Ship as a Wave Buoy: Sea State Estimation Using a Brute Force Approach

Abstract Accurate sea state data is essential for safe and efficient marine operations in the offshore energy sector. This paper presents a method for estimating sea state parameters directly from vessel motions measured by shipboard motion response units (MRUs), reducing the need for dedicated wave measurement equipment. The brute-force approach, developed by researchers at NTNU (Norway) and DTU (Denmark), iteratively solves the fundamental equation R = RAO * S, where R is the vessel response, RAO is the Response Amplitude Operator, and S is the wave spectrum. The algorithm is fast, solving for the sea state in less than 0.1 second per case. The inputs are the vessel response time series and the vessel RAO. The output is a 1D spectrum and a direction estimate. Additionally, the authors propose several techniques to improve the sea state estimates further. The method was tested on real life data from an offshore service vessel. Validation was performed using co-located data from a wave buoy within 20 km of the vessel position. The resulting dataset comprises 3,824 2D wave spectra measured over 7 months. The baseline algorithm and modified variants were compared against buoy-measured significant wave height (Hs), peak period (Tp), and mean direction (β). Results show strong agreement for Hs and Tp, with median errors below 0.25 m and 0.55 s, respectively. Direction estimates were less accurate, with a median error of 49°, largely due to ambiguity between port and starboard wave incidence.