Fault Detection Observer Design Research Articles

Fault detection observer design for Takagi–Sugeno fuzzy systems with finite-frequency specifications

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno fuzzy systems with finite-frequency specifications. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. Peak-to-peak analysis is used to derive a dynamic threshold. To further reduce the conservatism caused by predefined parameters, an iterative algorithm is developed. Both theoretical proof and simulation results show that the performance of the proposed method is not worse than the existing works.

Fuzzy Fault Detection Observer Design for Unmanned Marine Vehicles Based on Membership-Function-Dependent H∞/H_ Performance

This paper studies the design problem of fault detection (FD) observer for unmanned marine vehicles (UMVs) based on the T-S fuzzy model. Firstly, T-S fuzzy systems are used to approximate the nonlinear dynamics in UMVs. Secondly, to improve the FD performance of UMVs, a new H∞/H_ performance index, which depends on the membership functions, is defined. Then, based on the membership-function-dependent H∞/H_ performance index, a new fuzzy FD observer strategy, where the fuzzy submodels are not all required to be with the same H_ performance index, is developed to detect the sensor fault in UMVs; the corresponding synthesis conditions of the FD observer are derived based on the Lyapunov theory. Different from the conventional FD strategies, in the proposed membership-function-dependent FD method, the fuzzy submodels—which the system always works on—can have a larger H_ performance index, such that the performance of the FD can be improved. In the end, an example is given to show the effectiveness of the presented method.

WITHDRAWN: Towards robust fault detection for Takagi–Sugeno nonlinear systems

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno nonlinear systems. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. The peak-to-peak analysis is used to derive a dynamic threshold. An iterative algorithm is further developed to reduce conservatism. Theoretical proof shows that the performance of the proposed method is not worse than some existing works. Simulation results demonstrate the validity and viability of the proposed method.

Formula omitted] fault detection observer design for nonlinear conformable fractional-order systems

This study is concerned with the design of fault detection observers for nonlinear conformable fractional-order systems. An H∞/H− fault detection scheme is applied to maximize the sensitivity of faults and minimize the effect of disturbances. Based on basic fractional calculus lemmas and fractional-order Lyapunov stability theory, sufficient conditions are obtained to design a fault detection observer. Finally, the advantages and effectiveness of the proposed fault detection method are illustrated through a numerical example.

Fault detection of fractional‐order system based on finite frequency H−/H∞${{H}_{-}}/{{H}_{\infty }}$ unknown input observer

AbstractThis study is about fault detection observer design in finite frequency domain for fractional‐order systems with unknown input disturbances. In order to make the generated residuals fault‐sensitive, robust to the non‐decoupling parts of unknown input disturbances, and guarantee the stability requirements of fractional‐order error systems, the authors derive the fault detection conditions of unknown input observers. First, using the condition of observer, the unknown input is decomposed into decoupling part and non‐decoupling part, and the decoupling part is eliminated from the estimation error. Second, the residuals generator of the unknown input observer is designed by using the finite frequency performance indicator, so that the residuals are robust to the non‐decoupling part of the unknown input and sensitive to fault signals. In particular, variable linearization methods are introduced to convert design conditions into a series of LMIs. Finally, the simulation results show the effectiveness of the designed method.

L 1/L – Observer-Based Fault Detection for 2-D Delayed Positive Continuous-Time Systems

This study focuses on the design of fault detection observer for continuous 2D delayed positive systems. Firstly, the L1-gain and L–index of the 2D positive delayed systems are calculated by 2D Laplace transform; secondly, necessary and sufficient conditions for the system to satisfy the L1/L-performance are derived; finally, sufficient conditions for the existence of a mixed L1/L-observer are derived. The solution to the observer gain is given by an iterative linear programming algorithm. An example is given to demonstrate the validity of the proposed theoretical results.

A generalized proportional‐integral observer for fault detection: An approximate input disturbance decoupling approach

SummaryThis article proposes a generalized PI observer with approximate disturbance decoupling (ADD‐GPIO) for detecting incipient actuator faults of a system subject to periodic input disturbances. Robustness to disturbances and sensitivity to faults is achieved through dynamic configuration of the disturbance transmission zeros and pole‐optimization respectively. By incorporating the ‐gap metric with index, a novel interpretable fault sensitivity optimization objective function is proposed. It is the first time in the fault detection observer design that the difference between the transfer function matrices (TFMs) relating fault detection residual to the disturbances and faults is quantified by the proposed ‐gap metric, which allows a more differentiated treatment of the disturbance and fault signals for better fault detection. Then, the optimal design of the ADD‐GPIO is modeled as a mixed‐integer optimization problem and the Lagrangian relaxation is adopted to find the near‐optimal parameters of the ADD‐GPIO at less computation costs in real application. Finally, both simulation and lab experiments of a two‐wheeled self‐balancing robot are carried out to validate the improved performance of the proposed method.

Asynchronous Fault Detection Observer for 2-D Markov Jump Systems.

In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the H∞ attenuation index and H_ increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach.

Mixed [formula omitted] fault detection observer design for delayed 2D positive systems in FM LSS Models

This study is concerned with the problem of the mixed l1/l− fault detection (FD) observer for delayed two-dimensional (2D) positive systems (PSs). The necessary and sufficient conditions (NSCs) are derived under which the residual error system is asymptotically stable (AS) and has the prescribed performance level. The conservatism is greatly reduced compared to the existing results. A new performance analysis method and the mixed l1/l− FD observer design are presented. Firstly, the calculation of l1/l− index for delayed 2D PSs is proposed by establishing the equivalence between the delayed system and the higher dimensional delay-free system in sense of l1 and l− indexes. Secondly, NSCs are developed such that the delayed 2D PS is AS with a desired mixed l1/l− performance. Thirdly, the sufficient conditions of the observer design are further developed based on linear programming. An iterative algorithm is formulated to minimize and maximize the impact of system disturbances and faults on the output signal, respectively. Finally, we present two examples to verify the superiority of the obtained results.

Adaptive Event-Triggered Finite-Frequency Fault Detection With Zonotopic Threshold Analysis for LPV Systems.

This article investigates a class of multiobjective optimization fault detection observer design problems for linear parameter varying (LPV) systems considering the unknown but bounded disturbance with an adaptive event-triggered scheme. In this study, the actuator faults are considered in the low-frequency domain. First, to save the communication bandwidth and improve communication efficiency, an adaptively adjusted event-triggered (AAET) mechanism is proposed. Then, in order to make the designed observer gain satisfy both fault sensitivity and disturbance robust conditions, an H-/L∞ multiobjective optimization problem is proposed and solved by appropriate linear matrix inequalities. Next, the upper and lower bounds of the generated residual are calculated by the zonotope method when considering the estimation uncertainty. Fault detection can be achieved by judging whether the zero value belongs to the generated range of the residual signal. Finally, a simulation case is used to verify the effectiveness of the proposed method.

Actuator fault detection for a PEMFC system based on delta operator approach

This paper proposes an actuator fault detection observer design method for a proton exchange membrane fuel cell (PEMFC) system described by delta operator form. In the first, a nonlinear mathematical model for the PEMFC system is proposed by using the mechanism analysis method, which includes the time delay, external disturbance and uncertainty to reduce the conservatism of the design. Then, in order to detect the actuator fault, the functional observer is constructed as the residual generator, and sufficient conditions for the stability of the error system are obtained by using the Lyapunov-krasovsky functional theory in terms of linear matrix inequalities (LMIs), so as to ensure the design of the required functional observer. Finally, simulation results are provided to show the effectiveness of the approach.

Formula omitted] fault detection observer design for fractional-order singular systems in finite frequency domains

This paper investigates the robust fault detection observer design problem in finite frequency domains for fractional-order singular systems. An H−/H∞ fault detection observer for fractional-order singular systems is designed to meet the system admissibility, disturbance robustness and fault sensitivity indices in finite frequency domains simultaneously. Four theorems and four corollaries about the system admissibility and the performance index H−/H∞ in different frequency ranges are given, and then the sufficient conditions are obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to verify the validity of the presented methods.

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.

Fault detection observer design in finite-frequency domain for networked interconnected systems

With the development of network technology, information can flow flexibly, and the research of interconnected systems are booming. The article proposes an H ∞ / H - fault detection observer design means for a networked interconnected system. First, convert a linear networked interconnection systems to linear network systems. Next, the H − index is accustomed to measuring the worst-case sensitivity to failure and H ∞ norm from ungiven inputs to residuals is accustomed to measure disturbance robustness performance, so that the residuals generated by the designed fault detection observer are sensitive to failures and robust to disturbance in finite-frequency domain. Besides, sufficient conditions of the observer design are derived and transformed by a set of LMIs. Lastly, numerical simulations are provided to demonstrate the correctness and effectiveness of the designed means.

Event-triggered H–/L∞ fault detection observer design for discrete-time Lipschitz nonlinear networked control systems in finite-frequency domain

This paper proposes an event-triggered fault detection observer (FDO) design method for discrete-time Lipschitz nonlinear networked control systems (NCSs) in finite-frequency domain. First, a discrete event-triggered transmission scheme is proposed to mitigate the utility of limited network bandwidth. Second, with the aid of a reformulated Lipschitz property, the nonlinear error dynamics are converted into a linear parameter varying (LPV) networked system model. Third, based on this model, the finite-frequency index is used to measure the worst-case fault sensitivity performance and the norm from unknown disturbance to residual is used to measure disturbance robustness performance. Next, a residual evaluation and a dynamic threshold are synthesised based on the norm. Furthermore, sufficient conditions of the FDO design are derived and transformed by a set of linear matrix inequalities (LMIs). The proposed FDO design method can significantly reduce the data transmission to relieve the communication pressure, and can also achieve better FD performance than the full frequency domain. Finally, A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

On mixed [formula omitted] fault detection observer design for positive 2D Roesser systems: Necessary and sufficient conditions

This paper addresses the problem of fault detection observer design for positive two-dimensional (2D) systems in the Roesser model. Firstly, an analytical method is presented to compute the exact value of ℓ− index for positive 2D systems, where ℓ− index measures the sensitivity to faults. Necessary and sufficient conditions are developed under which the ℓ1-gain from noise to residuals is not larger than a prescribed level γ and the ℓ1-gain from faults to residuals is not less than a prescribed level β. Secondly, based on above results, necessary and sufficient conditions for the existence of mixed ℓ1/ℓ− fault detection observer are derived such that the effect of disturbance on the residual output is minimized and the effect of faults on the residual output is maximized. Thirdly, an iterative algorithm is proposed to solve the convex optimization conditions. Finally, an example is provided to show the effectiveness and correctness of the theoretical results.

Robust H−/H∞ fault detection observer design for polytopic spatially interconnected systems over finite frequency domain

SummaryThis article aims at solving the problem of robust H−/H∞ fault detection (FD) over finite frequency domain for spatially interconnected systems (SISs) with polytopic uncertainties. A fault detection observer is designed to generate the residual signal, and in order for the observer to work, the well‐posedness, robust stability, and finite frequency H−/H∞ indexes are properly defined for the error systems. A sufficient condition for the well‐posedness and robust stability of error systems is given based on the theory of continuous semigroup. Then, to obtain the H−/H∞ performance indexes conditions, a reformed generalized Kalman‐Yakubovich‐Popov (GKYP) lemma for polytopic SISs is derived, which takes the noncasual structure of SISs into account. It turns out that the reformed GKYP lemma is an extension of some existing results in traditional multidimensional casual systems. By resorting to Finsler's lemma and a linearization technique, the existence conditions of finite frequency H−/H∞ FD observer for polytopic SISs are given in terms of linear matrix inequalities. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Event-Triggered Fault Detection Observer Design for T–S Fuzzy Systems

This article is concerned with the problem of event-triggered (ET) fault detection (FD) observer design for Takagi-Sugeno (T-S) fuzzy systems. The nonlinear systems considered are presented as T-S models, and the system outputs are selected as the premise variables (PV) of T-S models. New types of observers, namely, switched fuzzy FD observers, are designed, which are switched at different triggering instants based on the online asynchronous premise reconstruction (APR) method. By employing new triggering instants-dependent Lyapunov functions (LFs) established via the idea of event interval partitioning, it is proved that the proposed FD observers can guarantee the stability and desired performance of the systems. Finally, a simulation example is applied to show that the proposed FD scheme can achieve better FD results than the existing design methods.

Fault detection observer design for periodic piecewise linear systems

This article deals with the problem of fault detection observer design for continuous-time periodic piecewise linear systems. Mixed performance index is introduced, which results in a trade-off between robustness to unknown input and sensitivity to a fault. Based on a class of Lyapunov functions with time-varying Lyapunov matrices, sufficient conditions are developed to investigate the existence of periodic piecewise fault detection observer with weighted performance. A tractable iterative algorithm is proposed to establish the desired periodic piecewise fault detection observer. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Distributed finite frequency fault detection observer design for spatially interconnected time-delay systems with interconnected chains

This paper proposes an $$H_{-}/H_{\infty }$$ fault detection observer method for a class of spatially interconnected time-delay systems (SITSs) with interconnected chains in finite frequency domain. As one of the main contribution, a delay-dependent generalized Kalman–Yakubivich–Popov (GKYP) lemma for SITSs with interconnected chains is proposed. Based on the giving GKYP lemma, sufficient conditions for the existence of the observers to guarantee the fault sensitivity and disturbance robustness in finite frequency domain are presented. Finally, an example is provided to demonstrate the effectiveness of the proposed method.