Distributed Fault Diagnosis With Overlapping Decompositions: An Adaptive Approximation Approach

This technical note deals with the problem of designing a distributed fault detection methodology for distributed (and possibly large-scale) nonlinear dynamical systems that are modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a local fault detector is designed, based on the measured local state of the subsystem as well as the transmitted variables of neighboring states that define the subsystem interconnections. The local detection decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the interconnection with neighboring subsystems. The use of a specially-designed consensus-based estimator is proposed in order to improve the detectability of faults affecting variables shared among different subsystems. Simulation results provide an evidence of the effectiveness of the proposed distributed fault detection scheme.     

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.     

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.     

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 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.     

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.     

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     

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.     

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.     

Multiobjective performance-based designs in fault estimation and isolation for discrete-time systems and its application to wind turbines

In this work, we develop a performance-based design of model-based observes and statistical-based decision mechanisms for achieving fault estimation and fault isolation in systems affected by unknown inputs and stochastic noises. First, through semidefinite programming, we design the observers considering different estimation performance indices as the covariance of the estimation errors, the fault tracking delays and the degree of decoupling from unknown inputs and from faults in other channels. Second, we perform a co-design of the observers and decision mechanisms for satisfying certain trade-off between different isolation performance indices: the false isolation rates, the isolation times and the minimum size of the isolable faults. Finally, we extend these results to a scheme based on a bank of observers for the case where multiple faults affect the system and isolability conditions are not verified. To show the effectiveness of the results, we apply these design strategies to a well-known benchmark of wind turbines which considers multiple faults and has explicit requirements over isolation times and false isolation rates.     

Distributed Model Predictive Control for Networked Plant-wide Systems With Neighborhood Cooperation

For large-scale networked plant-wide systems composed by physically (or geographically) divided subsystems, only limited information is available for local controllers on account of region and communication restrictions. Concerning the optimal control problem of such subsystems, a neighbor-based distributed model predictive control (NDMPC) strategy is presented to improve the global system performance. In this scheme, the performance index of local subsystems and that of its neighbors are minimized together in the determination of the optimal control input, which makes the local control decision also beneficial to its neighboring subsystems and further contributes to improving the convergence and control performance of overall system. The stability of the closed-loop system is proved. Moreover, the parameter designing method for distributed synthesis is provided. Finally, the simulation results illustrate the main characteristics and effectiveness of the proposed control scheme.      

Distributed sensor fault diagnosis for a formation system with unknown constant time delays

In this paper, a distributed velocity sensor fault diagnosis scheme is presented for a formation of a second-order multi-agent system with unknown constant communication time delays. An existing distributed proportion-derivation (DPD) formation control law is adopted and a delay-independent condition is proposed to guarantee the asymptotical formation stability of the formation system based on the Nyquist stability criterion. Then a distributed fault diagnosis scheme is developed. In each agent, a distributed fault detection residual generator (DFDRG) and a bank of distributed fault isolation residual generators (DFIRGs) are designed based on the closed-loop model of the whole system. Each DFIRG is built up on the basis of a reduced-order unknown input observer (UIO) which is robust to the fault of one neighboring agent. According to the robust relationship between DFIRGs and faults, distributed fault isolation can be achieved. Conditions are presented to guarantee that each agent is able to diagnose faults of itself and its neighbors despite the disturbance of time delays. Finally, outdoor experimental results illustrate the effectiveness of the proposed schemes.     

Fault tolerant control using a fuzzy predictive approach

This paper proposes the application of fault-tolerant control (FTC) using fuzzy predictive control. The FTC approach is based on two steps, fault detection and isolation (FDI) and fault accommodation. The fault detection is performed by a model-based approach using fuzzy modeling and fault isolation uses a fuzzy decision making approach. The information obtained on the FDI step is used to select the model to be used in fault accommodation, in a model predictive control (MPC) scheme. The fault accommodation is performed with one fuzzy model for each identified fault. The FTC scheme is used to accommodate the faults of two systems a container gantry crane and three tank benchmark system. The fuzzy FTC scheme proposed in this paper was able to detect, isolate and accommodate correctly the considered faults of both systems.     

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.     

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.     

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.     

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 detection and isolation for discrete-time switched linear systems based on average dwell-time method

This article is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched linear systems based on the average dwell-time method. The proposed FDI framework consists of a bank of FDI filters, which are divided into N groups for N subsystems. The FDI filters belonging to one group correspond to the faults for a subsystem, and generate a residual signal to guarantee the fault sensitivity performance for the subsystem, the fault attenuation performance for other subsystems and the disturbance attenuation performance for all subsystems. Different form employing the weighting matrices to restrict the frequency ranges of faults for each subsystem, the finite-frequency H _? performance for switched systems is first defined. Sufficient conditions are established by linear matrix inequalities (LMIs), and the filter gains are characterised in terms of the solution of a convex optimisation problem. Two examples are used to demonstrate the effectiveness of the proposed design method.     

Robust parameter-dependent fault-tolerant control for actuator and sensor faults

In this article, we study a robust fault-tolerant control (FTC) problem for linear systems subject to time-varying actuator and sensor faults. The faults under consideration are loss of effectiveness in actuators and sensors. Based on the estimated faults from a fault detection and isolation scheme, robust parameter-dependent FTC will be designed to stabilise the faulty system under all possible fault scenarios. The synthesis condition of such an FTC control law will be formulated in terms of linear matrix inequalities (LMIs) and can be solved efficiently by semi-definite programming. The proposed FTC approach will be demonstrated on a simple faulty system with different fault levels and fault estimation error bounds.