A geometric approach to nonlinear fault detection and isolation in a hybrid three-cell converter

In this paper, the problem of fault detection and isolation in a three-cell converter is investigated using a nonlinear geometric approach. This powerful method based on the unobservability distribution is used to detect and isolate the faulty cell in the three-cell converter. First, a model describing the faults in the cells is presented. The geometric approach is then applied on this faulty model to generate residual signals based on a sliding-mode observer that allows the detection of faults in the three-cell converter. Numerical results show the effectiveness of the proposed sliding-mode residual generators for fault detection and isolation in the three-cell converter.     

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     

Active fault detection and isolation in linear time-invariant systems: A geometric approach

In this work, a novel approach on active fault detection and isolation for linear time-invariant systems, named forced diagnosability, is proposed. This approach computes a continuous state feedback law to render a fault diagnosable, even when it cannot be diagnosed by using passive diagnosis methods. To do that, this work derives novel geometric relationships between unobservability and $(A,B)$-invariant subspaces that, under certain conditions, guarantee the existence of such state feedback law. The objective of the state feedback law is to force all the faults, except the one required to be diagnosed, named $L_d$, to reside in an unobservability subspace. This effectively decouples the effect of $L_d$ on the system output, from the effect of the other faults, allowing the design of a residual generator to detect and isolate the desired fault. The proposed state feedback law continuously forces diagnosability, and it can be computed in polynomial time. This avoids testing faults only at fixed time intervals and solving complex optimization problems required in other active diagnosis approaches. A numerical example is presented to illustrate the efficiency of the proposed approach.     

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 possibilistic clustering approach to novel fault detection and isolation

In this paper, a new approach for fault detection and isolation that is based on the possibilistic clustering algorithm is proposed. Fault detection and isolation (FDI) is shown here to be a pattern classification problem, which can be solved using clustering and classification techniques. A possibilistic clustering based approach is proposed here to address some of the shortcomings of the fuzzy c-means (FCM) algorithm. The probabilistic constraint imposed on the membership value in the FCM algorithm is relaxed in the possibilistic clustering algorithm. Because of this relaxation, the possibilistic approach is shown in this paper to give more consistent results in the context of the FDI tasks. The possibilistic clustering approach has also been used to detect novel fault scenarios, for which the data was not available while training. Fault signatures that change as a function of the fault intensities are represented as fault lines, which have been shown to be useful to classify faults that can manifest with different intensities. The proposed approach has been validated here through simulations involving a benchmark quadruple tank process and also through experimental case studies on the same setup. For large scale systems, it is proposed to use the possibilistic clustering based approach in the lower dimensional approximations generated by algorithms such as PCA. Towards this end, finally, we also demonstrate the key merits of the algorithm for plant wide monitoring study using a simulation of the benchmark Tennessee Eastman problem.     

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     

A graph-theoretic approach to fault detection and isolation for structured bilinear systems

In this paper, using a graph-theoretic approach, we address some issues related to the fault detection and isolation for structured bilinear systems. Considering a structured bilinear system submitted to faults and disturbances, we give necessary and sufficient conditions to the solvability of the so-called bilinear fundamental problem of residual generation. We also treat the cases where the system is submitted to multiple failures occurring simultaneously or only one at a time. One of the main advantages of the proposed analysis tool is that all the given conditions are easy to check because they deal with finding paths in a digraph. This makes our approach well suited to studying large scale systems.     

A robust fault detection approach for nonlinear systems

In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided, and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.     

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     

Actuator and sensor fault detection and isolation for nonlinear systems subject to uncertainty

This work addresses the problem of simultaneous actuator and sensor fault detection and isolation (FDI) for control affine nonlinear uncertain systems in the absence of measurement noise. The FDI is achieved by using a bank of filters, which utilize a subset of the measurements along with prescribed values of the control actuators to estimate states and compute expected process behavior. Residuals are next defined as the difference between the observed and expected behavior. Detectability conditions are developed, which, upon satisfaction, ensure that each residual remains sensitive to a subset of fault scenarios in the presence of uncertainty. To this end, first the ability of observers in providing bounded estimation error for a generalized class of nonlinear uncertain systems is rigorously established. These bounds allow determining thresholds that account for the impact of uncertainty on each residual. Finally, the ability of the proposed framework to achieve FDI by ensuring a unique residual breaching pattern for each fault scenario is established. The efficacy of the FDI framework subject to uncertainty and measurement noise is illustrated using a chemical reactor example.     

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.     

Sensor fault detection and isolation: a game theoretic approach

This paper studies sensor fault detection using a game theoretic approach. Sensor fault detection is considered as change point analysis in the coefficients of a regression model. A new method for detecting faults, referred to as two-way fault detection, is introduced which defines a game between two players, i.e. the fault detectors. In this new strategic environment, assuming that the independent states of the regression model are known, the test statistics are derived and their finite sample distributions under the null hypothesis of no change are derived. These test statistics are useful for testing the fault existence, as well as, the pure and mixed Nash equilibriums are derived for at-most-one-change and epidemic change models. A differential game is also proposed and solved using the Pontryagin maximum principle. This solution is useful for studying the fault detection problem in unknown state cases. Kalman filter and linear matrix inequality methods are used in finding the Nash equilibrium for the case of unknown states. Illustrative examples are presented to show the existence of the Nash equilibriums. Also, the proposed fault detection scheme is numerically evaluated via its application on a practical system and its performance is compared with the cumulative sum method.     

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.     

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     

Sensor fault detection, isolation and reconstruction using nonlinear principal component analysis

State reconstruction approach is very useful for sensor fault isolation, reconstruction of faulty measurement and the determination of the number of components retained in the principal components analysis (PCA) model. An extension of this approach based on a Nonlinear PCA (NLPCA) model is described in this paper. The NLPCA model is obtained using five layer neural network. A simulation example is given to show the performances of the proposed approach.     

Robust nonlinear analytic redundancy for fault detection and isolation in mobile robot

A robust nonlinear analytical redundancy (RNLAR) technique is presented to detect and isolate actuator and sensor faults in a mobile robot. Both model-plant-mismatch (MPM) and process disturbance are considered during fault detection. The RNLAR is used to design primary residual vectors (PRV), which are highly sensitive to the faults and less sensitive to MPM and process disturbance, for sensor and actuator fault detection. The PRVs are then transformed into a set of structured residual vectors (SRV) for fault isolation. Experimental results on a Pioneer 3-DX mobile robot are presented to justify the effectiveness of the RNLAR 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.