Probabilistic estimation of directional wave spectrum using onboard measurement data

Ocean wave spectrum is the key to the response estimation of seagoing vessel whose structural integrity is of utmost importance. Efforts have been made by researchers to correctly estimate the ocean wave spectrum using so called ‘wave-buoy analogy’ concept, where the vessel is considered to behave as a wave buoy. The aim of this study is to develop a methodology through which the directional wave spectrum can be estimated using the concept of ‘wave-buoy analogy’. To achieve the objective, ocean wave was modeled with 10-parameter bimodal wave spectrum combining long- and short-wave component. These 10 parameters of bimodal wave spectrum were targeted by solving non-linear least square problem, which is formulated by error function quantifying the difference between model prediction and onboard measurement data. Model prediction is based on the linear relationship between the wave spectrum and response spectra and measurement data are directly from the sensors installed on the vessel. To solve the non-linear least square problem, Bayesian statistics-based probabilistic approaches, Markov-Chain Monte Carlo simulation (MCMC), were utilized. Well-known adaptive Metropolis–Hastings algorithm which is one of the most popularly used MCMC techniques was utilized to derive the spectrum parameters that best describe the directional wave spectrum. To validate the proposed methodology, pseudo measurement data generated by numerical analysis with different loading conditions were used. The application of the proposed methodology to the numerical analysis data confirmed that it accurately estimates the response at locations where sensors are not installed.