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A metocean study : Theoretical bases



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Theoretical bases for the statistical analysis of responses experienced by a vessel during a voyage.

Statement of the problem
State of the Art - Old and new
Links and references

These web pages are based on a report prepared by Anastasia Baxevani, of the Mathematical statistics Department of Lund University, Krzysztof Podgórski, of the Mathematical statistics Department of Indiana University - Purdue University Indianapolis and Igor Rychlik, of the Mathematical statistics Department of Lund University.


Statement of the problem

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This theoretical study reported here was prepared in relationship with the COMKISS European project.

Let us consider a ship which is undertaking voyages over a certain relatively long period of time. The load she experiences and consequently her response to this load are random and thus they would be best analyzed by some reliable statistical methods. Clearly, from the engineering point of view, the most important is to find an accurate approach to study the extremal events occuring during this period of exploration. The principal methodological challenge in the so-posed problem comes from several different sources of the involved random variation. They are directly related to temporal-spatial scale within which one considers the sea surface. Yet, conditions occuring on the sea surface are changing continuously in time and in space, and the randomness is different in different scales and thus different methods should be chosen depending on the scale and combined together.

Most of the material included in the considerations here appeared in some form in the literature but this is, as far as we know, the first attempt to put together the consistent methodological framework which, as we hope, will be helpful for future advances in research on these topics.

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General description

We consider the following three different scale threshold levels. First, there is randomness related to short-time variability of the sea surface in time intervals measured in minutes or in few hours at most and in a restricted region in which the weather conditions appear to be the same. Another level of variability is due to the change of the sea states which is the consequence of changes of weather conditions occuring within several hours or even several days and also due to different conditions in distant regions of the sea. Then there is a stochastic variability of different journeys which are undertaken at different times and possibly along different routes. Of course, these are only few of many possible factors and the complete analysis would be extremely complex if possible at all. In these notes we focus on these factors which are most important for the statistical properties of extremal waves (or responses). However, the proposed methods can be also applied to studies of arbitrary, not only extremal, waves.

Typical applications

In various practical problems, for example in safety considerations, it is important to determine the probability that the response -- for instance the heave amplitude, or the acceleration at a given location of a ship, or the stress in a given member -- exceeds some critical level over some time interval (one voyage, the duration of a storm, the lifetime of the vessel).

The concepts and notions which allow for the precise formulation of the corresponding research problems are discussed in the report.

State of the Art - Old and new

Present methodology

The conventional method is presently to oversimplify the problem, assuming that the random influencing variables are uncorrelated and of known simple distributions, and/or to use Monte Carlo type simulations of numerous potential histories for the time interval of interest, and accept the statistics of their results as a valid basis for the safety assessment.




Recent improvements

Satellite measurements provide data at time intervals such that the conventional method of history reconstruction can not be used with them. The report sets the definitions and theory for methods that rely on parameters which may be estimated from the satellite measurements.




Analysis of the example

The following concepts and notions are defined and discussed:

Sea state and its duration.
Route, as a time-indexed trajectory, and as an unknown variable apart from its end-points.
Response process, on the basis of a conditional Gaussian model.
Periods of stationarity.
Distribution of response and probabilities of exceedances.
Crossing intensity and oscillations density function.
Height of the crest of an oscillation.
Distribution of rainflow cycles.
Poisson approximation for the number and the probability of exceedances.
Connection of route segments.
Estimation of the probabilities mentionned above.



The Theoretical statistical bases are set for analysis and estimation of response level exceedance and of rainflow damage accumulation experienced by a vessel.


Research actions

The report raises many questions, and we refer the reader to it.

The most important issues are the validation of the assumptions, and the practical estimation of the parameters used in the theoretical formulae. Such practical estimation should not be limited to satellite data, but should of course consider them as one of the potential sources of information.

User persuasion

Safety assessment needs to be understood in a stochastic manner. This is not yet current practice everywhere, but the models presented here are essentially stochastic, and they are a compelling stage in the process, all the more if satellite data are to be used.

Expected improvements

Collaborative research actions should be able to shed light on the ways to solve the problem of extracting information on the time-histories of sea state processes from the almost instantaneous space lines of the orbital path.

Links and references

 The COMKISS project:

Project objectives 

The main objectives of the project are: 

to demonstrate to major segments of the marine transport industry the benefits of integrating satellite-derived information on sea state such as wave height and direction. 
to raise awareness of the usefulness of satellite data in increasing the safety and overall efficiency of shipping operations by using the EWSE (at CEO) as the principal channel for communicating progress. 

The results should be of interest for enterprises such as ship certification, fast ship/coastal traffic, and transportation of unconventional loads.

Project partners 

Satellite Observing Systems , Godalming, UK (David Cotton, project manager)
Mathematical Statistics, Lund University, Sweden (Georg Lindgren, project
Bureau Veritas, Paris-La Defense, France (Guy Parmentier)
Dockwise, Meer, Belgium (Cees Leenaars)
IFREMER, Brest, France (Michel Olagnon)
OPTIMER, Brest, France (Raymond Nerzic), 
Corsica Ferries, Bastia, France

Project period 

September 1, 1998 - August 31, 2000


Mise jour 09/10/00
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