Measuring configuration of multi-setup ambient vibration test

Abstract

In the ambient vibration test (AVT) of structures, when the number of desired locations for mode shapes to be measured is larger than that of available sensors, a ‘multi-setup’ strategy is often adopted. That is, sensors are ‘roved’ (placed) at different locations in different setups while ‘reference’ sensors are placed at common locations to provide information for estimating the ‘global’ mode shape covering all desired locations from ‘local’ information in individual setups. Currently, multi-setup AVTs are often planned based on experience. Naturally, questions on how to judge the performance of the test configuration are relevant, e.g., number and location of reference/rover sensors. This paper proposes metrics to quantify a multi-setup configuration by comparing the identification uncertainty of mode shapes with its best achievable one. The latter is informed by recent theoretical findings, i.e., ‘uncertainty law’ of multi-setup in operational modal analysis. Two indices are proposed to measure the overall configuration and the placement of reference sensors. They are also simplified to aid the design of multi-setup AVT. Two examples, a laboratory shear-type building model and a (full-scale) suspension footbridge, are presented to illustrate the usage of the proposed indices for performance quantification. The theory and examples reveal that the placement of reference sensors has a decisive influence. Notably, it is found that as long as the reference sensors are in ‘good’ positions, the identification uncertainty of the global mode shape is insensitive to the choice of rover sensors. Practically, and somewhat consistent with conventional wisdom, this suggests that reference sensors should be placed with due consideration to signal-to-noise ratio and the modes that can be detected, but rover sensors can be planned primarily based on logistics constraints/considerations.