Continuous motion response prediction of offshore flexible risers based on temporal and spatial-scale modal decomposition

Offshore flexible risers are critical components in deepwater oil and gas production systems, but the reconstruction of their continuous motion response from limited sensor data remains a significant challenge. Additionally, current reconstruction methods are limited by the available observations. Thus, this study introduces a novel dual-scale modal decomposition approach that integrates temporal and spatial scale analyses for precise prediction of riser responses. On the temporal scale, a Variational Mode Decomposition-Long Short-Term Memory (VMD-LSTM) model decomposes discrete displacement data into Intrinsic Mode Functions (IMFs) and forecasts their evolution using a rolling decomposition method to avoid information loss. On the spatial scale, theoretical modal shapes are incorporated as physical constraints within the VMD framework to reconstruct continuous spatial displacement from discrete measurements. The proposed method is validated using experimental data obtained from high-mode-number vortex-induced vibration tests on a flexible riser model. Simulation results show an RMSE of 0.004 m in temporal predictions and spatial reconstruction errors within 0.1 m, confirming the method's effectiveness for structural health monitoring and fatigue life estimation.