Nonlinear function selection and parameter estimation of structures with localised nonlinearities, part 1: Numerical analysis
Authors: Safari, S. and Londono Monsalve, J.M.
Journal: Conference Proceedings of the Society for Experimental Mechanics Series
Pages: 139-149
eISSN: 2191-5652
ISBN: 9783030476250
ISSN: 2191-5644
DOI: 10.1007/978-3-030-47626-7_23
Abstract:Although techniques for system identification of linear dynamical systems are well developed, for nonlinear systems, it is still an open research question. Particularly, finding the correct form of the nonlinear functions (e.g. polynomial, multi-linear) and their parameters for dynamic systems with unknown nonlinearities still represents a crucial aspect to be addressed. Many methods have been presented in the literature to characterize and estimate the parameters of nonlinear dynamical systems; yet, most of them require pre-assumption of the form of the nonlinear function. In order to overcome this issue, in this study a data driven nonlinear autoregressive with exogenous inputs (NARX) model is considered together with a polynomial basis of model terms. We present here the mathematical background and numerical simulations of the proposed methodology. We use Forward Regression Orthogonal Least Square (FROLS) algorithm to select the terms in the NARX model considered. FROLS is a recursive algorithm able to find the more significant model terms based on the Error Reduction Ratio (ERR) criterion. We also explore ways to improve the selection of nonlinear terms using an optimization procedure during which models corresponding to various candidate structures are estimated based on Prediction Error Method (PEM), and the one providing the best fitness to the simulation data is selected. The procedure is motivated by the desire to quantify the degree of nonlinearity of a system, with the ultimate goal of updating a finite-element or other mathematical model to capture the nonlinear effects accurately. Single and multi-degrees of freedom systems that include a wide variety of nonlinearities are considered in this study. The results show that selecting the nonlinear function based on ERR is not affected by noise while the coefficient estimation depends on signal-to-noise ratio (SNR) value and the combination of different nonlinear functions. Discussions are made on sufficiency and efficiency of various optimization tools dealing with the coefficient estimation for MDOF system with localised nonlinearities.
Source: Scopus