Identifying the stiffness parameters of a structure using a subspace approach and the Gram-Schmidt process in a wavelet domain

This article presents a procedure to improve the accuracy of calculated stiffness matrix of a structure based on the identified modal parameters from its measured responses. First, a continuous wavelet transform is applied to the measured responses of a structure, and the state–space model can be reconstructed by the wavelet coefficients of acceleration that can be obtained from the measured noisy responses. The modal parameters are identified using the subspace approach. Second, the identified mode shapes are corrected via Gram–Schmidt process. Finally, the identified natural frequencies and the corrected mode shapes in previous steps are utilized to build the stiffness matrix of structure. The accuracy of the proposed approach is numerically confirmed, and the noise effects on the ability to precisely identify the stiffness matrix are also investigated. The measured data of two eight-story steel frames in a shaking table test are analyzed to demonstrate the applicability of the procedure to real structures.