# Parameter reduction in nonlinear state-space identification of hysteresis

## TL;DR

This paper introduces a decoupling approach to reduce parameters in nonlinear state-space models of hysteresis, maintaining accuracy while halving the model complexity, thus improving efficiency in system identification.

## Contribution

The paper proposes a novel polynomial decoupling method that significantly reduces parameter count in hysteresis modeling without sacrificing accuracy.

## Key findings

- Parameter reduction of up to 50% achieved.
- Maintains comparable output error levels.
- Connects polynomial decoupling with neural network modeling.

## Abstract

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree, as well as the connections with neural network modeling. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50\%, while maintaining a comparable output error level.