A geometric approach to fault detection and isolation for bilinearsystems

In this paper, a geometric approach to the synthesis of a residual generator for fault detection and isolation (FDI) in bilinear systems is considered. A necessary and sufficient condition to solve the so-called fundamental problem of residual generation is obtained. The proposed approach resorts to extensions of the notions of (C, A)-invariant and unobservability subspaces, and it yields a constructive design 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.     

Robust fault detection and isolation of time-delay systems using a geometric approach

This paper investigates the development of Fault Detection and Isolation (FDI) filters for both retarded and neutral time-delay systems with unknown time-varying delays. Using a geometric framework, the notion of a finite unobservability subspace is introduced for time-delay systems and an algorithm for its construction is presented. A bank of residual generators is then designed so that each residual is affected by one fault and is partially decoupled from the others while the H_∞ norm of the transfer function between the disturbances and the uncertainties in delays and the residuals are guaranteed to remain less than a prescribed value. Furthermore, it is shown that in the case of known delays it is possible to generate residuals that enjoy perfect decoupling properties among faults. Simulation results presented demonstrate the effectiveness of our proposed FDI algorithms.     

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.     

Observer-based approach to fault detection and isolation fornonlinear systems

The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied, First, the problem statement used for linear systems is extended, and a set of sufficient conditions for the existence of a solution is given. Next, circumstances under which high-gain observers for uniformly observable systems can be used in the synthesis of the residual generator are provided     

Structured residual vector-based approach to sensor fault detection and isolation

This paper proposes a novel approach to detection and isolation of faulty sensors in multivariate dynamic systems. After formulating the problem of sensor fault detection and isolation in a dynamic system represented by a state space model, we develop the optimal design of a primary residual vector for fault detection and a set of structured residual vectors for fault isolation using an extended observability matrix and a lower triangular block Toeplitz matrix of the system. This work is, therefore, a vector extension to the earlier scalar-based approach to fault detection and isolation. Besides proposing a new algorithm for consistent identification of the Toeplitz matrix from noisy input and output observations without identifying the state space matrices {A, B, C, D} of the system, the main contributions of this newly proposed fault detection and isolation scheme are: (1) a set of structured residual vectors is employed for fault isolation; (2) after determination of the maximum number of multiple sensors that are most likely to fail simultaneously, a unified scheme for isolation of single and multiple faulty sensors is proposed; and (3) the optimality of the primary residual vector and the structured residual vectors is proven. We prove the advantage of our newly proposed vector-based scheme over the existing scalar element-based approach for fault isolation and illustrate its practicality by simulated and experimental evaluation on a multivariate pilot scale, computer interfaced system.     

A geometric approach to edge detection

This paper describes edge detection as a composition of four steps: conditioning, feature extraction, blending, and scaling. We examine the role of geometry in determining good features for edge detection and in setting parameters for functions to blend the features. We find that: (1) statistical features such as the range and standard deviation of window intensities can be as effective as more traditional features such as estimates of digital gradients; (2) blending functions that are roughly concave near the origin of feature space ran provide visually better edge images than traditional choices such as the city-block and Euclidean norms; (3) geometric considerations ran be used to specify the parameters of generalized logistic functions and Takagi-Sugeno input-output systems that yield a rich variety of edge images; and (4) understanding the geometry of the feature extraction and blending functions is the key to using models based on computational learning algorithms such as neural networks and fuzzy systems for edge detection. Edge images derived from a digitized mammogram are given to illustrate various facets of our approach     

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.     

Causal fault detection and isolation based on a set-membership approach

This paper presents a diagnostic methodology relying on a set-membership approach for fault detection and on a causal model for fault isolation. Set-membership methods are a promising approach to fault detection because they take into account a priori knowledge of model uncertainties and measurement errors. Every uncertain model parameter and/or measurement is represented by a bounded variable. In this paper, detection consists of verifying the membership of measurements to an interval. First order discrete time models are used and their output is explicitly computed with interval arithmetic. Fault isolation relies on a causal analysis and the exoneration principle, which allows focusing the consistency tests on simple local models. The isolation strategy consists of two steps: performing minimal tests found with the causal graph and determining on line additional relevant tests that reduce the final diagnosis. An application for a nuclear process is used in order to illustrate the method's efficiency.     

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.     

A differential geometric approach to nonlinear filtering: theprojection filter

This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem     

A geometric approach to feedback stabilization of nonlinear systems with drift

The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov type function, but requires the solution of a nonlinear programming satisficing problem stated in terms of the logarithmic coordinates of flows. As opposed to other approaches, point-to-point steering is not required to achieve asymptotic stability. Instead, the flow of the controlled system is required to intersect periodically a certain reachable set in the space of the logarithmic coordinates.     

A fault detection and isolation method for complex industrialsystems

A method for the fault detection in complex industrial systems is presented. The plant devices, the sensors, the actuators, and diagnostic tests are described as discrete-event systems. A formal composition rule of these models is given and an inference procedure for the identification and isolation of the faults is discussed. Temporal information is also considered to speed up the fault isolation procedure and, in some cases, to uniquely identify faults with the same static fault signature     

A geometric approach to the synthesis of failure detection filters

A geometric formulation of Beard's failure detection filter problem is stated using the concepts of(C, A)-invariant and unobservability subspaces. The notions of output separable and mutually detectable families of subspaces introduced by Beard are also clarified. It is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum. Moreover, it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions. Finally, the complete duality between a generalization of Beard's detection filter problem and the restricted control decoupling problem is illustrated.     

A geometric approach to nonlinear dissipative balanced reduction II: internal isometries

This Part II provides structural aspects of the internal signals and operators used in the unified geometric theory for nonlinear dissipative and Hankel balanced reduction using the differential-geometric framework based on dissipativity theory, Lie-semigroups and submanifold Hilbert theory. In particular, a novel characterization of the nonlinear Gramians is presented along with an alternative view of some concepts of the theory of nonlinear balanced reduction and the Hankel operator, namely eigenvalue problems and eigenfunction decomposition, etc.     

A geometric approach to nonlinear dissipative balanced reduction I: exogenous signals

This paper is divided into two parts and provides a unified geometric theory for nonlinear dissipative and Hankel balanced reduction with the help of a framework based on differential geometry, dissipativity theory, Lie-semigroups and sub manifold Hilbert theory. Part I presents a theory for the invariants of the behavior using classical Gauss’ curvature theory. Furthermore, known concepts of the theory of balanced reduction like the Hankel operator, Schmidt decomposition, etc., can be understood in a proper and general perspective.     

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.     

A frequency domain approach to fault detection in sampled-data systems

This paper deals with fault detection problems in sampled-data (SD) systems. A tool is first introduced for the analysis of intersample behavior of SD systems in the frequency domain from the viewpoint of fault detection and isolation. Based on it, a direct design approach of fault detection systems for SD systems is proposed, and further the problem of full decoupling from unknown disturbances is studied.     

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 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.