Instrumental variable methods for identifying partial differential equation models of distributed parameter systems

Schorsch, Julien; Garnier, Hugues; Gilson, Marion

doi:10.3182/20120711-3-be-2027.00421

Cited by 7 publications

(9 citation statements)

References 13 publications

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“…Recently, the IV technique for identification of continuous 2-D and discrete systems has been used in [17], [19], and [20]. However, this paper has used the IV technique for the first time to estimate the input shifts in a shifted continuous 2-D system.…”

Section: Shift and Parameter Estimationmentioning

confidence: 98%

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Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable

Shafieirad

Shafiee

Abedi

2014

Can. J. Electr. Comput. Eng.

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This paper develops an algorithm to estimate the space shift, time shift (or time delay), and parameters in a shifted continuous 2-D system described by a 2-D partial differential equation. Using the linear filter method, the simultaneous estimation of shifts and parameters is achieved. Also, the instrumental variable technique is used to remove the least square estimation bias, which is due to measurement noise. There are some methods to estimate the time shift in 1-D systems. However, no method has been proposed so far to estimate the shifts in 2-D systems. To show the performance of the proposed algorithm, one illustrative numerical example is discussed.Résumé-Cet article présente un algorithme pour estimer le décalage spatiale et temporal (ou delais), et les paramètres dans un système bidimensionnel continue et décalé décrit par une équation différentielle partielles 2-D. En utilisant la méthode de filtrage linéaire, l'estimation simultanée des décalages et des différents paramètres est réalisée en utilisant la méthode de filtrage linéaire. En outre, la technique basée sur la variable instrumentale est utilisée pour éliminer l'erreur d'estimation des moindres carrés, qui est due au bruit de mesure. Il existe des méthodes pour estimer le décalage temporel dans les systèmes unidimensionnels. Cependant, aucune méthode n'a été proposée à ce jour pour estimer les décalages dans les systèmes bidimensionnels. Pour démontrer la performance de l'algorithme proposé, un exemple numérique illustratif est présenté et discuté.Index Terms-Continuous 2-D systems, instrumental variable (IV), parameter estimation, partial differential equations (PDEs), space and time input shifts.

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Section: Shift and Parameter Estimationmentioning

confidence: 98%

“…In previous years, the use of the IV technique together with the filtering has been increased for continuous 1-D system identification [10], [15], [16]. However, there is only one IV-based method to estimate the parameters of a PDE using the output error model [17].…”

mentioning

confidence: 99%

Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable

Shafieirad

Shafiee

Abedi

2014

Can. J. Electr. Comput. Eng.

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“…According to Equations (8-a), (25), and Remark 5, noisefree system parameter vector and the ARMA noise process parameter vector are given as follows:…”

Section: Simulationmentioning

confidence: 99%

“…Some of the continuous 2-D identification methods reduce the PDE model to an algebraic equation using basis functions such as Fourier series, Walsh series and wavelet and then use an identification technique to estimate the parameters of this algebraic equation [19À22]. Also, there are some other identification methods which are based on optimization techniques [23] and use integration to avoid the differentiation of data [24,25].…”

Section: Introductionmentioning

confidence: 99%

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Recursive Identification of Continuous Two-Dimensional Systems in the Presence of Additive Colored Noise

Shafieirad

Shafiee

Abedi

2014

IETE Journal of Research

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In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is modelled as hybrid BoxÀJenkins model. No comprehensive algorithm for identification of continuous 2-D systems simultaneous with noise process parameter estimation has been proposed so far. Also, there is no recursive method to identify the continuous 2-D systems. The proposed algorithm estimates the noise-free system parameters and colored noise process parameters based on the instrumental variable method simultaneously. Finally, the performance of the proposed method is evaluated by a numerical example.

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On the Closed-Loop System Identification with Fractional Models

Yakoub

Amairi

Chetoui

et al. 2015

Circuits Syst Signal Process

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Instrumental variable methods for identifying partial differential equation models of distributed parameter systems

Cited by 7 publications

References 13 publications

Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable

Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable

Recursive Identification of Continuous Two-Dimensional Systems in the Presence of Additive Colored Noise

On the Closed-Loop System Identification with Fractional Models

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