Time-varying hydrodynamics of a flexible riser under multi-frequency vortex-induced vibrations

This paper proposes the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible riser under multi-frequency vortex-induced vibrations (VIV). Differing from the traditional least squares method used to identify hydrodynamics, with equal weights on all sampled data, this method introduces a forgetting factor to give higher weight to data closer to the present moment. FF-LS allows the possibility of handling the time-varying parameters. By following this procedure for all sampled data of a flexible riser undergoing multi-frequency VIV, the corresponding time-varying hydrodynamics in the Cross-Flow (CF) direction will be obtained considering multi-frequency coupling. The results show that, under multi-frequency coupling, vortex-induced force coefficients of flexible risers change periodically and differ from coefficients at the basic frequency usually used in VIV prediction. This difference is a result of the coupling effect between the basic frequency and high frequency. Time-varying coefficients considering multi-frequency coupling contain steady components and vibration components whose frequencies are the sum of coupling frequencies and the difference of coupling frequencies. To show the advantages of time-varying hydrodynamics, we compare forces reconstructed from different vortex-induced force coefficients, assuming vortex-induced force obtained from the inverse analysis is the real force. The results show that time-varying vortex-induced force coefficients considering a coupling effect between multiple frequencies can accurately reconstruct vortex-induced force, while the sum of vortex-induced force coefficients under multiple frequencies will produce the cross-term that overestimates the vortex-induced force.