Bayesian operational modal analysis of offshore rock lighthouses: Close modes, alignment, symmetry and uncertainty

•The paper describes a unique exercise in modal testing of functioning iconic heritage structures.•This paper provides a rare presentation of full 3D modes for tall quasi-axisymmetric structures.•Measurements showed mode shape orientations were not always perpendicular within a pair.•An extended recording shows how closeness of modes trades with precision in their identification.•A recording of extreme response shows BAYOMA to be unexpectedly robust to non-stationarity in the data.