Modal identification using spectral moments

Abstract The use of spectral moments has been proposed for estimating natural frequencies of vibration and equivalent viscous modal damping ratios from ambient response measurements of dynamically excited structures. The moments tend to be relatively more stable than spectral ordinates and may be derived from raw, unsmoothed periodograms. Central to the analysis are the assumptions of white noise excitation, small damping, and uncoupled modes. Partial spectral moments are recommended for multi-degree-of-freedom dynamic systems, deviations from white noise excitation, and to ignore noisy regions of the spectrum at the frequency extremes. This paper presents an iterative algorithm for implementing the concept which eliminates severe bias errors that are identified in damping estimates obtained with the originally proposed algorithm based on partial spectral moments. An error analysis of the new algorithm, which does not make the small damping assumption, is conducted to evaluate the sensitivity of the parameter estimates to (i) presence of additive noise in the response measurements, and (ii) the non-whiteness of the excitation spectral density function. The results are compared with those from a similar analysis for the well-known maximum response natural frequency and half-power bandwidth damping estimators. Information is provided to help in selecting appropriate integration intervals for computing partial spectral moments.