1. MARINTEK Efficient prediction of extreme ship responses by MingKang Wu Centre for Ships and Ocean Structures, NTNU Norwegian Marine Technology Research Institute

2. MARINTEK Outline Predictions of long-term and short-term extreme ship responses (nonlinear VBMs and VSFs) Time-domain nonlinear simulation Sensitivity study Statistical uncertainty

3. MARINTEK Prediction of long-term extreme ship responses Probability of exceedance Separation of wave heading and sea state Equal probability of different wave headings Scatter diagram

4. MARINTEK Prediction of long-term extreme ship responses Minimum steering speed is about 5 knots Head seas is the most critical wave heading as far as VBMs and VSFs are concerned Only a few sea states are relevant to the extreme ship responses Part of the IACS scatter diagram (Total number of occurrences is 100,000) H s (m) T z (s) 9.510.511.512.513.514.5 8.5 255.9350.6296.9174.677.627.7 9.5 101.9159.9152.299.248.318.7 10.5 37.967.571.751.527.311.4 11.5 13.326.631.424.714.26.4 12.5 4.49.912.811.06.83.3 13.5 1.43.55.04.63.11.6

5. MARINTEK Prediction of short-term extreme ship responses Probability of exceedance per unit time for extreme linear rigid-body responses Probability of exceedance per unit time for extreme nonlinear flexible-body responses (hydroelastic responses)

6. MARINTEK Evaluation of distribution parameters Method of moments Assumes equal importance of all peak values Distribution function for an overall fit to all peaks may fail to accurately describe the high peaks Weighted curve fitting Force the distribution function closer to the simulated one in the high-value region No theoretical method for selecting the best weighing function Larger weight in the high-value region can produce better distribution tail but will also increase the statistical uncertainty due to the randomness of individual time-domain simulations of limited period

7. MARINTEK Peak Over Threshold (POT) Conditional distribution function of the peaks over sufficiently high threshold asymptotically approaches generalized Pareto distribution (Pickands, 1975) Probability of exceedance

8. MARINTEK Time-domain nonlinear simulation Computer program WINSIR (Wave-INduced ShIp Responses). Potential flow theory. Total response=linear response + nonlinear modification. Linear response. 3D approach 2.5D approach (high-speed strip theory) 2D approach (conventional strip theory) Nonlinear modification. Nonlinear Froude-Krylov and restoring forces Slamming force Viscous roll damping

9. MARINTEK Time-domain nonlinear simulation Calculation of slamming force Wagner Von Karman + correction for pile-up water Von Karman (momentum slamming)

10. MARINTEK Time-domain nonlinear simulation Calculation of load effects Conventional approach for rigid ship hull Modal superposition for flexible ship hull Hybrid method (mode acceleration) Hydrodynamic force Inertia force

11. MARINTEK Time-domain nonlinear simulation Example Main particulars of the SL-7 containership and the LNG ship Parameter SL-7LNG Length between perpendiculars (m)270324 Breadth (m)32.250.0 Draught amidships (m)9.9511.7 Displacement (tonnes)50500148350 Block coefficient0.5850.753 Centre of gravity aft of amidships (m)9.801.37 Centre of gravity above base line (m)13.716.3 Radius of gyration in pitch (m)65.580.8 Moment of inertia amidships (m 4 )3501200

12. MARINTEK Time-domain nonlinear simulation Example

13. MARINTEK Time-domain nonlinear simulation Example

14. MARINTEK Time-domain nonlinear simulation Example

15. MARINTEK Time-domain nonlinear simulation Example

16. MARINTEK Time-domain nonlinear simulation Example

17. MARINTEK Time-domain nonlinear simulation Example

18. MARINTEK Time-domain nonlinear simulation Example

19. MARINTEK Time-domain nonlinear simulation Example

20. MARINTEK Time-domain nonlinear simulation Example

21. MARINTEK Time-domain nonlinear simulation Example

22. MARINTEK Time-domain nonlinear simulation Example

23. MARINTEK Time-domain nonlinear simulation Example

24. MARINTEK Time-domain nonlinear simulation Example

25. MARINTEK Sensitivity study Sensitivity of short-term extreme load effects to changes in Stiffness distribution Modal damping ratio (0.005, 0.01, 0.015) Stiffness level

26. MARINTEK Sensitivity study Influence of stiffness distribution Influence of stiffness distribution on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; damping ratio=0.01; P 3hrs (R e >r)=0.01; U=5knots; H s =7.5m, T z =10.5s Stiffness distribution SaggingHogging VBM f /VBM r Amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp 11.1771.1161.0981.1341.1301.097 21.1781.1141.0971.1371.1281.101 31.1751.1141.1001.1341.1271.104

27. MARINTEK Sensitivity study Influence of stiffness distribution Influence of stiffness distribution on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; damping ratio=0.01; P 3hrs (R e >r)=0.01; U=10knots; H s =7.5m, T z =10.5s Stiffness distribution SaggingHogging VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp 11.3351.3641.1871.1901.3601.130 21.3331.3601.1871.1931.3601.137 31.3321.3601.1891.1971.3671.136

28. MARINTEK Sensitivity study Influence of modal damping Influence of modal damping on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; Stiffness distribution 2; P 3hrs (R e >r)=0.01; U=5knots; H s =7.5m, T z =10.5s Damping ratio SaggingHogging VBM f /VBM r Amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp 0.0051.1831.0931.0991.1571.1581.122 0.011.1781.1141.0971.1371.1281.101 0.0151.1681.1051.0951.1181.1061.087

29. MARINTEK Sensitivity study Influence of modal damping Influence of modal damping on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; Stiffness distribution 2; P 3hrs (R e >r)=0.01; U=10knots; H s =7.5m, T z =10.5s Damping ratio SaggingHogging VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp VBM f /VBM r amidships VBM f /VBM r at 0.25L pp VSF f /VSF r at 0.25L pp 0.0051.3461.3571.1911.2401.4841.164 0.011.3331.3601.1871.1931.3601.137 0.0151.3161.3551.1841.1621.2771.110

30. MARINTEK Sensitivity study Variations in the longitudinal stiffness distribution do not produce any noticeable difference in the extreme vertical hydroelastic load effects. Using the simplest constant longitudinal stiffness distribution over the whole ship length is totally acceptable. 50% decrease or increase in the modal damping ratio cause less than 2% changes in the extreme sagging hydroelastic load effects but slightly larger changes in the extreme hogging hydroelastic load effects. Those changes are not considered to be significant in practice. Therefore, using 0.01 as the modal damping ratio can be justified.

31. MARINTEK Statistical uncertainty (on-going research work) Selection of the threshold in the POT method and its impact on the prediction of the short-term extreme load effects Scattering of the predicted short-term extreme load effects due to the time-domain simulations of limited period

32. MARINTEK