Journal of Applied Mathematics
Volume 2013 (2013), Article ID 759102, 7 pages
Research Article

A Probabilistic Damage Identification Approach for Structures under Unknown Excitation and with Measurement Uncertainties

1Department of Civil Engineering, Xiamen University, Xiamen 361005, China
2Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received 26 December 2012; Revised 4 May 2013; Accepted 26 May 2013

Academic Editor: Xiaojun Wang

Copyright © 2013 Ying Lei 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.


Recently, an innovative algorithm has been proposed by the authors for the identification of structural damage under unknown external excitations. However, identification accuracy of this proposed deterministic algorithm decreases under high level of measurement noise. A probabilistic approach is therefore proposed in this paper for damage identification considering measurement noise uncertainties. Based on the former deterministic algorithm, the statistical values of the identified structural parameters are estimated using the statistical theory and a damage index is defined. The probability of identified structural damage is further derived based on the reliability theory. The unknown external excitations to the structure are also identified by statistical evaluation. A numerical example of the identification of structural damage of a multistory shear-type building and its unknown excitation shows that the proposed probabilistic approach can accurately identify structural damage and the unknown excitations using only partial measurements of structural acceleration responses contaminated by intensive measurement noises.