Erdem Acar, Raphael T. Haftka, Nam-Ho Kim, Deepti

[Steve Yenisch]

Paper: www.mae.ufl.edu/nkim/ISSMO/KimPaper.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/KimPresentation.pdf

Including the Effects of Future Tests in Aircraft Structural Design
Erdem Acar¹, Raphael T. Haftka², Nam-Ho Kim², Deepti Buchi²

1 TOBB University of Economics and Technology, Söğütözü, Ankara, Turkey
[e-mail]
2 University of Florida, Gainesville, Florida, USA.
[e-mail]
[e-mail]
[e-mail]

ABSTRACT
In this paper, we investigate the effects of future tests on aircraft structural safety, focusing on the numbers of coupon tests and structural element tests. The mean failure stress is assumed to be predicted by a failure criterion (e.g. Tsai-Wu), and the initial distribution of this mean failure stress reflects the uncertainty in the analysis procedure that uses coupon test data to predict structural failure. In addition to the uncertainty in the mean failure stress, there is also uncertainty in its variability due to the finite number of coupon tests. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. We consider structural design based on point stress analysis following the FAA regulations (using B-basis allowables), and show tradeoffs between the number of tests and the weight of the structure for a given probability of failure. We found that element tests are more influential than coupon tests. This indicates that aircraft companies may reduce the number of coupon tests by moving to reliability-based design optimization (RBDO).

[Stratos]

May 13, 2009 23:06:07 GMT -5 Steve Yenisch said:

Paper: www.mae.ufl.edu/nkim/ISSMO/KimPaper.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/KimPresentation.pdf

Including the Effects of Future Tests in Aircraft Structural Design
Erdem Acar¹, Raphael T. Haftka², Nam-Ho Kim², Deepti Buchi²

1 TOBB University of Economics and Technology, Söğütözü, Ankara, Turkey
[e-mail]
2 University of Florida, Gainesville, Florida, USA.
[e-mail]
[e-mail]
[e-mail]

ABSTRACT
In this paper, we investigate the effects of future tests on aircraft structural safety, focusing on the numbers of coupon tests and structural element tests. The mean failure stress is assumed to be predicted by a failure criterion (e.g. Tsai-Wu), and the initial distribution of this mean failure stress reflects the uncertainty in the analysis procedure that uses coupon test data to predict structural failure. In addition to the uncertainty in the mean failure stress, there is also uncertainty in its variability due to the finite number of coupon tests. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. We consider structural design based on point stress analysis following the FAA regulations (using B-basis allowables), and show tradeoffs between the number of tests and the weight of the structure for a given probability of failure. We found that element tests are more influential than coupon tests. This indicates that aircraft companies may reduce the number of coupon tests by moving to reliability-based design optimization (RBDO).

1) The title is not descriptive of the paper. The paper investigates the effect of certification tests on reliability -- it does not present a design method that that accounts for anticipated future test results.
2) Are the conclusions on pages 22 and 23 general or are they based on the examples in this paper?
3) On page 16, it is assumed that the variables describing the geometry and material properties are independent. I do not think that the independence assumption is realistic.
4) What is the performance function in the calculation of the probability of failure? Is it Eq. 23 in the paper?
5) On page 8, justify the assumption that the stress at failure is normal. Uncertainty in the type of the distribution of the stress at failure can be important.

[Nam Ho Kim]

Stratos:

1) The title is not descriptive of the paper. The paper investigates the effect of certification tests on reliability -- it does not present a design method that that accounts for anticipated future test results.

R) We anticipate the situation that the coupon/element tests are not performed yet at the design stage.Thus, the design engineer must consider their effect using distributions of distributions. We will reinforce this aspect in the paper.

2) Are the conclusions on pages 22 and 23 general or are they based on the examples in this paper?

R) The conclusions are based on our assumption on distributions types. We will invstigate the effect of other distribution types in the near future.

3) On page 16, it is assumed that the variables describing the geometry and material properties are independent. I do not think that the independence assumption is realistic.

R) Could you suggest what would be the reasonable way of modeling them? If you have any examples, that will help us a lot.

4) What is the performance function in the calculation of the probability of failure? Is it Eq. 23 in the paper?

R) Yes, it is the probability of failure at the certification tests in Eq. (23). We will make cross-reference in the paper.

5) On page 8, justify the assumption that the stress at failure is normal. Uncertainty in the type of the distribution of the stress at failure can be important.

R) There is no particular reason of using normal distriution. We agree that the type of distribution will be important. We will investigate the effect of distribution type in the near future.

Thanks,

Nam-Ho

[Stratos]

May 21, 2009 15:16:13 GMT -5 @Nam Ho Kim said:

Stratos:

1) The title is not descriptive of the paper. The paper investigates the effect of certification tests on reliability -- it does not present a design method that that accounts for anticipated future test results.

R) We anticipate the situation that the coupon/element tests are not performed yet at the design stage.Thus, the design engineer must consider their effect using distributions of distributions. We will reinforce this aspect in the paper.

2) Are the conclusions on pages 22 and 23 general or are they based on the examples in this paper?

R) The conclusions are based on our assumption on distributions types. We will investigate the effect of other distribution types in the near future.

3) On page 16, it is assumed that the variables describing the geometry and material properties are independent. I do not think that the independence assumption is realistic.

R) Could you suggest what would be the reasonable way of modeling them? If you have any examples, that will help us a lot.

4) What is the performance function in the calculation of the probability of failure? Is it Eq. 23 in the paper?

R) Yes, it is the probability of failure at the certification tests in Eq. (23). We will make cross-reference in the paper.

5) On page 8, justify the assumption that the stress at failure is normal. Uncertainty in the type of the distribution of the stress at failure can be important.

R) There is no particular reason of using normal distribution. We agree that the type of distribution will be important. We will investigate the effect of distribution type in the near future.

Thanks,

Nam-Ho

Nam-Ho,

Thank you.

Regarding your response about the independence assumption, you could describe the dependence of the random variables using a copula. This is a function of the marginal CDFs of the random variables that is defined in terms of one or more parameters. For two random variables, their joint CDF can be expressed in the form C(U,V, theta) where U and V are the values of the CDFs of the random variables and theta is a vector of parameters. I will email you a paper on copulas.

[Stratos]

May 21, 2009 16:56:11 GMT -5 @Stratos said:

May 21, 2009 15:16:13 GMT -5 @Nam Ho Kim said:

Stratos:

1) The title is not descriptive of the paper. The paper investigates the effect of certification tests on reliability -- it does not present a design method that that accounts for anticipated future test results.

R) We anticipate the situation that the coupon/element tests are not performed yet at the design stage.Thus, the design engineer must consider their effect using distributions of distributions. We will reinforce this aspect in the paper.

2) Are the conclusions on pages 22 and 23 general or are they based on the examples in this paper?

R) The conclusions are based on our assumption on distributions types. We will investigate the effect of other distribution types in the near future.

3) On page 16, it is assumed that the variables describing the geometry and material properties are independent. I do not think that the independence assumption is realistic.

R) Could you suggest what would be the reasonable way of modeling them? If you have any examples, that will help us a lot.

4) What is the performance function in the calculation of the probability of failure? Is it Eq. 23 in the paper?

R) Yes, it is the probability of failure at the certification tests in Eq. (23). We will make cross-reference in the paper.

5) On page 8, justify the assumption that the stress at failure is normal. Uncertainty in the type of the distribution of the stress at failure can be important.

R) There is no particular reason of using normal distribution. We agree that the type of distribution will be important. We will investigate the effect of distribution type in the near future.

Thanks,

Nam-Ho

Nam-Ho,

Thank you.

Regarding your response about the independence assumption, you could describe the dependence of the random variables using a copula. This is a function of the marginal CDFs of the random variables that is defined in terms of one or more parameters. For two random variables, their joint CDF can be expressed in the form C(U,V, theta) where U and V are the values of the CDFs of the random variables and theta is a vector of parameters. I will email you a paper on copulas.

Additional comment: KK Choi has modeled dependence using copulas. His paper at this conference has some information.