Fundamental laws of operational modal analysis

Ambient modal identification, commonly known as 'operational modal analysis', allows the modal properties of a structure to be identified based on 'output-only' measurements without knowing explicitly the loading time history. Because of its economy in implementation, there is an increasing number of ambient vibration tests performed with industrial applications. As the modal properties are frequently used for subsequent analysis or decision making it is of vital importance to quantify and manage their uncertainties, which can be significant because no loading information is used in the identification. One fundamental question of both scientific and engineering relevance is, 'how much data do we need to achieve a specified accuracy in the modal parameters?' This is by no means a simple question and one would not expect an explicit answer. Common sense suggests that it is related to a variety of factors such as the sensor and data acquisition hardware, the number and location of sensors, the environment, the nature of the mode of interest, etc. This paper gives a fundamental answer to this question via a set of 'uncertainty laws' for the asymptotic behavior of the posterior covariance matrix in Bayesian modal identification derived under typical situations of small damping and sufficiently long data duration. The uncertainty laws give the fundamental laws of operational modal analysis governing the accuracy that can be achieved by any method, Bayesian or non-Bayesian, under the same set of assumptions and data. Scientific and practical implications shall be discussed.