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Wavelet transform has been used for detecting the singularities in structural response, which are caused by sudden changes in the system parameters. If the structure is subject to broadband random excitation like earthquakes, however, the singularities could also be caused by the excitation process. The isolation method based on wavelet transform was investigated to separate the singularities due to the excitation and the singularities due to the structural damages. An FEM model for the American Society of Civil Engineers (ASCE) structural health monitoring benchmark problem was used to demonstrate the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]