Wave Time History Realisations – Pitfalls and Solutions

Louise Devaney, Trevor Hodgson, Mark Manzocchi, Mohammad Saif, Narasimhan Sampathkumar
Atkins Ltd, Glasgow, UK


When performing coupled analysis of a WTG using the time history approach, it is necessary to generate many different realisations of wave and wind conditions, each lasting typically 10-minutes. Each realisation is a different representation of the environment over this time history, generated using different seeds to define the random relative phasing of the frequency components of wind or wave action.

Based on studies undertaken on recent projects, it became apparent to the authors that 6 random 10-minute wave realisations, as recommended by ICE 61400-3, do not necessarily produce statistically reliable data for the purposes of fatigue assessment and hence can lead to inaccurate fatigue lives. Either many more random simulations are required, else some form of constraint or testing of the time histories to be used is required.

This presentation uses the results of further research to create simple rules which, if followed, will ensure that wave time history realisations are indeed statistically reliable, and may therefore be used with confidence in the prediction of fatigue lives. This in turn will increase confidence in the resultant design and reduce the risk that premature fatigue failure will occur.


It is feasible to identify suitable wave time histories by assessing their contribution to fatigue life, comparing this with fatigue lives calculated over a statistically reliable large number of time histories. The problem with this approach is that it is time consuming, requiring the solution of the structure (albeit with only wave loads) for a large number of cases.

The approach adopted has therefore been as follows:

• generate a large number of realisations that are demonstrably statistically reliable, and produce fatigue lives from these;

• show that six randomly selected realisations do not necessarily produce sufficiently accurate fatigue lives;

• identify constraints that can be applied to the water surface time history only that restrain the wave realisations so that they are statistically reliable.


It has been found possible to identify wave time history realisations that are a good representation of long term statistics by assessing statistics of the water surface elevation.

Significant wave height alone is not necessarily sufficient, as a relatively even distribution of waves does not contain the peaks necessary to generate sufficient fatigue damage (due to the power law dependence). Parameters such as skewness and kurtosis should also be considered.

The results also show the significance of sea state wave zero up-crossing period and the method of time history generation from individual wavelets. Large waves at the end of a time history may be omitted for longer period seas, so that statistical reliability must be demonstrated over varying sea state periods.


Pitfalls possible in wave time history selection for fatigue analysis have been identified. It has been shown that the simple provision of six random 10-minute simulations, as recommended in the codes, is not necessarily sufficient to produce reliable fatigue lives.

It has further been demonstrated that simple checks on the statistics of the generated water surface are sufficient to reinstate confidence in the selected time histories. These checks can be used to ensure that the resultant time histories and fatigue damages are not overly conservative.

Depending on the time history generation method, it may be necessary to perform these checks on sea states with varying wave periods, since the statistics will vary depending how the time history is cropped to the required duration (typically 10-minutes).


The learning objectives of this presentation are as follows:

• to demonstrate the care that should be taken in the creation of wave time histories for fatigue life evaluation;

• to show how reliable time histories can be generated given simple checks on the water surface elevation;

• to present simple criteria for these checks for that resultant fatigue life calculations are reliable.

Application of these checks in design will result in more reliable fatigue life calculations and prevent one source of under-prediction of fatigue damage.