Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012 recorded max MW is used
100 120 140
20 40 60 80
0
histogram for max M(W,h,1)
Gamma (3P) PDF
The results refer only to max MW,h,1 ; POO = 10-1; POE design MW,h ≈ 0
portion of design M(W, h) [-]
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Figure. 7 POE of the design MW when POO = 10-1 of the recorded max MW is used
0.0 0.1 0.2 0.3 0.4 0.5 0.6
histogram for max M(W,h,0)
Beta PDF
The results refer only to max MW,h,0 ;
i.e. POO = 1; POE design MW,h = 3.24x10-7
portion of design M(W, h) [-]
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Figure. 8 POE of the design MW, h when POO = 1 of the recorded max MW, h is used
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
histogram for max M(W,hog) Kumaraswami PDF
The results refer to all max MW,h when POO of max MW,h is neglected; POE
design MW,h = 0.0185
portion of design M(W, h) [-]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Figure. 9 POE of the design MW,h when the POO of the
recorded max MW,h is neglected Step IV: Replacing each histogram containing maximal amplitudes
with the same POE with theoretical
distribution The POE of the design MW,h is calculated by the formula:
PP max M designMd, hht W, W, Step V: Calculating the POE of any given value
In the paper, the design MW is taken as a given value. Because the probabilistic distributions of maximal MW,h,i in each group “i” are not identical, the POE of the design
MW,h is calculated in the following way: max i
PP 10
d, i i0
i (17) One should emphasize here that the design MW,h is
calculated by the formulas given in class societies’ rules, (e.g., ABS Rules, 2011) which is the most probable extreme value of MW derived with amplitude statistics.
the individual
The multiplier 10 - i serves as weight coefficient to take into consideration the conditional probability for the data “to get in the corresponding i-group” in which the POE
of the design MW,h is calculated. The notation of the groups in the example for MW.h is:
Group 0 corresponds to POO = 1 Group 1 corresponds to POO = 0.1 Group 2 corresponds to POO = 0.01 Group 3 corresponds to POO = 0.001
The change of the final POE of the design MW,h is illustrated in Figure. 10 and Figure. 11.
3.0E-02 The time window of the 2.0E-02
records is 60 minutes over one year. The probabilistic ranges are treated as independent. Then, POE design M(W,h) = 2.64E-02
1.0E-02 (16)
0.0E+00
32 1 group number
Figure. 10 POE of 0 the design MW,h when the
©2012: The Royal Institution of Naval Architects
A-93
PDF [-]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
PDF [-] frequency [-]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
frequency [-]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
PDF [-]
frequency [-]
POE of design M(W,hog) [-]
2.61E-02
3.32E-04 0.00E+00 3.24E-07
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