Comparative study of data-based and covariance-based methods for flutter derivative identification of a trussed deck suspension bridge model with wind tunnel validation

Abstract

This study presents a comprehensive comparative analysis of two stochastic system identification methods—SSI_data and SSI_cov—for extracting flutter derivatives (FDs) of a trussed deck suspension bridge section under turbulent wind conditions. Numerical simulations and wind tunnel experiments were conducted to evaluate each method's robustness to noise, identification accuracy, and computational efficiency. Results show that while both methods reliably estimate natural frequencies, SSI_data achieves greater precision in damping ratio identification and offers a significant computational advantage—reducing runtime compared to SSI_cov. A detailed signal-to-noise ratio (SNR) analysis reveals that SSI_data excels in vertical mode identification, while SSI_cov is more resilient in estimating torsional damping under low SNR conditions. Experimental validation confirms that the critical flutter wind speeds estimated using both methods under turbulent flow conditions closely match the results observed in wind tunnel tests. These findings provide practical guidance for selecting suitable identification strategies and underscore the potential of SSI methods—particularly SSI_data—for real-time aeroelastic analysis of long-span bridges operating in complex, turbulence-prone wind environments.

Keywords

Flutter derivatives / SSI_cov / SSI_data / Turbulent wind / Wind tunnel / Critical flutter wind speed

References

[1] BarniN, ManniniC. Parametric effects of turbulence on the flutter stability of suspension bridges. J Wind Eng Ind Aerodyn, 2024, 240. 105553

[2] ChenX, KareemA. Wind-induced responses of long-span bridges: advances in flutter and buffeting theories. J Wind Eng Ind Aerodyn, 2020, 204. 104319

[3] ChowdhuryAG, SarkarPP. Identification of flutter and buffeting characteristics of long-span bridges using system identification techniques. Eng Struct, 2003, 25: 1763-1772.

[4] D’Antuono P, Weijtjens W, Devriendt C, Rizzo P, Milazzo A (2023) European Workshop on Structural Health Monitoring EWSHM 2022 - Volume 1 On the Minimum Required Sampling Frequency for Reliable Fatigue Lifetime Estimation in Structural Health Monitoring. How Much is Enough? Springer International Publishing Cham 133–42. https://doi.org/10.1007/978-3-031-07254-3_14

[5] GeY, WenZ, FangG, LouW, XuH, WangG. Explicit solution framework and new insights of 3-DOF linear flutter considering various frequency relationships. Eng Struct, 2024, 307. 117883

[6] GuM, ZhangR, XiangH. Identification of flutter derivatives of bridge decks. J Wind Eng Ind Aerodyn, 2000, 84: 151-162.

[7] HaanFL. Experimental study of the wind-induced vibrations of suspension bridges. J Wind Eng Ind Aerodyn, 2000, 88: 69-84.

[8] Han Y, Li K, Cai CS (2020) Study of central buckle effects on flutter of long-span suspension bridges. Wind and Structures 31:403–417. https://doi.org/10.12989/WAS.2020.31.5.403

[9] Honshu-Shikoku Bridge Authority (HSBA) (1992) Wind tunnel testing manual for long-span bridges. Internal technical document, Kobe, Japan (in Japanese)

[10] HuP, HanY, CaiCS, ChengW. Wind characteristics and flutter performance of a long-span suspension bridge located in a deep-cutting gorge. Eng Struct, 2021, 233. 111841

[11] Hu P, Yuan B, Han Y, Li K, Cai CS, Chen X (2024) Study on nonlinear flutter characteristics of single-box section and twin-box section as a three-degree-of-freedom system. International Journal of Structural Stability and Dynamics 24(5). https://doi.org/10.1142/S0219455425502475

[12] JakobsenJB, Hjorth-HansenE. Determination of the aerodynamic derivatives by a system identification method. J Wind Eng Ind Aerodyn, 1995, 57: 295-305.

[13] Juang JN, Pappa RS (1985) An eigensystem realization algorithm (ERA) for modal parameter identification and model reduction. J Guid Control Dyn 299–318. https://doi.org/10.2514/3.20031

[14] LamHT, KatsuchiH, YamadaH. Investigation of turbulence effects on the aeroelastic properties of a truss bridge deck section. Engineering, 2017, 3: 845-853.

[15] LiM, SunY, LeiY, LiaoH, LiM. Experimental study of the nonlinear torsional flutter of a long-span suspension bridge with a double-deck truss girder. Int J Struct Stab Dyn, 2021, 212150102.

[16] LiS, et al.. Experimental and numerical investigation of aerodynamic performance of suspension bridges under yawed wind. J Wind Eng Ind Aerodyn, 2021, 215. 104655

[17] LiK, HanY, CaiCS, SongJ, HuP, QiuZ. Three-dimensional nonlinear flutter analysis of long-span bridges by multimode and full-mode approaches. J Wind Eng Ind Aerodyn, 2023, 242. 105554

[18] LiK, HanY, CaiCS, SongJ, HuP. Study on the influence of structural parameters and 3D effects on nonlinear bridge flutter using amplitude-dependent flutter derivatives. J Fluids Struct, 2024, 125. 104085

[19] MatsumotoM, et al.. Aerodynamic characteristics of bridge decks and flutter analysis. J Wind Eng Ind Aerodyn, 1999, 83: 133-146.

[20] PeetersB, De RoeckG. Reference-based stochastic subspace identification for output-only modal analysis. Mech Syst Signal Process, 1999, 13: 855-878.

[21] ReyndersE, De RoeckG, DegrandeG. Operational modal analysis using the stochastic subspace identification method: a practical guideline. Eng Struct, 2008, 31: 1507-1516.

[22] ReyndersE, PintelonR, De RoeckG. Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mech Syst Signal Process, 2008, 22: 948-969.

[23] SarkarPP, et al.. System identification-based approach for the determination of flutter derivatives of long-span bridges. J Wind Eng Ind Aerodyn, 2009, 97: 147-158.

[24] ScanlanRH. The action of flexible bridges under wind: flutter theory. J Sound Vib, 1978, 60: 187-199.

[25] ShokraviH, et al.. Output-only modal identification of structures under non-stationary excitations: a comprehensive review. Mech Syst Signal Process, 2020, 139. 106625

[26] SongJ, LiK, HanY, WangX, LiC. Investigation on nonlinear flutter modes competition of a long-span suspension bridge based on full-bridge aeroelastic model tests. Eng Struct, 2025, 322. 119073

[27] Theodorsen T (1935) General theory of aerodynamic instability and the mechanism of flutter. NACA Report 496. https://ntrs.nasa.gov/citations/19930091840

[28] WuB, WangQ, LiaoH, MeiH. Hysteresis response of nonlinear flutter of a truss girder: experimental investigations and theoretical predictions. Comput Struct, 2020, 238. 106267

[29] WuY, ChenX, WangY. Identification of linear and nonlinear flutter derivatives of bridge decks by unscented Kalman filter approach from free vibration or stochastic buffeting response. J Wind Eng Ind Aerodyn, 2021, 214. 104650

[30] WuB, ZhouQ, WangY, ShenH, LiaoH, LiuJ. Post critical characteristics of a side-box steel concrete composite girder. J Wind Eng Ind Aerodyn, 2023, 240. 105513

[31] YangY, ZhouR, GeY, ZhangL. Flutter characteristics of twin-box girder bridges with vertical central stabilizers. Eng Struct, 2017, 133: 33-48.

[32] YingX, XuF, ZhangM, ZhangZ. Numerical explorations of the limit cycle flutter characteristics of a bridge deck. J Wind Eng Ind Aerodyn, 2017, 169: 30-38.

[33] ZhangM, XuF, ZhangZ, YingX. Energy budget analysis and engineering modeling of post-flutter limit cycle oscillation of a bridge deck. J Wind Eng Ind Aerodyn, 2019, 188: 410-420.

[34] ZhangZ, WangZ, ZengJ, ZhuL, GeY. Experimental investigation of post-flutter properties of a suspension bridge with a π-shaped deck section. J Fluids Struct, 2022, 112. 103592

[35] ZhuL, GaoG, ZhuQ. Recent advances, future application, and challenges in nonlinear flutter theory of long-span bridges. J Wind Eng Ind Aerodyn, 2020, 206. 104307

[36] ZhuJ, YangY, XuH, ZhangJ, SuR, GeY. An investigation into the modal effect mechanism of multi-mode coupled flutter with modality-driven method. Eng Struct, 2023, 296. 116925

Funding

Trường Đại học Bách khoa, Đại học Đà Nẵng(T2024-02-45)

RIGHTS & PERMISSIONS

The Author(s)