element model in conjunction with a recently proposed damage detection technique, referred to as the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI). The identification process is divided into two steps. In the first step, static condensation technique is used to reduce the order of the equations of motion of the finite-element model. In the second step, the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI) is used for the on-line system identification and damage detection of the reduced order system. The proposed approach is capable of identifying time-varying parameters of linear or nonlinear hysteresis structures. The capability of the proposed damage detection technique is demonstrated by shake table test data using large-scale structures. A 1/3-scaled 6-story steel frame, a 1/3-scaled 2-story RC frame and a 1/2-scaled
one-story two-bay RC frame have been tested experimentally on the shake table at NCREE (The National Center for Research on Earthquake Engineering), Taiwan. For the 1/3-scaled 6-story steel frame structure, the damages of the joints were simulated by loosening the connection bolts. The 1/3-scaled 2-story RC frame was subject to a sequence of earthquake excitations back to back. Both RC frames are modeled by a series of finite elements and plastic hinges following the generalized Bouc-Wen model. Experimental results demonstrate that the proposed damage detection technique is quite accurate and effective for the tracking of: (i) the stiffness degradation of linear structures, and (ii) the non-linear hysteretic parameters with stiffness and strength degradations.
The versatile Bouc–Wen model has been used extensively to describe hysteretic phenomena in various fields of engineering. Nevertheless, it is known that it exhibits displacement drift, force relaxation and nonclosure of hysteretic loops when subjected to short unloading–reloading paths. Consequently, it locally violates Drucker’s or Ilyushin’s postulate of plasticity. In this study, an effective modification of the model is proposed which eliminates these problems. A stiffening factor is introduced into the hysteretic differential equation which enables the distinction between virgin loading and reloading. Appropriate reversal points are utilized effectively to guide the entire process. It is shown that the proposed modification corrects the nonphysical behavior of the model under short unloading–reloading paths without affecting its response in all other cases. It is further demonstrated that the original and modified model exhibit significantly different response under seismic excitation. r 2008 Elsevier Ltd. All rights reserved.
