Calibration of mass-spring-damper equivalent systems for real time assessment of the dynamics of trees

In-situ tests and numerical models represent valuable tools for deriving the main dynamic characteristics of trees and for studying their response to dynamic actions. Regarding the numerical models, a key aspect is their calibration. Most procedures available in the literature generally suggest the use of a significant number of instruments (accelerometers placed on both the trunk and branches), which results in high costs and is time-consuming. The aim of this paper is to propose a two-phase approach to calibrate multiple mass-spring-damper systems for studying the dynamics of trees. The proposal aims to support the monitoring and stability assessment of trees through an efficient procedure that combines techniques and methods derived from the field of structural dynamics. Some of these techniques are already used for trees, while others are newly applied in this context. In particular, the experimental data deduced from pull-release tests performed using a single accelerometer placed only on the trunk are assumed as the input data for the approach. The approach is presented in the first part of the paper. In the second part, the approach is implemented in the computer code Matlab to validate it with reference to both numerical models and real tree cases. Finally, a user-friendly graphical application of the approach is developed to make it a practical and expedient tool for researchers and practitioners, allowing real-time evaluation of the dynamics of trees, conducted simultaneously with in-situ tests.