Karimov, Artur I. and Kopets, Ekaterina and Nepomuceno, Erivelton and Butusov, Denis (2021) Integrate-and-Differentiate Approach to Nonlinear System Identification. Mathematics, 9 (23). pp. 1-19. ISSN 2227-7390

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Abstract

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions.

Item Type:	Article
Keywords:	system identification; least squares; accelerometry; integration; differentiation; ordinary differential equation; nonlinear system; piece-wise linear system;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16844
Identification Number:	https://doi.org/10.3390/math9232999
Depositing User:	Erivelton Nepomuceno
Date Deposited:	11 Jan 2023 12:21
Journal or Publication Title:	Mathematics
Publisher:	MDPI
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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