Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012 F = CDF (both functions are calculated for ye = )


The other approach is to use numerical methods when records of the random process are available. In this case, the basic steps in the application of the EVT are shown in Figure. 1.


Step 1: A new histogram is built that contains only the maximal amplitudes in each time window.


Available records of the random process


1


2 3


Building histogram containing only maximal amplitudes


Replacing the histogram of


maximal amplitudes with theoretical probabilistic distribution


Calculating the probability of exceedance of any given value


Figure. 1 Basic steps in EVT approach


Step 2: The histogram of all maximal amplitude is replaced by theoretical probabilistic distribution obtained by some of the available computer programs or analytical formulas. No doubt, the new histogram will be located much further towards the large corresponding


values of the random variance under consideration


relative to the original histogram built with the individual amplitude statistics.


Step 3: As one can expect, when the POE of the originally given permissible limit (used in the case when individual statistics are applied) is calculated, it is much higher than the originally calculated POE with the individual amplitude statistics. In some publications (e.g., Faulkner, Sadden 1979; Ochi 1973) on design wave bending moments given in classification societies’ rules, its POE is calculated as 63.2% when extreme value statistics is applied. In mathematical terms, this number refers to the POE of the most probable extreme value. In a special case when the design wave bending moment is chosen such that its POE is 1/N (N is the number of cycles) it is treated as the most probable extreme value. Hence, the 63.2% POE of the most probable extreme value


Mathematically, the result


becomes 63.2% POE of the is correct


design MW. within the


assumptions made in the EVT (i.e. when the random variables in each time window are independent and identically distributed and the design MW is equal to the


A-90


most probable extreme MW). Whatever the interpretation of this 63.2%, if the POE of the


design MW in


classification societies’ rules is calculated by the traditional EVT following the above described procedure, then its POE will be much larger than if the individual amplitude statistics are used. Therefore, the proponents of the application of the EVT for assessing the hull girder bending moments propose increases of the design hull girder wave induced bending moments. Prior to doing that some aspects of the EVT application should be analyzed considering also the experience from real ship’s operation. If the calculations with the EVT of the POE of this design hull girder bending moment are correct, ships would suffer more severe casualties than previously observed.


To avoid misinterpretations of the obtained numerical results with the EVT, it would be useful to address the above mentioned fundamental assumptions. One should either make some changes in the EVT or improve its application and interpretation.


2.


PROPOSAL FOR A PROCEDURE CONSIDERING THE PROBABILITY OF OCCURRENCE OF THE MAXIMAL VALUE IN EACH TIME WINDOW


The basic steps in the proposed procedure are shown in Figure. 2. However, before commencing the explanation of each step in the proposed procedure, some information for the analysis of the available records of the random process should be given. In the paper, records of full scale measurements of a container ship are


used.


Comprehensive information for the multi-year full scale measurements can be found in (Yu H C et al 2006, 2008; Lee S J et al 2010). The strain gauges mounted on the hull girder of a container ship provide information for the recorded stresses. Based on the geometric properties of the hull girder at sections though the gauging’ location, the records of the total bending moments (B.M.) are obtained. Since the study targets only vertical hull girder bending moment


(VWBM), high-frequency horizontal and torsion bending moments are filtered.


The wave B.M. (MW) and still water B.M. (MSW) are extracted from the records of the total B.M. taking into consideration the ratio between wave-induced hogging


B.M. (MW,h) and sagging B.M. (MW,s) as a function of block coefficient. For


real ships, the sagging wave


bending moment is always greater than hogging wave bending moment because the block coefficient (CB) is always smaller than unity. This fact is reflected in all class rules. What causes this difference is the side structure flair in bow and stern part of the ship. The two bending moments will be equal only in the case when the block coefficient is equal to unity.


Abrahamsen and Vedeler (1957, 1958) derived the


following formulas for the dimensionless coefficients,  , for sagging and hogging wave bending moments:


©2012: The Royal Institution of Naval Architects load,


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