Cross-attention based frequency-domain prediction method for buffeting response of long-span bridges

Du Wu , Xiaolong Li , Nan Xu , Yanru Li , Yao Jin , Shaoyang He , Wencheng Xu , Na Li , Wenli chen , Shujin Laima

Advances in Bridge Engineering ›› 2026, Vol. 7 ›› Issue (1) : 36

PDF
Advances in Bridge Engineering ›› 2026, Vol. 7 ›› Issue (1) :36 DOI: 10.1186/s43251-026-00227-2
Original Innovation
research-article
Cross-attention based frequency-domain prediction method for buffeting response of long-span bridges
Author information +
History +
PDF

Abstract

The prediction of wind-induced buffeting response in long-span bridges is a fundamental scientific challenge in bridge wind engineering. Conventional buffeting analysis methods are constrained by simplifying theoretical assumptions, high experimental costs, and inherent model errors, making accurate full-scale prediction difficult. This study focuses on the Xihoumen Bridge, a representative long-span suspension bridge, and utilizes five-year multi-source heterogeneous monitoring data acquired from its structural health monitoring (SHM) system. By integrating deep learning techniques with classical buffeting theory, a frequency-domain, data-driven buffeting response prediction framework is proposed. Guided by the Davenport–Scanlan buffeting theory, the physical mapping relationship between wind field features and structural acceleration power spectral density (PSD) is first established, which motivates the design of an Attention-embedded Frequency Convolutional Network (Att-FCN) and a Residual Bidirectional Gated Recurrent Unit (Res-BiGRU) module. The prediction process is then physically decomposed into two sequential mapping stages—wind field to buffeting force spectrum and buffeting force spectrum to structural response spectrum—yielding a Cross-Attention Buffeting Network (CA-Buffeting Net). Experimental results demonstrate that CA-Buffeting Net reduces the mean squared error (MSE) by 29.7%, the mean absolute error (MAE) by 20.2%, and improves the cosine similarity (CS) by 1.2% points relative to the baseline model. Visualization of the channel and frequency attention coefficients further validates the physical interpretability of the proposed model, offering an effective technical tool for wind-resistance analysis and structural safety assessment of long-span bridges.

Keywords

Data-driven / Deep learning / Long-span bridge / Buffeting response / Attention mechanism / Power spectral density

Cite this article

Download citation ▾
Du Wu, Xiaolong Li, Nan Xu, Yanru Li, Yao Jin, Shaoyang He, Wencheng Xu, Na Li, Wenli chen, Shujin Laima. Cross-attention based frequency-domain prediction method for buffeting response of long-span bridges. Advances in Bridge Engineering, 2026, 7 (1) : 36 DOI:10.1186/s43251-026-00227-2

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Bai S, Kolter JZ, Koltun V (2018) An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:180301271

[2]

Castellon DF, Fenerci A, Iseth O. A comparative study of wind-induced dynamic response models of long-span bridges using artificial neural networks, support vector regression and buffeting theory. J Wind Eng Ind Aerodyn, 2021, 209: 104484.

[3]

Cho K, Van Merri E, Nboer B, Gul CC, Ehre CCAU, Bahdanau D, Bougares F, Schwenk H, Bengio Y (2014) Learning phrase representations using RNN encoder–decoder for statistical machine translation, in: 1724–1734

[4]

Davenport AG. Buffetting of a suspension bridge by storm winds. J Struct Div, 1962, 88(3): 233-270.

[5]

Fenerci A, Lystad TM, Iseth O. Full-scale monitored wind and response characteristics of a suspension bridge compared with wind tunnel investigations at the design stage. J Wind Eng Ind Aerodyn, 2023, 242: 105583.

[6]

Feng H, Qian W, Laima S. A machine learning-based probabilistic wind speed prediction model with multi-resolution data, quantile regression and bound estimation. Eng Struct, 2025, 322: 119098.

[7]

Feng H, Qian W, Li S, Jin Y, Han F, Xu W, Li N, Laima S (2026) A novel interval prediction model for buffeting response of a long-span bridge based on machine learning. Mech Syst Signal Proc 244:113734. https://doi.org/10.1016/j.ymssp.2025.113734

[8]

Goswami S, Giovanis DG, Li B, Spence SMJ, Shields MD. Neural operators for stochastic modeling of nonlinear structural system response to natural hazards. Eng Struct, 2025, 345: 121284.

[9]

He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition, in:770–778

[10]

He X, Wu Y, Peng G, Zou Y, Jing H, Yan L, Guo H, Dong Z, Li H. Recent developments in the wind resistance of railway bridges in china. Adv Wind Eng, 2024, 1(2): 100027.

[11]

Hu P, Cheng W, Xu G, Han Y, Yan N, Wang N. Prediction of buffeting responses of the thin plate under joint action of wave and wind using LSTM and transfer learning. Appl Ocean Res, 2023, 134: 103514.

[12]

Hu C, Li M, Li Y, Zhang M, Huang Y, Liu Y (2026) Near-surface wind field in coastal mountain terrain under typhoon influence. Adv BRIDGE Eng 7 (1). https://doi.org/10.1186/s43251-025-00203-2

[13]

Jain A, Jones NP, Scanlan RH. Coupled flutter and buffeting analysis of long-span bridges. J Struct Eng, 1996, 122(7): 716-725.

[14]

Kavrakov I, McRobie A, Morgenthal G. Data-driven aerodynamic analysis of structures using gaussian processes. J Wind Eng Ind Aerodyn, 2022, 222: 104911.

[15]

Laima S, Feng H, Li H, Jin Y, Han F, Xu W. A buffeting-net for buffeting response prediction of full-scale bridges. Eng Struct, 2023, 275: 115289.

[16]

Li Z, Kovachki NB, Azizzadenesheli K, Liu B, Bhattacharya K, Stuart AM, Anandkumar A (2020) Fourier neural operator for parametric partial differential equations. CoRR abs/2010.08895.

[17]

Li S, Li S, Laima S, Li H (2021) Data-driven modeling of bridge buffeting in the time domain using long short-term memory network based on structural health monitoring. Struct Control Health Monit 28 (8):e2772

[18]

Li S, Jin X, Laima S, Li H. Efficient data-driven nonlinear system identification for structural health monitoring: a proof-of-principle study. Adv Struct Eng, 2024, 27(16): 2950-2961.

[19]

Lianghao Z, Jian W, Jie S, Rui Z, Hao W (2025) Analysis of wind-induced vibration response characteristics of multispan double-layer cable photovoltaic support structure. J Southeast Univ 41 (1)

[20]

Lu L, Jin P, Pang G, Zhang Z, Karniadakis GE. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat Mach Intell, 2021, 3(3): 218-229.

[21]

Lu Z, Li S, Fu J, Li Q, Xu Z. Wind-induced vibration control of bridge girders by aerodynamic and mechanical methods: a literature review. Adv Bridge Eng, 2025, 6(1): 34.

[22]

Nie Y, Zhang Z, Zeng J (2025) Wind-resistant performances comparison between a long-span CFRP and a steel cable-stayed. Adv Bridge Eng 6 (1). https://doi.org/10.1186/s43251-025-00177-1

[23]

Scanlan RH. The action of flexible bridges under wind, II: buffeting theory. J Sound Vibr, 1978, 60(2): 201-211.

[24]

Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser LU, Polosukhin I. Attention is all you need, 2017. Red Hook, NY, USA, in: NIPS’17: 6000-6010

[25]

Woo S, Park J, Lee J, Kweon IS (2018) Cbam: convolutional block attention module, in:3–19

[26]

Xing L, Zhang M, Li Y, Zhang Z, Yin D. Large eddy simulation of the fluctuating wind environment at a bridge site in the mountainous area. Adv Bridge Eng, 2021, 2(1): 23.

[27]

Xu YL, Sun DK, Ko JM, Lin JH. Fully coupled buffeting analysis of tsing ma suspension bridge. J Wind Eng Ind Aerodyn, 2000, 85(1): 97-117.

[28]

Yuanfeng D, Zhengteng D, Hongmei Z, Others (2024) Bridge damage identification based on convolutional autoencoders and extreme gradient boosting trees. J Southeast Univ 40 (3)

[29]

Zhang Z, Li S, Feng H, Zhou X, Xu N, Li H, Laima S, Chen W. Machine learning for bridge wind engineering. Adv Wind Eng, 2024, 1(1): 100002.

[30]

Zhao L, Cui W, Fang G, Cao S, Zhu L, Song L, Ge Y. State-of-the-art review on typhoon wind environments and their effects on long-span bridges. Adv Wind Eng, 2024, 1(1): 100007.

Funding

Key Technologies Research and Development Program(2022YFC3005303)

RIGHTS & PERMISSIONS

The Author(s)

PDF

0

Accesses

0

Citation

Detail

Sections
Recommended

/