Integration of a mechano-probabilistic optimization module in the COLIBRI tool
Creators: name:  O. BRAYDI 
name:   A. DUMAS 
name:   Y. GUERIN 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: STRUCTURES
MATERIALS
DESIGN
OPTIMIZATION

description: As part of the search for mass gain in space vehicle structures, while ensuring their reliability, CNES called on Phimeca to develop a mechano-probabilistic optimization module integrated into their COLIBRI design tool. The ultimate objective of this study is to perform a reliability-based design optimization of a part of a launcher. The developed tool makes it possible to take into account the uncertainty inherent of the input parameters. These are modeled by random variables which can represent intrinsic variabilities of the geometry, the material properties or the in-flight loading. These variabilities are then propagated within the physical model in order to analyze the variability resulting from one or more quantities of interest. This module allows several functionalities to be carried out, in particular, the analysis of the sensitivity of the outputs with respect to the uncertainty of the input parameters. The sensitivity analysis aims to determine which input parameters have the greatest influence on the outputs. Another functionality is the reliability analysis where the goal is to estimate probabilities that an output exceeds a given threshold. Finally the tool integrates a reliability-based design optimization module that can optimize a deterministic objective function with respect to deterministic and probabilistic constraints. For each of these functionalities, the developed module is based on existing methods in the bibliography, such as the Morris and Sobol [1] methods for sensitivity analysis, Monte Carlo simulation, Importance sampling, Subset sampling and the AK-MCS [2], AK-IS and AK-SYS [3] methods for the computation of probabilities, and Kriging and polynomial chaos expansion for optimization coupled with meta-models. It is developed in the Python language and most of the methods are based on tools proposed in the OpenTURNS library [4], which is especially developed for the treatment of uncertainties, risks and statistics. This work also shows an innovative character in the field of launchers, through the application of methods proven in industrial fields strongly constrained by reliability aspects. The module is applied as part of the CALLISTO project, which is a reusable vehicle demonstrator for which CNES is the prime contractor in partnership with the DLR and the JAXA. This study follows on from a first study of the vehicle equipment bay, the first goal of which was to prioritize the random variables. Results from this first study allowed to reduce the number of the random input parameters, selecting only the most influential ones. Then Sobol indices were estimated using the polynomial chaos expansion. And the estimation of the probability of failure was set up using the Kriging-based algorithms. The difficulty of this study is in particular to consider several failure situations due to different loading configurations corresponding to several flight phases of the launcher. This is therefore a system reliability issue. In addition, the quantities of interest studied are multiple: stresses, buckling, displacements, fluxes. These quantities are calculated by a finite element model which also increases the complexity. Therefore, the use of meta-model coupled with optimization will be applied. The results show the relevance of taking into account the uncertain context in the design and sizing phase of space launchers.