Spacecrafts such as Stardust (NASA, 2006) are protected by an ablative Thermal Protection System (TPS) for their hypersonic atmospheric entry. A new generation of TPS material, called Phenolic Impregnated Carbon Ablator (PICA), has been introduced with the Stardust mission. This new generation of low density carbon-phenolic composites is now widely used in the aerospace industry. Complex heat and mass transfer phenomena coupled to phenolic pyrolysis and pyrolysis gas chemistry occur in the material during atmospheric entry. Computer programs, as the Porous material Analysis Toolbox based on OpenFoam (PATO) released open source by NASA, allow to study the material response. In this study, a non-intrusive Anchored Analysis of Variance (Anchored-ANOVA) method has been interfaced with PATO to perform low-cost sensitivity analysis on this problem featuring a large number of uncertain parameters. Then, a Polynomial-Chaos method has been employed in order to compute the statistics of some quantities of interest for the atmospheric entry of the Stardust capsule, by taking into account uncertainties on effective material properties and pyrolysis gas composition. This first study including pyrolysis gas composition uncertainties shows their key contribution to the variability of the quantities of interest.

This paper is devoted to tackling constrained multi-objective optimisation under uncertainty problems. A Surrogate-Assisted Bounding-Box approach (SABBa) is formulated here to deal with robustness and reliability measures, which can be computed with tunable and refinable fidelity. A Bounding-Box is defined as a multi-dimensional product of intervals centred on the estimated objectives and constraints that contains the true underlying values. The fidelity of these estimations can be tuned throughout the optimisation so as to reach high accuracy only on promising designs, which allows quick convergence toward the optimal area. In SABBa, this approach is supplemented with a Surrogate-Assisting (SA) strategy, which is very useful to reduce the overall computational cost. The adaptive refinement within the Bounding-Box approach is based on the computation of a Pareto Optimal Probability (POP) for each box. We first assess the proposed method on several analytical uncertainty-based optimisation testcases with respect to an a priori metamodel approach in terms of a probabilistic modified Hausdorff distance to the true Pareto optimal set. The method is then applied to two engineering applications: the design of two-bar truss in structural mechanics and the design of a thermal protection system for atmospheric reentry.