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.     

A robust detection and isolation scheme for abrupt and incipientfaults in nonlinear systems

This paper presents a robust fault diagnosis scheme for abrupt and incipient faults in nonlinear uncertain dynamic systems. A detection and approximation estimator is used for online health monitoring. Once a fault is detected, a bank of isolation estimators is activated for the purpose of fault isolation. A key design issue of the proposed fault isolation scheme is the adaptive residual threshold associated with each isolation estimator. A fault that has occurred can be isolated if the residual associated with the matched isolation estimator remains below its corresponding adaptive threshold, whereas at least one of the components of the residuals associated with all the other estimators exceeds its threshold at some finite time. Based on the class of nonlinear uncertain systems under consideration, an isolation decision scheme is devised and fault isolability conditions are given, characterizing the class of nonlinear faults that are isolable by the robust fault isolation scheme. The nonconservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and of faults for which these conditions are also necessary for fault isolability. Moreover, the analysis of the proposed fault isolation scheme provides rigorous analytical results concerning the fault isolation time. Two simulation examples are given to show the effectiveness of the fault diagnosis methodology     

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.     

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.     

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.     

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.     

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.     

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.     

Incipient sensor fault isolation based on augmented Mahalanobis distance

Incipient sensor fault diagnosis is important to an efficient and optimal operating condition for modern industrial systems. Recently, a new fault detection index called augmented Mahalanobis distance (AMD) has been proposed in our previous work for incipient fault detection. Following detection, fault isolation is also quite desired so as to investigate root causes of the occurred fault. In the present work, the AMD statistic is first revisited and a geometric illustration of AMD is provided, which intuitively shows its superiority for incipient fault detection. Then, with available fault direction information, an incipient sensor fault isolation approach is proposed. Its fault isolability condition is analyzed theoretically and compared with that of the conventional method. For complex sensor faults whose fault direction information is unknown, a corresponding fault isolation strategy is also briefly discussed. Case studies on a high-speed train air brake system and the continuous stirred tank reactor (CSTR) process are carried out, which demonstrate the effectiveness of the AMD based fault detection and isolation methods, in comparison with conventional approaches.     

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.     

Fault‐Tolerant Control Allocation for Overactuated Nonlinear Systems

This paper addresses the problem of fault‐tolerant control allocation for input affine nonlinear systems. The proposed scheme is divided in three main tasks: fault detection and estimation using a nonlinear observer, fault isolation through a bank of unknown input observers with a resetting policy to reduce the effects of nonlinearities and control reconfiguration based on reduced order allocation. Analytical results regarding the isolability and reconfigurability of actuator faults are derived and a simulation example is used to illustrate the the proposed fault tolerant control methodology.     

Kalman filters in non-uniformly sampled multirate systems: For FDI and beyond

The first part of the paper is the development of a data-driven Kalman filter for a non-uniformly sampled multirate (NUSM) system. Algorithms for both one-step predictor and filtering are developed and analysis of stability and convergence is conducted in the NUSM framework. The second part of the paper investigates a Kalman filter-based methodology for unified detection and isolation of sensor, actuator, and process faults in the NUSM system with analysis on fault detectability and isolability. Case studies using data respectively collected from a pilot experimental plant and a simulated system are conducted to justify the practicality of the proposed theory.     

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.     

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.     

Novel MPC‐Based Fault Tolerant Tracking Control Against Sensor Faults

The problem of active fault‐tolerant tracking control with control input and system output constraints is studied for a class of discrete‐time systems subject to sensor faults. A time‐varying fault‐tolerant observer is first developed to estimate the real system state from the faulty sensor output and control input signals. Then by using the estimated state at each time step, a model predictive control (MPC)‐based fault‐tolerant tracking control scheme is presented to guarantee the desired tracking performance and the given input and output constraints on the faulty system. In comparison with many existing fault‐tolerant MPC methods, its main contribution is that the proposed state estimator is designed by the simple and online numerical computation to tolerate the possible sensor faults, so that the regular MPC algorithm without fault information can be adopted for the online calculation of fault‐tolerant control signal. The potential recursive infeasibility and computational complexity due to the faults are avoided in the scheme. Additionally, the closed‐loop stability of the post‐fault system is discussed. Simulative results of an electric throttle control system verify the effectiveness of the proposed method.     

Online fault diagnosis using recursive subspace identification: Application to a dam-gallery open channel system

The paper presents an online strategy for sensor and/or actuator fault detection and isolation applied to a dam-gallery. A recursive subspace identification algorithm is used to estimate the dam-gallery model parameters. The main contribution consists in developing a specific identification scheme, insensitive to a certain type of faults. That is, the identified parameters are invariant to the faults. A fault estimation procedure is proposed to detect potential faults. The proposed approach appears to be suitable for open channel systems for which the characteristics are not easily measurable.     

Fault isolation schemes for a class of continuous-time stochastic dynamical systems

In this paper a new method for fault isolation in a class of continuous-time stochastic dynamical systems is proposed. The method is framed in the context of model-based analytical redundancy, consisting in the generation of a residual signal by means of a diagnostic observer, for its posterior analysis. Once a fault has been detected, and assuming some basic a priori knowledge about the set of possible failures in the plant, the isolation task is then formulated as a type of on-line statistical classification problem. The proposed isolation scheme employs in parallel different hypotheses tests on a statistic of the residual signal, one test for each possible fault. This isolation method is characterized by deriving for the unidimensional case, a sufficient isolability condition as well as an upperbound of the probability of missed isolation. Simulation examples illustrate the applicability of the proposed scheme.     

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.     

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.     

Sensor fault diagnosis in a chemical process via RBF neural networks

Radial basis function (RBF) neural networks are investigated here for process fault diagnosis. The use of the output prediction error, between a neural network model and a non-linear dynamic process, as a residual for diagnosing actuator, component and sensor faults is analysed. It is found that this residual for a dependent neural model is less sensitive to sensor faults than actuator or component faults. This is confirmed in experiments for a real, multivariable chemical reactor. A scheme is then developed utilising a semi-independent neural model to generate enhanced residuals for diagnosing the sensor faults in the reactor. A second neural-network classifier is developed to diagnose the sensor faults from the residuals generated, and results are presented to demonstrate the satisfactory detection and isolation of sensor faults achieved using this approach.