Directional wave spectrum estimation through onboard measurement data utilizing B-spline basis functions

The utilization of digital twin technology, which integrates real-world measurement data with a digital representation of the vessel, is garnering increasing attention within the realm of structural integrity management. Due to limitations in sensor deployment on ships, the integration of the digital twin framework, which merges measurement data with the ship's digital design model, becomes crucial for ensuring the effectiveness of structural integrity management. This investigation introduces a methodological approach for estimating localized responses at unmeasured locations, leveraging both measurement and design datasets. To approximate the response at unobserved sites, the directional wave spectrum is initially determined utilizing the least squares method, thereby, minimizing the disparity between the estimated and measured response spectra. The methodology notably incorporates cubic B-spline interpolation specifically to smooth the directional wave spectrum deployed on the heading-frequency domain. This deliberate choice of employing cubic B-spline interpolation underscores the emphasis on achieving a refined and continuous representation of the directional wave spectrum, thus enhancing the accuracy and reliability of the estimation process. To validate the proposed methodology, synthetic pseudo-measurement data derived from the wave spectrum and RAO of a 13,000 TEU container ship are employed. Subsequently, the directional wave spectrum is estimated utilizing the pseudo-measurement data, and the estimated directional wave spectrum, in conjunction with the Response Amplitude Operator (RAO), is harnessed to approximate the response spectrum at the location where sensors are not installed.