Probabilistic Framework with Bayesian Optimization for Predicting Typhoon-Induced Dynamic Responses of a Long-Span Bridge

Bridges are important transportation arteries, improving accessibility and convenience. However, with the rapid surge in the number of long-span bridges, the main concern to design engineers is their increasing vulnerability to extreme wind events such as hurricanes and typhoons. Specifically, long-span bridges experience extreme vibrations when subjected to typhoons, threatening their safety and serviceability. Generally, predicting the typhoon-induced response (TIR) is deemed the most efficient and reliable means of mitigating the possible threats. Besides wind tunnel experiments and field measurements, finite-element (FE) simulations are commonly used as an effective traditional method for predicting TIR of long-span bridges. However, the inadequacies associated with the assumptions involved in establishing the wind model and formulation of the model undermines the accuracy of FE methods. Consequently, formulating reliable models representing in-service bridges using the FE method is difficult.

Following the rapid increase in long-span bridges with structural monitoring systems, data-driven methods based on field measurement data are becoming attractive for accurate TIR prediction. For instance, machine learning (ML) methods such as random forest (RF), though sparsely explored in structural wind engineering, can be used to model the relationship between wind and its associative structural responses. The limitations of ML methods, especially in solving nonlinear optimization problems, can be addressed by using the quantile random forest (QRF) approach. By combining the advantages of quantile regression and RF, QRF can effectively measure the prediction uncertainties. Notably, to ensure high prediction performance, QRF requires hyperparameter optimization, which can be achieved via Bayesian optimization. Unlike grid and random search methods, Bayesian optimization is highly efficient and can determine the optimal hyperparameters with few iterations.

On this account, Postdoctoral fellow Dr. Yi-Ming Zhang, Professor Hao Wang, Professor Jian-Xiao Mao, Zi-Dong Xu from Southeast University together with Yu-Feng Zhang from the Jiangsu Transportation Research Institute Co., Ltd. employed a data-driven framework combining Bayesian optimization and QRF for probabilistic prediction of typhoon-induced dynamic responses of long-span bridges. Through Bayesian optimization implementation, the hyperparameters of the QRF were obtained. Moreover, the presented approach allowed for the characterization of uncertainties involved in the TIR prediction, especially those with high variability. The feasibility of the proposed method was validated using a long-span cable-stayed bridge with the main span extending for 1088m. Additionally, other optimization algorithms, random and grid search, and response surface methods were implemented for comparison purposes. The original research article is published in the Journal of Structural Engineering.

Results showed that using QRF with Bayesian optimization provided reliable and more accurate probabilistic estimations, enabling the quantification of uncertainties associated with the TIR prediction. Furthermore, the typhoon characteristics, including those exhibiting variability, were successfully analyzed and the parameters associated with the wind characteristics were regarded as QRF predictor variables. Moreover, the importance of the predictor variables was evaluated and the average wind velocity and direction were identified as the most important parameters for vertical TIR prediction. Compared with other optimization methods, the presented method was superior in terms of cost and accuracy.

In summary, a probabilistic model comprising QRF and Bayesian optimization for predicting TIR from a data-driven perspective rather than FE method was developed. The probabilistic model exhibited superior performance than the existing optimization algorithms and models. The improved computational efficiency could be attributed to the advantages of QRF that allowed for the accurate prediction of uncertainties in TIR predictions without assumptions and hypotheses. Furthermore, as a powerful tool for modeling nonlinear systems, the present method also exhibited superior performance than the response surface methodology. In a statement to Advances in Engineering, first author Dr. Yi-Ming Zhang stated that the predictive framework and analysis for TIR provided useful insights that would advance data-driven structural wind engineering.