Diane Villanueva, A. Sharma, RT. Haftka, BV.Sankar

[Steve Yenisch]

Paper: dl.getdropbox.com/u/473092/WCSMO8.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/Diane_internetconf.htm

Risk Allocation by Optimization of an Integrated Thermal Protection System
Diane Villanueva¹, Anurag Sharma², Raphael T. Haftka³, Bhavani V. Sankar⁴

1 Graduate Research Assitant, University of Florida, Gainesville, FL, U.S.A
[e-mail]
2 PhD Candidate, University of Florida, Gainesville, FL, U.S.A
[e-mail]
3 Distinguished Professor, University of Florida, Gainesville, FL, U.S.A
[e-mail]
4 Ebaugh Professor, University of Florida, Gainesville, FL, U.S.A
[e-mail]

ABSTRACT
Space vehicles traveling at hypersonic speeds through a planetary atmosphere experience severe aerodynamic heating. An integrated thermal protection system (ITPS) serves to protect the vehicle from this aerodynamic heating, while also providing some structural load bearing function. The design of an ITPS is a compromise between structural requirements of robust structural members and the need to limit the heat conducted through these members. This compromise is an exercise in risk allocation between structural and thermal failures.
In deterministic approaches, risk allocation between failure modes is implicit in the choice of safety factors and margins. Probabilistic optimization can be used to allocate risk explicitly between failure modes. Previous work has shown the differences in risk allocation between deterministic and probabilistic optimization with constraints on the maximum temperature and buckling of the ITPS web. In this study, the effect of addition of a constraint on the maximum von Mises stress in the web on the risk allocation is examined. The ABAQUS finite element program is used to generate transient thermal response under reentry heating loads, and the structural response is calculated at critical times (e.g., time at which temperature gradient is maximum) during the re-entry process. Separable Monte Carlo is used to evaluate the limit states corresponding to the three failure modes. Probabilistic optimization reduced the mass of the ITPS by 1.2% while maintaining the same level of reliability as the deterministic design. More risk was allocated to thermal and stress failures after optimization and the probability of buckling failure was greatly reduced. The presence of only a few combined thermal-stress and buckling-stress failure modes were noted in the deterministic design, and even fewer were found in the probabilistic design.

[Nam Ho Kim]

Dear Diane:

In your example, the three failure modes are almost separated. In such a case, you can define your system failure as a sum of three individual failure modes. Will your method still work of the overlaps between different failure modes are significant? In such as case, will the allocation of different faiure probability be possible?

[dvillanueva]

May 18, 2009 17:34:20 GMT -5 @Nam Ho Kim said:

Dear Diane:

In your example, the three failure modes are almost separated. In such a case, you can define your system failure as a sum of three individual failure modes. Will your method still work of the overlaps between different failure modes are significant? In such as case, will the allocation of different faiure probability be possible?

Dr. Kim,

This method should still work. Calculating the probability of failure through Monte Carlo sampling allows us to keep track of failures of each random set and because of this the method should work when there are a large number of combined failures. If the points on the Pareto front that are used in the interpolation have overlapping failure modes, the optimum should then have the same failure characteristics.

If the failure modes are highly coupled for all possible designs, I'm not exactly sure what kind of risk allocation we would see. I expect that the allocation would not be so obvious. Since the mechanisms that cause failure in our study are so different, we can see the risk allocation clearly.