DRIFTING RESCUE UNITS HAZARD’S
IMPORTANCE ESTIMATION
Smolarek L.
Gdynia Maritime University, Gdynia, Poland
Abstract: In many cases the system structure of drifting rescue units (DRU) is not as
important as its operational possibility [1,3]. The DRU failure, especially capsizing, is caused not only by DRU system changes but is strongly effected by environment negative influences (the action of wind, currents, and waves), [ 4, 7].
1. Introduction
1The international regulations presented at the IMO papers describe technical parameters and general stability criteria for Drifting Rescue Units (DRU). Unfortunately the experiences obtained during SAR action shows that such criteria are not sufficient [9]. Risk, in this context, is defined as reductions in DRU stability due to changes of loading and the environment influence.
All methods established to measure the stability of DRU take into account only hydrostatic forces. There are situations where the capsizing depends seriously on the actual kind of wave motion. A way to get an understanding of the DRU capsizing is to investigate dynamical systems with periodic or stochastic excitations.
The major sources of stability loss are [5,8]:
gust risk is the momentum change of heeling force due to changes in wind speed; heeling risk is the change in DRU horizontal position due to the trim and changes of
a wave slope;
loading risk results from distribution of survivors inside DRU [11];
performance risk is the DRU stability losses resulting from the DRU movements on waves.
1 This research was conducted within the research grant number 4T12C 03827 financially
supported by the State Committee for Scientific Research, 2004/2005.
The Tail Value at Risk (TailVaR) is defined as the average of all capsizing scenarios over the 100th percentile, where is a selected probability level, such as 0.992. This
measure is larger than the Value at Risk for the same probability level because it is the average of all capsizing events that are over the Value at Risk, i.e. the 100th percentile. The Standard Deviation risk measure, for selected constant K (K=3), is defined as:
). (
3 ) (
3 E capsizing StdDevcapsizing
StdDev
These risk measures can be applied after (Post) and before (Pre) changes of the DRU system and the risk reduction measures is defined as follows:
eTailVaR R PostTailVa reduction TailVaR Pr 1 , (1) 3 3 3 1 PreStdDev PostStdDev reduction StdDev .
The standard deviation is often used to measure the risk of dynamic systems. The standard deviation is a measure of volatility it means that if system stability parameters more vary from the average return than the more volatile is the DRU stability.
The Tail Value at Risk reflects both the probability and magnitude of the capsizing probability. This measure is looking at one side of the possible outcomes. The stationarity of a system means:
in the statistical sense - that the mean, variance, skew and kurtosis of the system parameter distributions are taken to be stable through time;
in the dynamical sense - that the forms of the equations that describe a system’s dynamics are assumed to be constant through time.
2. Examples
The statistical analysis of water pocket and trim importance’s for 10 life raft.
Table 1. Statistical parameters for life raft without water pocket
Trim [deg] 0 1 2 4 6 8 10
Average 0,5809 0,5879 0,5938 0,6022 0,6066 0,6073 0,6049 Median 0,5749 0,5826 0,5903 0,6061 0,6113 0,6225 0,6061 Var 0,0788 0,0756 0,0736 0,0726 0,0737 0,0756 0,0775
2 REPORT TO AMERICAN ACADEMY OF ACTUARIES INDEX SECURITIZATION TASK FORCE by
CASUALTY ACTUARIAL SOCIETY VALUATION, FINANCE AND INVESTMENTS COMMITTEE, Harvey A. Sherman.
Stdev 0,2807 0,2749 0,2714 0,2694 0,2714 0,2750 0,2784 Skew -0,2059 -0,1820 -0,1889 -0,2420 -0,2848 -0,2897 -0,2616 Kurt -1,0410 -1,0805 -1,0591 -0,9889 -0,9853 -1,0345 -1,0879 Range 0,9760 0,9649 0,9649 0,9649 0,9649 0,9649 0,9649 1st Quartile 0,3751 0,3831 0,3909 0,3982 0,4010 0,3959 0,3909 3rd Quartile 0,8430 0,8439 0,8448 0,8517 0,8587 0,8671 0,8755 80th percentile 0,8853 0,8885 0,8918 0,8957 0,8995 0,9026 0,9048
Table 2. Statistical parameters for life raft with water pocket
Trim [deg] 0 1 2 4 6 8 10 Average 0,5410 0,5475 0,5529 0,5607 0,5651 0,5665 0,5652 Median 0,5280 0,5312 0,5343 0,5409 0,5413 0,5490 0,5413 Var 0,0420 0,0390 0,0370 0,0353 0,0353 0,0362 0,0371 Stdev 0,2050 0,1974 0,1923 0,1878 0,1880 0,1902 0,1926 Skew -0,6075 -0,5351 -0,5152 -0,5648 -0,6263 -0,6419 -0,6166 Kurt 0,0550 -0,0463 0,0081 0,2507 0,3570 0,3078 0,2172 Range 0,8298 0,8136 0,8136 0,8136 0,8136 0,8136 0,8136 1st Quartile 0,4569 0,4629 0,4682 0,4770 0,4831 0,4814 0,4792 3rd Quartile 0,7073 0,7100 0,7127 0,7181 0,7251 0,7320 0,7341 80th percentile 0,7483 0,7509 0,7535 0,7588 0,7595 0,7602 0,7627 199
Fig. 1. Plot of importance measures for water pocket as a function of life raft trim; TailVar1reduction, TailVar3reduction, StaDev3reduction
Fig. 2. Trim importance measures of 10 person life raft
The equation of the fitted model is
Fig. 3. Plot of fitted model
Table 3. Regression Analysis for GZz and GZbez
Parameter Estimate StandardError StatisticT P-Value
Intercept 0,150411 0,0051698 29,0943 0
Slope 0,700559 0,00589 118,94 0
Correlation Coefficient = 0,998484, R-squared = 99,697 percent, Standard Error of Est. = 0,0143633
Table 4. Analysis of Variance for GZz and GZbez
Source Sum of Squares Df SquareMean F-Ratio P-Value
Model 2,91854 1 2,91854 14146,79 0
Residual 0,00887109 43 0,000206
Total (Corr.) 2,92742 44
The equation of the fitted model is
CMz(with) = 0,115654 + 0,714268*CMbez(without) (3)
Fig. 4. Plot of fitted model for critical moment, 10-person life raft Table 5. Regression Analysis for CMz and CMbez
Parameter Estimate StandardError StatisticT P-Value Intercept 0,115654 0,0054045 21,3996 0
Slope 0,714268 0,006626 107,798 0
Table 6. Analysis of Variance
Source SquaresSum of Df SquareMean F-Ratio P-Value
Model 2,6529 1 2,6529 11620,45 0
Residual 0,0098167 43 0,0002283
Total (Corr.) 2,66272 44 Correlation Coefficient = 0,998155 R-squared = 99,6313 percent Standard Error of Est. = 0,0151095
Fig. 5. Plot of difference for righting arm Table 7. Kolmogorov-Smirnov Test
Estimated overall statistic DN 0,288889
Two-sided large sample K-S statistic 1,37032
Approximate P value 0,046775
In the Kolmogorov-Smirnov test, the maximum distance is 0,288889. The approximate P-value for the test is less than 0,05, there is a statistically significant difference between the two distributions at the 95,0% confidence level.
Fig. 6. Importance of life raft trim and influence of water pocket for righting moment
3. Summary
There is a relation between the capsizing of DRU and bifurcation scenarios of appropriated excited dynamical systems. Because of the
complexity of such problems a first step is to analyses these systems numerically [10].
The excitation forces and moments in the DRU system will be generated by wind and waves. Trim will play an important part in the stability of a DRU which is influenced by the wind.
The risk importance measure can help to analyze how the environment parameters affected the DRU as a system and its components and how such behavior may change over time.
Identification and hierarchisation of risk factors lead to identifying single causal factors or variables. Factors which influence a DRU safety can be split into three groups:
system parameters; environment factors; human factor.
Storm conditions can bring dynamic forces (wind and waves) into play so the water pockets play important role in a DRU stability.
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