Parity relation based fault estimation for nonlinear systems: An LMI approach

Nguang, Sing Kiong; Zhang, Ping; Ding, Steven X.

doi:10.1007/s11633-007-0164-7

Cited by 40 publications

(14 citation statements)

References 25 publications

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“…Also, a comparison made between our method, linear parity and the method proposed in Nguang et al (). A mass‐spring‐damper dynamical system from Nguang et al () without disturbance is considered. The state‐space system model with non‐linear spring is

\begin{matrix} left \\ {\overset{x}{true}}_{1} (t) = x_{2} (t), \\ {\overset{x}{true}}_{2} (t) = - x_{1} (t) - 2 x_{1}^{3} (t) - x_{2} (t) + f_{1} (t) + u (t), \\ y_{1} (t) = x_{1} (t), \\ y_{2} (t) = x_{2} (t), \end{matrix}

where x 1 ( t ) is the spring displacement, x 2 ( t ) is the spring velocity, u ( t ) is the input force, y 1 ( t ) , y 2 ( t ) are the outputs, and f 1 ( t ) is the actuator fault.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…For comparison, two other methods are used, a method for fault estimation and linear parity. In Nguang et al (), a residual for fault estimation is generated as the following…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Also, a comparison made between our method, linear parity and the method proposed in Nguang et al (2007). A mass-spring-damper dynamical system from Nguang et al (2007) without disturbance is considered. The state-space system model with non-linear spring is…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Hence, motivated by capabilities of a T.S fuzzy system and its simplicity, parity relations for linear systems can be extended to detect faults in non‐linear systems. In Juan (), Nguang, Zhang, and Ding (, ), and Zhang, Hu, and Hu (), the parity space approach has been generalized to the fault estimation of T.S fuzzy models, but only sufficient conditions for the existence of a fault estimator have been obtained.…”

Section: Introductionmentioning

confidence: 99%

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Generalization of parity space to fault detection based on Takagi‐Sugeno fuzzy models for non‐linear dynamic systems

Zarch

Shoorehdeli

2017

Expert Systems

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Fault detection in non‐linear system has drawn a lot of attention recently. A typical solution is the generalization of linear methods to include non‐linear dynamics. This study addresses fault detection in non‐linear systems by extending parity relations using Takagi‐Sugeno (T.S) fuzzy models. Parity equations for linear systems are a residual generation method that has appealing capabilities in fault detection. T.S fuzzy systems are also extensively used in modelling of non‐linear systems. In this paper, parity equations are rewritten in the form of non‐linear systems that can be modelled by T.S fuzzy system. An advantage of this approach is that parity vector can be derived from relations explicitly. An algorithm is proposed to show how a residual can be generated in this manner. Simulation results on the fault detection of a mass‐spring‐damper system show the effectiveness of the proposed method.

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\begin{matrix} left \\ {\overset{x}{true}}_{1} (t) = x_{2} (t), \\ {\overset{x}{true}}_{2} (t) = - x_{1} (t) - 2 x_{1}^{3} (t) - x_{2} (t) + f_{1} (t) + u (t), \\ y_{1} (t) = x_{1} (t), \\ y_{2} (t) = x_{2} (t), \end{matrix}

where x 1 ( t ) is the spring displacement, x 2 ( t ) is the spring velocity, u ( t ) is the input force, y 1 ( t ) , y 2 ( t ) are the outputs, and f 1 ( t ) is the actuator fault.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…For comparison, two other methods are used, a method for fault estimation and linear parity. In Nguang et al (), a residual for fault estimation is generated as the following…”

Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalization of parity space to fault detection based on Takagi‐Sugeno fuzzy models for non‐linear dynamic systems

Zarch

Shoorehdeli

2017

Expert Systems

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“…The parity relation approach can be applied to either time-domain state-space model or frequency-domain input-output model, which is well revisited by the books [40,41,82]. Recently, the parity relation method is extended for fault diagnosis for more complex models such as TS fuzzy nonlinear systems [83] and fuzzy tree models [84], and applied to various industrial systems such as aircraft control surface actuators [85] and electromechanical brake systems [86].…”

Section: Fig 3 Scheme Of Model-based Fault Diagnosismentioning

confidence: 99%

A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches

Gao

Cecati

Ding

2015

IEEE Trans. Ind. Electron.

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2,421

937

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.) IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Abstract-With the ever increase of complexity and expense of industrial systems, there is less tolerance for performance degradation, productivity decrease and safety hazards, which greatly stimulates to detect and identify any kinds of potential abnormalities and faults as early as possible, and implement realtime fault-tolerant operation for minimizing performance degradation and avoiding dangerous situations. During the last four decades, fruitful results were reported about fault diagnosis and fault-tolerant control methods and their applications in a variety of engineering systems. The three-part survey paper aims to give a comprehensive review for real-time fault diagnosis and fault tolerant control with particular attention on the results reported in the last decade. In the first-part review, fault diagnosis approaches and their applications are reviewed comprehensively from model-based and signal-based perspectives, respectively.

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Fault‐Tolerant Nonlinear Control Systems

Mahmoud

Xia

2013

Analysis and Synthesis of Fault‐Tolerant Control Systems

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Parity relation based fault estimation for nonlinear systems: An LMI approach

Cited by 40 publications

References 25 publications

Generalization of parity space to fault detection based on Takagi‐Sugeno fuzzy models for non‐linear dynamic systems

Generalization of parity space to fault detection based on Takagi‐Sugeno fuzzy models for non‐linear dynamic systems

A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches

Fault‐Tolerant Nonlinear Control Systems

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