2014 |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Abdelkrim, Mohamed Naceur 2014, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Additive noise, Additives, commensurate order, Continuous time systems, Continuous-time, Differential equations, Electronic systems, Errors in variables, Fourth-order cumulants, Fractional differentiation, Higher order statistics, Identification (control systems), Nonlinear programming, Religious buildings, Signal processing @conference{Chetoui2014b,This paper considers the problem of identifying continuous-time fractional systems from noisy input/output measurements. Firstly, the differentiation orders are fixed and the differential equation coefficients are estimated using an estimator based on Higher-Order Statistics: fractional fourth-order cumulants based least squares (ffocls). Then, the commensurate order is estimated along with the differential equation coefficients using a non linear optimization technique combined to the ffocls algorithm (co-ffocls). Under some assumptions on the distributional properties of additive noises and the noise-free input signals, the developed estimators give consistent results. Hence, the noise-free input signal is assumed to be non gaussian, whereas the additive noises are assumed to be gaussian. The performances of the developed algorithms are assessed through a practical application for modeling a real electronic system. © 2014 IEEE. |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Abdelkrim, Mohamed Naceur 2014, (Cited by: 0). Résumé | Liens | BibTeX | Étiquettes: Additive noise, Additives, commensurate order, Continuous time systems, Continuous-time, Differential equations, Electronic systems, Errors in variables, Fourth-order cumulants, Fractional differentiation, Higher order statistics, Identification (control systems), Nonlinear programming, Religious buildings, Signal processing @conference{Chetoui2014,This paper considers the problem of identifying continuous-time fractional systems from noisy input/output measurements. Firstly, the differentiation orders are fixed and the differential equation coefficients are estimated using an estimator based on Higher-Order Statistics: fractional fourth-order cumulants based least squares (ffocls). Then, the commensurate order is estimated along with the differential equation coefficients using a non linear optimization technique combined to the ffocls algorithm (co-ffocls). Under some assumptions on the distributional properties of additive noises and the noise-free input signals, the developed estimators give consistent results. Hence, the noise-free input signal is assumed to be non gaussian, whereas the additive noises are assumed to be gaussian. The performances of the developed algorithms are assessed through a practical application for modeling a real electronic system. © 2014 IEEE. |
2013 |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur; Oustaloup, Alain New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models Article de journal Dans: Computers and Mathematics with Applications, vol. 66, no. 5, p. 860 – 872, 2013, (Cited by: 30; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Algorithms, commensurate order, Differential equations, Errors, Errors in variables, Estimation, Fractional differentiation, Higher order statistics, Identification (control systems), Identification problem, Iterative least squares, Least squares algorithm, Non-linear optimization algorithms, Third-order cumulant @article{Chetoui2013860b,The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example. |
Chetoui, Manel; Thomassin, Magalie; Malti, Rachid; Aoun, Mohamed; Najar, Slaheddine; Abdelkrim, Mohamed Naceur; Oustaloup, Alain New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models Article de journal Dans: Computers and Mathematics with Applications, vol. 66, no. 5, p. 860 – 872, 2013, (Cited by: 30; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Algorithms, commensurate order, Differential equations, Errors, Errors in variables, Estimation, Fractional differentiation, Higher order statistics, Identification (control systems), Identification problem, Iterative least squares, Least squares algorithm, Non-linear optimization algorithms, Third-order cumulant @article{Chetoui2013860,The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example. |
Publications
2014 |
2014, (Cited by: 0). |
2014, (Cited by: 0). |
2013 |
New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models Article de journal Dans: Computers and Mathematics with Applications, vol. 66, no. 5, p. 860 – 872, 2013, (Cited by: 30; All Open Access, Bronze Open Access). |
New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models Article de journal Dans: Computers and Mathematics with Applications, vol. 66, no. 5, p. 860 – 872, 2013, (Cited by: 30; All Open Access, Bronze Open Access). |