Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012
probabilistic ranges are treated as independent 3.0E-05
The time window of the 2.0E-05
records is 60 minutes over one year. The probability of getting into each group is considered. Then, POE design M(W,h) = 2.97E-05
1.0E-05 1.E+00 1 year records
1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01
0.0E+00
3 210 group number
Figure. 11 POE of the design MW,,h considering the probability of getting into each probabilistic group
The final POE of the design Mw,h is calculated by Eq. (17). In this case P = 2.97E-05
When this result is compared with the result shown in Figure. 9, one can observe that the POE of the design
MW,h obtained with the proposed procedure is around 620 times smaller than the POE of
the same MW,h obtained by the traditional EVT (i.e., when the POO/POE
of the maximal MW,h in each time window is neglected and the probabilistic distributions are assumed as independent and identical).
Although this result is valid only for this example, it clearly shows that the 63.2% POE of the design MW,h
(derived for the special case where the design MW,h is chosen such that the POE is equal to 1/N) should be substantially reduced. If one assumes that the same ratio between the two results exists for the case when 63.2%
POE of the design MW,h is calculated, the new POE would be around 0.10 % instead of 63.2%. The graphs of
the POE of any given MW,h are shown in Figure. 12 in log-scale. They illustrate the big difference between the
POE of any given value, including design MW,h , when the traditional EVT and the proposed procedure are applied. One can also observe the fact that, in this particular case, the maximum contributions come from Group 3 (i.e., POO = 0.001). In this group, the POE of
the design MW,h is even greater than the POE of the design MW,h obtained
by the conventional EVT.
However, when Eq. (17) is applied, the contribution of Group 3 drops substantially.
60 min time window
0.0 0.2 0.4 0.6 0.8 1.0 1.2 portion of design M(W,h)
POO neglected POO 0.01 POO 1
POO 0.001 POO 0.1
POO considered Figure. 12 POE of MW,h when the probabilistic ranges
are treated as independent and POE of MW,h derived by conventional EVT and the proposed procedure
Similar calculations were performed with time windows of 60 minutes for the total hull girder bending moment
Mt over 3.5 years of records. The design Mt was calculated by the formula:
Mt σ Z (18)
where [] = permissible total hull girder bending stress given in class societies’ rules (e.g., ABS Rules, 2011), Z = hull girder section modulus (deck).
The results of the calculations confirmed the same trend
as for the design MW,h, i.e. the POE of the design Mt derived by the proposed procedure is much lower (around ten times lower) than the POE calculated by the traditional EVT approach.
Since the example refers to records from relatively moderate seaway which results in a very low POE of the
design Mt, this obstructs the quantitative comparison between the results obtained by the traditional EVT and the proposed procedure. Considering the fact that the
recorded Mt practically does not exceed 70 – 80% of the
design Mt, numerical comparison between the results obtained by the two approaches was made for the POE of
two limit values = 70% and 80% of the design Mt. When the former limit is used, the proposed procedure leads to around 550 times reduction of the POE. When the latter limit is used, the proposed procedure leads to around 220 times reduction of the POE.
Although the numerical results refer design MW,h and only
particular case, a conclusion can be made that of the
to this the
reduction of the POE (calculated with the proposed procedure)
design Mt is
A-94
©2012: The Royal Institution of Naval Architects
POE of design M(W,hog) [-]
2.61E-05 3.32E-06 0.00E+00 3.24E-07
POE [-]
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