In this paper, Forgetting Factor Recursive Least Squares (FF-LS) method is proposed to identify time-varying vortex-induced force coefficients of the flexible riser under multi-frequency VIV. FF-LS method introduces the forgetting factor, which gives more weight to the data closer to the present. This modification improves the method’s sensitivity to the time-varying parameters, and enables it to identify the time-varying parameters under multi-frequency coupling. In this paper, the mass-spring-dashpot model is used to verify FF-LS method’s ability to accurately identify time-varying parameters under multi-frequency coupling. Then, this methodology is used to identify the vortex-induced force coefficients of flexible riser at the basic frequency when vortex-induced vibration occurs. Identified coefficients are consistent with the result obtained from Least Squares method, which indicates that the proposed FF-LS method retrogrades to the Least Squares method when VIV response and the vortex-induced force contains only one single frequency. Finally, this methodology is used to identify the time-varying vortex-induced force coefficients of a flexible riser under VIV considering the coupling effect between the basic frequency and high frequency. The vortex-induced force reconstructed from identified time-varying coefficients is consistent with real vortex-induced force, which verifies the validity and applicability of this methodology in identifying time-varying vortex-induced force coefficients considering multi-frequency coupling effect. The results show that when the flexible riser is subjected to multi-frequency VIV, its vortex-induced force coefficients change periodically, the time-averaged values of these time-varying coefficients are different from the vortex-induced force coefficients at the basic frequency, which results from the coupling effect between the basic frequency and high frequency. Linear superposition of vortex-induced force coefficient at basic frequency and high frequency are different from time-varying coefficients considering coupling effect of multi-frequency and cannot reconstruct vortex-induced force correctly.

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