Model structure detection and system identification of metal rubber devices

Metal rubber (MR) devices, a new wire mesh material, have been extensively used in recent years due to several unique properties especially in adverse environments. Although many practical studies have been completed, the related theoretical research on metal rubber is still in its infancy. In this paper, a semi-constitutive dynamic model that involves nonlinear elastic stiffness, nonlinear viscous damping and bilinear hysteresis Coulomb damping is adopted to model MR devices. After approximating the bilinear hysteresis damping using Chebyshev polynomials of the first kind, a very efficient procedure based on the orthogonal least squares (OLS) algorithm and the adjustable prediction error sum of squares (APRESS) criterion is proposed for model structure detection and parameter estimation of an MR device for the first time. The OLS algorithm provides a powerful tool to effectively select the significant model terms step by step, one at a time, by orthogonalizing the associated terms and maximizing the error reduction ratio, in a forward stepwise procedure. The APRESS statistic regularizes the OLS algorithm to facilitate the determination of the optimal number of model terms that should be included into the dynamic model. Because of the orthogonal property of the OLS algorithm, the approach leads to a parsimonious model. Numerical ill-conditioning problems confronted by the conventional least squares algorithm can also be avoided by the new approach. Finally by utilising the transient response of a MR specimen, it is shown how the model structure can be detected in a practical application. The identified model agrees with the experimental measurements very well.