Ikjin Lee, K.K. Choi, Yoojeong Noh

[Steve Yenisch]

Paper: www.mae.ufl.edu/nkim/ISSMO/IkjinLeePaper.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/IkjinLeePresentation.pptx

Comparison Study between Probabilistic and Possibilistic Approaches for Problems with Correlated Input and Lack of Input Statistical Information
Ikjin Lee, K.K. Choi, and Yoojeong Noh
Department of Mechanical & Industrial Engineering
College of Engineering
The University of Iowa, Iowa City, IA 52242, U.S.A.
Email: [e-mail]
[e-mail]
[e-mail]

ABSTRACT
Due to expensive experimental testing costs, in most industrial engineering applications, only limited statistical information is available to describe the input uncertainty model. It would be unreliable to use an estimated input uncertainty model, such as distribution types and parameters including the standard deviations for the distributions, that is obtained from insufficient data for the design optimization. Furthermore, when input variables are correlated, we would obtain non-optimum design if we use the assumption of independency for the design optimization.
In this paper, two methods for problems with lack of input statistical information – possibility-based design optimization (PBDO) and reliability-based design optimization (RBDO) with confidence level on the input model – are compared using a mathematical example and Abrams roadarm of an M1A1 tank. The comparison study shows that the PBDO could provide an unreliable optimum design when the number of samples is very small and that it provides an optimum design that is too conservative when the number of samples is relatively large. Furthermore, the optimum design does not converge to the optimum design obtained using the true input distribution as the number of samples increases. On the other hand, the RBDO with confidence level on the input model provides a conservative and reliable optimum design in a stable manner, and the optimum design converges to the optimum design obtained using the true input distribution as the number of samples increases.

[Christian Gogu]

Dear authors,

For the analytical example did you also do the RBDO with the true values of the distributions? If yes I would be interested in the average cost with the true values of the distributions.
I would also find it interesting to have the min and max of the cost. That way one would have a direct mapping of what is gained in cost by the increase in probability of failure for this particular problem.
Thank you.

Christian Gogu

[Ikjin Lee]

Using true distribution, there is only one cost value, which is
-3.127. The optimum design is (6.264, 3.138). Again, when the
true distribution is used, then there is no need to do statistical
test. So, there is no min and max for the true distribution.
Thank you.

May 18, 2009 18:30:18 GMT -5 Christian Gogu said:

Dear authors,

For the analytical example did you also do the RBDO with the true values of the distributions? If yes I would be interested in the average cost with the true values of the distributions.
I would also find it interesting to have the min and max of the cost. That way one would have a direct mapping of what is gained in cost by the increase in probability of failure for this particular problem.
Thank you.

Christian Gogu

[Christian Gogu]

Thanks.
What I meant was to also have the min and max of the cost for the three methods of Table 3. Basically that will show how much is gained on the cost function by being unconservative. For example for RBDO with estimated parameters (with 500 samples) I assume the most unconservative case is either the one which led to PF2=3.1161 or to PF3=3.1172. Do you have the cost value for this most unconservative case? This will give the gain on the cost function corresponding to having a Pf of about 3.1 instead of 2.3. I think it is interesting information to have.

May 18, 2009 20:14:57 GMT -5 @Ikjin Lee said:

Using true distribution, there is only one cost value, which is
-3.127. The optimum design is (6.264, 3.138). Again, when the
true distribution is used, then there is no need to do statistical
test. So, there is no min and max for the true distribution.
Thank you.

May 18, 2009 18:30:18 GMT -5 Christian Gogu said:

Dear authors,

For the analytical example did you also do the RBDO with the true values of the distributions? If yes I would be interested in the average cost with the true values of the distributions.
I would also find it interesting to have the min and max of the cost. That way one would have a direct mapping of what is gained in cost by the increase in probability of failure for this particular problem.
Thank you.

Christian Gogu

[Ikjin Lee]

For the most unconservative case, RBDO with estimated parameter shows PF2=3.1161 or to PF3=3.1172 with the cost =
-3.2869. It seems that the cost value is not much different from the true cost = -3.127. But, the cost value depends on the cost function shape. In this case, we used linear cost function. If this function becomes highly nonlinear, then we could see different result.
For the same data set, using RBDO with upper bound, then the cost is -3.1411 and using PBDO, the cost is -2.430. So, we can see that even for the worst case, RBDO with upper bound shows very close result to the true one, whereas PBDO is too conservative.
Thank you.

May 19, 2009 9:29:18 GMT -5 Christian Gogu said:

Thanks.
What I meant was to also have the min and max of the cost for the three methods of Table 3. Basically that will show how much is gained on the cost function by being unconservative. For example for RBDO with estimated parameters (with 500 samples) I assume the most unconservative case is either the one which led to PF2=3.1161 or to PF3=3.1172. Do you have the cost value for this most unconservative case? This will give the gain on the cost function corresponding to having a Pf of about 3.1 instead of 2.3. I think it is interesting information to have.

May 18, 2009 20:14:57 GMT -5 @Ikjin Lee said:

Using true distribution, there is only one cost value, which is
-3.127. The optimum design is (6.264, 3.138). Again, when the
true distribution is used, then there is no need to do statistical
test. So, there is no min and max for the true distribution.
Thank you.