Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior

A system identification technique suitable for single degree of freedom (SDOF) and multiple degree of freedom (MDOF) structural systems with either nonlinear elastic or inelastic/hysteretic behavior is proposed in this paper. The method is a parametric modeling technique based on sparse regularization. The proposed framework is capable of discovering the underlying governing equations of the system of interest from input-output data. We build on the work of Brunton et al. (2016) by including functions that allow the discovery of significant nonlinearities, and hystertic or inelastic behavior with permanent deformation. We also present model selection using sparse regularization and cross validation using Akaike criteria. We demonstrate through experimental validation that the technique presented in this paper is applicable to a significantly broader class of problems. The effectiveness of the proposed method is evaluated through numerical examples of a 2-story nonlinear or inelastic building with a adjustable stiffness device. We also present experimental validation using a unique nonlinear structural system that consists of a MDOF structural system and a nonlinear negative stiffness device (NSD) to illustrate the significant ability of the proposed framework. We successfully identify the following structural systems from experimental data: a SDOF yielding frame without NSD; a SDOF yielding frame with NSD; and a 3-DOF frame with NSD. The extracted sparse model also shows potential for generalization.