Fig. 5.3 Cumulative distribution of simulated 10-min load maxima, which is plotted as a function of the
return period (average ice thickness: 0.165 m)
5.3 Correlation between the distribution of load maxima and the ice thickness
Fig. 5.4 shows the simulation results in the ice where the thickness is assumed to be uniformly distributed along the route. The Gumbel I distribution is fitted to the simulated 10-min load maxima, within each ice thickness class (except for class 8 and class 9, as the maximum icebreaking capacity of MS Kemira is about 0.5 m):
where J is Euler’s constant, 0.577. The cumulative distribution function given in Eq.
(5.1) is defined as conditional because the parameters ci and ui are correlated with the classified ice thickness, hi.
As shown in Fig. 5.5, the correlation betweenci, ui and hi can be determined by an approximate linear or quadratic regression. The conditional cumulative distribution function can then be translated into:
Fig. 5.3 Cumulative distribution of simulated 10-min load maxima, which is plotted as a function of the
return period (average ice thickness: 0.165 m)
5.3 Correlation between the distribution of load maxima and the ice thickness
Fig. 5.4 shows the simulation results in the ice where the thickness is assumed to be uniformly distributed along the route. The Gumbel I distribution is fitted to the simulated 10-min load maxima, within each ice thickness class (except for class 8 and class 9, as the maximum icebreaking capacity of MS Kemira is about 0.5 m):
where J is Euler’s constant, 0.577. The cumulative distribution function given in Eq.
(5.1) is defined as conditional because the parameters ci and ui are correlated with the classified ice thickness, hi.
As shown in Fig. 5.5, the correlation betweenci, ui and hi can be determined by an approximate linear or quadratic regression. The conditional cumulative distribution function can then be translated into:
Short-Term Distribution of Maximum Ice Loads on a Frame 59
Fig. 5.3 Cumulative distribution of simulated 10-min load maxima, which is plotted as a function of the
return period (average ice thickness: 0.165 m)
5.3 Correlation between the distribution of load maxima and the ice thickness
Fig. 5.4 shows the simulation results in the ice where the thickness is assumed to be uniformly distributed along the route. The Gumbel I distribution is fitted to the simulated 10-min load maxima, within each ice thickness class (except for class 8 and class 9, as the maximum icebreaking capacity of MS Kemira is about 0.5 m):
where J is Euler’s constant, 0.577. The cumulative distribution function given in Eq.
(5.1) is defined as conditional because the parameters ci and ui are correlated with the classified ice thickness, hi.
As shown in Fig. 5.5, the correlation betweenci, ui and hi can be determined by an approximate linear or quadratic regression. The conditional cumulative distribution function can then be translated into:
Short-Term Distribution of Maximum Ice Loads on a Frame 59
Fig. 5.3 Cumulative distribution of simulated 10-min load maxima, which is plotted as a function of the
return period (average ice thickness: 0.165 m)
5.3 Correlation between the distribution of load maxima and the ice thickness
Fig. 5.4 shows the simulation results in the ice where the thickness is assumed to be uniformly distributed along the route. The Gumbel I distribution is fitted to the simulated 10-min load maxima, within each ice thickness class (except for class 8 and class 9, as the maximum icebreaking capacity of MS Kemira is about 0.5 m):
where J is Euler’s constant, 0.577. The cumulative distribution function given in Eq.
(5.1) is defined as conditional because the parameters ci and ui are correlated with the classified ice thickness, hi.
As shown in Fig. 5.5, the correlation betweenci, ui and hi can be determined by an approximate linear or quadratic regression. The conditional cumulative distribution function can then be translated into:
that these parameters are dependent on the hull shape and the frame angle. The assumed correlation in Fig. 5.5 is fit for a specified frame on a specified ship hull, herein further validations are needed.
The final cumulative distribution function of w can be obtained by integrating the conditional cumulative distribution function over the relevant statistics of hi:
,1 ,2 2
icebreaking capacity of the ship.
Fig. 5.4 Fitted Gumbel distribution to the simulated 10-min load maxima within each ice thickness class
Fig. 5.5Parameters of fitted Gumbel distribution as a function of the classified ice thickness
that these parameters are dependent on the hull shape and the frame angle. The assumed correlation in Fig. 5.5 is fit for a specified frame on a specified ship hull, herein further validations are needed.
The final cumulative distribution function of w can be obtained by integrating the conditional cumulative distribution function over the relevant statistics of hi:
,1 ,2 2
icebreaking capacity of the ship.
Fig. 5.4 Fitted Gumbel distribution to the simulated 10-min load maxima within each ice thickness class
Fig. 5.5Parameters of fitted Gumbel distribution as a function of the classified ice thickness
60 Chapter 5 that these parameters are dependent on the hull shape and the frame angle. The assumed correlation in Fig. 5.5 is fit for a specified frame on a specified ship hull, herein further validations are needed.
The final cumulative distribution function of w can be obtained by integrating the conditional cumulative distribution function over the relevant statistics of hi:
,1 ,2 2
icebreaking capacity of the ship.
Fig. 5.4 Fitted Gumbel distribution to the simulated 10-min load maxima within each ice thickness class
that these parameters are dependent on the hull shape and the frame angle. The assumed correlation in Fig. 5.5 is fit for a specified frame on a specified ship hull, herein further validations are needed.
The final cumulative distribution function of w can be obtained by integrating the conditional cumulative distribution function over the relevant statistics of hi:
,1 ,2 2
icebreaking capacity of the ship.
Fig. 5.4 Fitted Gumbel distribution to the simulated 10-min load maxima within each ice thickness class
The empirical studies (e.g. Kujala, 1994) have shown that the best correlation between measured winter maximum ice load values and prevailing ice conditions is obtained when the equivalent level ice thickness is used to describe the annual ice conditions instead of parameters such as the maximum ice extent, fast or pack ice thickness. In view of this, Eq. (5.5) indicates a potential way to evaluate the long-term ice load statistics based on short-term simulations.
The empirical studies (e.g. Kujala, 1994) have shown that the best correlation between measured winter maximum ice load values and prevailing ice conditions is obtained when the equivalent level ice thickness is used to describe the annual ice conditions instead of parameters such as the maximum ice extent, fast or pack ice thickness. In view of this, Eq. (5.5) indicates a potential way to evaluate the long-term ice load statistics based on short-term simulations.
Short-Term Distribution of Maximum Ice Loads on a Frame 61
The empirical studies (e.g. Kujala, 1994) have shown that the best correlation between measured winter maximum ice load values and prevailing ice conditions is obtained when the equivalent level ice thickness is used to describe the annual ice conditions instead of parameters such as the maximum ice extent, fast or pack ice thickness. In view of this, Eq. (5.5) indicates a potential way to evaluate the long-term ice load statistics based on short-term simulations.
Short-Term Distribution of Maximum Ice Loads on a Frame 61
The empirical studies (e.g. Kujala, 1994) have shown that the best correlation between measured winter maximum ice load values and prevailing ice conditions is obtained when the equivalent level ice thickness is used to describe the annual ice conditions instead of parameters such as the maximum ice extent, fast or pack ice thickness. In view of this, Eq. (5.5) indicates a potential way to evaluate the long-term ice load statistics based on short-term simulations.
62 Chapter 5 62 Chapter 5
63