Fault Detection Dynamics Research Articles

Distributed H∞ Consensus Fault Detection for Uncertain T‐S Fuzzy Systems with Time‐Varying Delays Over Lossy Sensor Networks

AbstractThis paper investigates the issue of distributed H∞ consensus fault detection (FD) for uncertain T‐S fuzzy systems with time‐varying delays over lossy sensor networks. One set of Bernoulli distributed white sequence is introduced to govern the multiple probabilistic packet losses over sensor network. The augment fault detection dynamics system is first transformed into the form of interconnect ion of two subsystems by applying an input‐output method. Through available output measurements from not only the individual sensor but also its neighboring sensors, a sufficient condition is established for the desired of distributed H∞ consensus fuzzy fault detection filter (FFDF) to ensure the fault detection dynamics system to be mean‐square asymptotically stable with an average performance. At the same time, the solution of the parameters for the distributed H∞ consensus FFDF is characterized in terms of the feasibility of a convex optimization problem. Finally, an illustrative example is provided to illustrate the effectiveness of the proposed approaches over the lossy sensor networks.

Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

This paper is concerned with the fault detection (FD) problem for a class of discrete-time stochastic systems with channel fadings, randomly occurring multiple communication delays, and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD 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. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.

Event-based fault detection for T–S fuzzy systems with packet dropouts and (x, v)-dependent noises

This paper deals with the event-based fault detection problem for T–S fuzzy systems with packet dropouts as well as state- and disturbance-dependent noises ((x, v)-dependent noises for short). To utilize limited network resources efficiently, the event-triggered mechanism is employed such that only selected valuable data is transmitted to the filter according to whether specific events happen or not. The aim of the addressed problem is to design a fuzzy fault detection filter which guarantees the stochastic stability of the overall fault detection dynamics as well as the robustness against disturbances and sensitivity to faults of the residual signal. Some sufficient criteria are obtained for the existence of the desired fault detection filter which can be designed by solving a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the validity of the derived results.

On Design of Robust Fault Detection Filter in Finite-Frequency Domain With Regional Pole Assignment

This brief is concerned with the fault detection (FD) filter design problem for an uncertain linear discrete-time system in the finite-frequency domain with regional pole assignment. An optimized FD filter is designed such that: 1) the FD dynamics is quadratically D-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> -norm. With the aid of the generalized Kalman-Yakubovich-Popov lemma, the mixed H-/H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and the D-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired FD filter is proposed by evaluating the threshold on the generated residual function. A simulation result is exploited to illustrate the effectiveness of the proposed design technique.

Fault detection for a class of non‐linear networked control systems with data drift

In this paper, the fault detection problem is studied for a class of non-linear discrete-time networked control systems (NCSs). An individual stochastic variable satisfying a certain probabilistic distribution is utilised to describe the data drift of each sensor. The random transmission delays with the upper bound and the data drift phenomena are taken into account in a unified framework. By augmenting the states of the original non-linear NCS and the constructed full-order fault detection filter, the resulting fault detection dynamics is converted into an H ∞ filtering problem of a non-linear time-delay system. A sufficient condition for the existence of the designed fault detection filter is given in terms of a feasible linear matrix inequality, guaranteeing that the fault detection dynamics is stochastically stable and attains the prescribed H ∞ attenuation level. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Robust Fault Detection for Nonlinear Networked Systems with Multiple Fading Measurements

In this paper, the fault detection problem is investigated for a class of nonlinear networked systems with multiple fading measurements. A stochastic Rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients. Attention is focused on the design of a full-order fault detection filter such that the overall fault detection dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a prescribed level by means of the $$H_{\infty }$$H? performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for the existence of the desired fault detection filter, and the corresponding optimal filter parameters can be easily derived by solving a convex optimization problem via a semi-definite program method. Finally, a numerical example is exploited to illustrate the effectiveness of the proposed method.

Fault detection for a class of nonlinear networked control systems with Markov sensors assignment and random transmission delays

The paper investigates the fault detection problem for a class of nonlinear networked control systems with both communication constraints and random transmission delays. The access status of the sensors is governed by a stochastic event, which is modeled as a Markov chain taking matrix values in a certain set. The main task of this paper is to design a mode-dependent fault detection filter, such that for Markov sensors assignment, random network-induced delays and the unknown input signal, the error between the fault and the residual signal is minimized. And the resulting fault detection dynamics is formulated as an H∞ filtering problem of a Markov jump system. The linear matrix inequality-based sufficient conditions for the existence of the fault detection filter are obtained. Finally, two examples are given to show the effectiveness of the developed method.

Input–output method to fault detection for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses

The fault detection (FD) problem for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses is investigated in this paper. The communication links between the plant and the FD filter (FDF) are assumed to be imperfect, and the missing probability is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time delayed fuzzy networked system is first transformed into the form of interconnect ion of two subsystems by applying an input–output method and a two-term approximation approach, which are employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy FDF (FFDF) such that, for all data missing conditions, the overall FD dynamics are input–output stable in mean square and preserves a guaranteed performance. Sufficient conditions are first established via H∞ performance analysis for the existence of the desired FFDF; meanwhile, the corresponding solvability conditions for the desired FFDF gains are characterised in terms of the feasibility of a convex optimisation problem. Moreover, we show that the obtained criteria based on the input–output approach can also be established by applying the direct Lyapunov method to the original time-delay systems. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed approaches.

Fault detection for singular networked control systems with randomly occurring delays and partially known distribution transmission delays

In this paper, the fault detection problem is discussed for a class of discrete-time singular networked control systems with randomly occurring delays and network-induced delays. The considered randomly occurring delays include the multiple state delays and the infinite-distributed delay. Both of them are assumed to occur in random ways, which are governed by two independent stochastic variables satisfying the Bernoulli binary distribution. Network-induced delays are modeled as a discrete-time homogeneous Markov chain, and the transition probabilities of the Markov chain are partially known. A stochastic Lyapunov functional is constructed to design a full-order fault detection filter guaranteeing that the fault detection dynamics is stochastically admissible with a prescribed [Formula: see text] performance index. Hence, the fault detection filter design problem is converted into a convex optimization problem in terms of a set of linear matrix inequalities. If these linear matrix inequalities are feasible, the corresponding parameters of the designed fault detection filter are determined. Finally, a numerical example is addressed to demonstrate the effectiveness of the developed method.

Fault Detection for a Class of Nonlinear Singular Systems Over Networks with Mode-Dependent Time Delays

In this paper, the fault detection problem is investigated for a class of nonlinear discrete-time singular systems over networks with mode-dependent time delays. The transmission delays are modeled as a Markov chain with partly known distribution, which takes values in a finite state space. By augmenting the original nonlinear singular system and the fault detection filter, the resulting fault detection dynamics is formulated as an $$H_{\infty }$$ H ? filtering problem of a singular Markov jump system. Regular, casual, stochastically stable of the fault detection dynamics and the prescribed $$H_{\infty }$$ H ? attenuation level are obtained by the mode-dependent Lyapunov functional approach. The desired fault detection filter is obtained in terms of a series of feasible LMIs. A numerical example is presented to show the effectiveness of the developed technique.

H∞ fault detection with randomly occurring nonlinearities and channel fadings

In this paper, the H∞ fault detection problem is investigated for a class of discrete-time stochastic systems with both channel fadings and randomly occurring nonlinearities. Due to Doppler effect and multi-path delays, channel fadings are inevitable and also cause unpredictable dynamic behaviour. The Lth Rice fadings model, which is accounted for both channel fadings and time delays, can be employed to describe this phenomenon. Meanwhile, by using a Bernoulli distributed white sequence, a kind of non-linear disturbance appearing in a random way is also considered in the H∞ fault detection issue. The purpose of the addressed problem is to design a fault detection filter such that, in the presence of channel fadings, the overall fault detection dynamics is stochastically stable and, at the same time, the error between the residual (generated by the fault detection filter) and the fault signal is made as small as possible. By utilising the Lyapunov stability theory associated with the intensive stochastic analysis techniques, sufficient conditions are established under which the addressed H∞ fault detection problem is recast as solving a convex optimisation problem via the semi-definite programme method. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.

Fault Detection for Network Control Systems with Multiple Communication Delays and Stochastic Missing Measurements

This paper is concerned with fault detection problem for a class of network control systems (NCSs) with multiple communication delays and stochastic missing measurements. The missing measurement phenomenon occurs in a random way and the occurrence probability for each measurement output is governed by an individual random variable. Besides, the multiple communication delay phenomenon reflects that networked control systems have different communication delays when the signals are transferred via different channels. We aim to design a fault detection filter so that the overall fault detection dynamics is exponentially stable in the mean square. By constructing proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the fault detection filter for the discrete systems, and the filter parameters are also derived by solving linear matrix inequality. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

Fault Detection Filter Design for Stochastic Systems with Mixed Time-Delays and Parameter Uncertainties

This paper purposes the design of a fault detection filter for stochastic systems with mixed time-delays and parameter uncertainties. The main idea is to construct some new Lyapunov functional for the fault detection dynamics. A new robustly asymptotically stable criterion for the systems is derived through linear matrix inequality (LMI) by introducing a comprehensive different Lyapunov-Krasovskii functional. Then, the fault detection filter is designed in terms of linear matrix inequalities (LMIs) which can be easily checked in practice. At the same time, the error between the residual signal and the fault signal is made as small as possible. Finally, an example is given to illustrate the effectiveness and advantages of the proposed results.

Fault Detection for Markovian Jump Systems With Sensor Saturations and Randomly Varying Nonlinearities

This paper addresses the fault detection problem for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities, randomly varying nonlinearities and sensor saturations. For the Markovian mode jumping, the transition probability matrix is allowed to have partially unknown entries, while the cases with completely known or completely unknown transition probabilities are also investigated as two special cases. The randomly varying nonlinearities and the sensor saturations are introduced to reflect the limited capacity of the communication networks resulting from the noisy environment, probabilistic communication failures, measurements of limited amplitudes, etc. Two energy norm indices are used for the fault detection problem in order to account for, respectively, the restraint of disturbance and the sensitivity of faults. The purpose of the problem addressed is to design an optimized fault detection filter such that 1) the fault detection dynamics is stochastically stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm. The characterization of the gains of the desired fault detection filters is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the fault detection filtering scheme proposed in this paper.

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.

Fuzzy-Model-Based Robust Fault Detection With Stochastic Mixed Time Delays and Successive Packet Dropouts

This paper is concerned with the network-based robust fault detection problem for a class of uncertain discrete-time Takagi-Sugeno fuzzy systems with stochastic mixed time delays and successive packet dropouts. The mixed time delays comprise both the multiple discrete time delays and the infinite distributed delays. A sequence of stochastic variables is introduced to govern the random occurrences of the discrete time delays, distributed time delays, and successive packet dropouts, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fuzzy fault detection filter such that 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 fuzzy fault detection filters, and then, the corresponding solvability conditions for the desired filter gains are established. In addition, the optimal performance index for the addressed robust fuzzy fault detection problem is obtained by solving an auxiliary convex optimization problem. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.