nonlinear loads. Whereas the former method is well established and proven to be valid in a variety of cases, the latter one allows much stronger compression of the simulation time, but it requires further development and validation.

[1] Söding, H. and Tongue, E., “Computing Capsizing Frequencies of Ships in Seaway,” Third Stability Conference, Gdansk 1986

[2] Söding, H. “Current Problems in Ship Loads” (in German), Jahrbuch Schiffbaut. Ges. (STG) 1991.


You are correct that different responses require different simulations when using the presented wave conditioning technique. However, we do not agree that the methods which you mentioned are more efficient with respect to both the required simulation time and the accuracy of the results. A principal difference between the approach followed in [1] and our approach is that we are not looking for the probability of occurrence of a non-linear event rather than the magnitude of the non-linear event. The probability of this event is defined in an earlier stage as the most probable largest value according to linear theory. The Most Likely Extreme Response method was presented to calculate the non-linear response in a well-defined condition, which is known to give the largest response in a linear calculation. The required simulation time depends on the shape of the auto-correlation function of the response. For vertical bending, this is typically 4 to 5 cycles whereas the length can be more than 10 cycles for roll motions. The procedure as described in [1] required the simulation of 30 events and 400 cycles to predict the probability of capsizing. Spending a similar simulation time using the MLER-method, it is possible to calculate the non-linear extremes for about 40 to 80 responses. The method mentioned in your second reference [2] shows more similarity with our method although the wave-conditioning process is much easier to understand and to realise in the Most Likely Extreme Response method. In addition, the Most Likely Extreme Response method is very flexible to slight modifications of the mean period at the instant of occurrence of the extreme response. This allows the user to control the instantaneous wave steepness to be within physical limits.

[1] Söding, H. and Toguc, E. “Computing Capsizing Frequencies of Ships in a Seaway,” Third Stability Conference, Gdansk 1986.

[2] Söding, H. “Recent Problems in Ship Loads (in German),” Jahrbuch Schiffbaut. Ges. (STG) 1991.

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