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Risk Allocation

The design of an integrated thermal protection system (ITPS) is challenging in that thermal and structural requirements are often satisfied by conflicting changes in design.  For example, the webs of the ITPS play an important role in transferring heat from the top face sheet to the bottom face sheet.  As the web thickness is decreased, we successfully decrease the temperature of the bottom face sheet.  However, this design change makes the web more susceptible to buckling, therefore making it less structurally sound.  

Risk allocation shifts probabilities of failure between the failure modes
 through changes in design while considering the cost of these design changes.  In determininstic optimization, risk is allocated implicity by the choice of safety factors.  Probabilistic optimization allocates risk explicity by considering the probability of failure in each mode.

The table below compares designs found through deterministic and probabilistic optimization for minimum mass of the ITPS with constraints on the thermal, buckling, and stress in the web.  Notice that, for the same level of reliability (i.e. 2.28), the mass is reduced by probabilistic design.  It is noted that probabilistic optimization shifts most risk to the thermal failure mode, while eliminating almost all buckling failure.

The figure below shows a comparison of the deterministic and probabilistic optima on an empirical Pareto front for reliability index and mass.  While the deterministic optimum is not on the Pareto front, the probabilistic optimum is.

Learn more:  Villanueva, D., Sharma, A., Haftka, R.T., Sankar, B.V. (2009). "Risk Allocation by Optimization of an Integrated Thermal Protection System," 8th World 
                   Congress for Structural and Multidisciplinary Optimization, Lisbon, Portugal (PDF)(Presentation with Audio)(Poster)