Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012
substantial relative to results obtained by the traditional EVT.
3. DISCUSSION The key reason for the present discussion of the
applicability of the EVT in shipbuilding is the calculated POE of the design MW in class societies’ rules by 63.2% by several researchers (e.g., Faulkner and Sadden 1979). From the mathematical point of view, this POE refers to the POE of the most probable
extreme value. The
proponents of EVT argue that, since the POE of the design MW in class societies’ rules is equal to unity divided by the number of load cycles within given time period (e.g., 25 years), it becomes equal to the most probable extreme value. Hence, they conclude that the design MW in class societies’ rules can be exceeded by 63.2%.
When the individual amplitude statistics are used (i.e., when all amplitudes are taken into consideration), the POE of the design MW is 10-8. The difference between the POE of the design MW obtained by the individual amplitude statistics and extreme value statistics is tremendous
but not surprising. The method for
calculating the POE of MW is significantly changed and as a result – the POE also changes significantly.
The mixture of two types of statistical analysis of MW (i.e., individual amplitude and extreme value statistics) leads to situation where the design MW is always interpreted as equal to the most probable extreme value of MW . Thus, following the traditional EVT, it can be exceeded by 63.2% for any value of n (number of cycles). It means that the most probable extreme value of MW will vary with the variation of number of cycles n while the design MW in class societies rules is a fixed value for given ship’s service life. Therefore, when EVT is applied, it is more reasonable to place on the derived probabilistic distribution of extreme MW (derived by following the proposed procedure) the fixed number of class rules’ design MW.
In the design stages, there are no records of MW to be used for the newly designed ship. The only option is to follow the conventional approach
described in the
Introduction, i.e. to use as accurate as possible parent distribution to calculate the needed parameters of the extreme value distribution by the formulas available e.g., in (Ochi, 1989). In these formulas, the parameter n (e.g. number of cycles) plays a governing role together with accuracy of the parent probabilistic distributions.
Many efforts are devoted to obtain as accurate as possible parent probabilistic distributions, to verify and calibrate them against records of full-scale measurements. Usually, the duration of full-scale measurements lasts around 3-4 years. Unavoidably, using the data from these measurements automatically implies the assumption that the future ship’s operation (e.g., 25 years service life)
The time windows’ duration has a strong effect on the final results obtained with the present EVT. The same is valid for the proposed procedure as well. A parametric study is needed to explore the quantitative effect of different durations of the time-windows on the final POE of any given limit. However, in any case,
consideration the POE of the maximal values of MW,h or Mt will contribute to a more accurate calculation of the POE of any value of the design MW,h or Mt. This could result in better understanding classification societies’ rules and may help avoiding possible misinterpretations.
Another issue is the sensitivity of the results when different criteria are used in the EasyFit computer program (or in any other computer program). In the example presented here, Kolmogorov-Smirnov criterion is used. When the Anderson – Darling criterion is used, the obtained numerical results are different from those given in the paper. To have an idea about the difference,
one could refer to the POE of the design MW,h calculated using both criteria in the proposed procedure.
In the
example, the POE of the design MW,h is equal to 2.97E- 05 when Kolmogorov – Smirnov criterion is used and equal to 7.52E-05 when Anderson – Darling criterion is used.
When the two criteria are used to calculate the POE of the design MW,h following the conventional EVT, the
POE of the design MW,h is equal to 0.0185 when Kolmogorov – Smirnov criterion is used and equal to 0.3469 when Anderson – Darling criterion is used.
Obviously, more studies of the sensitivity of the numerical results are needed,
e.g. - when different
durations of the time windows and 2 fitness criterion are used. Whatever differences are obtained resulting from the use of different time windows and criteria for fitness, the two major issues in the proposed procedure will remain i.e. a) one should consider the POE of the recorded maximal B.M. in each time window; b) one should not use the design MW in class societies’ rules as the most probable extreme value to be applied in conventional EVT approach.
4. CONCLUSION
A procedure is proposed for application of the EVT in ship’s strength calculations considering not only the maximal value of the corresponding random variable
©2012: The Royal Institution of Naval Architects A-95
will repeat the environment in which the full-scale measurements were carried out. Once the probabilistic distributions are verified, they can be used for any scenario of ship’s operation in the future. The trouble is that it is almost impossible to predict accurately all details of the future ship’s operation (operational regions, head angles, speed, Beaufort scale, etc.) despite the efforts and right intention. Hence, the prediction of number of load cycles n (see Eq. (5)) which the ship will be exposed to in the future also contains uncertainties.
taking into
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