Probabilistic Model for Modal Properties Based on Operational Modal Analysis

Operational modal analysis allows one to identify the modal properties (natural frequencies, damping ratios, mode shapes, etc.) of a constructed structure based on output vibration measurements only. For its high economy in implementation, it has attracted great attention in theory development and practical applications. In the absence of specific loading information and under uncertain operational environments that can hardly be controlled, the identified modal properties have significantly higher uncertainties than their counterparts based on free or forced vibration tests where the signal-to-noise ratio can be directly controlled. A recent result connecting mathematically the frequentist and Bayesian quantification of identification uncertainty opens up opportunities for modeling the variability of modal properties over time when taking into account identification uncertainty. This paper presents a probabilistic model for the modal properties of a structure under operating environment, which incorporates the identification information from past data to yield the total uncertainty that can be expected in the future with similar structural and environmental characteristics in the past. The developed concepts are illustrated using synthetic, laboratory, and field data.