Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

Abstract

This study proposes a direct parameter estimation approach from observed input-output data of a stochastic singleinput-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 continuoustime 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 nonlinear 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.

A lumped thermal model of lithium-ion battery cells considering radiative heat transfer

“…Steps II to V are repeated for four iterations where convergence of the parameter is very rapid. It requires two or three iterations, for convergence analysis, see [39]. The test data are collected under two different heat dissipation conditions.…”

Parameter Estimation of Hybrid Fractional-Order Hammerstein-Wiener Box-Jenkins Models Using RIVCF Method

“…where the order ofD q −1 is selected to be twelve in the illustrative example. (19) leads to rearrange (18) such that:…”

“…The fractional-order continuous-time Hammerstein, Wiener and Hammerstein-Wiener (HFC, WFC and HWFC) models were introduced in [18]. A direct parameter estimation approach from observed input-output data of a stochastic single-input single-output fractional-order continuous-time Hammerstein-Wiener model was also proposed in [18] by extending the iterative simplified refined instrumental variable (SRIV) algorithm. They are termed SRIV for HFC, WFC and HWFC models which are abbreviated as HSRIVCF, WSRIVCF and HWSRIVCF, respectively.…”

Modeling and parameter learning method for the Hammerstein–Wiener model with disturbance

“…[33][34][35] Based on the hierarchical identification principle and the auxiliary model identification idea, Wang and Ding 33 presented hierarchical least squares method to learn the Hammerstein-Wiener output error model parameter. Bias compensation principle is combined with the singular value decomposition method for learning the Hammerstein-Wiener model, and an improved online two-stage identification algorithm is introduced in the work by Li et al 34 By extending the simplified and refined instrumental variable method, Allafi et al 35 studied the instrumental variable least squares parameter estimation algorithm for the fractional-order Hammerstein-Wiener model. It should be noted that the abovementioned results assumed that unknown static nonlinearities are of polynomial forms.…”