Cumulative power spectral density-based damping estimation

Damping is one of the critical factors in evaluating the performance of a structure under loads resulting from winds, waves, and earthquakes. Due to significant uncertainties associated with the damping mechanism and methods of its evaluation, its accurate estimation remains a challenging task. Therefore, many studies have focused on the development of damping estimation schemes. In this study, a simple yet effective scheme based on "Dynamics 101" for estimating damping in structures that draws upon attributes of the cumulative power spectral density (CPSD) function is proposed. The underlying principle is that the damping ratio can be estimated by comparing the computed CPSD of the modal response derived from measured data with the corresponding theoretical CPSD that is, defined by natural frequency and damping ratio. Unlike the jaggedness often observed in the power spectral density (PSD) that leads to uncertainty in damping estimates, the CPSD is characterized by its smoothness as it stems from the integration of the PSD. Theoretical characteristics of CPSD were utilized for extracting damping, and it was also extended to include non-classically damped systems. Using numerically simulated data and full-scale measurements, the validity and efficacy of the proposed scheme have been demonstrated. It is also demonstrated that this simplistic approach, requiring elementary knowledge of dynamics, yields results of the quality that match those of more advanced techniques. This offers an attractive scheme for practical applications with a promise of automation through a simple algorithm or a machine learning-based environment.