On Nonlinear Parameter Estimation

Document type: Conference Papers
Peer reviewed: No
Full text:
Author(s): Martin Magnevall, Andreas Josefsson, Kjell Ahlin
Title: On Nonlinear Parameter Estimation
Conference name: ISMA International Conference on Noise and Vibration Engineering
Year: 2006
ISBN: 90-73802-83-0
City: Leuven
ISI number: 000246669504025
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mechanical Engineering (Sektionen för teknik – avd. för maskinteknik)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
Authors e-mail: martin.magnevall@bth.se, andreas.josefsson@bth.se
Language: English
Abstract: The industrial demand on good dynamical simulation models is increasing. Since most structures show
some form of nonlinear behavior, linear models are not good enough to predict the true dynamical
behavior. Therefore nonlinear characterization, localization and parameter estimation becomes important
issues when building simulation models. This paper presents identification techniques for nonlinear
systems based on both random and harmonic excitation signals.

The identification technique based on random excitation builds on the well known reverse-path method
developed by Julius S. Bendat. This method treats the nonlinearity as a feedback forcing term acting on an
underlying linear system and the parameter estimation is performed in the frequency domain by using
conventional MISO/MIMO techniques. Although this method provides a straightforward and systematic
way of handling nonlinearities, it has been somewhat limited in use due to the complexity of creating
uncorrelated inputs to the model. As is shown in this paper, the parameter estimation will not be improved
with conditioned inputs and the nonlinear parameters and the underlying linear system can still be
estimated with partially correlated inputs.

This paper will also describe a parameter estimation method to be used with harmonic input signals. By
using the principle of harmonic balance and multi-harmonic balance it is possible to estimate an analytical
frequency response function of the studied nonlinear system. This frequency response function can, in
conjunction with measured nonlinear transfer functions, be used to estimate the nonlinearity present in the
system. This method is also applicable on nonlinear systems with memory, e.g. systems with hysteresis

The above mentioned methods are applied to multi-degree-of-freedom and single-degree-of-freedom
systems with different types of nonlinearities. Also, techniques for locating nonlinearities are discussed.
Subject: Mechanical Engineering\Structural Dynamics
Keywords: parameter estimation, nonlinear, characterization, localization, reverse-path, harmonic balance