Identifying modal properties of trees with Bayesian inference - Burcham, Daniel C. (2022)
In forested landscapes, the presence of trees enhances turbulent airflow governing the exchange of momentum, heat, and gas between the atmosphere and biosphere, especially when horizontal motion dominates near-surface winds, and tree vibration is a prominent feature of the dynamic interaction between wind and trees. The vibration characteristics of trees reflect their underlying mechanical properties (i.e., mass, stiffness, damping) and govern their response to dynamic loads. Despite numerous investigations of tree vibration, there have been few studies examining methodological improvements for identifying and characterizing variability in the modal properties of trees during ambient wind excitation. In the engineering disciplines, however, there are several techniques commonly used to estimate the modal properties of a structure from its ambient vibration, often called ‘operational modal analysis’ (OMA). Operating in the frequency domain, this study examined the use of Bayesian OMA for identifying several important modal properties, including frequencies, damping ratios, and partial mode shapes, as well as their identification uncertainty. Using the ambient vibration recorded on a mature Hopea odorata Roxb. (Dipterocarpaceae) tree over a one-week period, the identified modal properties and associated uncertainties were physically reasonable and consistent with previous measurements for trees, and the identification uncertainty was much greater for damping ratio than frequency, which can be explained theoretically. Beyond the consistency with existing measurements, the analysis also yielded new insight about the vibration behavior of large trees. The modal properties varied considerably over consecutive one-hour intervals, and the changes were likely related to differences in wind excitation during each period, suggesting the existence of amplitude dependence in the modal properties of trees. Over the same periods, there were consistently two close modes (i.e., with similar frequencies), oriented approximately orthogonal to one another, near the tree’s fundamental frequency. With additional evaluation and refinement, the techniques can be used for OMA of trees in different settings.