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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems

This paper considers observer-based actuator fault detection and reconstruction problems for uncertain nonlinear systems. Based on a kind of full-order observer which is robust to disturbances but sensitive to actuator faults, a single detection observer is constructed to produce a residual which can be used to alarm the occurrence of the actuator faults when at least one actuator fault occurs indeed. The full-order observer is adaptive one because an adaptation law which can adjust the Lipschitz constant of Lipschitz term is introduced. For this reason, the Lipschitz constant can be unknown in our design. After this, a kind of reduced-order observer is developed by choosing a special observer gain matrix. Based on the reduced-order observer, we provide a kind of unknown information estimating method which can be used to not only reconstruct the actuator faults but also estimate the disturbances of the system. In simulation, a real model of the seventh-order aircraft is used to illustrate the effectiveness of the proposed methods.     

Relaxed fault detection and isolation: An application to a nonlinear case study

Given a number of possibly concurrent faults (and disturbances) that may affect a nonlinear dynamic system, it may not be possible to solve the standard fault detection and isolation (FDI) problem, i.e., to detect and isolate each single fault from all other, possibly concurrent faults and disturbances, due to the violation of the available necessary conditions of geometric nature. Motivated by a robotic application where this negative situation structurally occurs, we propose some relaxed formulations of the FDI problem and show how necessary and sufficient conditions for their solution can be derived from those available for standard FDI. The design of a hybrid residual generator follows directly from the fulfillment of the corresponding solvability conditions. In the considered nonlinear case study, a robotic system affected by possible actuator and/or force sensor faults, we detail the application of these results and present experimental tests for validation.     

Two fault detection and isolation schemes for robot manipulators using soft computing techniques

With growing technology, fault detection and isolation (FDI) have become one of the interesting and important research areas in modern control and signal processing. Accomplishment of specific missions like waste treatment in nuclear reactors or data collection in space and underwater missions make reliability more important for robotics and this demand forces researchers to adapt available FDI studies on nonlinear systems to robot manipulators, mobile robots and mobile manipulators.In this study, two model-based FDI schemes for robot manipulators using soft computing techniques, as an integrator of Neural Network (NN) and Fuzzy Logic (FL), are proposed. Both schemes use M-ANFIS for robot modelling. The first scheme isolates faults by passing residual signals through a neural network. The second scheme isolates faults by modelling faulty robot models for defined faults and combining these models as a generalized observers scheme (GOS) structure. Performances of these schemes are tested on a simulated two-link planar manipulator and simulation results and a comparison according to some important FDI specifications are presented.     

Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach

Active fault detection and isolation (AFDI) is used for detection and isolation of faults that are hidden in the normal operation because of a low excitation signal or due to the regulatory actions of the controller. In this paper, a new AFDI method based on set-membership approaches is proposed. In set-membership approaches, instead of a point-wise estimation of the states, a set-valued estimation of them is computed. If this set becomes empty the given model of the system is not consistent with the measurements. Therefore, the model is falsified. When more than one model of the system remains un-falsified, the AFDI method is used to generate an auxiliary signal that is injected into the system for detection and isolation of faults that remain otherwise hidden or non-isolated using passive FDI (PFDI) methods. Having the set-valued estimation of the states for each model, the proposed AFDI method finds an optimal input signal that guarantees FDI in a finite time horizon. The input signal is updated at each iteration in a decreasing receding horizon manner based on the set-valued estimation of the current states and un-falsified models at the current sample time. The problem is solved by a number of linear and quadratic programming problems, which result in a computationally efficient algorithm. The method is tested on a numerical example as well as on the pitch actuator of a benchmark wind turbine.     

Structural analysis for the sensor location problem in fault detection and isolation

In this paper we tackle the sensor location problem for fault detection and isolation based on structural analysis for linear systems with faults. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. With such structured systems one can associate a graph. A dedicated residual set is designed using a bank of observers for solving the problem. A major tool in this analysis is the notion of input separator in the associated graph, these separators form a lattice structure. The main contribution of this paper is the formulation of necessary and sufficient solvability conditions for the problem in terms of number of additional sensors measuring variables between faults and input separators in the associated graph.     

Subspace-based fault detection robust to changes in the noise covariances

The detection of changes in the eigenstructure of a linear time invariant system by means of a subspace-based residual function has been proposed previously. While enjoying some success in its applicability in particular in the context of vibration monitoring, the robustness of this framework against changes in the noise properties has not been properly addressed yet. In this paper, a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown. The complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided.