The Uncertainty of Damping Ratios Obtained Using Modal Identification Techniques and Full-Scale Acceleration Data

Abstract

The damping ratio of a structure has a large influence on its ability to meet serviceability and habitability requirements under dynamic loading. In practice, design analysis relies on estimates of damping ratios from measurements on existing structures, which can display significant variation even between nominally similar buildings. Overestimates of damping arising from uncertainty in the damping ratio can lead to tall buildings experiencing acceleration responses during wind and seismic events that cause human discomfort. This uncertainty is greater with modern methods of construction such as modular buildings that have limited previous vibration monitoring history. Better understanding of the damping ratio of these structures is necessary to realise their full potential. Whilst structural calculations, computational models and wind tunnel tests can be used to estimate the damping ratio of a structure, full scale testing is the only true way to investigate the actual damping displayed by a given structure. Modal analysis techniques can be applied to acceleration data obtained in full scale tests or ambient vibration to identify the damping ratio value. However, this value is associated with significant ambiguity as it depends on both response conditions during monitoring and the modal analysis techniques applied to the measured data. One commonly applied modal analysis method is the Random Decrement Technique (RDT) coupled with a mode decomposition method such as Analytical Mode Decomposition (AMD). The application of the RDT yields values of the damping ratio, however, it does not provide insight into the error associated with these values. It has been shown that by integrating bootstrapping techniques within the RDT, the uncertainty of the damping estimate can be evaluated. This paper compares the error [HM1] [BB2] of the AMD-RDT method using bootstrapping with the error of another prominent modal identification technique, the Bayesian Fast Fourier Transform (BFFT). Full-scale acceleration response signals obtained during ambient vibration monitoring of the worldﾒs tallest modular building are processed using both bootstrapping AMD-RDT[HM3] [BB4] and BFFT methods. The coefficient of variation (CV) for the two methods is compared, providing insights into the uncertainty of the dynamic response of structures and enabling better selection of mitigation measures to ensure compliance with habitability requirements.