Probabilistic Regression Model for OMA-Based Damping Estimates of a Cable-Stayed Bridge Under Environmental and Operational Variability

Modal parameters are key factors in vibrational serviceability assessments of long-span cable-supported bridges. The recent development of automated operational modal analysis (OMA) has enabled modal tracking according to environmental and operational conditions (EOCs). However, in contrast to the successful implementations for natural frequencies, there are still challenges in the investigation of damping ratio due to (1) inherent errors in damping estimates and (2) epistemic uncertainties on the effects of EOCs. In this regard, this study proposes the framework to establish a reliable probabilistic regression model for the damping ratio of an actual cable-stayed bridge by incorporating various machine learning (ML) algorithms. First, a conventional automated OMA algorithm is improved by employing a displacement reconstruction algorithm and the optimized unsupervised clustering method. These approaches can reduce the model-order dependencies in OMA-based damping estimates with minimum user intervention. The proposed framework is then employed to estimate the long-term damping ratio from 2.5 years of structural health monitoring data. The monthly fluctuation and amplitude dependency of long-term damping characteristics are discussed. Subsequently, the deep Gaussian Process (DGP) model is applied to damping estimates for developing a probabilistic regression model. A statistic-based and knowledge-based data cleansing strategies are proposed to enhance the model’s regression performance. A comparative study with different regression models validates the robustness of DGPs. Finally, the predictability of the trained model is validated using the actual monitoring datasets.