A probabilistic machine learning framework of flutter critical wind velocity prediction for cable-stayed bridges based on a calibrated finite element model
Email:
hxnam@utc.edu.vn
Từ khóa:
flutter instability, cable-stayed bridge, critical wind velocity, Gaussian process regression, finite element model updating, machine learning
Tóm tắt
Flutter is a self-excited aeroelastic instability that controls the wind design of long-span cable-stayed bridges. It is usually assessed by wind tunnel tests or costly simulations. This study examines whether a probabilistic machine learning model can give a first estimate of the flutter critical wind velocity, based on flat-plate theory, from preliminary design parameters, for a family of bridges derived from one existing bridge. A finite element model of the Dakrong cable-stayed bridge in Vietnam is updated to match ten of the twelve natural frequencies measured on site (root-mean-square error 4.7%). Three hundred bridge configurations are generated from the updated model by Latin Hypercube Sampling of eleven variables within slenderness limits, and their critical velocity is estimated with the Selberg formula and checked with the Rocard formula. On a test set of 61 configurations, Gaussian process regression with automatic relevance determination, trained only on span, width, depth, mass and inertia, reproduces the Selberg estimate with R2 = 0.92 and a mean absolute percentage error of 6.4%, and 95.1% of the test values fall inside its 95% confidence intervals. These values measure agreement with the formula-based labels, not with the actual flutter speed. The labels assume flat-plate aerodynamics and a single pair of modes, and additional checks suggest that, for this open-girder deck, their uncertainty is larger than the prediction error. The model is therefore intended only for comparing deck alternatives within the sampled family and does not replace a flutter check.Tài liệu tham khảo
[1]. E. Simiu, R. H. Scanlan, Wind Effects on Structures: Fundamentals and Applications to Design, 3rd ed., John Wiley & Sons, New York, 1996.
[2]. R. H. Scanlan, J. J. Tomko, Airfoil and bridge deck flutter derivatives, Journal of the Engineering Mechanics Division, 97 (1971) 1717-1737. https://doi.org/10.1061/JMCEA3.0001526
[3]. A. Larsen, Aerodynamic aspects of the final design of the 1624 m suspension bridge across the Great Belt, Journal of Wind Engineering and Industrial Aerodynamics, 48 (1993) 261-285. https://doi.org/10.1016/0167-6105(93)90141-A
[4]. E. López-Núñez, M. Ogueta-Gutiérrez, O. Gómez-Ortega, R. Manzanares-Bercial, E. Roibás-Millán, S. Franchini, Effect of wind barriers on the aeroelastic instabilities of a hinged-deck cross-section cable-stayed bridge, Engineering Structures, 287 (2023) 116112. https://doi.org/10.1016/j.engstruct.2023.116112
[5]. A. Selberg, Oscillation and aerodynamic stability of suspension bridges, Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series No. 13, Trondheim, 1961.
[6]. Y. Rocard, Instabilité des ponts suspendus dans le vent - expériences sur modèle réduit, National Physical Laboratory Paper No. 10, 1963.
[7]. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter, NACA Report No. 496, National Advisory Committee for Aeronautics, 1935.
[8]. T. Abbas, I. Kavrakov, G. Morgenthal, Methods for flutter stability analysis of long-span bridges: a review, Proceedings of the Institution of Civil Engineers - Bridge Engineering, 170 (2017) 271-310. https://doi.org/10.1680/jbren.15.00039
[9]. F. Rizzo, L. Caracoglia, Artificial neural network model to predict the flutter velocity of suspension bridges, Computers & Structures, 233 (2020) 106236. https://doi.org/10.1016/j.compstruc.2020.106236
[10]. H. X. Nam, V. M. Trung, N. N. Son, N. N. Long, Vibration-based damage detection in cable-stayed bridges using a novel 1D-ConvNeXt-LSTM network, Transport and Communications Science Journal, 77 (2026) 485-499. https://doi.org/10.47869/tcsj.77.4.11
[11]. H. X. Nam, T. N. Hoa, B. T. Thanh, B. P. Loc, V. Q. Tuyen, A. Nguyen, A positional encoding-enhanced Kolmogorov-Arnold convolutional network for structural health monitoring, Structures, 89 (2026) 111970. https://doi.org/10.1016/j.istruc.2026.111970
[12]. N. L. M. Dang, H. X. Nam, V. M. Trung, N. K. N. Bao, Detection of damage in steel truss bridges using a hybrid 1DCNN-BIGRU model and time-series data augmentation techniques, Transport and Communications Science Journal, 76 (2025) 1281-1295 (in Vietnamese). https://doi.org/10.47869/tcsj.76.9.11
[13]. T. Canor, L. Caracoglia, V. Denoël, Application of random eigenvalue analysis to assess bridge flutter probability, Journal of Wind Engineering and Industrial Aerodynamics, 140 (2015) 79-86. https://doi.org/10.1016/j.jweia.2015.02.001
[14]. S. Arangio, F. Bontempi, Structural health monitoring of a cable-stayed bridge with Bayesian neural networks, Structure and Infrastructure Engineering, 11 (2015) 575-587. https://doi.org/10.1080/15732479.2014.951867
[15]. E. Cheynet, FlutterBridge_FD: the coupled flutter velocity of a single-span suspension bridge computed in the frequency domain. https://github.com/ECheynet/FlutterBridge_FD, 2023, (accessed 25/09/2026).
[16]. S. Liu, C. S. Cai, Y. Han, Time-domain simulations of turbulence effects on the aerodynamic flutter of long-span bridges, Advances in Bridge Engineering, 1 (2020) 7. https://doi.org/10.1186/s43251-020-00007-6
[17]. I. Khan, D. Shan, Q. Li, J. He, F. L. Nan, Data interpretation and continuous modal parameter identification of cable stayed bridge, The Open Civil Engineering Journal, 9 (2015) 577-591. https://doi.org/10.2174/1874149501509010577
[18]. H. Tran-Ngoc, S. Khatir, G. De Roeck, T. Bui-Tien, L. Nguyen-Ngoc, M. Abdel Wahab, Model updating for Nam O bridge using particle swarm optimization algorithm and genetic algorithm, Sensors, 18 (2018) 4131. https://doi.org/10.3390/s18124131
[19]. R. Storn, K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11 (1997) 341-359. https://doi.org/10.1023/A:1008202821328
[20]. M. D. McKay, R. J. Beckman, W. J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979) 239-245. https://doi.org/10.1080/00401706.1979.10489755
[21]. C. E. Rasmussen, C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, Cambridge, 2006.
[22]. L. Breiman, Random forests, Machine Learning, 45 (2001) 5-32. https://doi.org/10.1023/A:1010933404324
[23]. T. Chen, C. Guestrin, XGBoost: a scalable tree boosting system, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (San Francisco, 13-17/08/2016), 2016, ACM, 785-794. https://doi.org/10.1145/2939672.2939785
[24]. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, E. Duchesnay, Scikit-learn: machine learning in Python, Journal of Machine Learning Research, 12 (2011) 2825-2830.
[25]. A. Jain, N. P. Jones, R. H. Scanlan, Coupled flutter and buffeting analysis of long-span bridges, Journal of Structural Engineering, 122 (1996) 716-725. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:7(716)
[26]. A. Šarkić, R. Fisch, R. Höffer, K.-U. Bletzinger, Bridge flutter derivatives based on computed, validated pressure fields, Journal of Wind Engineering and Industrial Aerodynamics, 104-106 (2012) 141-151. https://doi.org/10.1016/j.jweia.2012.02.033
[2]. R. H. Scanlan, J. J. Tomko, Airfoil and bridge deck flutter derivatives, Journal of the Engineering Mechanics Division, 97 (1971) 1717-1737. https://doi.org/10.1061/JMCEA3.0001526
[3]. A. Larsen, Aerodynamic aspects of the final design of the 1624 m suspension bridge across the Great Belt, Journal of Wind Engineering and Industrial Aerodynamics, 48 (1993) 261-285. https://doi.org/10.1016/0167-6105(93)90141-A
[4]. E. López-Núñez, M. Ogueta-Gutiérrez, O. Gómez-Ortega, R. Manzanares-Bercial, E. Roibás-Millán, S. Franchini, Effect of wind barriers on the aeroelastic instabilities of a hinged-deck cross-section cable-stayed bridge, Engineering Structures, 287 (2023) 116112. https://doi.org/10.1016/j.engstruct.2023.116112
[5]. A. Selberg, Oscillation and aerodynamic stability of suspension bridges, Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series No. 13, Trondheim, 1961.
[6]. Y. Rocard, Instabilité des ponts suspendus dans le vent - expériences sur modèle réduit, National Physical Laboratory Paper No. 10, 1963.
[7]. T. Theodorsen, General theory of aerodynamic instability and the mechanism of flutter, NACA Report No. 496, National Advisory Committee for Aeronautics, 1935.
[8]. T. Abbas, I. Kavrakov, G. Morgenthal, Methods for flutter stability analysis of long-span bridges: a review, Proceedings of the Institution of Civil Engineers - Bridge Engineering, 170 (2017) 271-310. https://doi.org/10.1680/jbren.15.00039
[9]. F. Rizzo, L. Caracoglia, Artificial neural network model to predict the flutter velocity of suspension bridges, Computers & Structures, 233 (2020) 106236. https://doi.org/10.1016/j.compstruc.2020.106236
[10]. H. X. Nam, V. M. Trung, N. N. Son, N. N. Long, Vibration-based damage detection in cable-stayed bridges using a novel 1D-ConvNeXt-LSTM network, Transport and Communications Science Journal, 77 (2026) 485-499. https://doi.org/10.47869/tcsj.77.4.11
[11]. H. X. Nam, T. N. Hoa, B. T. Thanh, B. P. Loc, V. Q. Tuyen, A. Nguyen, A positional encoding-enhanced Kolmogorov-Arnold convolutional network for structural health monitoring, Structures, 89 (2026) 111970. https://doi.org/10.1016/j.istruc.2026.111970
[12]. N. L. M. Dang, H. X. Nam, V. M. Trung, N. K. N. Bao, Detection of damage in steel truss bridges using a hybrid 1DCNN-BIGRU model and time-series data augmentation techniques, Transport and Communications Science Journal, 76 (2025) 1281-1295 (in Vietnamese). https://doi.org/10.47869/tcsj.76.9.11
[13]. T. Canor, L. Caracoglia, V. Denoël, Application of random eigenvalue analysis to assess bridge flutter probability, Journal of Wind Engineering and Industrial Aerodynamics, 140 (2015) 79-86. https://doi.org/10.1016/j.jweia.2015.02.001
[14]. S. Arangio, F. Bontempi, Structural health monitoring of a cable-stayed bridge with Bayesian neural networks, Structure and Infrastructure Engineering, 11 (2015) 575-587. https://doi.org/10.1080/15732479.2014.951867
[15]. E. Cheynet, FlutterBridge_FD: the coupled flutter velocity of a single-span suspension bridge computed in the frequency domain. https://github.com/ECheynet/FlutterBridge_FD, 2023, (accessed 25/09/2026).
[16]. S. Liu, C. S. Cai, Y. Han, Time-domain simulations of turbulence effects on the aerodynamic flutter of long-span bridges, Advances in Bridge Engineering, 1 (2020) 7. https://doi.org/10.1186/s43251-020-00007-6
[17]. I. Khan, D. Shan, Q. Li, J. He, F. L. Nan, Data interpretation and continuous modal parameter identification of cable stayed bridge, The Open Civil Engineering Journal, 9 (2015) 577-591. https://doi.org/10.2174/1874149501509010577
[18]. H. Tran-Ngoc, S. Khatir, G. De Roeck, T. Bui-Tien, L. Nguyen-Ngoc, M. Abdel Wahab, Model updating for Nam O bridge using particle swarm optimization algorithm and genetic algorithm, Sensors, 18 (2018) 4131. https://doi.org/10.3390/s18124131
[19]. R. Storn, K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11 (1997) 341-359. https://doi.org/10.1023/A:1008202821328
[20]. M. D. McKay, R. J. Beckman, W. J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979) 239-245. https://doi.org/10.1080/00401706.1979.10489755
[21]. C. E. Rasmussen, C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, Cambridge, 2006.
[22]. L. Breiman, Random forests, Machine Learning, 45 (2001) 5-32. https://doi.org/10.1023/A:1010933404324
[23]. T. Chen, C. Guestrin, XGBoost: a scalable tree boosting system, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (San Francisco, 13-17/08/2016), 2016, ACM, 785-794. https://doi.org/10.1145/2939672.2939785
[24]. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, E. Duchesnay, Scikit-learn: machine learning in Python, Journal of Machine Learning Research, 12 (2011) 2825-2830.
[25]. A. Jain, N. P. Jones, R. H. Scanlan, Coupled flutter and buffeting analysis of long-span bridges, Journal of Structural Engineering, 122 (1996) 716-725. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:7(716)
[26]. A. Šarkić, R. Fisch, R. Höffer, K.-U. Bletzinger, Bridge flutter derivatives based on computed, validated pressure fields, Journal of Wind Engineering and Industrial Aerodynamics, 104-106 (2012) 141-151. https://doi.org/10.1016/j.jweia.2012.02.033
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25/09/2026
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02/11/2026
Chấp nhận đăng
09/11/2026
Xuất bản
15/11/2026
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Kiểu trích dẫn
Ho Xuan, N., & Nguyen Ngoc, L. (1794675600). A probabilistic machine learning framework of flutter critical wind velocity prediction for cable-stayed bridges based on a calibrated finite element model. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(9), 1185-1197. https://doi.org/10.47869/tcsj.77.9.5
