A Non-Parametric Approach for Identification of Parameter Varying Hammerstein Systems

Ehsan Sobhani Tehrani,Robert E Kearney

doi:10.1109/access.2022.3141704

Ehsan Sobhani Tehrani, Robert E Kearney

Open Access

https://doi.org/10.1109/access.2022.3141704

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Abstract

This paper presents a novel method for non-parametric identification of parameter-varying (PV) Hammerstein systems where the parameters of both the static nonlinearity and the linear dynamics change with a scheduling variable. The proposed method estimates the individual elements of the PV Hammerstein system by describing the static nonlinear element using a PV Chebychev basis expansion and the linear dynamic element as a non-parametric PV impulse response function with Laguerre basis expansion. The method was validated using Monte-Carlo simulations of a PV Hammerstein model of ankle reflex stiffness during large movements. Results demonstrated that the method is simple, effective, and robust; it accurately identified the PV Hammerstein system in the presence of relatively large colored, time-varying measurement noise (average SNR of 15dB). These results demonstrate the two main contributions of the method: (1) It accurately and precisely estimates both the linear and nonlinear elements of the PV Hammerstein cascade as they vary with a scheduling variable; and (2) Models identified with the method accurately predict the response of the PV Hammerstein system to novel scheduling variable trajectories. To our knowledge, no other Hammerstein method can achieve these.

Highlights

Methods for the identification of linear systems are well developed and there is a good understanding of the effects of measurement noise, disturbances, uncertainties, and other practical considerations on their accuracy and precision [1]
This paper presents an efficient non-parametric nonlinear identification method for PV Hammerstein systems named as non-parametric PV-H method that estimates how both the static nonlinear and linear dynamic elements vary with a scheduling variable
This paper describes a new non-parametric, nonlinear parameter-varying identification method that estimates the changes in both elements of SISO PV Hammerstein systems with a scheduling variable

Summary

INTRODUCTION

Methods for the identification of linear systems are well developed and there is a good understanding of the effects of measurement noise, disturbances, uncertainties, and other practical considerations on their accuracy and precision [1]. This paper extends nonlinear identification to situations where the underlying model structure is inherently nonlinear whose parameters change with a scheduling variable; to the case of PV Hammerstein systems. Methods for the identification of time-varying (TV) Hammerstein systems have used one of four approaches: (1) Ensemble-based (e.g., [14]), which require many input-output trials having the same TV behaviour. Acquisition of such data is tedious at best and is impossible for many physiological systems during functional activities. Sobhani Tehrani et al [34] developed a subspace method to identify a class of PV Hammerstein systems where the static nonlinearity is parameter varying but the linear dynamics is time invariant.

PROBLEM FORMULATION

IDENTIFICATION ALGORITHM

SIMULATION STUDIES

Findings

DISCUSSION AND CONCLUSION