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In vessel performance analysis, reliable information about speed-through-water (STW) is key for realistic modeling of the single ship’s fuel efficiency. It is paramount that STW measurements are reliable such that they can be adopted as input in fuel consumption forecast models. This paper presents a study where three variations of a Dynamic Factor Model are used to estimate the STW. A simulation study is presented to demonstrate the estimation and smoothing techniques for the Dynamic Factor Model. The model variations are then applied to real vessel data, including STW and propeller measurements, in combination with metocean data (sea currents). The present study suggests that the developed model can minimize the systematic STW measurement error even under highly non-stationary conditions.

Predicting the wave-induced response in the near-future is of importance to ensure safety of ships. To achieve this target, a possible method for deterministic and conditional prediction of future responses utilizing measured data from the most recent past has been developed. Herein, accurate derivation of the autocorrelation function (ACF) is required. In this study, a new approach for deriving ACFs from measurements is proposed by introducing the Prolate Spheroidal Wave Functions (PSWF). PSWF can be used in two ways: fitting the measured response itself or fitting the sample ACF from the measurements. The paper contains various numerical demonstrations, using a stationary heave motion time series of a containership, and the effectiveness of the present approach is demonstrated by comparing with both a non-parametric and a parametric spectrum estimation method; in this case, Fast Fourier Transformation (FFT) and an Auto-Regressive (AR) model, respectively. The present PSWF-based approach leads to two important properties: (1) a smoothed ACF from the measurements, including an expression of the memory time, (2) a high frequency resolution in power spectrum densities (PSDs). Finally, the paper demonstrates that a fitting of the ACF using PSWF can be applied for deterministic motion predictions ahead of current time.

A practical estimation methodology of the mean added resistance in irregular waves is shown, and the present paper provides statistical analyses of estimates for ships in actual conditions. The study merges telemetry data of more than 200 in-service container vessels with ocean re-analysis data from ERA5. Theoretical estimates relying on spectral calculations of added resistance are made for both long- and short-crested waves and are based on a combination of a parametric expression for the wave spectrum and a semi-empirical formula for the added resistance transfer function. The theoretical estimates are compared to predictions from an indirect calculation of added resistance relying on shaft power measurements and empirical estimates of the remaining resistance components. Overall, the comparison reveals a bias in bow oblique waves and higher sea states of the spectral estimates as well as the large variance of the empirically derived predictions — particularly in beam-to-following waves. One of the study’s main findings, confirming previous studies but based on a much larger dataset than in earlier similar studies, is that added resistance assessment based on in-service data is complex due to significant associated uncertainties.

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 minutes), 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 hours likely is violated for ships sailing the typical service speed (15 – 20+ knots).

This study assesses the relationship between speed and power of ships, and is based on operational data derived from more than 50,000 noon reports retrieved from 88 tankers. The analysis is made with a data-driven model based on principles from naval architecture and an econometric framework. The model facilitates the determination of a draught- and speed-dependent exponent. It is shown that the exponent is significantly lower than 3 at speed intervals below the design speed. The finding of a (much) smaller exponent, relative to 3, at low speed intervals is important in the slow steaming debate, since slow steaming will not be as good as often stated when the cubic speed-power relationship does not hold. On a practical level, the developed method can be used to set a more reliable benchmark in the performance monitoring of ships.

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.

The present paper examines a semi-empirical framework for the estimation of added resistance in arbitrary wave heading under consideration of uncertainty quantification. In this respect, the calibration of the formula's parameter vector is conducted based on particle swarm optimization as well as a database of model test results comprising 25 different ships and around 1100 samples. In the first iteration, the minimization of reducible systematic uncertainty is of interest and the effect of four objective functions on prediction accuracy is evaluated. Moreover, two different parameter combinations were obtained for blunt (CB≥0.70) and slender-type ships. Conversely, the irreducible statistical uncertainty, i.e. the inherent noise of the experimental data, is taken into account by a quantile regression procedure. Applying this approach, a 90% prediction interval for the formula's estimates is implemented using the skewed version of the superior loss function in the previous iteration. The practical relevance of an uncertainty estimate for the prediction of the added resistance is emphasized in the final part, in which the proposed approach is validated in regular waves against model test data and other well-established prediction methods. In general, the validation studies suggest satisfactory performance and reliability of the adapted semi-empirical formulation. Published version The financial support from The Danish Maritime Fund (Projekt 2019-043), A/S D/S Orient’s Fond and the Department of Mechanical Engineering (DTU) is highly appreciated. The second author received funding by the Research Council of Norway through the Centres of Excellence scheme, project number 223254 AMOS.

This paper is concerned with a machine learning-based approach for sea state estimation using the wave buoy analogy. In-situ sensor data of an advancing medium-size container vessel has been utilized for the prediction of integral sea state parameters. The main novelty of this contribution is the rigorous comparison of time and frequency domain models in terms of accuracy, robustness and computational cost. The frequency domain model is trained on sequences of spectral ordinates derived from cross response spectra, while the time domain model is applied to 5-minute time series of ship responses. Multiple deep neural networks were trained and the sensitivity of individual sensor recordings, sample length, and frequency discretization on estimation accuracy was analysed. An Inception Architecture adapted for sequential data yields the highest out of sample performance in both considered domains. Additionally, multi-task learning was employed, as it is known for increased generalization capability and diminished uncertainty. Overall, it was found that the frequency domain method provides both superior performance and significantly less computational effort for training.

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.

This paper investigates a semi-empirical model used to estimate added-wave resistance on a ship sailing in waves. The model relies on measurements from a continuous monitoring system, and produces an estimate - the indirect measurement - of added-wave resistance, based on the difference between, on the one side, the measured power and, on the other side, a summation of theoretically calculated resistance contributions but neglecting the component because of seaway. Hence, the added-wave power is obtained as the surplus. The model has been applied to more than three months of full-scale data recorded on an in-service operating container ship. The results indicate reasonable levels of the added-wave power, emphasising that both positive and negative values are obtained, since the model is not restricted to relative wave directions forward of beam. It is found that following waves often lead to ‘negative resistance’, in fact creating a thrust, but, importantly, following waves can also increase the total resistance significantly.

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.

This paper addresses the connection between added wave resistance and required propulsion power of ships, having focus on the early stage of new ship designs, notably tankers and bulk carriers. The paper investigates how mean added wave resistance affects the required torque of a fixed pitch propeller and thus also the operational conditions of a directly coupled main engine. The interest of the study has its background in the assessment of minimum propulsion power, and the study considers the prescriptive guidelines of the IMO as basis. Specifically, the study focuses on an assessment of the minimum forward speed attainable under consideration of the propeller light running margin and static load limits of engines in the early phase of new ship designs, where details of hull geometry are not available. The study considers three semi-empirical methods for predicting mean added wave resistance. All methods are known to be applied in the industry, emphasising that only methods relying solely on main particulars, together with information about sea state and advance speed, are of interest. The paper contains a case study used to illustrate the importance of the added wave resistance prediction with respect to the loading of the main engine. It is shown that, despite small absolute differences, the consequence in relation to the loading of the propeller and hereby the directly coupled main engine can be relatively large. Furthermore, the study illustrates that the propeller light running margin of a fixed pitch propeller directly coupled to the main engine has crucial influence on the attainable speed during adverse weather conditions.

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.

Extreme value statistics can often be based on the assumption that exceedance events of a high threshold level are statistically independent and identically distributed (i.i.d. process), which further implies the Poisson assumption to be valid. This makes it possible to express the extreme response statistics through the mean up-crossing rate. For non-linear processes, analytic expressions of the mean up-crossing rate do not in general exist. Reliable statistics of mean up-crossing rate based on the brute-force approach, e.g. Monte Carlo simulation (MCS) require long time domain simulations considering a number of different ensemble input. The associated computations can be very time consuming especially when a detailed physical (e.g. hydrodynamic) model is applied. The First Order Reliability Method (FORM) has previously been found efficient for estimation of extreme value prediction of stationary stochastic time domain processes, However, if the non-linearity in a response is significant, the accuracy of the FORM linearized mean up-crossing rate can be limited.

Active monitoring of transverse stability in fishing vessels is paramount due to its significant incidence in operational accidents. Access to systems for automatic detection of changes in vessel’s stability related parameters would better support the crew during fishing and navigation operations. The paper presents an initial experimental validation of a signal-based transverse stability monitoring system, which consists of an estimator-detector kernel that solely uses measurements of roll motion to identify changes in vessel’s metacentric height by estimating the roll natural frequency. Its performance is evaluated based on experimental data from a towing tank scale model test campaign. The proposed transverse stability monitoring system well performs by identifying the potential risks and changes in loading condition.

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).

The present paper implements machine learning methods for the prediction of the added-wave resistance of ships in head to beam wave conditions. The study is focused on non-linear regression algorithms namely Random Forests, Extreme Gradient Boosting Machines and Multilayer Perceptrons. The employed dataset is derived from results of three different potential flow methods covering a wide range of operational conditions and 18 hull forms in total. The rational data preprocessing makes up the core part of the paper having its focal point on practical application. Moreover, a rigorous hyperparameter study based on Bayesian optimization is conducted, and the validation of the final models for three case studies against numerical and experimental data as well as two established prediction techniques shows satisfactory generalization in case of the neural network. The tree-based ensemble methods, on the other hand, are not able to generalize sufficiently from the given parameter discretization of the underlying dataset.

This paper presents a novel method for estimating the sea state parameters based on the heave, roll and pitch response of a vessel conducting station keeping automatically by a dynamic positioning (DP) system, i.e., without forward speed. The proposed algorithm finds the wave spectrum estimate from the response measurements by iteratively solving a set of linear equations, and it is computationally efficient. The main vessel parameters are required as input. Apart from this the method is signal-based, with no assumptions on the wave spectrum shape. Performance of the proposed algorithm is demonstrated on full-scale experimental DP data of a vessel in three different sea states at head, bow quartering, beam, stern quartering and following sea waves, respectively.

Transfer functions are often used together with a wave spectrum for analysis of wave–ship interactions, where one application addresses the prediction of wave-induced motions or other types of global responses. This paper presents a simple and practical method which can be used to tune the transfer function of such responses to facilitate improved prediction capability. The input to the method consists of a measured response, i.e. time series sequences from a given sensor, the 2D wave spectrum characterising the seaway in which the measurements are taken, and an initial estimate of the transfer function for the response in study. The paper presents results obtained using data from an in-service container ship. The 2D wave spectra are taken from the ERA5 database, while the transfer function is computed by a simple closed-form expression. The paper shows that the application of the tuned transfer function leads to predictions which are significantly improved compared to using the transfer function without tuning.

The article presents a practical approach to transform a wave energy spectrum from encounter domain to absolute domain. This problem has its specific relevance, when shipboard sea state estimation is conducted by the wave buoy analogy; notably for some particular implementation solving for the sea state directly in the encounter domain. In this context, the encounter domain is that observed from a ship when it advances in a seaway, whereas the absolute domain is that corresponding to making observations from a fixed point in the inertial frame. Spectrum transformation can be uniquely carried out if the ship sails “against” the waves (beam to head sea) but in following sea conditions there exists no unique solution to the problem. Instead, a reasonable approach valid for practical engineering must be applied, and the article outlines one viable solution that can be used to transform a wave spectrum from encounter to absolute domain. Specifically, two pseudo algorithms are presented, and good performance is achieved with both algorithms when they are tested at different operational scenarios.

The international Maritime Organization (IMO) Weather Criterion has proven to be the governing stability criteria regarding minimum metacentric height for e.g., small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessarily representative for current new buildings with large superstructures. Thus, it seems reasonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here, it is combined with the first order reliability method (FORM) to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The FORM results for a fictitious vessel are compared with Monte Carlo simulations, and good agreement is found at a much lesser computational effort. Finally, the results for an existing small ferry will be discussed in the light of the current weather criterion. 1. Introduction Recently, the International Maritime Organization (IMO) has initiated a thorough revision of the intact stability rules in the framework of goal-based design, e.g., Peters et al. (2013). Several draft guidelines have been issued, e.g., SDC 1/INF.8 (IMO 2013) discussing in details the requirements for the hydrodynamic software to be applied including qualitative and quantitative assessment procedures. The focus so far has been mostly on failure modes related to the change of righting lever in waves, notably parametric rolling and pure loss of stability, whereas the dead ship behavior in beam sea still is based on the existing Weather Criterion issued by IMO (1985) as Resolution A.562. This criterion is based to a large extent on model tests of older hull forms and does not provide any probability of capsize for a given vessel, just a pass/no pass result. Furthermore, the wave environment is not explicitly specified in the criterion thus leading to the same requirement whether the ship is sailing in restricted areas or not. A very detailed and precise description of the drawbacks in the IMO Weather Criterion, as applied to modern ships, is given in Bulian and Francescutto (2004). In a recent study by Tompuri et al. (2015), a detailed investigation on application of the second generation intact stability criteria has been done. However, the criterion for dead ship condition is excluded from this thorough study because the criterion is thought to be still in the early phase of development.

This article is about the use of measured wave-induced vessel motions for estimation of ocean wave spectra by application of the wave buoy analogy. In the study, data from a larger, in-service container ship is considered. The estimation of wave spectra, equivalently sea state parameters, is based on measurements from, respectively, a gyro and two accelerometers leading to the simultaneous use of the pitching motion together with the horizontal and vertical accelerations in a position close to the forward perpendicular. The study of in-service data leads to contemplations about the vessel's advance speed, as the possible existence of sea current means that speed-over-ground (SOG) and speed-through-water (STW) will be different. The article discusses aspects related to advance speed in the context of the wave buoy analogy, and a smaller sensitivity study is conducted. Preceding to the sensitivity study, a comparison is made between sea state estimates by the wave buoy analogy and estimates obtained from a hindcast study. The article shows an acceptable agreement between the two sets of estimates. Following, the main conclusion from the sensitivity study on advance speed is that errors and uncertainties in the speed log have an effect on the estimates of the wave buoy analogy. In fact, the effect can be severe if reliable STW measurements are not available. In the final part, the article includes a few discussions about (non)stationary conditions in the context of the wave buoy analogy, and, although the effect on results is not necessarily detrimental, care must be shown when the wave buoy analogy is applied during in-service conditions.

This paper presents a study focused on sea state estimation along the route of an in-service container ship. The paper is concerned with the wave buoy analogy in which wave-induced motions of the ship are processed and analysed together with corresponding motion transfer function to give the directional wave spectrum exactly at the point of operation. In this study, a simple and inexpensive instrumentation of the vessel is considered, and wave spectrum estimation is based on measurements from one motion response unit mounted close to the forward perpendicular of the ship. The estimates by the wave buoy analogy are compared with two sets of results from third generation spectral wave models, with one set provided by a commercial supplier and with another set obtained from the Copernicus Climate Change Service Information. Motion measurements from a seven-days voyage across the Pacific Ocean are studied, and it is shown that the wave buoy analogy estimates wave conditions, in terms of sea state parameters, in good agreement with the reports by the sets of ocean wave hindcasts. Along with the comparisons, the paper discusses some of the inherent drawbacks of the wave buoy analogy, notably the fact that a ship acts as a low-pass filter.

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.

Shipboard wave estimation has been of interest in recent years for the purpose of decision support. In this paper, estimation of sea state is studied using ship responses and a parametric description of directional wave spectra. A set of parameters, characterising a given wave spectrum is estimated through an optimisation problem using global search basin with proper constraints. The cost function is established based on the difference between the energies of a set of measured ship responses and the corresponding theoretical spectral moments. A partitioning procedure is applied, which is able to separate swell components from wind seas.

Ice sounding radars are able to measure ice sheets by profiling their glaciological features from the surface to the bedrock. The current airborne and, in particular, future space-based systems are suffering from off-nadir surface clutter, which can mask the depth signal of interest. The most recent surface clutter suppression techniques are based on multi-phase-center systems combined with sophisticated coherent postprocessing. The performance of the techniques can be improved by accurate direction-of-arrival (DOA) estimates of the surface clutter. This paper deals with data-driven DOA estimation for surface clutter signals, which includes a formulation of the mathematical foundation of spatial aliasing. DOA estimation is applied to data acquired with the P-band POLarimetric Airborne Radar Ice Sounder at the Jutulstraumen Glacier, Antarctica. The effects of spatial aliasing related to a large phase center spacing are analyzed, and an unwrapping procedure is presented and applied to the data. Finally, DOA estimation of full-scene data is analyzed and used to show an along-track and incidence (off-nadir) angle dependent variation of the effective scattering center of the surface return, which is caused by a varying penetration depth.

The article introduces a spectral procedure for sea state estimation based on measurements of motion responses of a ship in a short-crested seaway. The procedure relies fundamentally on the wave buoy analogy, but the wave spectrum estimate is obtained in a direct - brute-force - approach, and the procedure is simple in its mathematical formulation. The actual formulation is extending another recent work by including vessel advance speed and short-crested seas. Due to its simplicity, the procedure is computationally efficient, providing wave spectrum estimates in the order of a few seconds, and the estimation procedure will therefore be appealing to applications related to realtime, onboard control and decision support systems for safe and efficient marine operations. The procedure's performance is evaluated by use of numerical simulation of motion measurements, and it is shown that accurate wave spectrum estimates can be obtained for all wave directions in short-crested waves, taking the wave system to be composed by both wind generated sea and swell. Furthermore, the procedure is tested using full-scale motion data obtained from sea trials. Good wave estimations are achieved as compared to corresponding results from a free-floating (classical) wave buoy.

The objective of ship motion-based wave spectrum estimation is to provide the distribution of wave energy densities in absolute domain. However, as a ship generally advances relative to the progressing waves, any spectrum estimate inherently dates back to the encounter domain and, consequently, the spectrum estimate must be transformed to absolute domain. In following sea conditions, spectrum transformation from encounter to absolute domain has no unique (mathematical) solution. This article presents an optimisation-based technique to carry out the particular transformation in following sea conditions. The optimisation relies on an object function established using (wave) spectral moments; calculated directly using the estimated encounter-wave spectrum on the one side and by using a parameterised wave spectrum valid in absolute domain on the other side. The simplicity of the transformation technique is a strength in itself as it leads to an insignificant computational effort in the transformation to absolute domain. Equally important, the specific technique proves capable to provide accurate results in the majority of cases, when comprehensive testings with numerically simulated data of following sea conditions are performed. Furthermore, the technique is tested successfully using experimental full-scale sea trials data.

This paper presents a study focused on a newly developed procedure for wave spectrum estimation using wave-induced motion recordings from a ship. The particular procedure stands out from other existing, similar ship motion-based procedures by its computational efficiency and - at the same time - providing accurate estimates of the on-site wave conditions. In the paper, the procedure is applied to full-scale experimental data obtained from dedicated sea trial runs. The results show favorable agreement with corresponding wave spectrum estimates by a directional wave buoy. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Short-term variability of ship responses is investigated by cross-spectrum analysis. In a steady state condition, it is well known that a certain length of sampled data is required for stable results of the spectral analysis. However, the phase lag between responses, in terms of the phase angle of the cross-spectra, has not been discussed in detail. Using long stationary time series, the transition of amplitudes and relative phase angles of the cross-spectra has been investigated by iterative analyzes with a few seconds of time shifting. In the results, the short-term variability of the relative phase angle was observed. In effect, the variability may compromise the accuracy of the wave buoy analogy.

In this paper, we analyze the direction-of-arrival (DOA) of the ice-sheet data collected over Jakobshavn Glacier with the airborne Multichannel Radar Depth Sounder (MRDS) during the 2006 field season. We extracted weak ice–bed echoes buried in signals scattered by the rough surface of the fast-flowing Jakobshavn Glacier by analyzing the DOA of signals received with a five-element receive-antenna array. This allowed us to obtain ice thickness information, which is a key parameter when generating bed topography of glaciers. We also estimated ice–bed roughness and bed slope from the combined analysis of the DOA and radar waveforms. The bed slope is about 8° and the roughness in terms of rms slope is about 16°.

This article gives a review of techniques applied to make sea state estimation on the basis of measured responses on a ship. The general concept of the procedures is similar to that of a classical wave buoy, which exploits a linear assumption between waves and the associated motions. In the frequency domain, this assumption yields the mathematical relation between the measured motion spectra and the directional wave spectrum. The analogy between a buoy and a ship is clear, and the author has worked on this wave buoy analogy for about fifteen years. In the article, available techniques for shipboard sea state estimation are addressed, but with a focus on only the wave buoy analogy. Most of the existing work is based on methods established in the frequency domain but, to counteract disadvantages of the frequency-domain procedures, newer studies are working also on procedures formulated directly in the time domain. Sample results from several studies are included, and the main findings from these are mentioned.

Previous research has shown that the First Order Reliability Method (FORM) can be an efficient method for estimation of outcrossing rates and extreme value statistics for stationary stochastic processes. This is so also for bifurcation type of processes like parametric roll of ships. The present paper discusses this solution procedure with a focus on the computational efficiency of FORM as compared with Monte Carlo Simulation (MCS).

Fault detection and isolation are very important elements in the design of fault-tolerant decision support systems for ship operator guidance. This study outlines remedies that can be applied for fault diagnosis, when the ship responses are assumed to be linear in the wave excitation. A novel numerical procedure is described for the calculation of residuals using the ship's transfer functions which correlate the wave excitation and the ship responses. As tests, multiplicative faults have artificially been imposed to full-scale motion measurements and it is shown that the developed model is able to detect and isolate all faults.

Onboard sea state estimation is relevant for evaluation of ship operations at sea. Means to obtain the sea state at a fixed position include a traditional wave rider buoy, where motion measurements of the buoy are processed to give the (directional) wave spectrum. The analogy between a ship and a buoy is clear, although the ship is moving with a forward speed and, in general, is characterised by a more complex underwater geometry. Thus, it is possible to obtain an estimate of the wave spectrum at the location of an advancing ship by processing its wave-induced responses similar to the situation of a traditional wave rider buoy. The paper studies the ‘wave buoy analogy’, and a large set of full-scale motion measurements is considered. It is shown that the wave buoy analogy gives fairly accurate estimates of integrated sea state parameters when compared to corresponding estimates from real wave rider buoys. The complete distribution of wave energy is also compared, however, with poorer agreement. Finally, it is shown that the wave buoy analogy, for the studied data, provides, on average, slightly better sea state estimates than a wave radar system.

The paper studies parametric wave estimation based on the ‘wave buoy analogy’, and data and results obtained from the training ship Shioji-maru are compared with estimates of the sea states obtained from other measurements and observations. Furthermore, the estimating characteristics of the parametric model are discussed by considering the results of a similar estimation concept based on Bayesian modelling. The purpose of the latter comparison is not to favour the one estimation approach to the other but rather to highlight some of the advantages and disadvantages of the two approaches.

Most new advanced ships have extensive data collection systems to be used for continuous monitoring of engine and hull performance, for voyage performance evaluation etc. Such systems could be expanded to include also procedures for stress monitoring and for decision support, where the most critical wave-induced ship extreme responses and fatigue damage accumulation can be estimated for hypothetical changes in ship course and speed in the automatically estimated wave environment. The aim of this paper is to outline a calculation procedure for fatigue damage rate prediction in hull girders taking into account whipping stresses. It is conceptually shown how such a method, which integrates onboard estimation of sea states, can be used to deduce decision support with respect to the accumulated fatigue damage in the hull girder. The paper firstly presents a set of measured full-scale wave-induced stress ranges in a container ship, where the associated fatigue damage rates calculated from a combination of the rain-flow counting method and the Palmgren-Miner damage rule are compared with damage predictions obtained from a computationally much faster frequency fatigue analysis using a spectral method. This analysis verifies the applied multi-modal spectral analysis procedure for fatigue estimation for cases where hull girder flexibility plays a role. To obtain an automated prediction method for the fatigue damage rates it is in the second part of the paper shown how a combination of the full-scale onboard acceleration and stress measurements can be used to calculate sea state parameters. These calculated environmental data are verified by a comparison to hindcast data. In the third part of the paper the full-scale fatigue stress ranges are compared to results from an analytical design oriented calculation procedure for flexible ship hulls in short-term estimated sea states. Altogether, it is conceptually shown that by a combination of the onboard estimated sea state parameters with the described analytical fatigue damage prediction procedure a method can be established for real-time onboard decision support which includes estimates of fatigue damage rates.

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.

In this paper nonlinear fault detection for in-service monitoring and decision support systems for ships will be presented. The ship is described as a nonlinear system, and the stochastic wave elevation and the associated ship responses are conveniently modelled in frequency domain. The transformation from time domain to frequency domain has been conducted by use of Volterra theory. The paper takes as an example fault detection of a containership on which a decision support system has been installed.

An estimate of the on-site wave spectrum can be obtained from measured ship responses by use of Bayesian modelling, which means that the wave spectrum is found as the optimum solution from a probabilistic viewpoint. The paper describes the introduction of two hyperparameters into Bayesian modelling so that the prior information included in the modelling is based on two constraints: the wave spectrum must be smooth directional-wise as well as frequency-wise. Traditionally, only one hyperparameter has been used to control the amount of smoothing applied in both the frequency and directional ranges. From numerical simulations of stochastic response measurements, it is shown that the optimal hyperparameters, determined by use of ABIC (a Bayesian Information Criterion), correspond to the best estimate of the wave spectrum, which is not always the case when only one hyperparameter is included in the Bayesian modelling. The paper includes also an analysis of full-scale motion measurements where wave spectra estimated by the Bayesian modelling are compared with results from ocean surface measurements by satellite and from a wave radar. The agreement is found to be reasonable.

The paper continues a study on the wave buoy analogy that uses shipboard measurements to estimate sea states. In the present study, the wave buoy analogy is formulated directly in the time domain and relies only partly on wave-vessel response amplitude operators (RAOs), which is in contrast to all previous works that either are formulated in the frequency domain and/or depend entirely on RAOs. Specifically, the paper evaluates a novel concept for wave estimation based on combined techniques using a wave frequency estimator, not dependent on RAOs, to detect wave frequency and, respectively, nonlinear least squares fitting to estimate wave amplitude and phase. The concept has been previously tested with only numerical simulations but in this study the techniques are applied to model-scale experiments. It is shown that the techniques successfully can be used to estimate the wave parameters of a regular wave train. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Uncertainties related to numerical modelling of parametric roll have been investigated by using a 6-DOFs model with nonlinear damping and roll restoring forces. At first, uncertainty on damping coefficients and its effect on the roll response is evaluated. Secondly, uncertainty due to the “effective (equivalent) wave” concept in calculation of restoring moment is studied. Finally, uncertainty to roll response from different methods of GZ calculation has been checked. It is found that the equivalent wave concept is sufficiently accurate for the purpose of GZ calculation. Two different GZ approximations give a good agreement with direct calculation method if relevant coefficients have been properly found in the fitting.

One method to estimate the wave spectrum onboard ships is to use measured ship responses. In this method, known also as Wave Buoy Analogy, amongst various responses that are available from sensor measurements, a couple of responses (at least three) are usually utilized. Selec-tion of the best combination of ship responses is important. Optimally, this selection should not be implemented manually in onboard applications. Therefore, availability of an automatic response selection procedure would be a great advantage for decision support. In this paper, a local sensitivity analysis is applied to evaluate the importance of individual responses in sea state estimation. The sensitivity factor is defined by calculation of the partial derivatives of wave parameters with respect to the variance of individual responses.

Reliable estimation of the on-site sea state parameters is essential to decision support systems for safe navigation of ships. The wave spectrum can be estimated from procedures based on measured ship responses. The paper deals with two procedures—Bayesian Modelling and Parametric Modelling—which both use complex-valued frequency response functions (FRF) to estimate the wave spectrum. It is therefore interesting to investigate how the filtering aspect, introduced by FRF, affects the final outcome of the estimation procedures. In order to do this, extensive numerical simulations—with known wave parameters—are carried out for a large container vessel. The study shows that filtering has an influence on the estimations, since high-frequency components of the wave excitations are not estimated as accurately as lower frequency components.

This paper presents a trend analysis for prediction of sea state parameters onboard ships during voyages. Given those parameters, a JONSWAP model and also the transfer functions, prediction of wave induced ship responses are thus made. The procedure is tested with full-scale data of an in-service container ship. Comparison between predictions and the actual measurements, implies a good agreement in general. This method can be an efficient way to improve decision support onboard ships.