Identification of an Equivalent Linear Model for a Non-Linear Time-Variant RC-Structure

This paper considers estimation of the maximum softening for a RC-structure subjected to earthquake excitation. The so-called Maximum Softening damage indicator relates the global damage state of the RC-structure to the relative decrease of the fundamental eigenfrequency in an equivalent linear model with slowly varying stiffness properties, displaying the combined damage effects of the maximum displacement ductility of the structure during extreme plastic deformations and the stiffness deterioration in the elastic regime, also called final softening. In order to use the Maximum Softening damage indicator robust estimates of the fundamental eigenfrequency of the equivalent linear structure is required. Among many methods available for system identification application the Recursive Prediction Error Method (RPEM) and the Recursive Least Square (RLS) estimation using ARMAX models are investigated and compared with ARMAX models used on a running window. The techniques are evaluated using simulated data generated by the non-linear finite element program SARCOF modeling a 10-storey 3-bay concrete structure subjected to amplitude modulated Gaussian white noise filtered through a Kanai-Tajimi filter. The results show that an ARMAX model used on a running window seems to give the most robust estimate of the fundamental eigenfrequency.