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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. [ABSTRACT FROM AUTHOR]

The article presents a study investigating the level of variation in sea state parameters encountered by sailing ships crossing the oceans. The sea state parameters have been obtained from a reanalysis, in this case the ERA5. The study is based on the use of different interpolation schemes to compute parameters in geographical positions off the fixed grid. It is shown that the variation in sea state parameters can be significant. Consequently, in case of sailing ships, covering relatively long distances in a short time (30–60 min), it is recommended to rely on bilinear interpolation rather than nearest neighbour. The variation in the sea state parameters is, in fact, at a level which means that the normal assumption of a stationary seaway in periods up to 3 h likely is violated for ships sailing the typical service speed (15–20+ kt). [ABSTRACT FROM AUTHOR]

• Nonlinear roll damping identification method using onboard measurements is proposed. • Incident wave reconstruction method is incorporated into the present approach. • Numerical and experimental investigations in long- and short-crested waves are made. • Short-term variability was mitigated by taking averages of individual results. Accurate estimation of the roll damping of a ship is important for reliable prediction of roll motions. In particular, characterization and prediction of parametric roll incidence and other events associated with large roll angles require detailed knowledge about the damping terms. In the present paper, an approach to identify the stability parameters, i.e. linear and nonlinear roll damping coefficients in conjunction with the natural roll frequency, based on onboard response measurements is proposed. The method starts by estimating the encountered wave profile using wave-induced response measurements other than roll, e.g., heave, pitch, and sway motions. The estimated wave profile is then fed into a physic-based nonlinear roll estimator, and then the stability parameters that best reproduce the measured roll motion are identified by optimization. In turn, in-situ identification can be achieved while simultaneously collecting the response measurements. A numerical investigation using synthetic response measurements is made first, then follows an experimental investigation using a scaled model ship. Good results have been obtained in both long-crested and short-crested irregular waves. [ABSTRACT FROM AUTHOR]

Abstract The article presents initial ideas towards a network-based approach for sea state estimation used for marine operations and other maritime applications. In principle, all available means, ranging from in situ buoys, fleet of ships to remote sensing by satellite and aircraft, could be considered, emphasising that each means and any combinations among may act simultaneously. This study focuses on just one of the means; the use of ships as sailing wave buoys. The article introduces the wave buoy analogy, i.e. ship-as-a-wave-buoy, and it makes a proposal on how to impose (different) weights to the single ship-specific wave spectrum estimates obtained from multiple ships. Moreover, the work includes a discussion about the importance to associate a measure to reflect the (un)certainty of the wave spectrum estimate. The article presents a numerical case study, where multiple ships act simultaneously as wave spectrum-estimators. The case study relies on numerical motion simulations, as appropriate full-scale data is not yet available. In the analysis, it is shown that the use of simultaneous data from multiple ships leads to more accurate wave spectrum estimations. [ABSTRACT FROM AUTHOR]

This article studies a procedure that facilitates short- time , deterministic predictions of the wave-induced motion of a marine vessel, where it is understood that the future motion of the vessel is calculated ahead of time. Such predictions are valuable to assist in the execution of many marine operations (crane lifts, helicopter landings, etc.), as a specific prediction can be used to inform whether it is safe, or not, to carry out the particular operation within the nearest time horizon. The examined prediction procedure relies on observations of the correlation structure of the wave-induced response in study. Thus, predicted (future) values ahead of time for a given time history recording are computed through a mathematical combination of the sample autocorrelation function and previous measurements recorded just prior to the moment of action. Importantly, the procedure does not need input about the exciting wave system, and neither does it rely on off-line training. In the article, the prediction procedure is applied to experimental data obtained through model-scale tests, and the procedure's predictive performance is investigated for various irregular wave scenarios. The presented results show that predictions can be successfully made in a time horizon corresponding to about 8–9 wave periods ahead of current time (the moment of action). [ABSTRACT FROM AUTHOR]

The ever-changing sea state constitutes an integral part of situational awareness for vessels at sea. In this paper, a computationally efficient sea state estimation algorithm is extended by (1) automatic gain and tolerance calculation, and (2) trust measure for wave filtering condition identification. The resulting algorithm can run online in a control system without the need of user input, producing estimates of sea state parameters (significant wave height, peak wave frequency and main propagation direction), while simultaneously monitoring the quality of the estimates produced by identifying when wave filtering occurs. The algorithm is developed for application in dynamic positioning (DP) control systems, where the vessel has zero (or low) forward speed. The estimation method is tested with realistic values of measurement noise and sampling in terms of comprehensive time series simulations based on both long- and short-crested wave conditions. The sea state estimates correspond well with a state-of-the-art Bayesian estimation approach. This indicates that the simplifications made in order to enhance the computational speed, has not affected the quality of the estimates to any significant extent. The trust measure correctly identifies when wave filtering occurs in all simulated scenarios. [ABSTRACT FROM AUTHOR]

Abstract: Mean outcrossing rates can be used as a basis for decision support for ships in severe sea. The article describes a procedure for calculating the mean outcrossing rate of non-Gaussian processes with stochastic input parameters. The procedure is based on the first-order reliability method (FORM) and stochastic parameters are incorporated by carrying out a number of FORM calculations corresponding to combinations of specific values of the stochastic parameters. Subsequently, the individual FORM calculation is weighted according to the joint probability with which the specific combination of parameter values is expected to occur, and the final result, the mean outcrossing rate, is obtained by summation. The derived procedure is illustrated by an example considering the forces in containers stowed on ships and, in particular, results are presented for the so-called racking failure in the containers. The results of the procedure are compared with brute force simulations obtained by Monte Carlo simulation (MCS) and good agreement is observed. Importantly, the procedure requires significantly less CPU time compared to MCS to produce mean outcrossing rates. [Copyright &y& Elsevier]

Abstract: Onboard decision support systems (DSS) are used to increase the operational safety of ships. Ideally, DSS can estimate future ship responses within a time scale of the order of 1–3h taking into account speed and course changes, assuming stationary sea states. In principle, the calculations depend on a large amount of operational and environmental parameters, which will be known only in the statistical sense. The present paper suggests a procedure to incorporate random variables and associated uncertainties in the calculations of the outcrossing rates that are the basis for risk-based DSS. The procedure is based on parallel system analysis, and the paper derives and describes the main ideas. The concept is illustrated by an example, where the limit state of a non-linear ship response is considered. The results from the parallel system analysis are in agreement with corresponding Monte Carlo simulations. However, the computational speed of the parallel system analysis proved slower than expected. [Copyright &y& Elsevier]

Abstract: In general, two main concepts can be applied to estimate the on-site directional wave spectrum on the basis of ship response measurements: (1) a parametric method which assumes the wave spectrum to be composed by parameterised wave spectra; or (2) a non-parametric method where the directional wave spectrum is found directly as the values in a completely discretised frequency-directional domain without a priori assumptions on the spectrum. The paper outlines the theory of these two concepts, and it is shown how to deal with the speed-of-advance problem for operating ships. In addition, the methods include an equivalence of energy in the governing equations and, as regards the parametric concept, a frequency-dependent spreading of the waves is introduced. The paper includes an extensive analysis of full-scale measurements for which the directional wave spectra are estimated by the two ship response-based methods. Hence, comparisons are made between these estimates and, moreover, the agreement with the corresponding directional wave spectra produced by the wave radar system WAVEX is studied. The agreement between the two methods is reasonable, as well is the agreement between the results of these methods and those of WAVEX. It is difficult to propose one of the ship response-based methods in favour of the other, since they perform equally well. [Copyright &y& Elsevier]

• 50,000 noon reports from 88 tankers analysed to assess speed-power relationship • Data-driven model combining principles from naval architecture and econometrics • Speed-power exponent is significantly lower than 3 at speeds below the design speed • Environmental effect of slow steaming is overestimated • Imparts attention to speed optimization and not reduction for reducing CO 2 emissions This study investigates the speed-power relationship of ships, and is based on a combined econometric and naval architectural data-driven model fed with operational data from more than 50,000 noon reports obtained from 88 tankers. It is shown that the speed-power exponent is significantly lower than 3 at speed intervals below the design speed. This finding, including the study itself, affects the environmental discussions related to slow steaming, since it implies that slow steaming will not be as good as often stated. As such, the study imparts attention to speed optimisation, rather than reduction, in the political and environmental debate focused on the reduction of carbon emissions from shipping. [ABSTRACT FROM AUTHOR]

This study reports about the wave conditions encountered by the fleet of Maersk Line. Herein, wave conditions refer to integral wave parameters in terms of significant wave height, zero-upcrossing period, and wave direction (equivalently relative wave heading), but main focus is on the significant wave height. The study includes data from 189 container ships, where auto-logged data has been collected over a three-years period (2017–2020) during operations in the majority of the world's larger oceans. In total, the data corresponds to 1 million hours of operation. The encountered wave heights are compared with the information from wave scatter diagrams given by the Global Wave Statistics (British Maritime Technology, 1986). The study shows that weather routing and seamanship have an effect, but the effect is not as pronounced as reported in a previous study (Olsen et al., 2006). The study also presents findings in relation to the temporal and spatial variation in encountered wave height along ship routes at consecutive wave points spaced by the sailing distance in 30–120 min. It is shown that the variation can be large and, as such, the concept of "stationary conditions" might be compromised sometimes in the analysis of wave-ship interactions. • An account of the wave conditions encountered by ships based on ERA5. • Observations from 189 ships based on data collected over more than 3 years (2017–2020). • Assessment of encountered wave heights compared to the Global Wave Statistics. • Insight about the spatial and temporal variation of encountered wave height along ships' routes. [ABSTRACT FROM AUTHOR]

This paper studies real-time deterministic prediction of wave-induced ship motions using the autocorrelation functions (ACFs) from short-time measurements, namely the instantaneous ACFs. The Prolate Spheroidal Wave Functions (PSWF) are introduced to correct the large lag time errors in the instantaneous sample ACF, together with a modification of the autocorrelation (AC) matrix for ensuring its positive definiteness. The validity of the PSWF-based ACFs is first examined by using the ship motion measurements from model experiment under stationary wave excitations. It is shown that the use of PSWF-based ACFs leads to better prediction accuracy than direct use of sample ACFs. The validation is then extended to ship motion prediction using in-service data from a container ship, and an improvement of the prediction accuracy by PSWF-based ACFs is again found. Finally, the effectiveness of use of the instantaneous ACFs for non-stationary wave-induced responses is highlighted by comparing with the prediction results based on the ACFs from long-time measurements. • Real-time prediction method of wave-induced ship motions is addressed. • Prolate Spheroidal Wave Functions (PSWF) are introduced to correct autocorrelations. • Improvement of prediction accuracy by PSWF-based autocorrelations is presented. • Effectiveness of short-term autocorrelation on non-stationary measurements is shown. [ABSTRACT FROM AUTHOR]

The real-time provision of high-quality estimates of the ocean wave parameters at appropriate spatial resolutions are essential for the sustainable operations of marine structures. Machine learning affords considerable opportunity for providing additional value from sensor networks, fusing metocean data collected by various platforms. Exploiting the ship-as-a-wave-buoy concept, this article proposes the integration of vessel-based observations into a wave-nowcasting framework. Surrogate models are trained using a high-fidelity physics-based nearshore wave model to learn the spatial correlations between grid points within a computational domain. The performance of these different models are evaluated in a case study to assess how well wave parameters estimated through the spectral analysis of ship motions can perform as inputs to the surrogate system, to replace or complement traditional wave buoy measurements. The benchmark study identifies the advantages and limitations inherent in the methodology incorporating ship-based wave estimates to improve the reliability and availability of regional sea state information. • Sea state parameters are estimated by spectral analysis of wave-induced ship motions. • Vessel-based observations can complement buoy measurements in a wave sensor network. • A random-forest surrogate model is trained using historical wave hindcast data. • The hybrid ship–buoy network employs the surrogate model to output spatial wave data. • Inclusion of ship-based wave estimates improved the nowcasting accuracy and precision. [ABSTRACT FROM AUTHOR]