Subspace method aided data-driven design of fault detection and isolation systems

This paper deals with data-driven design of fault detection and isolation (FDI) systems. The basic idea is to identify a primary form of residual generators, instead of the process model, directly from test data and, based on it, to design advanced FDI systems. The proposed method can be applied for the parity space and observer based detection and isolation of sensor and actuator faults as well as the construction of soft-sensors. The application of the proposed method is illustrated by a simulation study on the Tennessee Eastman process.     

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.     

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.     

A risk adjusted approach to robust simultaneous fault detection and isolation

This paper addresses the problem of detecting and isolating faults in noisy MIMO uncertain-systems, subject to structured dynamic uncertainty. Its main result shows that this problem can be efficiently solved using a combination of sampling and LMI optimization tools. These results are illustrated with two examples and benchmarked against existing methods.     

On the disturbed fault detection and isolation problem

In this paper we study the fault detection and isolation problem in presence of disturbances. In the case of observer-based residual generation, the problem amounts to finding two gain matrices such that two problems are simultaneously solved. These problems are insensitivity of the residuals to disturbances and the existence of some special structure for the transfer from faults to residuals. We prove in this paper that this joint problem can be solved if and only if the usual (undisturbed) fault detection and isolation problem can be solved for a system with a reduced number of outputs.     

Distributed data-driven optimal fault detection for large-scale systems

This paper is concentrated on two new distributed data-driven optimal fault detection approaches in large-scale systems using a group of sensor blocks, each of which accesses part of the process variables. Towards this end, an optimal fault detection problem is first formulated and solved, which lays a foundation for further distributed studies. Based on it, the first distributed data-driven optimal fault detection scheme, consisting of offline distributed learning and online distributed detection, is developed using the average consensus algorithm. To further reduce communication and computation efforts, the second average consensus based fault detection is investigated. Considering that the iteration computations for average consensus algorithm can lead to fault detection delay, a variation of the average consensus based fault detection scheme is proposed with iterative estimation of the covariance matrices of random variables and implementation of the distributed test statistic during the consensus iteration. A numerical example and a case study on the PRONTO heterogeneous benchmark dataset are used to demonstrate the proposed approaches.     

Distributed fault detection for interconnected second-order systems

In this paper, the existence of unknown input observers for networks of interconnected second-order linear time invariant systems is studied. Two classes of distributed control systems of large practical relevance are considered. It is proved that for these systems, one can construct a bank of unknown input observers, and use them to detect and isolate faults in the network. The result presents a distributed implementation. In particular, by exploiting the system structure, this work provides further insight into the design of UIO for networked systems. Moreover, the importance of certain network measurements is shown. Infeasibility results with respect to available measurements and faults are also provided, as well as methods to remove faulty agents from the network. Applications to power networks and robotic formations are presented. It is shown how the developed methodology apply to a power network described by the swing equation with a faulty bus. For a multi-robot system, it is illustrated how a faulty robot can be detected and removed.     

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.     

A distribution independent data-driven design scheme of optimal dynamic fault detection systems

In this paper, design issues of data-driven optimal dynamic fault detection systems for stochastic linear discrete-time processes are addressed without precise distribution knowledge of unknown inputs and faults. Concerning a family of faults with different distribution profiles in mean and covariance matrix, we introduce a bank of parameter vectors of parity space and construct the parity relation based residual generators using process input and output data. In the context of minimizing the missed detection rate for a prescribed false alarm rate, the design of fault detection system is formulated as a bank of distribution independent optimization problems without posing specific distribution assumption on unknown inputs and faults. It is proven that the optimal selection of individual parameter vector can be formulated as a generalized eigenvalue–eigenvector problem in terms of the means and covariance matrices of residuals in fault-free and each faulty cases, and is thus solved via singular value decomposition. The tight upper bounds of false alarm rate and missed detection rate are simultaneously achieved quantitatively. Besides, the existence condition of the optimal solutions is investigated analytically. Experimental study on a three-tank system illustrates the application of the proposed scheme.     

Disturbance decoupling in fault detection of linear periodic systems

This paper studies fault detection problems of linear discrete-time periodic systems. The aim is to design residual generators, which deliver a residual signal fully decoupled from unknown disturbances. First, a periodic parity relation based full decoupling residual generator with a periodically varying parity vector is established. Then, the relation between periodic parity vectors and periodic observer-based residual generators is investigated. It is shown that a periodic observer-based full decoupling residual generator can be obtained from a periodic full decoupling parity vector. Finally, the condition of disturbance decoupling is discussed and an example is given to illustrate the proposed approaches.     

Sensor fault detection and isolation for aircraft control systems by kinematic relations

This paper presents a new approach to Fault Detection and Isolation (FDI) for sensors of aircraft. In the most general case, fault detection of these sensors on modern aircraft is performed by a logic that selects one of, or combines, the three redundant measurements. Such a method is compliant with current airworthiness regulations. However, in the framework of the global aircraft optimization for future and upcoming aircraft, it could be required, e.g., to extend the availability of sensor measurements. Introducing a form of analytical redundancy of these measurements can increase the fault detection performance and result in a weight saving of the aircraft. This can be achieved by exploiting the knowledge of the kinematic relations between the measured variables. These relations are exactly known giving the advantage that no model-mismatches need to be accounted for. Furthermore these relations are valid over the whole flight envelope and general for any type of aircraft. Two example applications will be presented, showing the applicability of the method for the FDI of air data sensors and measurements of the inertial reference unit.     

A fuzzy inference system for fault detection and isolation: Application to a fluid system

This work focuses on the design and implementation of a fuzzy inference system for fault detection and isolation (FDI) which can learn from example fault data, and the determination of a suitable optimisation strategy for the membership functions. A FDI system was developed which is based on adaptive fuzzy rules. A number of optimisation strategies were then applied; it was found that an evolutionary algorithm not only produced the best results but did so with relatively little processing effort and with excellent consistency.The adaptive fuzzy system, thus optimised, was tested against a neural network, which was trained to produce analogue outputs as an indication of fault magnitude. The fuzzy solution produced the best accuracy.We can conclude that an adaptive fuzzy inference system for FDI, using an evolutionary algorithm to learn from examples, can provide an accurate and readily comprehensible solution to diagnosing and evaluating fluid process plant faults.     

Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems

In this article, an actuator fault detection and isolation scheme for a class of nonlinear systems with uncertainty is considered. The uncertainty is allowed to have a nonlinear bound which is a general function of the state variables. A sliding mode observer is first established based on a constrained Lyapunov equation. Then, the equivalent output error injection is employed to reconstruct the fault signal using the characteristics of the sliding mode observer and the structure of the uncertainty. The reconstructed signal can approximate the system fault signal to any accuracy even in the presence of a class of uncertainty. Finally, a simulation study on a nonlinear aircraft system is presented to show the effectiveness of the scheme.     

Online fault detection and isolation of nonlinear systems based on neurofuzzy networks

An online fault detection and isolation (FDI) technique for nonlinear systems based on neurofuzzy networks (NFN) is proposed in this paper. Two NFNs are used. The first one trained by data obtained under normal operating condition models the system and the second one trained online models the residuals. Fuzzy rules that are activated under fault free and faulty conditions are extracted from the second NFN and stored in the symptom vectors using a binary code. A fault database is then formed from these symptom vectors. When applying the proposed FDI technique, the NFN that models the residuals is updated recursively online, from which the symptom vector is obtained. By comparing this symptom vector with those in the fault database, faults are isolated. Further, the fuzzy rules obtained from the symptom vector can also provide linguistic information to experienced operators for identifying the faults. The implementation and performance of the proposed FDI technique is illustrated by simulation examples involving a two-tank water level control system under faulty conditions.     

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 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.     

Auxiliary signal design for robust active fault detection of linear discrete-time systems

In this paper, algorithms are proposed to design auxiliary signals for active fault detection based on a multi-model formulation of discrete-time systems. Two different scenarios are considered for this problem; the first one assumes there is no a priori information on initial conditions and no exogenous input signal, while the second allows for having a priori information and the possibility of having a known input in addition to the test signal. Approaches are proposed for solving these two types of problems which are capable of solving the problems efficiently. This is achieved by using a recursive approach based on the use of special Riccati equations. These algorithms can be used for systems of higher dimension and on longer time horizons than the existing methods.     

UIO design for singular delayed LPV systems with application to actuator fault detection and isolation

In this paper, the unknown input observer (UIO) design for singular delayed linear parameter varying (LPV) systems is considered regarding its application to actuator fault detection and isolation. The design procedure assumes that the LPV system is represented in the polytopic framework. Existence and convergence conditions for the UIO are established. The design procedure is formulated by means of linear matrix inequalities (LMIs). Actuator fault detection and isolation is based on using the UIO approach for designing a residual generator that is completely decoupled from unknown inputs and exclusively sensitive to faults. Fault isolation is addressed considering two different strategies: dedicated and generalised bank of observers’ schemes. The applicability of these two schemes for the fault isolation is discussed. An open flow canal system is considered as a case study to illustrate the performance and usefulness of the proposed fault detection and isolation method in different fault scenarios.     

Survey and application of sensor fault detection and isolation schemes

Model-based sensor fault detection, isolation and accommodation (SFDIA) is a direction of development in particular with UAVs where sensor redundancy may not be an option due to weight, cost and space implications. SFDIA via neural networks (NNs) have been proposed over the years due to their nonlinear structures and online learning capabilities. The majority of papers tend to consider single sensor faults. While useful, this assumption can limit application to real systems where sensor faults can occur simultaneously or consecutively. In this paper we consider the latter scenario, where it is assumed that a 1 s time gap is present between consecutive faults. Furthermore few applications have considered fixed-wing UAVs where full autonomy is most needed. In this paper an EMRAN RBF NN is chosen for modelling purposes due to its ability to adapt well to nonlinear environments while maintaining high computational speeds. A nonlinear UAV model is used for demonstration, where decoupled longitudinal motion is considered. System and measurement noise is also included in the UAV model as wind gust disturbances on the angle of attack and sensor noise, respectively. The UAV is assumed to operate at an initial trimmed condition of speed, 32 m/s and altitude, 1000 m. After 30 separate SFDIA tests implemented on a 1.6 GHz Pentium processor, the NN-SFDIA scheme detected all but 2 faults and the NN processing time was 97% lower than the flight data sampling time.