Estimating waves via measured ship responses

Abstract

Optimisation of energy efficiency and operational performance as well as assessment of safety levels and emissions of marine operations require detailed information about the acting wave system. It is possible-with an analogy to classical wave buoys-to estimate the directional wave spectrum by processing sensor measurements of wave-induced responses (e.g., motions and structural responses) from a ship. Compared to other sources of wave data (e.g., buoys, satellites, third-generation wave models), estimation concepts using the ship itself as a buoy provide the wave spectrum at the exact spatio-temporal point, potentially increasing accuracy and with minimal associated cost. This paper gives an overview of the technology, discusses associated uncertainties, and highlights new developments made for estimating waves via measured ship responses.

Figure 1

Measuring ocean waves. Information about waves is of crucial importance in many applications considered by engineers and ocean scientists.

Figure 2

Snapshot of vessel positions, as of 27-06-2023 UTC 10:30, from AIS data with colour codes for identification of ship type, noticing that more than 300,000 ships appear. With permission by MarineTraffic (www.marinetraffic.com).

Figure 3

Sketch of the wave buoy analogy (WBA), alluding to frequency-domain frameworks.

Figure 4

The research vessel Gunnerus is owned and operated by NTNU. Data from a test campaign is studied in the preliminary assessment of the WBA.

Figure 5

Unconditioned Bayesian wave spectrum estimates obtained by analysis of dedicated sea trial experiments with a research vessel, cf. Fig. 4.

Figure 6

In-service data from a container ship has been analysed. In total, 7644 time series samples of 25 minutes duration have been studied.

Figure 7

Comparison of integral wave parameters ($H_s$, $T_z$, and $D_m$) from the ERA5 database and corresponding parameters derived from the unconditioned wave spectrum estimates by the WBA. The legends inform about the root-mean-squared error (RMSE) for $H_s$ and $T_z$, respectively, and the minimum-absolute error (MAE) for $D_m$.

Figure 8

Integral wave parameters from the ERA5 database against corresponding parameters derived from, respectively, the unconditioned wave spectrum estimates by the WBA (top row) and the conditioned estimates using the hybrid framework of the WBA (bottom row). Left-side plots: $H_s$, middle plots: $T_z$, right-side plots: $D_m$.

Figure 9

Directional wave spectra by the WBA and a wave radar system (Wavex), and with the corresponding point spectra below. In subplots (a) and (b), different time stamps (UTC) are considered (a: 24-09-2007 00:00; b: 06-03-2008 19:00), and the respective sub-captions inform about the corresponding ERA5 wave parameters for the given cases, including the wave encounter angle $\beta$.

Figure 10

Measured and estimated roll motions in long-crested irregular waves based on model-tests carried out by National Maritime Research Institute (Japan). The time axis is in the scale of the model (1:72).