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

Significance 

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.

Probabilistic Framework with Bayesian Optimization for Predicting Typhoon-Induced Dynamic Responses of a Long-Span Bridge - Advances in Engineering
Fig. 1. The framework of QRF for TIR prediction. (Quantile random forest: QRF, Typhoon-induced responses: TIR).
Probabilistic Framework with Bayesian Optimization for Predicting Typhoon-Induced Dynamic Responses of a Long-Span Bridge - Advances in Engineering
Fig. 2. Forecasting vertical TIR using QRF.

About the author

Dr. Yiming Zhang currently works as a Post-doctoral Fellow at the Hong Kong Polytechnic University. He earned Ph.D. degrees in Civil Engineering from Southeast University and Monash University in 2021. His research interests primarily lie in the field of SHM and wind engineering with probabilistic machine learning methods to address engineering problems from a data-driven perspective. He has published more than ten refereed articles in leading journals, such as ASCE Journal of Structural Engineering, Mechanical Systems and Signal Processing, Journal of Wind Engineering and Industrial Aerodynamics, and Structural Health Monitoring.

About the author

Dr. Hao Wang is currently a full professor affiliated with the School of Civil Engineering at Southeast University (SEU), Nanjing, China. He received a Ph.D. degree from SEU in 2007. In SEU, he leads a group dedicated to the research and development of wind effects and structural health monitoring (SHM) in Civil Engineering, with both fundamental investigations and real-world engineering applications. Dr. Wang is a Changjiang Scholarship Professor and vice-director of key laboratory of C&RC structures, ministry of education.

His research broadly involves the following themes: disaster prevention and mitigation, structural engineering with particular emphasis on wind effects, structural control and health monitoring, machine learning, smart sensing technology, and earthquake engineering. To date, Prof. Wang’s research efforts have resulted in more than 160 peer-reviewed journal articles, four books, and over 50 patents.

Reference

Zhang, Y., Wang, H., Mao, J., Xu, Z., & Zhang, Y. (2021). Probabilistic Framework with Bayesian Optimization for Predicting Typhoon-Induced Dynamic Responses of a Long-Span BridgeJournal of Structural Engineering, 147(1), 04020297.

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