Prediction of Extreme Sloshing Pressure Using Different Statistical Models

  • Cetin, Ekin Ceyda (Department of Naval Architecture & Ocean Engineering, Seoul National University) ;
  • Lee, Jeoungkyu (Department of Naval Architecture & Ocean Engineering, Seoul National University) ;
  • Kim, Sangyeob (Department of Naval Architecture & Ocean Engineering, Seoul National University) ;
  • Kim, Yonghwan (Department of Naval Architecture & Ocean Engineering, Seoul National University)
  • Received : 2018.10.11
  • Accepted : 2018.11.28
  • Published : 2018.12.31


In this study, the extreme sloshing pressure was predicted using various statistical models: three-parameter Weibull distribution, generalized Pareto distribution, generalized extreme value distribution, and three-parameter log-logistic distribution. The estimation of sloshing impact pressure is important in design of liquid cargo tank in severe sea state. In order to get the extreme values of local impact pressures, a lot of model tests have been carried out and statistical analysis has been performed. Three-parameter Weibull distribution and generalized Pareto distribution are widely used as the statistical analysis method in sloshing phenomenon, but generalized extreme value distribution and three-parameter log-logistic distribution are added in this study. Additionally, statistical distributions are fitted to peak pressure data using three different parameter estimation methods. The data were obtained from a three-dimensional sloshing model text conducted at Seoul National University. The loading conditions were 20%, 50%, and 95% of tank height, and the analysis was performed based on the measured impact pressure on four significant panels with large sloshing impacts. These fittings were compared by observing probability of exceedance diagrams and probability plot correlation coefficient test for goodness-of-fit.


E1GPC1_2018_v4n4_185_f0001.png 이미지

Fig. 1 Experiment setup

E1GPC1_2018_v4n4_185_f0002.png 이미지

Fig. 3 POE diagrams of 0.20H, P.19, No.5

E1GPC1_2018_v4n4_185_f0003.png 이미지

Fig. 2 Layout of sensor cluster panels

E1GPC1_2018_v4n4_185_f0004.png 이미지

Fig. 4 POE curves for 5-hour test

E1GPC1_2018_v4n4_185_f0006.png 이미지

Fig. 6 POE curves of 5-hour experiment(left, 0.20H, P.14, No.09) and 100-hour experiment(right)

Table 1. Parameter estimation method for distribution and notation for each fit

E1GPC1_2018_v4n4_185_t0001.png 이미지

Table 2. Plotting position formulas

E1GPC1_2018_v4n4_185_t0002.png 이미지

Table 3. Test conditions

E1GPC1_2018_v4n4_185_t0003.png 이미지

Table 4. Selected four panels according to load condition

E1GPC1_2018_v4n4_185_t0004.png 이미지

Table 5. PPCC test results of (0.20H, P.19, No.5)

E1GPC1_2018_v4n4_185_t0005.png 이미지

Table 6. PPCC test results for whole data

E1GPC1_2018_v4n4_185_t0006.png 이미지

Fig. 5 POE curves that show the difference of GP

E1GPC1_2018_v4n4_185_t0007.png 이미지

Table 7. PPCC test results of tail-only data

E1GPC1_2018_v4n4_185_t0008.png 이미지

Table 8. PPCC test result for 100 hours of whole data and tail-only data

E1GPC1_2018_v4n4_185_t0009.png 이미지


  1. Cousineau, D., "Nearly Unbiased Estimators For the Three Parameter Weibull Distribution With Greater Efficiency Than the Iterative Likelihood Method," Brit J Math Stat Psychology, 62, 167-191, 2009.
  2. Cunnane, C., "Unbiased Plotting Positions - A Review," J Hydrology, 37(3/4), 205-222, 1978.
  3. Filliben, JJ (1975). "The Probability Plot Correlation Coefficient Test For Normality," Technometrics, 17(1), 111-117.
  4. Fillon, B, Diebold, L, Henry, J, et al., "Statistical Post-Processing of Long-Duration Sloshing Test," Proc 21th Int Offshore and Polar Eng Conf, Hawaii, ISOPE, 46-53, 2011.
  5. Grazcyk, M, Moan, T and Rognebakke, O., "Probabilistic Analysis of Characteristic Pressure for LNG Tanks," J Offshore Mech Arct, 128, 133-134, 2006.
  6. Grazcyk, M and Moan, T., "A Probabilistic Assessment of Design Sloshing Pressure Time Histories in LNG Tanks," Ocean Eng, 35, 834-855, 2008.
  7. Gran, S., "Statistical Distributions of Local Impact Pressures," Norweg Marit Res, 8(2), 2-13, 1981.
  8. Gringorten, II., "A Plotting Rule for Extreme Probability Paper," J Geophysical Res, 68(3), 813-814, 1963.
  9. Heo, J-H, Kho, YW, Shin, H, Kim, S., "Regression Equations of Probability Plot Coefficenttest Statistics From Several Probability Distributions," J Hydrology, 355, 1-15, 2008.
  10. Hosking, JRM., "L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics," J Royal Stat Society Series (B) Method, 52(1), 105-124, 1990.
  11. Kim, SY, Kim, Y, Kim, KH., "Statistical Analysis of Sloshing-Induced Random Impact Pressures," Proc Inst Mech Eng, Part M: J Eng Maritime Environ, 228(3), 235-248, 2014.
  12. Kuo, JF, Campbell, RB, Ding, Z, et al., "LNG Tank Sloshing Assessment Methodology - The New Generation," Int J Offshore and Polar Eng, ISOPE, 19(4), 241-253, 2009.
  13. Mathiesen, J., "Sloshing Loads Due to Random Pitching," Norweg Marit Res, 3(2), 2-13, 1976.
  14. Myung, IJ., "Tutorial on Maximum Likelihood Estimation," J Math Psychology, 47, 90-100, 2003.
  15. Pickands, J III., "Statistical Inference Using Extreme Order Statistics," Ann Stat, 3(1), 119-131, 1975.
  16. Smith, RL., "Maximum Likelihood Estimation In A Class Of Nonregular Cases," Biometrika, 72, 67-90, 1985.
  17. Vogel, RM., "The Probability Plot Correlation Coefficient Test for Normal, Lognormal, and Gumbel Distributional Hypotheses," Water Resources Res, 22(4), 587-590, 1986.