System Identification and Damage Detection of Nonlinear Structures

Many civil and mechanical engineering structures exhibit nonlinear hysteretic behavior when subject to dynamic loads. The modeling and identification of non-linear hysteretic systems with stiffness and strength degradations is a practical but challenging problem encountered in the engineering field. Time domain analysis techniques, including the least square estimation (LSE) and the extended Kalman filter (EKF), have been used for the identification of structural parameters. However, the LSE approach may require the displacement measurements which are usually not measured in practice. With only the measurements of acceleration responses, the on-line system identification and damage detection is possible based on the EKF approach. However, for the EKF approach, the solutions may easily become unstable and may not converge. Furthermore, system identification approaches, such as LSE and EKF approaches, are usually more suitable for simple structures. For the finite element model (FEM) of a complex structure with a large number of degree-of-freedom (DOFs), it may require a large number of sensors and involve a heavy computational effort for the identification of structural damages.;To overcome such a challenge, we propose the application of a reduced-order finite 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.