Furthermore, the sensitivity to fault and the fault isolability condition are analyzed also in the paper. Simulations of a heating process for detecting and isolating an actuator gain fault and an additive fault show the proposed scheme is effective.     

基于高增益鲁棒滑模观测器的故障检测和隔离

针对一类同时具有执行器和传感器故障的不确定线性系统,讨论了基于观测器的故障检测和隔离方法.首先,通过引入增维向量,使得在构造的增维系统中,故障向量包含了原系统的执行器故障和传感器故障.通过构造辅助输出使增维系统的观测器匹配条件得以满足,同时设计高增益滑模观测器对辅助输出进行估计.然后,对增维系统构造鲁棒滑模观测器并用作故障检测观测器,通过滑模控制项来抑制干扰,使观测器具有鲁棒性.在此基础上,结合多观测器故障隔离思想,提出了可以同时对执行器故障和传感器故障进行检测和隔离的方法. 最后,通过对一个五阶飞行器模型进行仿真,证明了所提方法的有效性.     

Fault detection and estimation for a class of PIDE systems based on boundary observers

In this paper, we propose a simultaneous state estimation and fault estimation approach for a class of first‐order hyperbolic partial integral differential equation systems. Specifically, we consider the multiplicative boundary actuator and sensor faults, ie, unknown fault parameters multiplying by the boundary input or boundary state (ie, output). As a consequence, two difficulties arise immediately: (1) simultaneous estimation of both plant state and faults is a nonlinear problem due to the multiplication between fault parameters and plant signals; (2) no prior information is available to determine the type (actuator or sensor) of faults. To overcome these difficulties, this paper develops adaptive fault parameter update laws and embeds the resulting laws into the plant state observer design. First, we propose new approaches to estimate actuator fault and sensor fault, respectively. Next, we develop a novel method to simultaneously estimate actuator and sensor faults. The proposed observer and update laws, designed using only one boundary measurement, ensure both state estimation and fault parameter estimation. By choosing appropriate Lyapunov functions, we prove that the estimates of state and fault parameters converge to an arbitrarily small neighborhood of their true values. Numerical simulations are used to demonstrate the effectiveness of the proposed estimation approaches.     

Actuator fault diagnosis for a class of nonlinear systems and its application to a laboratory 3D crane

In this paper, an actuator fault diagnosis scheme is proposed for a class of affine nonlinear systems with both known and unknown inputs. The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators. The main advantages of the proposed approach are that it does not require a design of nonlinear observer and applies to systems not necessarily detectable. Conditions are provided to characterize the feasibility of fault detection and isolation using the proposed scheme and the maximum number of isolatable actuator faults. The efficacy of the proposed actuator fault diagnosis approach is tested through experiments on a laboratory 3D Crane, and the experimental results show that the proposed actuator fault diagnosis approach is promising and can achieve fault detection and isolation satisfactorily.     

Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator

A fault estimator for linear systems affected by disturbances is proposed. Faults appearing explicitly in the state equation and in the system output (actuator faults and sensor faults) are considered. With this design neither the estimation of the state vector nor the estimation of the disturbances is required, implying that the structural conditions are less restrictive than the ones required to design an unknown input observer. Furthermore, the number of unknown inputs (faults plus disturbances) may be greater than the number of outputs. The faults are written as an algebraic expression of a high-order derivative of a function depending on the output. Thus, the reconstruction of the fault signals is carried out by means of a sliding mode high-order differentiator, which requires the derivative of the faults to have a bounded norm.     

The joint optimal filtering and fault detection for multi-rate sensor fusion under unknown inputs

In multi-sensor fusion, it is hard to guarantee that all sensors have an identical sampling rate, especially in the distributive and/or heterogeneous case. Meanwhile, stochastic noise, unknown inputs (UIs), and faults may coexist in complex environment. To this end, we propose the problem of joint optimal filtering and fault detection (FD) for multi-rate sensor fusion subject to UIs, stochastic noise with known covariance, and faults imposed on the actuator and sensors. Furthermore, the new scheme of optimal multi-rate observer (MRO) is presented and applied to detect faults. The observer parameters are determined optimally in pursuit of the UI decoupling and maximizing noise attenuation under the causality constraint due to multi-rate nature. Finally, the output estimation error of the MRO is used as a residual signal for FD via a hypothesis test in which the threshold is adaptively designed according to the MRO parameters. One numerical example is given to show the effectiveness of our proposed method.     

Actuator fault detection and isolation in linear systems

A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.     

Sliding mode observers for detection and reconstruction of sensor faults

This paper proposes two methods for detecting and reconstructing sensor faults using sliding mode observers. In both methods, fictitious systems are introduced in which the original sensor fault appears as an actuator fault. The original sensor faults are then reconstructed using a ‘secondary’ sliding mode observer. For both methods, there are certain conditions which must be satisfied for successful fault detection and reconstruction. The methods are demonstrated using a chemical process example.     

Cascade filter structure for sensor/actuator fault detection and isolation of satellite attitude control system

This paper presents a new scheme for fault detection and isolation in a satellite system. The purpose of this paper is to develop detection, isolation and identification algorithms based on a cascade filter for both total and partial faults in a satellite attitude control system (ACS). The cascade filter consists of a decentralized Kalman filter (DKF) and a bank of interacting multiple model (IMM) filters. The cascade filter is utilized for detection and diagnosis of anticipated sensor and actuator faults in a satellite ACS. Other fault detection and isolation (FDI) schemes are compared with the proposed FDI scheme. The FDI procedure using a cascade filter was developed in three stages. In the first stage, two local filters and a master filter detect sensor faults. In the second stage, the FDI scheme checks sensor residuals to isolate sensor faults, and 11 Extended Kalman filters with actuator fault models detect wherever actuator faults occur. In the third stage of the FDI scheme, four filters identify the fault type, which is either a total or partial fault. An important feature of the proposed FDI scheme is that it can decrease fault isolation time and accomplish not only fault detection and isolation but also fault type identification using a scalar penalty in the conditional density function.