Modeling of vortex-induced vibration system based on sparse identification of nonlinear dynamics

doi:10.3785/j.issn.1008-973X.2025.02.018

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (2): 402-412 DOI: 10.3785/j.issn.1008-973X.2025.02.018

Modeling of vortex-induced vibration system based on sparse identification of nonlinear dynamics

Tingwei JI(

),Liang WANG,Fangfang XIE*(

),Xinshuai ZHANG,Changdong ZHENG

School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China

Download:

HTML

PDF(2443KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

Two-dimensional and three-dimensional cylindrical vortex-induced vibration (VIV) systems were analyzed, and the nonlinear dynamics sparse identification (SINDy) method was employed to identify the structural response model and wake oscillation model of the VIV system. The models were validated and analyzed, leading to the development of a fluid-structure interaction model for the VIV system. Then the prediction of displacement and velocity responses of the cylindrical VIV under varying reduced velocities was realized. Results showed that the structural response model of a 2D VIV system with added damping was identified by using the SINDy algorithm. The model exhibits a clear pattern with the dynamic characteristics of the fluid-structure interaction system. The added damping remains nearly constant as the reduced velocity increases, and the dimensionless maximum structural amplitude stays at a high level when the VIV system is within the lock-in region. The added damping decreases linearly with increasing reduced velocity, and the dimensionless amplitude of the structure remains low in the non-lock-in region. The fluid-structure interaction model of the 2D VIV system and the structural response model of the 3D VIV system identified by the SINDy method demonstrate good predictive capabilities. The 2D VIV system model shows some generalization ability. The model predictions effectively capture the motion characteristics of the original systems, with relative errors in the predicted structural displacement response of less than 6%, relative errors in the velocity response of less than 5%, and relative errors in the 3D VIV system’s displacement and velocity responses of less than 4%.

Key words： sparse identification vortex-induced vibration fluid-structure interaction reduced-order model nonlinear dynamics

Received: 13 December 2023 Published: 11 February 2025

CLC:

O 357

Corresponding Authors: Fangfang XIE E-mail: zjjtw@zju.edu.cn;fangfang_xie@zju.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Tingwei JI
	Liang WANG
	Fangfang XIE
	Xinshuai ZHANG
	Changdong ZHENG

Cite this article:

Tingwei JI,Liang WANG,Fangfang XIE,Xinshuai ZHANG,Changdong ZHENG. Modeling of vortex-induced vibration system based on sparse identification of nonlinear dynamics. Journal of ZheJiang University (Engineering Science), 2025, 59(2): 402-412.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.02.018 OR https://www.zjujournals.com/eng/Y2025/V59/I2/402

基于非线性动力学稀疏辨识的涡致振动系统建模

以二维和三维圆柱涡致振动(VIV)系统为研究对象，通过非线性动力学稀疏辨识(SINDy)的方法，识别VIV系统的结构响应模型和尾流振荡模型. 对模型进行验证和分析, 得到VIV系统的流固耦合模型，实现不同缩减速度下圆柱VIV位移和速度响应的预测. 结果表明，采用SINDy算法，识别了带有附加阻尼的二维VIV系统的结构响应模型. 该模型与流固耦合系统的动力学特征表现出明显的规律：当涡致振动系统处于锁定(lock-in)区域时，附加阻尼随缩减速度变大而基本保持不变，结构的无量纲最大振幅保持在较高水平；当涡致振动系统处于非锁定区域时，附加阻尼随缩减速度变大而呈现线性下降的特征，结构的无量纲振幅保持在较低水平. 基于SINDy方法识别的二维VIV系统流固耦合模型和三维VIV系统结构响应模型有较好的预测能力，其中二维VIV系统流固耦合模型有一定的泛化能力. 模型预测值能够表征原系统的运动特征，对二维VIV系统结构位移响应预测的相对误差小于6%，结构速度响应预测的相对误差小于5%，对三维VIV系统结构位移和速度响应预测的相对误差小于4%.

关键词： 稀疏辨识, 涡致振动, 流固耦合, 降阶模型, 非线性动力学

Fig.1 Schematic diagram of two-dimensional cylinder vortex-induced vibration system

Fig.2 Schematic diagram of x-y plane computational domain and grid　　　　　

Fig.3 Comparison between numerical simulation result of this article and literature result

Fig.4 Prediction error of two models for displacement and velocity

Fig.5 Added damping and dimensionless maximum amplitude versus reduced velocity

Fig.6 Peak frequency curve of vibration spectrum of structure at different reduced velocity

Fig.7 Structural response model prediction with additional damping

Fig.8 Change of wake oscillation model coefficient with reduced velocity

Tab.1 Value table of coefficient of fluid-structure interaction model in locked area

Fig.9 Results of displacement, velocity and dimensionless wake variable response of fluid-structure interaction model predicting system

Fig.10 Relative error in prediction of system displacement, velocity and dimensionless wake variable response by using fluid-structure interaction model

Tab.2 Verification of model generalization ability

Fig.11 Verification of generalization ability of fluid-structure interaction model

Fig.12 Numerical simulation example result of three-dimensional vortex-induced vibration system

Fig.13 Prediction value and relative error of unsteady model

Fig.14 Prediction value and relative error of steady model


[1]	EHAB B, MEHDI G, SAMIR E Flutter control and mitigation of limit cycle oscillations in aircraft wings using distributed vibration absorbers[J]. Nonlinear Dynamics, 2021, 106 (3): 1975- 2003

[2]	MENG X H, WANG Z C, FAN D X, et al A fast multi-fidelity method with uncertainty quantification for complex data correlations: application to vortex-induced vibrations of marine risers[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 386 (3): 114212

[3]	ZHU H J, TANG T, ZHOU T M, et al High performance energy harvesting from flow-induced vibrations in trapezoidal oscillators[J]. Energy, 2021, 236 (4): 121484

[4]	刘宗杰, 祝志文, 陈魏, 等跨长江特大桥拉索涡激振动与风特性观测[J]. 铁道科学与工程学报, 2020, 17 (7): 1760- 1768 LIU Zongjie, ZHU Zhiwen, CHEN Wei, et al Observation of vortex-induced vibration and wind characteristics of cables across the Yangtze River bridge[J]. Journal of Railway Science and Engineering, 2020, 17 (7): 1760- 1768

[5]	LIU G J, LI H Y, QIU Z Z, et al A comprehensive numerical analysis of cross-flow vortex-induced vibrations for top tension risers under different flows[J]. Physics of Fluids, 2020, 32 (2): 027102 doi: 10.1063/1.5139545

[6]	BISHOP R, HASSAN A Y The lift and drag forces on a circular cylinder oscillating in a flowing fluid[J]. Proceedings of the Royal Society A, 1964, 277 (1368): 32- 50

[7]	LISBOA M, CATALDO J, GONZÁLEZ A Noise annoyance due to wind flow interaction with a building's facade[J]. Open Journal of Acoustics, 2015, 5 (1): 1- 10 doi: 10.4236/oja.2015.51001

[8]	SARPKAYA T A critical review of the intrinsic nature of vortex-induced vibrations[J]. Journal of Fluids and Structures, 2004, 19 (4): 389- 447 doi: 10.1016/j.jfluidstructs.2004.02.005

[9]	BENAROYA H, WEI T, KUCHNICKI S, et al Extended Hamilton’s principle for fluid-structure interaction[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2003, 217 (2): 153- 170 doi: 10.1243/146441903321898647

[10]	NEWMAN D, KARNIADAKIS G E Simulations of flow over a flexible cable: a comparison of forced and flow-induced vibration[J]. Journal of Fluids and Structures, 1996, 10 (5): 439- 453 doi: 10.1006/jfls.1996.0030

[11]	EVANGELINOS C, KARNIADAKIS G E Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations[J]. Journal of Fluid Mechanics, 1999, 400: 91- 124 doi: 10.1017/S0022112099006606

[12]	BAO Y, PALACIOS R, GRAHAM M, et al Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders[J]. Journal of Computational Physics, 2016, 321 (2): 1079- 1097

[13]	张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望[J]. 航空学报, 2021, 42(4): 524689. ZHANG Weiwei, KOU Jiaqing, LIU Yilang. Prospect of artificial intelligence empowered fluid mechanics [J]. Acta Aeronautica et Astronautica Sinica , 2021, 42(4): 524689.

[14]	BERKOOZ G, HOLMES P, LUMLEY J The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual Review of Fluid Mechanics, 2003, 25 (1): 539- 575

[15]	ZANARDI I, VENTURI S, PANESI M Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows[J]. Scientific Reports, 2023, 13 (1): 15497 doi: 10.1038/s41598-023-41039-y

[16]	ISERTE S, GONZÁLEZ B A, BARREDA P, et al A study on the performance of distributed training of data-driven CFD simulations[J]. The International Journal of High Performance Computing Applications, 2023, 37 (5): 503- 515

[17]	JAEYEONG L, SUNJOONG K, HO-KYUNG K Using supervised learning techniques to automatically classify vortex-induced vibration in long-span bridges[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2022, 221 (11): 104904

[18]	WILLCOX K, PERAIRE J Balanced model reduction via the proper orthogonal decomposition[J]. American Institute of Aeronautics and Astronautics Journal, 2002, 40 (11): 2323- 2330 doi: 10.2514/2.1570

[19]	ROWLEY C W, COLONIUS T, MURRAY R M Model reduction for compressible flows using POD and Galerkin projection[J]. Physica D: Nonlinear Phenomena, 2004, 189 (2): 115- 129

[20]	QIU R D, HUANG R F, WANG Y W, et al Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil[J]. Theoretical and Applied Mechanics Letters, 2020, 10 (5): 327- 332

[21]	洪泽宇, 董国朝, 韩艳, 等基于DMD方法的矩形断面涡振模态分析[J]. 动力学与控制学报, 2023, 21 (4): 48- 58 HONG Zeyu, DONG Guochao, HAN Yan, et al Modal analysis of vortex-induced vibration in rectangular section based on DMD method[J]. Journal of Dynamics and Control, 2023, 21 (4): 48- 58

[22]	ZHANG X S, JI T W, XIE F F, et al Unsteady flow prediction from sparse measurements by compressed sensing reduced order modeling[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 393 (1): 114800

[23]	MARZOCA P, SILVA W A, LIBRESCU L Nonlinear open-/closed-loop aeroelastic analysis of airfoils via Volterra series[J]. American Institute of Aeronautics and Astronautics Journal, 2004, 42 (4): 673- 686 doi: 10.2514/1.9552

[24]	OBEID S, AHMADI G, JHA R NARMAX identification based closed-loop control of flow separation over NACA 0015 airfoil[J]. Fluids, 2020, 5 (3): 100 doi: 10.3390/fluids5030100

[25]	YAO W, JAIMAN R K Model reduction and mechanism for the vortex-induced vibrations of bluff bodies[J]. Journal of Fluid Mechanics, 2017, 827 (1): 357- 393

[26]	EIVAZI H, VEISI H, NADERI M H, et al Deep neural networks for nonlinear model order reduction of unsteady flows[J]. Physics of Fluids, 2020, 32 (10): 105104 doi: 10.1063/5.0020526

[27]	BRUNTON S L, PROCTOR J L, KUTZ J N Discovering governing equations from data by sparse identification of nonlinear dynamical systems[J]. Proceedings of the National Academy of Sciences of the United States of America, 2016, 113 (15): 3932- 3937

[28]	ZHANG X S, JI T W, XIE F F, et al Data-driven nonlinear reduced-order modeling of unsteady fluid–structure interactions[J]. Physics of Fluids, 2022, 34 (5): 053608 doi: 10.1063/5.0090394

[29]	SANTOSA F, SYMES W W Linear inversion of band-limited reflection seismograms[J]. SIAM Journal on Scientific and Statistical Computing, 1986, 7 (4): 1307- 1330 doi: 10.1137/0907087

[30]	CANTWELL C D, MOXEY D, COMERFORD A, et al Nektar++: an open-source spectral/hp element framework[J]. Computer Physics Communications, 2015, 192 (3): 205- 219

[31]	倪问池. 低质量阻尼比圆柱涡激振动分岔特性数值模拟研究[D]. 哈尔滨: 哈尔滨工程大学, 2018. NI Wenchi. Numerical research on bifurcation characteristics for VIV of low mass damping ratio cylinder [D]. Harbin: Harbin Engineering University, 2018.

[32]	邹琳, 王家辉, 王程, 等基于速度和位移反馈的圆柱涡激振动主动控制研究[J]. 力学学报, 2023, 55 (9): 1834- 1846 ZOU Lin, WANG Jiahui, WANG Cheng, et al Active control of vortex-induced vibration of cylinder based on velocity and displacement feedback[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55 (9): 1834- 1846 doi: 10.6052/0459-1879-23-183

[33]	FACCHINETTI M L, LANGRE E D, BIOLLEY F Coupling of structure and wake oscillators in vortex-induced vibrations[J]. Journal of Fluids and Structures, 2004, 19 (2): 123- 140

[34]	NEWMAN D J, KARNIADAKIS G E. A direct numerical simulation study of flow past a freely vibrating cable [J]. Journal of Fluid Mechanics . 1997, 344: 95-136.

[35]	ZHENG C D, XIE F F, JI T W, et al Data-efficient deep reinforcement learning with expert demonstration for active flow control[J]. Physics of Fluids, 2022, 34 (11): 113603 doi: 10.1063/5.0120285

[36]	WILLIAMSON C H K, GOVARDHAN R Vortex-induced vibrations[J]. Annual Review of Fluid Mechanics, 2004, 36 (1): 413- 455 doi: 10.1146/annurev.fluid.36.050802.122128

[1]	Ya-xing YIN,Tong WANG,Cheng-yan WANG,Yan-kang ZHANG,Shi-cheng XU,Da-peng TAN. Mixing process modeling and flow-induced vibration characteristics based on lattice Boltzmann method[J]. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2217-2226.

[2]	Xia-lin LIU,Sheng-bin ZHANG,Quan CHEN,Heng SHU,Shang-ge LIU. Code development and verification for weak coupling of seepage-stress based on TOUGH2 and FLAC3D[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1485-1494.

[3]	Ke-lai YU,Zhen-jun YANG,Xin ZHANG,Guo-hua LIU,Hui LI. Hydraulic fracturing modeling of quasi-brittle materials based on pore pressure cohesive interface elements[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(11): 2151-2160.

[4]	Shuo HUANG,Shuang-qiang WANG,Peng WANG,Gui-yong ZHANG. Comparative study of application of smoothed point interpolation method in fluid-structure interactions[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1645-1654.

[5]	LI Xiao-chao, XU Wei, ZHOU Xi-lin, ZHAO Li-ping. Experimental study on hydrodynamic and power characteristics of vortex-induced vibration based power generator[J]. Journal of ZheJiang University (Engineering Science), 2018, 52(7): 1370-1375.

[6]	LI Meng-xuan, WU Jia, ZHENG Shui-ying, YING Guang-yao, LIU Shu-lian. Stability of bearing-rotor system with different bearing structures[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(11): 2239-2248.

[7]	WANG Lei, LIANG Shu-guo, ZOU Liang-hao, TANG Huai-qiang, WANG Shu-liang. Investigation on VIV system vibration frequency of super high-rise building[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(5): 805-812.

[8]	LI Qiang, LIU Shu-lian , YING Guang-yao, ZHENG Shui-ying. Numerical simulation for drop impact of PET bottle considering fluid-structure interaction[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(6): 980-986.

[9]	XIANG Yi-qiang, CHAO Chun-feng. Vortex-induced dynamic response for combined action of tube and cable of submerged floating tunnel[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(3): 409-415.

[10]	LI Qiang, LIU Shu-lian, YU Gui-chang, PAN Xiao-hong, ZHENG Shui-ying. Lubrication and stability analysis of nonlinear rotor-bearing system[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(10): 1729-1736.

[11]	GUO Zeng-wei, GE Yao-jun, LU An-ping. Parameter optimization of TMD for vortex-induced vibration control[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(1): 8-13.

Viewed

Full text

Abstract

Cited

Shared

Discussed