Given the random vibration of a linear and time-invariant system, the correlation function matrix is equivalent to free decays when the system is excited by Gaussian white noise. Correlation-driven Operational Modal Analysis utilises these properties to identify modal parameters from systems in operation based on the response only. Due to the finite length of the system response, the correlation function matrix must be estimated and this introduces statistical errors. This article focuses on the statistical errors due to this estimation process and the effect it has on the envelope and zero crossings of the estimated correlation function matrix. It is proven that the estimated correlation function matrix is a Gaussian stochastic process. Furthermore, it is proven that the envelope of the modal correlation function matrix is Rice distributed. This causes the tail region of the correlation function to become erroneous -called the noise tail. The zero crossings are unbiassed, but the random error related to the crossings increases fast in the noise tail. The theory is tested on a simulated case and there is a high agreement between theory and simulation. A new expression for the minimal time length is introduced based on the bias error on the envelope.

In operational modal analysis, the correlation function matrix is treated as multiple free decays from which system parameters are extracted. The finite time length of the measured system response, however, introduces statistical errors into the estimated correlation function matrix. These errors cause both random and bias errors that transfer to an identification process of the modal parameters. The bias error is located on the envelope of the modal correlation functions, thus violating the assumption that the correlation function matrix contains multiple free decays. Therefore, the bias error transmits to the damping estimates in operational modal analysis. In this paper, we show an automated algorithm that reduces the bias error caused by the statistical errors. This algorithm identifies erratic behaviour in the tail region of the modal correlation function and reduces this noise tail. The algorithm is tested on a simulation case and experimental data of the Heritage Court Building, Canada. Based on these studies, the algorithm reduces bias error and uncertainty on the damping estimates and increases stability in the identification process.

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