Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV) of marine risers, extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers. The problem is conventionally solved using the modal decomposition method, based on the principle that the response can be approximated by a weighted sum of limited vibration modes. However, the method is not valid when the problem is underdetermined, i.e., the number of unknown mode weights is more than the number of known measurements. This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP) algorithm, exploiting the sparsity of VIV in the modal space. In the validation study based on high-order VIV experiment data, the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed. A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem, which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.