Structural modal identification and enhancement of low-energy modes by successively variational extraction of high-energy modes

Accurate identification of modal properties for as much as possible modes from structural monitoring responses is an important part for structural health monitoring systems. Limited by the energy of external excitations, or influenced by the heavy noise, the energies of some modal components may be weak or buried in the energy of noise, giving rise to the difficulty for accurate modal identification. Variational mode decomposition method is a non-recursive decomposing procedure to decompose a signal into narrow-band sub-components. However, the difficulty for the decomposition of low-energy mode is determining the corresponding initial center frequencies. In this study, a new method for low-energy mode identification is proposed using the idea of locating, identifying, and subtracting the high-energy component to gradually enlarge the relative energy level of low-energy mode by substituting the original signal with residual signal repeatedly. First, the initial center frequency of the mode with maximum energy is determined by autoregressive power spectrum; second, the modal parameters including frequency, damping ratio and mode shape are identified by the singular value decomposition of Hankel matrix with low system order; third, vibrational mode extraction method is proposed to extract the modal component with maximum energy; subsequently, the modal component with maximum energy is subtracted from the original signal to construct the residual signal for the identification of next maximum energy component. The relative energy level of low-energy mode is enlarged gradually by repeating the subtraction of highenergy modal component. Then, the accuracy of low-energy mode identification is improved. The effectiveness of the proposed method is verified by the simulated structures under ambient and earthquake excitations with high-level noises. Besides, the capability for the application of practical structure is verified by the experimental data of a real bridge.