%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 }