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Shock and Vibration
Volume 2015 (2015), Article ID 193136, 12 pages
Research Article

Nonlinear Regression Based Health Monitoring of Hysteretic Structures under Seismic Excitation

1School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
2Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand

Received 19 March 2015; Revised 25 June 2015; Accepted 29 June 2015

Academic Editor: Mickaël Lallart

Copyright © 2015 C. Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a health monitoring method using measured hysteretic responses. Acceleration and infrequently measured displacement are integrated using a multirate Kalman filtering method to generate restoring force-displacement hysteresis loops. A linear/nonlinear regression analysis based two-step method is proposed to identify nonlinear system parameters. First, hysteresis loops are divided into loading/unloading half cycles. Multiple linear regression analysis is applied to separate linear and nonlinear half cycles. Preyielding stiffness and viscous damping coefficient are obtained in this step and used as known parameters in the second step. Then, nonlinear regression analysis is applied to identified nonlinear half cycles to yield nonlinear system parameters and two damage indicators: cumulative plastic deformation and residual deformation. These values are closely related to structural status and repair costs. The feasibility of the method is demonstrated using a simulated shear-type structure with different levels of added measurement noise and a suite of ground motions. The results show that the proposed SHM method effectively and accurately identifies physical system parameters with up to 10% RMS added noise. The resulting damage indicators can robustly and clearly indicate structural condition over different earthquake events.