多频涡激振动状态下柔性立管的时变水动力特性识别
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摘要
提出了遗忘因子最小二乘法识别柔性立管发生多频涡激振动下的时变涡激力系数。该算法在最小二乘法基础上,引入遗忘因子,其给予更接近当前时刻的数据更大的权重。这一修正提高了该算法对时变参数的敏感度,使其能够识别系统的时变参数。首先使用质量-弹簧-阻尼器模型验证了遗忘因子最小二乘法可准确识别系统的时变参数。随后使用该方法识别了柔性立管发生多频涡激振动时横流向的时变涡激力系数。结果显示柔性立管发生多频涡激振动时,其涡激力系数会周期性变化,其时间平均值亦不同于基频下的涡激力系数,这是基频与高频耦合作用的结果。根据识别的时变涡激力系数进行反演重构得到的涡激力与真实涡激力相吻合,验证了该方法识别多频耦合下的时变涡激力系数可以准确重构涡激力载荷。
Here,the forgetting factor least squares( FF-LS) method was proposed for identification of time-varying vortex-induced force coefficients of a flexible riser under multi-frequency vortex-induced vibrations( VIVs). This method introduced a forgetting factor to give a greater weight to the data closer to the present time instant. This modification improved the sensitivity of the algorithm to time varying parameters to make it be able to recognize a system's time-varying parameters. Here,a mass-spring-damping model was used to verify the FF-LS algorithm's ability to identify a system's time-varying parameters accurately. Then,the FF-LS algorithm was used to identify time-varying vortex-induced force coefficients in cross-flow( CF) direction of a flexible riser under multi-frequency VIVs. The results showed that under multi-frequency VIVs,vortex-induced force coefficients of the flexible riser change periodically,their time mean values are different from the riser's vortex-induced force coefficients under the fundamental frequency VIVs,this is due to coupling effect between fundamental frequency VIV and higher frequencies VIV; the vortex-induced force the reconstructed using identified time-varying vortex-induced force coefficients agrees well with the actual vortex-induced force to verify the time-varying vortex-induced force coefficients under multi-frequency coupling identified by the FF-LS algorithm being able to reconstruct vortex-induced force correctly.
Here,the forgetting factor least squares( FF-LS) method was proposed for identification of time-varying vortex-induced force coefficients of a flexible riser under multi-frequency vortex-induced vibrations( VIVs). This method introduced a forgetting factor to give a greater weight to the data closer to the present time instant. This modification improved the sensitivity of the algorithm to time varying parameters to make it be able to recognize a system's time-varying parameters. Here,a mass-spring-damping model was used to verify the FF-LS algorithm's ability to identify a system's time-varying parameters accurately. Then,the FF-LS algorithm was used to identify time-varying vortex-induced force coefficients in cross-flow( CF) direction of a flexible riser under multi-frequency VIVs. The results showed that under multi-frequency VIVs,vortex-induced force coefficients of the flexible riser change periodically,their time mean values are different from the riser's vortex-induced force coefficients under the fundamental frequency VIVs,this is due to coupling effect between fundamental frequency VIV and higher frequencies VIV; the vortex-induced force the reconstructed using identified time-varying vortex-induced force coefficients agrees well with the actual vortex-induced force to verify the time-varying vortex-induced force coefficients under multi-frequency coupling identified by the FF-LS algorithm being able to reconstruct vortex-induced force correctly.
引文
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[11]王俊高,付世晓,许玉旺,等.正弦振荡来流下柔性立管涡激振动发展过程[J].力学学报,2014,46(2):173-182.WANG Jungao,FU Shixiao,XU Yuwang,et al.VIVdeveloping process of a flexible under oscillatory flow[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):173-182.
[12]MARCOLLO H,HINWOOD J B.On shear flow single mode lock-in with both cross-flow and in-line lock-in mechanisms[J].Journal of Fluids and Structures,2006,22(2):197-211.
[13]SUMER B M,FREDSE J.Hydrodynamics around cylindrical structures[J].Coastal Engineering,2006,33(33):69.
[14]WU J,LIE H,LARSEN C M,et al.Vortex-induced vibration of a flexible cylinder:interaction of the in-line and cross-flow responses[J].Journal of Fluids&Structures,2016,63:238-258.
[15]SONG L,FU S,CAO J,et al.An investigation into the hydrodynamics of a flexible riser undergoing vortex-induced vibration[J].Journal of Fluids&Structures,2016,63:325-50.
[16]VANDIVER J K,JAISWAL V,JHINGRAN V.Insights on vortex-induced,traveling waves on long risers[J].Journal of Fluids and Structures.2009,25(4):641-653.
[17]LI L,FU S,YANG J,et al.Experimental investigation on vortex-induced vibration of risers with staggered buoyancy[C].American Society of Mechanical Engineers,2011.
[18]DING F,CHEN T.Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data[J].Circuits&Systems I Regular Papers IEEE Transactions on,2005,52(3):555-566.
[19]PALEOLOGU C,BENESTY J,CIOCHINA S.A robust variable forgetting factor recursive least-squares algorithm for system identification[J].IEEE Signal Processing Letters,2008,15:597-600.
[20]CHAVENT G.Identification of distributed parameter systems:about the output least square method,its implementation and identifiability[J].IFAC Proceedings Volumes,1979,12(8):85-97.
[21]LIE H,KAASEN K E.Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow[J].Journal of Fluids&Structures,2006,22(22):557-575.
[22]LIU C,FU S,ZHANG M,et al.Time-varying hydrodynamics of a flexible riser under multi-frequency vortexinduced vibrations[J].Journal of Fluids and Structures,2018,80:217-244.
[2]LARSEN C M,YTTERVIK R,ARONSEN K.Calculation of in-Line vortex induced vibrations of free spanning pipelines[C]∥2007 26th International Conference on Offshore Mechanics and Arctic Engineering.2007.
[3]范杰利,黄维平.细长立管两向自由度涡激振动数值研究[J].振动与冲击,2012,31(24):65-68.FAN Jieli,HUANG Weiping.The numerical research of twodegrees-of-freedom vortex-induced vibrations of long risers[J].Journal of Vibration and Shock,2012,31(24):65-68.
[4]唐友刚,樊娟娟,张杰,等.高雷诺数下圆柱顺流向和横向涡激振动分析[J].振动与冲击,2013,32(13):88-92.TANG Yougang,FAN Juanjuan,ZHANG Jie,et al.Analysis of in-line and transverse vortex-induced vibration for a circular cylinder at high Reynolds number[J].Journal of Vibration and Shock,2013,32(13):88-92.
[5]JAUVTIS N,WILLIAMSON C.The effect of two degrees of freedom on vortex-induced vibration at low mass and damping[J].Journal of Fluid Mechanics,2004,509:23-62.
[6]DAHL J J M.Vortex-induced vibration of a circular cylinder with combined in-line and cross-flow motion[D].Woods Hole,MA:Massachusetts Institute of Technology,2008.
[7]高云,任铁,付世晓,等.柔性立管涡激振动响应特性试验研究[J].振动与冲击,2015,34(17):6-11.GAO Yun,REN Tie,FU Shixiao,et al.Experimental study on response characteristics of VIV of a flexible riser[J].Journal of Vibration and Shock,2015,34(17):6-11.
[8]饶志标,付世晓,杨建民.钢悬链线的涡激振动分析[J].船舶力学,2011,15(3):245-258.RAO Zhibiao,FU Shixiao,YANG Jianmin.Vortex-induced vibration analysis of steel catenary riser[J].Journal of Ship Mechanics,2011,15(3):245-258.
[9]宋磊建,付世晓,任铁,等.均匀流下柔性立管涡激振动响应及涡激力载荷特性研究[J].振动与冲击,2017,36(22):14-21.SONG Leijian,FU Shixiao,REN Tie,et al.Structural responses and vortex-induced force of flexible risers undergoing vortex-induced vibration in uniform flow[J].Journal of Vibration and Shock,2017,36(22):14-21.
[10]王俊高,付世晓,许玉旺,等.振荡来流下柔性立管涡激振动“分时特性”试验研究[J].振动与冲击,2014,33(21):1-7.WANG Jungao,FU Shixiao,XU Yuwang,et al.Experimental investigation on“time sharing”of vortexinduced vibration of a flexible cylinder in oscillatory flow[J].Journal of Vibration and Shock,2014,33(21):1-7.
[11]王俊高,付世晓,许玉旺,等.正弦振荡来流下柔性立管涡激振动发展过程[J].力学学报,2014,46(2):173-182.WANG Jungao,FU Shixiao,XU Yuwang,et al.VIVdeveloping process of a flexible under oscillatory flow[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):173-182.
[12]MARCOLLO H,HINWOOD J B.On shear flow single mode lock-in with both cross-flow and in-line lock-in mechanisms[J].Journal of Fluids and Structures,2006,22(2):197-211.
[13]SUMER B M,FREDSE J.Hydrodynamics around cylindrical structures[J].Coastal Engineering,2006,33(33):69.
[14]WU J,LIE H,LARSEN C M,et al.Vortex-induced vibration of a flexible cylinder:interaction of the in-line and cross-flow responses[J].Journal of Fluids&Structures,2016,63:238-258.
[15]SONG L,FU S,CAO J,et al.An investigation into the hydrodynamics of a flexible riser undergoing vortex-induced vibration[J].Journal of Fluids&Structures,2016,63:325-50.
[16]VANDIVER J K,JAISWAL V,JHINGRAN V.Insights on vortex-induced,traveling waves on long risers[J].Journal of Fluids and Structures.2009,25(4):641-653.
[17]LI L,FU S,YANG J,et al.Experimental investigation on vortex-induced vibration of risers with staggered buoyancy[C].American Society of Mechanical Engineers,2011.
[18]DING F,CHEN T.Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data[J].Circuits&Systems I Regular Papers IEEE Transactions on,2005,52(3):555-566.
[19]PALEOLOGU C,BENESTY J,CIOCHINA S.A robust variable forgetting factor recursive least-squares algorithm for system identification[J].IEEE Signal Processing Letters,2008,15:597-600.
[20]CHAVENT G.Identification of distributed parameter systems:about the output least square method,its implementation and identifiability[J].IFAC Proceedings Volumes,1979,12(8):85-97.
[21]LIE H,KAASEN K E.Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow[J].Journal of Fluids&Structures,2006,22(22):557-575.
[22]LIU C,FU S,ZHANG M,et al.Time-varying hydrodynamics of a flexible riser under multi-frequency vortexinduced vibrations[J].Journal of Fluids and Structures,2018,80:217-244.