System identification methods for metal rubber devices

• Published in: Mechanical systems and signal processing 2013-08, Vol.39 (1-2), p.207-226
• Main Authors: Zhang, B., Lang, Z.Q., Billings, S.A., Tomlinson, G.R., Rongong, J.A.
• Format: Article
• Language: English
• Subjects: Algorithms; Bilinear hysteresis model; Devices; Dynamic models; Hysteresis; Least squares method; Mathematical models; Metal rubber; Nonlinear damping material; Nonlinear system identification; Nonlinearity
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2013.02.002

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. The model is first approximated by representing the bilinear hysteresis damping as Chebyshev polynomials of the first kind and then generalised by taking into account the effects of noises. A very efficient systematic procedure based on the orthogonal least squares (OLS) algorithm, the adjustable prediction error sum of squares (APRESS) criterion and the nonlinear model validity tests is proposed for model structure detection and parameter estimation of MR devices 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 orthogonalising the associated terms and maximising the error reduction ratio, in a forward stepwise manner. The APRESS statistic regularises the OLS algorithm to facilitate the determination of the optimal number of model terms that should be included into the model. And whether the final identified dynamic model is adequate and acceptable is determined by the model validity tests. Because of the orthogonal property of the OLS algorithm, the selection of the dynamic model terms and noise model terms are totally decoupled and the approach also leads to a parsimonious model. Numerical ill-conditioning problems which can arise in the conventional least squares algorithm can be avoided as well. The methods of choosing the sampling interval for nonlinear systems are also incorporated into the approach. Finally by utilising the response of a cylindrical MR specimen, it is shown how the model structure can be detected in a practical application. ► An approximated and generalised semi-constitutive dynamic model was proposed. ► A systematic method was then developed for metal rubber devices’ identification. ► The method can detect the model structure and leads to a parsimonious model. ► An identification example of a MR specimen under one set of conditions was given.