A new wave spectrum resembling procedure based on ship motion analysis
Introduction
The real-time knowledge of the environmental conditions, encountered by the ship along its route, is one of the key factors affecting the safety of navigation. In this respect, the assessment of sea state parameters is useful to minimize the risks of navigation and reduce the costs, as it provides an additional guidance to the onboard decision support systems and enables the crew to avoid potential dangerous phenomena in following and quartering seas, such as surf-riding, broaching and parametric rolling (Pascoal et al., 2007). Furthermore, the continuous monitoring of sea state conditions is helpful to improve the statistics of long-term wave data, providing additional information especially in open ocean waters, where the weather buoys are very scattered. Besides, the assessment of weather conditions, in terms of sea state parameters, is also required if the ship voyage is planned by means of weather routing methods in order to detect the optimal route, based on changeable weather conditions and navigational constraints (Krata and Szlapczynska, 2012). As concerns the safety of crew, additional advantages, coming from the knowledge of sea state parameters, are connected to the assessment of the risk level during the routine onboard operations that, in turn, are related to well-known seakeeping parameters, such as the Motion Induced Interruptions for sliding, longitudinal and lateral tipping events (Gaglione et al., 2016). Finally, additional benefits arise from the assessment of the onboard comfort level, mainly related to the Motion Sickness Incidence parameter, that needs to be continuously monitored to increase the seakeeping performances of passenger ships (Scamardella and Piscopo, 2014).
Based on previous remarks, since the mid-70s a variety of research activities were carried out to explore the possible analogy between ships and wave buoys, as some issues arise when assessing the sea state parameters based on onboard measurements, mainly related to the Doppler shift between the absolute and encounter wave frequencies. Besides, the ship hull doesn't have circular symmetry as regards the incoming waves, so as its dynamic behaviour is affected by the encounter angle between the vessel route and the prevailing wave direction. Furthermore, the ship size also affects the hydrodynamic behaviour of a vessel in a seaway, that acts as a low-pass filter, so reducing the capability of detecting the wave spectral energy at small wavelengths (Pascoal et al., 2007). All these factors negatively affect the reliability of sea state measurements, based on ship motion analysis, as it will be further discussed in Section 2, where a brief literature review of actual state-of-art is provided. In fact, some issues are still open and do not have a unique answer, such as: (i) the selection of the most suitable ship motions to be embodied in the wave spectrum resembling procedure; (ii) the employment of parametric or non-parametric techniques (Nielsen, 2017a) to detect the sea state parameters; (iii) the selection of the proper time duration of motion measurements, to obtain an almost real-time monitoring of weather conditions, without affecting the reliability of resembled sea state parameters; (iv) the incidence of heading angles and vessel speed on the effectiveness of sea state measurements, combined with the 1-to-3 multivalued problem between the absolute and encounter wave frequencies at quartering and following seas. All these issues were recently discussed by several researchers. In this respect, Montazeri et al. (2016a) carried out a local sensitivity analysis, devoted to assess the importance of individual responses in sea state estimation, and concluded that the wave bending moment is generally the most effective response to estimate both the wave period and direction and that the selection of the proper ship motions mainly depends on the heading angle between the vessel route and the prevailing wave direction. Brodtkorb et al. (2018) developed a signal-based algorithm, to detect the wave spectrum by iteratively solving a set of linear equations, based on heave, pitch and roll motion measurements. They also investigated the incidence of transient conditions, data overlapping and sampling frequency on the effectiveness of resembled sea spectra. Nielsen and Diez (2020) analysed the motion measurements of a large in-service containership, focusing on the incidence of the advance speed and performed a comparative analysis between sea state estimates obtained by motion measurements and a hindicast study. They also investigated the incidence of sample length, concluding that a sampling period between 15 and 30 min generally contains sufficient wave components and is of such a short duration that sea state conditions remains almost constant. Based on previous remarks, the main aims of current research are summarized as follows:
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A new wave spectrum resembling procedure, consisting of two subsequent steps and based on the analysis of heave and pitch motions, is developed in Section 2 and applied to the S175 containership, whose main data and hydrodynamic parameters are provided in Section 3. Hence, a preliminary analysis of some selected basic conditions is performed in Section 4, in order to investigate the effectiveness of the proposed procedure. Heave and pitch motion time histories are obtained by a set of time-domain simulations, carried out by a purposely programme developed in Matlab (MathWorks, 2017) that allows systematically varying the sea state parameters, the vessel speed and the heading angle between the ship route and the prevailing wave direction;
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The incidence of time duration of onboard measurements on resembled sea state parameters is investigated in a wide benchmark study carried out in Section 5, where the wave peak period, the significant wave height and the vessel speed are randomly selected at four heading angles, equally spaced from head to following seas. The whole benchmark study consists of 1200 data sets of heave and pitch motion time series, that also in this case are obtained by time-domain simulations carried out in Matlab (MathWorks, 2017). The main aim of the study is to investigate the effectiveness of the proposed procedure at different time intervals and heading angles, so also accounting for the 1-to-3 multivalued problem that occurs at quartering and following seas;
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The selection of the proper time duration, that allows balancing the need of an almost real-time monitoring of sea state parameters with the reliability of resembled data, is further investigated in Section 6, focusing on the statistics of errors between theoretical and resembled values of sea state parameters.
Obtained results are further discussed in Section 7, while additional information about the wave spectrum resembling procedure, the 1-to-3 multivalued problem and the time-domain simulations are provided in the attached Appendixes.
Section snippets
A brief literature review
The first pioneering works on wave spectrum resembling, based on ship motion measurements, were carried out in the mid-70s by Takekuma and Takahashi (1973), who applied a reverse analysis technique to ships without forward speed. In the following years, several attempts were performed to include the Doppler shift for ships advancing in head and bow seas (Isobe et al., 1984; Kobune and Hashimoto, 1986) and subsequently in quartering and following seas (Iseki and Ohtsu, 2000), so including the
The S175 containership
The S175 containership is assumed as reference vessel for the numerical calculations, carried out in Sections 4 Preliminary analysis, 5 Benchmark study, as it represents a basic design for seakeeping analysis, widely investigated in the past by several researchers (ITTC, 1978; Fonseca and Soares, 1998; Kim et al., 2017 among others). The main particulars of the reference ship are listed in Table 1, while its body plan is shown in Fig. 3. The frequency-dependent zero-speed added masses and
Selection of basic conditions
The wave spectrum resembling procedure, outlined in Section 2, is preliminarily applied to a set of heave and pitch motion data sets, obtained by time-domain simulations in a seaway, based on theoretical wave spectra with known input parameters. Time-domain analysis was performed by a dedicated code developed in Matlab (MathWorks, 2017), that solves the coupled heave/pitch motion equations, reported in Appendix D, based on random sea surface elevation. The time-series of heave and pitch
Preliminary remarks
In the preliminary analysis, carried out in Section 4, the duration of heave and pitch motion time-series was set equal to 1 h, in order to obtain a robust assessment of sea state parameters, even if this time interval is generally too high for practical purposes. Really, the selection of the proper time window is a quite challenging issue, provided that it needs to be chosen based on the proper balancing of different affecting factors. In fact, the minimum time window, required to perform the
Statistics of errors
After investigating the incidence of time duration on resembled sea state parameters, the statistics of errors need to be provided, in order to select the time duration that allows balancing the need of an almost real-time monitoring of sea state parameters with the reliability of the resembled sea state parameters. Hence, Fig. 8(a)-(f) show the frequency histograms of the percentage errors on wave peak periods and significant wave heights at head seas, based on different time durations. The
Combination of swell and wind waves
The wave spectrum resembling procedure, outlined in Sub-Section 2.3, is tested against more complex sea state conditions, characterized by a combination of swell and wind waves, coming from different directions. The double-peak wave spectrum is obtained by combining two JONSWAP spectra having different wave heights, peak periods and shape parameters, the latter generally ranging from 1 to 7 and from 7 to 10 for wind and swell waves, respectively (Boukhanovsky and Guedes Soares, 2009).
Really,
Conclusions
A new wave spectrum resembling procedure, based on the analysis of heave and pitch motion time series, was developed to assess the sea state parameters. The procedure was applied to the S175 containership, assumed as reference vessel, in order to investigate its effectiveness at different vessel speeds, heading angles and sea state conditions. The following main outcomes have been achieved:
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The new wave spectrum resembling procedure consists of two subsequent steps. At the first step the wave
CRediT authorship contribution statement
V. Piscopo: Conceptualization, Methodology, Software, Writing - original draft, Writing - review & editing. A. Scamardella: Conceptualization, Validation, Supervision, Data curation, Project administration. S. Gaglione: Methodology, Formal analysis, Data curation, Visualization, Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The research was partly funded by the Research Programme MOQAP “Maritime Operations Quality Assurance Platform” – Italian Ministry of Economic Development – PON Imprese e competitività 2014–2020, HORIZON 2020 and by the Research Programme DORA “Deployable Optics for Remote sensing Applications”, within the National Operational Program “Research and Innovation 2014–2020”.
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