A signal processing framework for operational modal analysis in time and frequency domain

In operational modal analysis (OMA), correlation functions, sometimes referred to as covariance functions, are commonly used for modal parameter extraction. Other techniques for parameter estimation use spectral density estimates. There are several known techniques for computing spectral density and correlation functions. The most common technique for spectral density estimates, is Welch's method. A more infrequently used technique, however, is based on computing the discrete Fourier transform (DFT) of the entire signals, and multiplying these DFTs into auto and cross-periodograms. To produce a correlation function, the inverse Fourier transform of the periodogram is used. To produce spectral density estimates, the periodogram may be smoothed. In the present paper this method of computing the spectral and correlation functions is investigated, and compared to other methods of spectral and correlation estimation. It is shown that the method has several advantages not only for estimation of spectra and correlation functions, but also because filtering, integration and differentiation, removal of harmonics, and compensation for non-ideal sensor characteristics are functions that can readily be encompassed in this technique, with high performance, at a minimum of computational cost. Furthermore, two methods to remove harmonics in spectral densities as well as in correlation functions, are developed in the paper. The first method, frequency domain editing (FDE), removes one or more stable harmonics, where variations of the frequency are small. The other method, order domain deletion (ODD), works in cases where the frequency of the harmonic, or harmonics, varies, and where the instantaneous frequency as a function of time is known, for example by processing a tacho signal. Based on the several advantages with using long DFTs as the estimation method for spectra and correlation functions, it is recommended as the standard framework for signal processing in OMA applications.