Multidisciplinary Optimization under Uncertainty for Preliminary Aircraft Sizing

The robust optimization allows designing an optimal system whose performances are insensitive to uncertainties. On the other hand reliability based optimization determines a minimum level of reliability but makes no guarantee regarding the performance sensitivity to uncertainties. In this paper a method combining both approaches is developed and is illustrated by an application to preliminary aircraft design. Uncertainties are taken into account through a probabilistic approach stemming from the use of historical data of aircraft (features, performances, etc.). Firstly, one shows that taking into account uncertainties with a constant standard deviation from the residual errors of the database, generates non-physical results because it leads to too large uncertainties in some regions. To overcome this problem one then develops an uncertainty model with a variable standard deviation which can take into account two factors: on one hand, the number of historical data in a given region varies; on the another hand some areas are less well predicted by the analytical model functions. The developed uncertainty modeling is applied to preliminary aircraft design optimization under both reliability and robustness constraints. It is found that the robust optimum point under reliability constraints for a short range aircraft is close to the deterministic optimum but the weight of the corresponding aircraft is higher because of additional margins taken.