Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty

Abstract

This study presents a methodology for the on-line identification of nonlinear hysteretic systems where not only the parameters of the system are unknown but also the nature of the analytical model describing the system is not clearly established. To this end a Bayesian approach using the Unscented Kalman Filter (UKF) method has been applied in order to investigate the effects of model complexity and parametrization. The latter can be especially challenging in the case of realistic applications involving limited information availability. The state space formulation incorporates a Bouc–Wen type hysteretic model properly modified with additional polynomial or exponential-type nonlinear terms that are properly weighted throughout the identification procedure. The parameters associated with the candidate models might be subjected to constraints that can affect the stability of the estimation process when violated. An adaptive gain technique is introduced in order to tackle the problem of parameter boundaries. In addition, a twofold criterion based on the smoothness of the parameter prediction and the accuracy of the estimation is introduced in order to investigate the required model complexity as well as to potentially rule out ineffective terms during the identification procedure (on-line). Previous work, Smyth et al. (1999) [1], has dealt with the adaptive on-line identification of nonlinear hysteretic systems using a least-squares based algorithm. The current work explores the case of more severe nonlinearities that call for the expansion of the hysteretic models commonly used in literature. The method is validated through the identification of the highly nonlinear hysteretic behavior produced by the experimental setup described in Tasbihgoo et al. (2007) [2] involving displacement and strain (restoring force) sensor readings.