Model-free damage localization of structures using wavelet based grey relational analysis

Damage detection of real-life civil structures is generally performed under a condition of poor information, mainly referring to our insufficient knowledge of structures, uncertainties and limited sensors. Moreover, most damage detection methods require the numerical or mathematical models of a structure, whose stiffness parameters are sought by inverse solutions such as model updating. However, ill-conditioning problems are often found when updating complex structures. Hence, a model-free damage localization strategy has been proposed incorporating wavelet packet transform with grey relation analysis. First acceleration response signals are decomposed into different frequency subbands using wavelet packet transform. The wavelet packet energies of specific frequency subbands corresponding to fundamental modal frequencies are extracted and then normalized by the total energy of all the accelerometers. After that, wavelet packet energy curvatures are constructed and incorporated with grey relation analysis to propose a wavelet grey correlation coefficient. Damage locations are determined according to magnitude changes in these coefficients. Lastly, the feasibility of the proposed method has been successfully verified against an experimental steel beam. The validation also found that direct damage localization based on mode shapes or modal curvatures could not provide effective judgment.