Inverse estimation of directional wave spectrum and response reconstruction using wave buoy analogy

초록

The structural performance of seagoing vessels is influenced by uncertainties arising from material variability, construction tolerances, and stochastic environmental loading. Since long-term operational conditions and fatigue accumulation cannot be fully captured at the design stage, increasing attention has been directed toward operational structural integrity management supported by onboard monitoring and digital twin concepts. Within such frameworks, structural responses at unmeasured locations must be estimated from limited onboard measurements. Directional wave spectrum estimation from ship responses has been widely investigated; however, it remains a fundamentally ill-posed problem due to limited independent information, weak directional sensitivity of response amplitude operators, and numerical instability associated with the nonlinear absolute–encounter frequency conversion under forward-speed conditions. This study extends a non-parametric directional wave spectrum estimation framework to improve robustness under realistic operational conditions. Building on a B-spline surface representation, an adaptive quadrature strategy is introduced to stabilize the absolute–encounter frequency conversion, particularly in regions where multiple absolute frequencies correspond to a single encounter frequency. In addition, a two-stage estimation procedure is employed to improve numerical stability and directional identifiability by separating the identification of energetically relevant regions from subsequent refinement. The proposed framework is validated using 64 full-scale measurement events obtained from an operational container vessel, and the estimated significant wave heights showed strong agreement with ERA5 reanalysis data, while reconstructed response spectral moments exhibited strong linear correlation with the measured responses, with correlation coefficients of approximately 0.93. The results indicate the applicability of the proposed framework under realistic operational conditions, although the estimation performance becomes more sensitive in low sea-state conditions due to the reduced signal-to-noise ratio of measured responses. © 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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