Accuracy Improvement of Directional Wave Spectrum Estimation Around Sea-Going Vessel

Abstract The application of digital twin technology, which integrates real-world measurement data with digital design information, is increasingly recognized as essential for effective structural integrity management. Given the limitations of onboard sensor installation, this study focuses on the inverse estimation of the directional wave spectrum using integrated design and measurement data, providing a foundation for accurately estimating local structural responses across the vessel. Building upon existing methodologies, this study introduces additional numerical schemes to enhance the accuracy of directional wave spectrum estimation. The directional wave spectrum is estimated by solving a quadratic programming problem that minimizes discrepancies between the estimated and measured response spectra. B-spline surface is utilized to ensure smoothness and continuity in the estimated spectrum. To address integral singularities arising in the encounter-to-absolute frequency conversion due to the Doppler effect, adaptive quadrature is employed. Additionally, a two-stage process is introduced to further refine the estimation results by pre-calculating hyperparameters and mitigating overfitting. To validate the proposed methodology, pseudo-measurement data generated from the wave spectrum and Response Amplitude Operator (RAO) of a 13,000 TEU container carrier were utilized. Using these pseudo-measurements, the directional wave spectrum was estimated. The RAO and estimated wave spectrum were then combined to estimate the response spectrum at locations without sensors.