## 1 Introduction
Conversely, based on the idea of inverse analysis, if the response of the structure is known, the external forces causing this response can be obtained by inverting the response of the structure with the finite element method. Based on this idea, [PERSON] [6] obtained the hydrodynamic forces acting on the vertically tensioned pipe model under shear flow in the CF and IF directions by using the strain information measured in the experiment and combining the pipe finite element equations. Based on the state vector space equations of pipe finite element, [PERSON] [7] used the Kalman filtering and recursive least-squares method to remove the noise of the experimental measurement signals and analyzed the hydrodynamic forces in the CF direction of the riser axial distribution under shear flow. [PERSON] [7] inversed the transverse vortex-induced force characteristics of the flexible riser under shear flow and uniform flow through the further application of the inverse analysis method based on the optimal control theory. This analysis method is to find forces which can cause the structure to produce the response closest to the actual response on the premise of meeting the governing equations for dynamic response at all times. Because this method will not cause time delays when constructing hydrodynamic force, it is superior to the hydrodynamic analysis method based on the state vector space equations of pipe finite element. [PERSON] [8] applied bandwidth filtering and the modal superposition method to reconstruct the single-frequency VIV response of a flexible riser under steady flow, and combined with the inverse finite element method, the vortex-induced forces and coefficients acting on each section of the riser were obtained. This method avoided the instability of load identification caused by the application of the optimization method. The identification coefficients of this method passed the \"double blind\" test with high accuracy. Using this method, [PERSON] [8] found that the vortex-induced force coefficients of the flexible riser were inconsistent with those obtained by the unidirectional forced oscillation test. [PERSON] [9] and [PERSON] [10] further extended this method to the identification of vortex-induced forces of the flexible riser with buoyancy modules, non-uniform structural characteristics and outer diameter under steady flow. The identification results show that the added mass coefficient of the bare pipe of the flexible riser with buoyancy modules is more than 10, which is much greater than the current specification value (1.0). [PERSON] [11] validated this finding by carrying out rigid cylindrical forced oscillation tests with buoyancy modules. Buoyancy modules and helical strakes are very common auxiliary components on marine risers, and their hydrodynamic shapes are quite different from those of bare pipes, resulting in the VIV forces and the response characteristics under ocean currents of them being different from those of bare pipes. Currently, the research on VIV of risers with buoyancy modules and helical strakes at home and abroad mainly focuses on the study of VIV response characteristics. Exxon Mobil carried out a series of unidirectional VIV experiments [12] on real-scale rigid bare cylinders and real-scale rigid cylinders with strakes; the results show that the VIV response after installing the suppression device could not be predicted with the existing VIV prediction method, but it was confirmed that the St number could predict vortex-shedding frequency. NDP also carried out a systematic VIV test of pipes with helical strakes at the MARINTEX tank in Norway [13], using a pipe model with a length of 1400 D. Both uniform flow and shear flow fields were considered. The sizes of the helical strakes were 17.5 D/0.25 D and 5.0 D/0.14 D. The results show that the 17.5 D/0.25 D helical stroke showed higher suppression efficiency in both uniform flow and shear flow, while the 5.0 D/0.14 D helical stroke had lower suppression efficiency in uniform flow.