On minimizing the influence of the noise tail of correlation functions in operational modal analysis

In operational modal analysis (OMA) correlation functions are used by all classical time-domain modal identification techniques that uses the impulse response function (free decays) as primary data. However, the main difference between the impulse response and the correlation functions estimated from the operational responses is that the latter present a higher noise level. This is due to statistical errors in the estimation of the correlation function and it causes random noise in the end of the function and this is called the noise tail. This noise might have significant influence on the identification results (random errors) when the noise tail is included in the identification. On the other hand, if the correlation function is truncated too much, then important information is lost. In other to minimize this error, a suitable truncation based on manual inspection of the correlation function is normally used. However, in automated OMA, an automated procedure is needed for the truncation. Based on known theoretical solutions from the literature, a model is proposed in this paper to automatically truncate the correlation function at the point where it starts to get dominated by the noise tail. The accuracy of the proposed truncation procedure is studied using a three degree of freedom simulation case.