Robust Fault Detection Problem Research Articles

H−/L∞Fault Detection Observer Design for Uncertain Lipschitz Nonlinear Systems

This paper deals with the robust fault detection problem in the finite frequency domain for a class of Lipschitz nonlinear systems with uncertain parameters. The design conditions ofH−/L∞fault detection observers are proposed. These conditions make the error estimation system stable, and the residual hasL∞disturbance attenuation performance for external disturbances and uncertain parameters. In addition, considering that fault occurs in the finite frequency domain, the residual also hasH−fault sensitivity performance. To ease of solution, the observer design conditions are further transformed into linear matrix inequalities. On this basis, a dynamic threshold design method based onL∞analysis is presented. Finally, simulation results demonstrate the superiority of the proposed method.

Robust Fault Detection using Set-based Approaches for LPV Systems: Application to Autonomous Vehicles

This paper addresses the problem of robust fault detection for Linear Parameter Varying (LPV) systems using set-based approaches. Two approaches are proposed, based respectively on set-based state and parameter estimation methods, for implementing direct and inverse test for robust fault detection (FD). The uncertainties are assumed to be unknown but bounded and their effect is propagated using zonotopic sets. These robust FD test methods aim at checking the consistency between the measured and estimated behaviour obtained from estimator in the parameter or output space considering the effect of the uncertainty. When an inconsistency is detected, a fault can be indicated. A case study based on an autonomous vehicle is employed to compare the performance of proposed FD tests.

Robust Fault Detection for Uncertain Delayed Systems With Measurement Outliers Under Stochastic Communication Protocol

In this paper, the robust fault detection (RFD) problem is studied for uncertain networked systems with time delay and measurement outliers under limited communication condition, where the time delay is presumed to occur randomly and the occurrence probability is considered to be uncertain. Specifically, in order to reduce the communication burden, the stochastic communication protocol (SCP) is introduced to adjust the transmission of measurement signals. Moreover, a fault detection filter (FDF) with saturation constraints is constructed to achieve the purpose of properly eliminating possible measurement outliers. Subsequently, a generalized sector condition is utilized to derive the stability criteria of the system on the basis of appropriate Lyapunov functional. In addition, a traditional FDF is also designed to compare with the saturation-constrained FDF. It is shown that the FDF with saturation constraints can properly avoid the influence of outliers on the detection effect. Finally, two simulations are presented to show the superiority and the practicality of the developed saturation-constrained fault detection (FD) filtering algorithm.

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

This study deals with the problem of robust fault detection for linear time-invariant fractional-order systems (FOSs) assumed to be affected by sensor, actuator and process faults as well as disturbances. The observer-based method was employed to solve the problem, where the detector is an observer. The problem was transformed into the mixed robust optimization problem to make the system disturbance-resistant on one hand and fault-sensitive on the other hand. Then, sufficient conditions were obtained to solve the problem in the linear matrix inequality (LMI) mode. Finally, the effectiveness and superiority of the method were demonstrated by simulating the solutions on a single-input multi-output thermal testing bench.

Event-triggered robust fault diagnosis and control of linear Roesser systems: A unified framework

In this paper, the problem of simultaneous robust fault detection and isolation and control in the presence of the stochastic, energy bounded, and peak bounded disturbances for linear Roesser systems through the network with limited resources is investigated. Toward this goal, a novel event-triggered integrated fault detection, isolation and control (IFDIC) framework is proposed where a time concept is considered for linear Roesser systems to define an event-triggered mechanism for data transmission of the output measurement to the IFDIC module and the control input to the plant through the network. Then, the sufficient conditions for the robust event-triggered fault detection and isolation observer, robust event-triggered H∞∕H2∕L1 control are derived using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed event-triggered IFDIC framework is demonstrated through simulation studies for thermal and gas absorption processes.

Spatial Decomposition-Based Fault Detection Framework for Parabolic-Distributed Parameter Processes.

Fault detection for distributed parameter processes (heat processes, fluid processes, etc.) is vital for safe and efficient operation. On one hand, the existing data-driven methods neglect the evolution dynamics of the processes and cannot guarantee that they work for highly dynamic or transient processes; on the other hand, model-based methods reported so far are mostly based on the backstepping technique, which does not possess enough redundancy for fault detection since only the boundary measurement is considered. Motivated by these considerations, we intend to investigate the robust fault detection problem for distributed parameter processes in a model-based perspective covering both boundary and in-domain measurement cases. A real-time fault detection filter (FDF) is presented, which gets rid of a large amount of data collection and offline training procedures. Rigorous theoretic analysis is presented for guiding the parameters selection and threshold computation. A time-varying threshold is designed such that the false alarm in the transient stage can be avoided. Successful application results on a hot strip mill cooling system demonstrate the potential for real industrial applications.

Optimized fault detection using bond graph in linear fractional transformation form

This article deals with the optimal robust fault detection problem using the bond graph in its linear fractional transformation form. Generally, this form of the bond graph allows the generation of two perfectly separate analytical redundancy relations, that are used as residual and threshold. However, the uncertainty calculation method gives overestimated thresholds. This may, for instance, lead to undetectable faults. Therefore, enhancing the robustness of fault detection and isolation algorithms is of utmost importance in designing a bond graph–based fault detection system. The main idea of this article is to develop optimized thresholds to ensure an optimal detection, otherwise this article proposes a method to detect tiny magnitude faults concerning parameter’s uncertainties. This work considers the issue of optimal fault detection as an optimization problem of the gap between the residuals and its threshold. New uncertainty values will be calculated in a way that these estimated parameters ensure the desired optimized gap between residuals and thresholds. These estimated uncertainty values will be used to generate optimized adaptive thresholds. Through these thresholds, we increase the sensitivity of the residuals to tiny magnitude faults, and we ensure an optimal and early detection.

Robust fault detection of singular Markov jump systems with partially unknown information

The problem of robust fault detection for singular Markov jump systems with partially unknown transition probabilities is investigated in the paper. A fault detection observer is designed such that the residual signal is sensitive to fault signals and robust to unknown disturbances. By using Lyapunov function approach, sufficient conditions under which the system is stochastic stable with robustness and sensitiveness are given. Furthermore, an optimization problem is also derived. A simulation example is given to show the effectiveness.

Robust Fault Detection for Permanent-Magnet Synchronous Motor via Adaptive Sliding-Mode Observer

In this paper, a robust fault detection problem is investigated for a permanent magnet synchronous motor (PMSM). By using the adaptive control and the sliding-mode control strategies, an observer is presented for estimating the amplitude demagnetization fault problem under inductance disturbance. The proposed method can effectively attenuate the inductance disturbance of the PMSM by the sliding-mode strategy. And the adaptive control estimation algorithm is adopted for guaranteeing that the real-time detection of demagnetization flux can be realized. The convergency is obtained by the Lyapunov stability theory. Finally, simulation is given for demonstrating the feasibility and effectiveness of the proposed method.

Robust Fault Detection for switched Takagi-Sugeno systems with unmeasurable premise variables: Interval-Observer-based approach

Abstract This paper deals with the problem of robust fault detection for continuous-time switched Takagi-Sugeno (T-S) fuzzy models. A procedure based on interval observers is proposed. First, an interval observer is designed under the assumption that the disturbances as well as the uncertainties are unknown but bounded. Stability and nonnegativity properties are given in terms of Linear Matrix Inequalities (LMIs) taking into account disturbances attenuation. Next, residual intervals generated by the interval observer are used for fault detection decision. Finally, a numerical example is provided to show the usefulness of this approach.

Robust Fault Detection of Nonlinear Uncertain Systems with Event-Triggered Communication

The robust fault detection problem for a class of nonlinear uncertain systems with event-triggered measurement communication is addressed in this study. The proposed event-triggered robust fault detection scheme has two steps. First, with the event-triggered measurement, an adaptive approximator is proposed to learn the unknown modeling uncertainty online. Second, after the learning procedure, an event-triggered residual generator is designed by integrating the adaptive approximator with the residual signal for fault detection. The adaptive threshold for fault detection decision is derived by taking the event-triggered scheme into consideration. The performance of the event-triggered fault detection system is rigorously analyzed by characterizing the event-triggered sampling error, including the stability of the adaptive approximation and the fault detectability.

An Event-Triggered Approach to Robust Fault Detection for Nonlinear Uncertain Markovian Jump Systems with Time-Varying Delays

In this paper, the problem of robust fault detection is investigated for nonlinear uncertain Markovian jump systems subject to time-varying delays, Lipschitz nonlinearities and parameter uncertainties under the event-triggered protocol. The event-triggered mechanism is introduced to adjust the transmission frequency of the data sent to the remote module. An event-based fault detection method is presented to guarantee the sensitivity of residual to fault and the attenuation of the effect from the disturbance on the residual. In this way, the considered fault detection problem is solvable by testifying the feasibility of $$H_\infty $$ filtering problem. By constructing the mode-dependent Lyapunov functional, new sufficient criteria are derived in terms of the linear matrix inequality technique, which insures the stochastic stability with prescribed performance for addressed MJSs. In the end, a numerical example is exploited and the validity of newly presented event-based fault detection method is shown.

Robust Fault Detection for Nonlinear Discrete Systems with Data Drift and Randomly Occurring Faults Under Weighted Try-Once-Discard Protocol

This paper is concerned with the robust fault detection (FD) problem for discrete uncertain systems with data drift, randomly occurring faults (ROFs) and randomly occurring nonlinearities (RONs) under weighted try-once-discard (WTOD) protocol. The phenomena of the RONs are characterized by the Bernoulli distributed variable. The Markov chain with two states is introduced to describe the ROFs in the system. The data drift is depicted by an array of mutually independent stochastic variables with individual probabilistic distribution functions. Moreover, the WTOD protocol is utilized to lessen the incidence of data collisions and enhance the communication efficiency. An FD filter is established, and sufficient conditions are proposed under which the resultant filtering error system is stochastically stable and achieves a prescribed $$H_{\infty }$$ performance irrespective of the simultaneous presence of the WTOD protocol mechanism, ROFs, RONs and data drift. Besides, the form of the desired filter parameters is presented in terms of the solutions to certain matrix inequalities. Finally, two examples are exploited to demonstrate the feasibility of the obtained robust FD algorithm.

A finite frequency approach for fault detection of fuzzy singularly perturbed systems with regional pole assignment

This paper investigates the robust fault detection problem for fuzzy singularly perturbed systems with pole assignment constraints. A finite frequency approach is proposed for the simultaneous achievement of the fault detection objectives and control objectives, which combines the computation of filter gains into a unified framework. By designing the fault detection filter, the residual signal for the detection of finite frequency faults can be produced, and the transient system behaviors can be improved to a satisfactory level based on the pole assignment. In addition, the estimated upper bound of the singular perturbation parameter is used to evaluate the performance of the proposed design method. Finally, a simulation example on an inverted pendulum controlled by a motor via a gear train is provided.

Simultaneous Disturbance Compensation and H1/H∞ Optimization In Fault Detection Of UAVs

Abstract This paper deals with the problem of robust fault detection (FD) for an unmanned aerial vehicle (UAV) flight control system (FCS). A nonlinear model to describe the UAV longitudinal motions is introduced, in which multiple sources of disturbances include wind effects, modeling errors and sensor noises are classified into groups. Then the FD problem is formulated as fault detection filter (FDF) design for a kind of nonlinear discrete time varying systems subject to multiple disturbances. In order to achieve robust FD performance against multiple disturbances, simultaneous disturbance compensation and H1/H∞ optimization are carried out in designing the FDF. The optimality of the proposed FDF is shown in detail. Finally, both simulations and real flight data are applied to validate the proposed method. An improvement of FD performance is achieved compared with the conventional H1/H∞-FDF.

Complete characterisation of disturbance estimation and fault detection for positive systems

This study considers the problem of disturbance estimation and fault detection for positive systems. Depending on the occurrences of disturbance and/or faults on positive systems, the authors use two types of observer structures and provide design strategies for reliable estimation of states, disturbance, and faults. Although various positive observers have been designed for positive systems, they fail to estimate the states in presence of unknown inputs. To realise simultaneous estimation of states and unknown inputs for positive systems, a special type of unknown input observer (UIO) called positive UIO (PUIO) is introduced and an linear matrix inequality (LMI) based approach is provided to make its design possible. The authors also show that simultaneous states and sensor fault estimation can be solved by a conversion scheme through a positive filtering process of the output. This allows to convert the sensor fault as an unknown input and employ the PUIO design. Finally, the problem of robust fault detection for positive systems is formulated and solved by combining the capability of UIO with proportional–integral (PI) observer. This integrated observer (PIUIO) decouples the unknown input disturbance through its UIO part while allowing PI part to estimate the fault. Several examples are constructed to support the theoretical results.

Robust fault detection filter design for interconnected systems subject to packet dropouts and structure changes

The problem of robust fault detection (FD) filter design for interconnected systems, and the problems of both packet dropouts and disconnected interconnections in these subsystems are studied. By modelling instances of disconnected interconnections among subsystems and packet dropouts in the measurement channel into independent subsystems, this study proposes a switched scheme that combines mode-dependent average dwell time with event-driven switching. A filter in which the FD system is exponentially stable and achieves a weighted performance can be derived from the optimal method of convex linear matrix inequalities. An example is given to demonstrate the effectiveness of the proposed method.

Robust Fault Detection of Uncertain Lipschitz Nonlinear Systems with Simultaneous Disturbance Attenuation Level and Enhanced Fault Sensitivity and Lipschitz Constant

In this paper, the problem of optimal robust fault detection (FD) for uncertain Lipschitz nonlinear systems is considered. A robust active fault detection approach for a class of the Lipschitz nonlinear systems in the presence of disturbances and parametric uncertainties is proposed, wherein the Lipschitz constant is assumed as one of the optimization parameters in the observer design. In addition to disturbance attenuation level, the fault sensitivity criterion based on \(H_-\) index is also defined in the FD system design. Different criteria are defined as a weighted multi-objective linear matrix inequality optimization problem, and the optimal variables of the FD system are derived based on a newly defined cost function. A numerical example is provided to demonstrate the effectiveness of the proposed FD system. The results show the robustness of the proposed method against parametric uncertainty and nonlinear uncertainty as well.

Robust Fault Detection H∞ Filter for Markovian Jump Linear Systems with Partial Information on the Jump Parameter

Abstract The present work focus on the Robust Fault Detection (RFD) problem in the Markovian Jump Linear System framework for the discrete-time domain, in which the Markov parameter θ(k) is considered not accessible. The assumption that the Markov Chain is not accessible brings a challenge where the filter designed for the RFD should not be dependent on the Markov Chain parameter. In order to represent this kind of situation, the implementation of a Hidden Markov Chain to model the system mode θ(k) and the estimated mode θˆ(k) is used. The main result presented in this work is the design of a H∞ MJLS Robust Fault Detection filter that depends only on the estimated mode θˆ(k) obtained through LMI formulation. In order to illustrate the feasibility of the proposed solution a numerical example is also included.

A Probabilistic Approach to Robust Fault Detection for a Class of Nonlinear Systems

This paper presents a probabilistic approach to fault detection (FD) for nonlinear systems subject to $l_{2}[0,N]$ -norm bounded unknown input. The major contribution is to design an evaluation function for robust FD in a unified framework of $l_{2}$ -norm estimation of unknown input and determine a threshold based on probabilistic analysis of FD performance. The problem of robust FD is first formulated as to find a minimal estimation of the $l_{2}[0,N]$ -norm of unknown input including unknown initial state. It is shown that such an estimation leads to a unified design of evaluation function for FD using extended Kalman filter or $H_{i}/H_{\infty }$ optimization-based FD filter. Based on this, a probabilistic approach to threshold determination and FD performance verification is proposed. In particular, if the $l_{2}[0,N]$ -norm boundedness of unknown input is not available, a choice of threshold can be made in the framework of probabilistic analysis for achieving a tradeoff between false alarm rate and FD rate. Finally, a nonlinear UAV control system model is given to demonstrate the effectiveness of the proposed method and show the feasibility of practical application.