Modal Parameters Directly Estimated from Power Spectral Densities or Correlation Functions in Output-Only Analysis

Abstract

Output-only analysis considers the system excited either by operative or by natural forces, in both cases the input loading which excites the structure is considered, at least in a limited frequency band, as a white noise. Because it is not possible to find directly the spectra, it is necessary to pass through the correlation functions so as to apply the Wiener–Khintchine theorem in order to find the power spectral densities (PSDs). In the past, the modal parameters have been essentially derived by approaches that manipulated the functions mentioned above. In this paper, the modal parameters will be directly estimated from the PSDs, in the frequency domain, and from the correlation functions in the time domain. A particular attention is devoted to the problems regarding the damping ratio overestimation. This effect due to the limited time window in the correlation function estimate is highly present in the low-frequency modes and could bring to large estimation errors. Experimental examples, carried out both on cantilever beams and on an helicopter blade, are presented. They show the problems related to the techniques using the PSDs, or the correlation functions and the possibility to overcome the overestimation of the damping factors due to the triangular window, also known as Bartlett window.