This study proposes a direct parameter estimation approach from observed input-output data of a stochastic single-input-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.
%0 Journal Article
%1 8047699
%A Allafi, W.
%A Zajic, I.
%A Uddin, K.
%A Burnham, K. J.
%D 2017
%J IET Control Theory Applications
%K HammersteinWiener estimation fractionalOrder
%N 15
%P 2591-2598
%R 10.1049/iet-cta.2017.0284
%T Parameter estimation of the fractional-order Hammerstein-Wiener model using simplified refined instrumental variable fractional-order continuous time
%U https://www.researchgate.net/publication/320145331_Parameter_estimation_of_the_fractional-order_Hammerstein-Wiener_model_using_simplified_refined_instrumental_variable_fractional-order_continuous_time
%V 11
%X This study proposes a direct parameter estimation approach from observed input-output data of a stochastic single-input-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.
@article{8047699,
abstract = {This study proposes a direct parameter estimation approach from observed input-output data of a stochastic single-input-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.},
added-at = {2018-01-24T09:47:01.000+0100},
author = {Allafi, W. and Zajic, I. and Uddin, K. and Burnham, K. J.},
biburl = {https://www.bibsonomy.org/bibtex/22b26ca1fcceccdaef73ba2007e9a605a/ristephens},
doi = {10.1049/iet-cta.2017.0284},
interhash = {37e58f0188f1671bc6b725e49dad4435},
intrahash = {2b26ca1fcceccdaef73ba2007e9a605a},
issn = {1751-8644},
journal = {IET Control Theory Applications},
keywords = {HammersteinWiener estimation fractionalOrder},
number = 15,
pages = {2591-2598},
timestamp = {2018-01-24T09:47:41.000+0100},
title = {Parameter estimation of the fractional-order Hammerstein-Wiener model using simplified refined instrumental variable fractional-order continuous time},
url = {https://www.researchgate.net/publication/320145331_Parameter_estimation_of_the_fractional-order_Hammerstein-Wiener_model_using_simplified_refined_instrumental_variable_fractional-order_continuous_time},
volume = 11,
year = 2017
}