Estimation error of the half-power bandwidth method in identifying damping for multi-DOF systems

The half-power bandwidth method is widely used for estimating damping in multi-DOF systems, although it was originally derived from the frequency response of a single-DOF system. This note aims to analyze the accuracy of the half-power bandwidth method in damping estimation for multi-DOF linear systems. More specifically, the damping ratios in a two-DOF linear system are estimated using its displacement frequency response curve for a wide range of important parameters that affect the shape of this response curve. It is found that the half-power bandwidth method may significantly overestimate the damping ratios of the two-DOF system in some cases. In particular, the damping estimation error for the first mode may be much larger than that in the single-DOF case even if two natural frequencies are spaced very far apart. Therefore, this method should be used with caution in damping estimation for multi-DOF systems.