Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

Design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems

This paper presents a unified fault isolation scheme for handling both process faults and sensor faults in a class of uncertain nonlinear systems. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular fault type. The design of the fault isolation decision scheme is based on the derivation of appropriate adaptive thresholds for each fault isolation estimator. Fault isolability conditions characterizing the class of process faults and sensor faults that are isolable by the proposed scheme are derived. A rigorous isolability analysis is presented via the use of the so-called fault mismatch functions, which are defined between pairs of possible faults. A simulation example is used to illustrate the proposed fault isolation scheme.     

Sensor bias fault isolation in a class of nonlinear systems

This note presents a robust fault isolation scheme for a class of nonlinear systems with sensor bias type of faults. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular output sensor. Based on the class of nonlinear systems and sensor bias faults under consideration, the stability and learning properties of the fault isolation estimators are obtained, adaptive thresholds are derived for the isolation estimators, and fault isolability conditions are rigorously investigated, characterizing the class of nonlinear faults that are isolable by the proposed scheme. A simulation example is used to illustrate the effectiveness of the sensor bias fault isolation methodology.     

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.     

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.     

Distributed fault diagnosis in a class of interconnected nonlinear uncertain systems

In this article, a distributed fault detection and isolation (FDI) method is developed for a class of interconnected nonlinear uncertain systems. In the distributed FDI architecture, a FDI component is designed for each subsystem in the interconnected system. For each subsystem, its corresponding local FDI component is designed by utilising local measurements and certain communicated information from neighbouring FDI components associated with subsystems that are directly interconnected to the particular subsystem under consideration. Under certain assumptions, adaptive thresholds for distributed FDI in each subsystem are derived, ensuring robustness with respect to interactions among subsystems and system modelling uncertainty. Moreover, the fault detectability and isolability conditions are rigorously investigated, characterising the class of faults in each subsystem that are detectable and isolable by the proposed distributed FDI method. Additionally, the stability and learning capability of the local adaptive fault isolation estimators designed for each subsystem is established. A simulation example of interconnected inverted pendulums mounted on carts is used to illustrate the effectiveness of the method.     

Distributed fault diagnosis for continuous-time nonlinear systems: The input–output case

In this paper, some new results on distributed fault diagnosis of continuous-time nonlinear systems with partial state measurements are proposed. By exploiting an overlapping decomposition framework, the dynamics of a nonlinear uncertain large-scale dynamical system is described as the interconnections of several subsystems. Each subsystem is monitored by a Local Fault Diagnoser: a set of local estimators, based on the nominal local dynamic model and on an adaptive approximation of the interconnection and of the fault function, allows to derive a local fault decision. A consensus-based protocol is used in order to improve the detectability and the isolability of faults affecting variables shared among different subsystems because of the overlapping decomposition. A sufficient condition ensuring the convergence of the estimation errors is derived. Finally, possibly non-conservative time-varying threshold functions guaranteeing no false-positive alarms and theoretical results dealing with detectability and isolability sufficient conditions are presented.     

Diagnosis of unknown parametric faults in non-linear stochastic dynamical systems

A new detection and isolation scheme for unknown parametric faults in non-linear stochastic systems is presented that is particularly suited for small parametric changes. The proposed residual is the moving angle between two stochastic processes: the error derived from the reference model and the expected error in case a certain fault has occurred. Since the fault is unknown, fault classes are defined. Most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class. As the moving angle itself is a stochastic process, an estimator is designed and characterised. Conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests. Finally, the theoretical results are confirmed by simulations and Monte Carlo tests.     

Adaptive fault detection and isolation approach for actuator stuck faults in closed-loop systems

This paper addresses the fault detection and isolation (FDI) problem for linear time-invariant (LTI) systems under feedback control. Considered all the possible actuator stuck faults, the closed-loop systems are modeled via multiple models, i.e., fault-free model and faulty models. A fault detection observer and a bank of fault isolation observers are designed by using adaptive estimation techniques. The explicit fault detectability and isolability conditions are derived for determining the class of faults that are detectable and isolable. An F-18 aircraft model is employed to illustrate the effectiveness of the proposed FDI approach.     

On-line fault detection in uncertain nonlinear systems using diagnostic observers: a survey

The paper discusses the principles of model-based fault detection and isolation (FDI) in nonlinear and time-varying uncertain dynamic systems. Such systems are typical for such complex plants as, for example, in the chemical process industries or in advanced transportation technology. For a model-based fault diagnosis in such situations, robust or even adaptive strategies are needed. In this paper the theory of robust linear observer-based residual generation for FDI is reviewed from a general point of view. The structural equivalence between the parity space approach and observer-based approach is shown in a new simple graphical way by showing that the observer-based FDI concept can easily be transformed into an equivalent extended parity space configuration, without claiming, however, equivalence of the underlying design techniques. The unknown input observer approach known as a most powerful and comprehensive framework for robust residual generation for FDI in uncertain linear systems is extended to classes of nonlinear and time-varying systems. For such plants an adaptive nonlinear unknown input observer scheme is proposed. Finally, appropriate residual evaluation techniques are outlined and suggestions are made to increase the robustness, for instance by using adaptive thresholds.     

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

Design of unknown input functional observers for nonlinear systems with application to fault diagnosis

This paper considers the design of low-order unknown input functional observers for robust fault detection and isolation of a class of nonlinear Lipschitz systems subject to unknown inputs. The proposed functional observers can be used to generate residual signals to detect and isolate actuator faults. By using the generalized inverse approach, the effect of the unknown inputs can be decoupled completely from the residual signals. Conditions for the existence and stability of reduced-order unknown input functional observer are derived. A design procedure for the generation of residual signals to detect and isolate actuator faults is presented using the proposed unknown-input observer-based approach. A numerical example is given to illustrate the proposed fault diagnosis scheme in nonlinear systems subject to unknown inputs.     

Small oscillation fault detection for a class of nonlinear systems with output measurements using deterministic learning

Early detection of small faults is an important issue in the literature of fault diagnosis. In this paper, for a class of nonlinear systems with output measurements, an approach for rapid detection of small oscillation faults is presented. Firstly, locally accurate approximations of unknown system dynamics and fault functions are achieved by combining a high gain observer and a deterministic learning (DL) theory. The obtained knowledge of system dynamics for both normal and fault modes is stored in constant RBF networks. Secondly, a bank of dynamical estimators are constructed for all the normal mode and oscillation faults. The knowledge obtained through DL is reused with a nonhigh-gain design. The occurrence of a fault can be detected if one of residual norms of a fault estimator becomes smaller than that of the normal estimator in a finite time. A rigorous analysis of the detectability properties of the proposed fault detection scheme is also given, which includes the fault detectability condition and the fault detection time. The attractions of the paper lie in that with output measurements, the knowledge of modeling uncertainty and nonlinear faults is obtained and then is utilized to enhance the sensitivity to small faults.     

Distributed fault detection and isolation scheme for abrupt and incipient faults in a class of nonlinear systems

This note developed a distributed fault detection and isolation scheme for a class of large-scale systems in discrete-time framework. The unstructured modeling uncertainty and abrupt and incipient faults are considered in this scheme. By using overlapping decompositions, the large-scale system is decomposed into a set of subsystems which are monitored by a network of local fault detectors (LFDs) and local fault isolation estimators (LFIEs). Specially, the LFIEs, corresponding the faults affecting the common components among different subsystems, may reach a cooperative (or consensus) isolation decision, based on the fact that they can exchange some knowledge about the local information of system by suitable communication links. As a result, for these LFIEs, the capability of isolating faults may be improved. Moreover, the derivation of rigorous analytical results for the detectability and isolability properties of the proposed scheme is given. Simulation results are provided to show the effectiveness of the presented scheme.     

Distributed sensor fault diagnosis in a class of interconnected nonlinear uncertain systems

In this paper, a distributed sensor fault detection and isolation (FDI) method is developed for a class of interconnected nonlinear uncertain systems. In the distributed FDI architecture, a FDI component is designed for each subsystem in the interconnected system. For each subsystem, its corresponding local FDI component is designed by utilizing local measurements and certain communicated information from neighboring FDI components associated with subsystems that are directly interconnected to the particular subsystem under consideration. Under certain assumptions, adaptive thresholds for distributed sensor fault detection and isolation in each subsystem are derived, ensuring robustness with respect to interactions among subsystems and system modeling uncertainty. Moreover, the fault detectability condition is rigorously investigated, characterizing the class of sensor faults in each subsystem that is detectable by the proposed distributed FDI method. Additionally, the stability and learning capability of the distributed adaptive fault isolation estimators is established. A simulation example of interconnected inverted pendulums mounted on carts is used to illustrate the effectiveness of the distributed FDI method.     

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.     

Quadrotor Sensor Fault Diagnosis with Experimental Results

This paper presents a fault detection, isolation, and estimation scheme for sensor bias faults in accelerometer and gyroscope measurements of quadrotor unmanned air vehicles (UAVs). Based on sliding-mode observer techniques, a robust estimation of the quadrotor roll and pitch angles is obtained by using only accelerometer measurements. Then, a diagnostic scheme is developed for detecting, isolating, and estimating sensor bias faults in the gyroscope and accelerometer measurements. Structured residuals are generated, allowing the detection and isolation of multiple simultaneous sensor faults under consideration. After the faults are detected and isolated, two nonlinear estimators are employed to provide an estimate of the unknown fault magnitude. The stability and estimation performance properties of the nonlinear estimators are established. The sensor fault diagnosis algorithm is implemented and evaluated through experimental results using a real-time indoor quadrotor test environment.     

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．     

Asymptotic tracking control of uncertain MIMO nonlinear systems with extended condition for controllability

For uncertain multiple-inputs multi-outputs nonlinear systems, it is nontrivial to achieve asymptotic tracking due to the intrinsic coupling among inputs, while the controllability conditions in most existing methods are rather restrictive or even impractical especially when unexpected actuator faults are involved. In this article, we focus on extending such controllability condition by resorting to the existence (instead of a priori knowledge) of some feasible auxiliary matrix, upon which a robust adaptive control scheme is first presented in the absence of actuator faults that is not only able to achieve asymptotic tracking even in the presence of non-parametric uncertainties with all the closed-loop signals globally ultimately uniformly bounded, but also able to deal with a larger class of system models. Furthermore, for the case with intermittent actuator faults, we develop a fault-tolerant control scheme with extended condition for controllability that is able to accommodate such faults automatically without using any fault detection or fault diagnosis unit. The effectiveness and benefits of the proposed method are verified via simulation on robotic systems.