On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

Multi-agent methodology for distributed and cooperative supervisory estimation subject to unreliable information

In this work, a novel multi-agent framework for cooperative supervisory estimation of linear time-invariant systems is proposed. This framework is developed based on the notion of subobservers and a discrete-event system (DES) supervisory control and is applicable to large-scale systems. We introduce a group of subobservers where each subobserver is estimating certain states that are conditioned on a given input, output and state information. The cooperation among the subobservers is managed by a DES supervisor. The supervisor makes decisions regarding the selection and configuration of a set of subobservers to successfully estimate all the system states, while the feasibility of the overall integrated cooperative subobservers is verified. When certain anomalies (faults) are present in the system, or the sensors and subobservers become unreliable, the supervisor reconfigures the set of selected subobservers so that the impacts of anomalies on the estimation performance are minimised to the extent that is possible. The application and capabilities of our proposed methodology in a practical industrial process is demonstrated through numerical simulations

A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems

This paper is concerned with development of novel fault detection and isolation (FDI) strategies for the Markovian jump linear systems (MJLS's) and the MJLS's with time-delays (MJLSD's). First a geometric property that is related to the unobservable subspace of MJLS's is presented. The notion of a finite unobservable subspace is then introduced for the MJLSD's. The concept of unobservability subspace is introduced for both the MJLS's and the MJLSD's and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for the MJLS's are developed by utilizing our introduced unobservability subspace. Furthermore, sufficient solvability conditions of the FPRG for the MJLSD's are also derived. Finally, sufficient conditions for designing an H∞-based FDI algorithm for the MJLS's with an unknown transition matrix that are also subject to input and output disturbances are developed

Model based fault diagnosis and prognosis of nonlinear systems

Rapid technological advances have led to more and more complex industrial systems with significantly higher risk of failures. Therefore, in this dissertation, a model-based fault diagnosis and prognosis framework has been developed for fast and reliable detection of faults and prediction of failures in nonlinear systems. In the first paper, a unified model-based fault diagnosis scheme capable of detecting both additive system faults and multiplicative actuator faults, as well as approximating the fault dynamics, performing fault type determination and time-to-failure determination, is designed. Stability of the observer and online approximator is guaranteed via an adaptive update law. Since outliers can degrade the performance of fault diagnostics, the second paper introduces an online neural network (NN) based outlier identification and removal scheme which is then combined with a fault detection scheme to enhance its performance. Outliers are detected based on the estimation error and a novel tuning law prevents the NN weights from being affected by outliers. In the third paper, in contrast to papers I and II, fault diagnosis of large-scale interconnected systems is investigated. A decentralized fault prognosis scheme is developed for such systems by using a network of local fault detectors (LFD) where each LFD only requires the local measurements. The online approximators in each LFD learn the unknown interconnection functions and the fault dynamics. Derivation of robust detection thresholds and detectability conditions are also included. The fourth paper extends the decentralized fault detection from paper III and develops an accommodation scheme for nonlinear continuous-time systems. By using both detection and accommodation online approximators, the control inputs are adjusted in order to minimize the fault effects. Finally in the fifth paper, the model-based fault diagnosis of distributed parameter systems (DPS) with parabolic PDE representation in continuous-time is discussed where a PDE-based observer is designed to perform fault detection as well as estimating the unavailable system states. An adaptive online approximator is incorporated in the observer to identify unknown fault parameters. Adaptive update law guarantees the convergence of estimations and allows determination of remaining useful life --Abstract, page iv

Geometric Fault Detection and Isolation of Infinite Dimensional Systems

A broad class of dynamical systems from chemical processes to flexible mechanical structures, heat transfer and compression processes in gas turbine engines are represented by a set of partial differential equations (PDE). These systems are known as infinite dimensional (Inf-D) systems. Most of Inf-D systems, including PDEs and time-delayed systems can be represented by a differential equation in an appropriate Hilbert space. These Hilbert spaces are essentially Inf-D vector spaces, and therefore, they are utilized to represent Inf-D dynamical systems. Inf-D systems have been investigated by invoking two schemes, namely approximate and exact methods. Both approaches extend the control theory of ordinary differential equation (ODE) systems to Inf-D systems, however by utilizing two different methodologies. In the former approach, one needs to first approximate the original Inf-D system by an ODE system (e.g. by using finite element or finite difference methods) and then apply the established control theory of ODEs to the approximated model. On the other hand, in the exact approach, one investigates the Inf-D system without using any approximation. In other words, one first represents the system as an Inf-D system and then investigates it in the corresponding Inf-D Hilbert space by extending and generalizing the available results of finite-dimensional (Fin-D) control theory. It is well-known that one of the challenging issues in control theory is development of algorithms such that the controlled system can maintain the required performance even in presence of faults. In the literature, this property is known as fault tolerant control. The fault detection and isolation (FDI) analysis is the first step in order to achieve this goal. For Inf-D systems, the currently available results on the FDI problem are quite limited and restricted. This thesis is mainly concerned with the FDI problem of the linear Inf-D systems by using both approximate and exact approaches based on the geometric control theory of Fin-D and Inf-D systems. This thesis addresses this problem by developing a geometric FDI framework for Inf-D systems. Moreover, we implement and demonstrate a methodology for applying our results to mathematical models of a heat transfer and a two-component reaction-diffusion processes. In this thesis, we first investigate the development of an FDI scheme for discrete-time multi-dimensional (nD) systems that represent approximate models for Inf-D systems. The basic invariant subspaces including unobservable and unobservability subspaces of one-dimensional (1D) systems are extended to nD models. Sufficient conditions for solvability of the FDI problem are provided, where an LMI-based approach is also derived for the observer design. The capability of our proposed FDI methodology is demonstrated through numerical simulation results to an approximation of a hyperbolic partial differential equation system of a heat exchanger that is represented as a two-dimensional (2D) system. In the second part, an FDI methodology for the Riesz spectral (RS) system is investigated. RS systems represent a large class of parabolic and hyperbolic PDE in Inf-D systems framework. This part is mainly concerned with the equivalence of different types of invariant subspaces as defined for RS systems. Necessary and sufficient conditions for solvability of the FDI problem are developed. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem. Finally, by generalizing the results that are developed for RS systems necessary and sufficient conditions for solvability of the FDI problem in a general Inf-D system are derived. Particularly, we first address invariant subspaces of Fin-D systems from a new point of view by invoking resolvent operators. This approach enables one to extend the previous Fin-D results to Inf-D systems. Particularly, necessary and sufficient conditions for equivalence of various types of conditioned and controlled invariant subspaces of Inf-D systems are obtained. Duality properties of Inf-D systems are then investigated. By introducing unobservability subspaces for Inf-D systems the FDI problem is formally formulated, and necessary and sufficient conditions for solvability of the FDI problem are provided