Fault detection based on fractional order models: Application to diagnosis of thermal systems

Aribi, Asma; Farges, Christophe; Aoun, Mohamed; Melchior, Pierre; Najar, Slaheddine; Abdelkrim, Mohamed Naceur

doi:10.1016/j.cnsns.2014.03.006

Cited by 28 publications

(13 citation statements)

References 13 publications

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“…We can distinguish four regions denoted R + 0 , R + 1 , R + 2 and R + 3 with respectively zero, one, two and three strictly positive real roots. In comparison with Figure 3, we observe that the curved colored lines (red and green) separating respectively the regions (1,3) and (4, 6) disappeared because each pair of regions has the same positive roots number. Figure 8.…”

Section: Problem Formulationmentioning

confidence: 76%

“…Recently, Fractional Order Systems (FOS) have received increasing attentions in many engineering applications [9] such as mechanics, electricity, chemistry, biology, and so on. FOS raise exciting challenges to develop new methodologies for modelling and identification [15,24,1,32,34,31,8], control [22,23,6,21,29,14] and diagnosis [2,3,4,33] by involving fractional order dynamics to physical systems. (1) where (a j , b i ) ∈ R 2 , differentiation orders α 1 < α 2 < ... < α m and β 1 < β 2 < ... < β n are allowed to be non-integer positive numbers.…”

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confidence: 99%

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Analytical study of resonance regions for second kind commensurate fractional systems

Boubidi¹,

Kechida²,

Tebbikh³

2021

DCDS-B

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The aim of this paper is to determine analytically the resonance limits for second kind commensurate fractional systems in terms of the pseudo damping factor ξ and the commensurate order v and in addition specify the different resonance regions. In the literature, these limits and regions have never been discussed mathematically, they are determined numerically. Second kind commensurate fractional systems are resonant if the equation : Ω 3v + 3ξcos(vπ/2)Ω 2v + (2ξ 2 + cos(vπ))Ω v + ξcos(vπ/2) = 0, obtained by setting the first derivative of the amplitude-frequency response equal to zero, has at last one strictly positive root. As in the conventional case, resonance limits correspond to zero discriminant of the last equation. This discriminant is a cubic equation in ξ 2 whose coefficients change depending on v. To resolve this equation, the tangent trigonometric solving method is used and the relationship between ξ and v is established, which represents the resonance limits expression. To search resonance regions, a mathematical study is conducted on the first equation to find the positive roots number for each (v, ξ) combination. Compared to works already achieved, a new region appeared in the region of single resonant frequency with an anti-resonant one. The results are tested through numerical examples and applied to a fractional filter.

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Section: Problem Formulationmentioning

confidence: 76%

mentioning

confidence: 99%

Analytical study of resonance regions for second kind commensurate fractional systems

Boubidi¹,

Kechida²,

Tebbikh³

2021

DCDS-B

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show abstract

“…Concerning fractional FD scheme, the second‐order sliding mode method is applied to deal with the FD problem of FOSs in [27]. Based on fractional order models, the generalised dynamic party space method and the Luenberger diagnosis observer are applied, respectively, in [28] to the diagnosis of thermal systems. In particular, a method of designing

H_{-} / H_{\infty}

FD observer is proposed in [29] for FOSs to ensure the sensitivity to fault input as well as the robustness to disturbances.…”

Section: Introductionmentioning

confidence: 99%

Fault detection for fractional‐order linear systems in finite frequency domains

Yang

2019

IET Control Theory & Applications

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“…In Aribi et al (2014) an approach is investigated to design a filter for FD with application in thermal systems, which is represented by fractional order model. Fractional Kalman filter (FKF) design framework is the best choice to handle the noise effect for linear fractional order systems.…”

Section: Introductionmentioning

confidence: 99%

Fractional order unknown input filter design for fault detection of discrete fractional order linear systems

Zarei

Tabatabaei

2018

Transactions of the Institute of Measurement and Control

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In this study, a new method is introduced to design an estimator for discrete-time linear fractional order systems, which are affected by unknown disturbances. The main goal of this study is decoupling disturbance and uncertainties from the true states for discrete fractional order systems in noisy environment. The fractional Kalman filter framework is exploited to develop a robust estimator against unknown inputs (UIs) in noisy environment. The proposed filter is exploited to detect faults in fractional order systems. Simulation results illustrate the advantages of this robust filter for state estimation and fault detection of fractional order model of ultra-capacitor (UC). The robustness of the designed filter is shown in the sense of disturbance decoupling in the presence of noise.

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Fault detection based on fractional order models: Application to diagnosis of thermal systems

Cited by 28 publications

References 13 publications

Analytical study of resonance regions for second kind commensurate fractional systems

Analytical study of resonance regions for second kind commensurate fractional systems

Fault detection for fractional‐order linear systems in finite frequency domains

Fractional order unknown input filter design for fault detection of discrete fractional order linear systems

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