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This paper presents an advanced time-frequency analysis technique based on the empirical mode decomposition (EMD) and a newly developed conjugate-pair decomposition (CPD) method for damage detection and health monitoring of dynamical systems.Responses of damaged dynamical systems are often nonlinear and nonstationary.EMD uses the apparent time scales revealed by the signals local maxima and minima to sequentially sift components of different time-varying scales, starting from high-frequency to low-frequency ones.