Investigating the statistical error on autocorrelation for operational modal analysis

Autocorrelation is commonly used in signal processing for analyzing time signals, however the shape and magnitude of its statistical error, caused by its estimation from finite length measurements, is rarely addressed. Previous research showed that in the general case, the error on the autocorrelation estimator of an arbitrary signal is inversely proportional to the square root of the signal length. For operational modal analysis of linear systems under unknown ambient excitation, this error seems to present a peculiar shape influencing the estimation of damping ratios. In this paper the error on autocorrelation for a linear, time-invariant system subjected to white Gaussian noise is analytically and numerically studied. It is found to be very similar to the system’s response to an ambient noise, thus with a frequency content close to that of the expected autocorrelation itself. An upper bound of error magnitude is found for each mode of the system. Then, the resulting error on damping computations is investigated through numerical simulations applied to a two degrees of freedom mechanical system. Numerical outcomes show good agreement with the theoretical part and are then supported by experimental data of a prestressed concrete bridge under ambient traffic. This study allows for a better understanding and quantification of the inaccuracy on damping ratios computation through techniques using autocorrelation in time domain, notably the logarithmic decrement or time–frequency domain decomposition based on wavelet analysis.