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Civil engineering structures, such as reinforced concrete frames, exhibit nonlinear hysteretic behavior when subject to dynamic loads, such as earthquakes. The ability to detect damages in structures after a major earthquake will ensure their reliability and safety. Innovative analysis techniques for damage detection of structures have been extensively studied recently. However, practical and effective damage identification techniques remain to be developed for nonlinear structures, in particular hysteretic reinforced concrete (RC) structures. In this paper, a smooth hysteretic model with stiffness and strength degradations and with the pinching effect is used to represent the dynamic characteristics of reinforced concrete (RC) frames. A system identification method capable of detecting damages in nonlinear structures, referred to as the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI), is used to detect damages in hysteretic RC frames. The performance of the AQSSE-UI technique is demonstrated by the experimental data. A 1/3 scale 2-story RC frame has been tested experimentally on the shake table at NCREE, Taiwan. This 2-story RC frame was subject to different levels of ground excitations back to back. The RC frame is firstly considered as a linear model with rotational springs and the tracking of the degradation of the stiffness parameters is carried out using the AQSSE-UI technique. Then the same RC frame is considered as a nonlinear structure with plastic hinges following a smooth hysteretic model. Experimental results show that the AQSSE-UI technique is quite effective for tracking of : (i) the stiffness degradation of linear structures, and (ii) the non-linear hysteretic parameters with stiffness and strength degradations.

An identification method for estimating the time varying excitation force acting on a structural system based on its response measurement is presented in this study. The method employs the simple Kalman filter to establish a regression model between the residual innovation and the input excitation forces. Based on the regression model, a recursive least-squares estimator is proposed to identify the input excitation forces incorporating with the measurement noise and the modeling error. In applying the method, the ambient vibration measurement of a structural system was used first. The stochastic subspace identification is applied to estimate the system matrix “A” and the m easurement matrix “C”. Then the Kalman filter with a recursive estimator is applied to determine the input excitation forces. The dynamic excitation forces are estimated from the measured structural responses by an inverse algorithm while least-square method with a recursive estimator is employed to update the estimation in the sense of real-time computation. Verification of the method with numerical simulation through MIMO system is conducted first. Identification of soil forces during the shaking table test of soil-pile interaction is also demonstrated. Keywords: Kalman filter, recursive least square, soil-pile interaction, MIMO dynamic system

This paper presents a damage assessment method using the measurement data of restoring force from a sub-structural system. A normalized hysteretic energy (NHE ) for bi-linear model is developed as a function structural period and system ductility, which serves as a reference-based model for damage assessment. The stiffness degradation, strength deterioration and pinching effect in the inelastic hysteretic model are then determined from a series of nonlinear time history analysis of an inelastic SDOF system. Next, modification factors on the NHE for sensitivities of the inelastic model parameters are developed. Based on the identified model parameters by measuring the inelastic hysteretic behavior of the restoring force incorporated with the reference-based NHE model and the modification factor, the percentage of structural damage in relating to strength and stiffness degradation can be evaluated. Verification of the proposed method by simulation and experimental data of the cyclic loading and shaking table tests of the RC frame are conducted. Keywords: Inelastic hysteretic model, strength degradation, sti ffness degradation, pinching effect, statistical analysis