Modal parameters are critical for wind resistant design and vibrational serviceability assessments of long-span cable-supported bridges. In contrast to the successful research efforts into natural frequencies, there are still challenges in modeling the damping ratio due to the following aspects: (1) inherent errors in damping estimates, (2) lack of insight into the damping mechanisms, and (3) epistemic uncertainties on the effects of environmental and operational conditions (EOCs). This paper proposes a probabilistic regression model for damping using Deep Gaussian Processes (DGP) on damping estimates compiled from 2.5 years of structural health monitoring (SHM) data from a cable-stayed bridge. Input features representative of EOCs theorized to be related to damping ratios from past literature were used. Two data cleaning strategies based on statistics and knowledge-based criteria were used for enhancing the model performance. A comparative study with DGPs and different regression models were carried out to confirm the robustness of DGPs across different datasets. A knowledge-based feature engineering process examined the most significant predictor of the damping ratios. The proposed data-driven regression model can enable a probabilistic consideration of damping in structural design and vibrational serviceability assessments.

The recent development of automated operational modal analysis (OMA) has enabled the modal tracking of environmental and operational conditions. Variations in these conditions have prevented investigations into the long-term characteristics of the damping ratio due to its inherently high degree of scattering. In this study, the long-term damping characteristics of a twin cable-stayed bridge under environmental and operational variations were investigated. A displacement reconstruction algorithm was applied to resolve the model-order dependency in OMA-based damping estimates. In order to automatically establish groups of modal estimates, optimal parameters for a density-based unsupervised clustering algorithm were proposed on the basis of gaps between target modal frequencies. The proposed clustering parameters were first validated by comparing the clustering results with those of manually determined ground truth classes. Next, the applicability of the clustering parameters for long-term damping estimation was demonstrated by quantifying the dispersion of modal estimates in each cluster. Subsequently, the framework was applied to 2.5 years of monitoring data to evaluate the long-term damping characteristics of the twin cable-stayed bridge that is often subjected to high variations in environmental and operational conditions. The following aspects are mainly discussed: (1) seasonal fluctuation in long-term damping ratios; (2) the effect that aerodynamic interference exerts on variations in the dynamic characteristics; and (3) the amplitude dependency of the damping ratio. The probability distribution of the modal damping ratio is provided based on the statistical analysis of reliable modal damping ratios.