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Multi-fidelity optimization under uncertainty, application to the design of complex systems

SDU2E

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In the context of complex system design, and particularly in the pre-project phases, the use of optimization methods is essential, enabling the search for optimal configurations taking into account performance criteria, as well as technical, economic and environmental constraints. Applied to the design of engineering systems (e.g. aerospace vehicles), they require the use of numerical solvers that are potentially costly in terms of computing time to assess performance and compliance with system specifications. More often than not, the designer has access to numerical solvers of different fidelity levels, characterized by different accuracy and computational cost. These levels of fidelity may derive from the modeling choices made, such as physical or numerical simplifications, mesh definition, etc. Numerous methods have been developed to offer the possibility of analyzing and optimizing a system while reducing the number of calls to expensive numerical solvers. These different levels of modeling fidelity mean that epistemic uncertainties have to be taken into account. In addition, certain variables or phenomena have a stochastic nature which is taken into account in design processes, adding random uncertainties to epistemic uncertainties. Integrating multiple sources of uncertainty into the optimization process then becomes a difficult task, and can result in a Reliability-Based Design Optimization (RBDO) problem involving a system reliability analysis (i.e., a calculation of the system’s probability of failure). This thesis aims to reduce the computational cost of RBDO problems in a multi-fidelity context by exploiting multiple sources of information. Two approaches are developed to reduce the cost of reliability analysis. Firstly, a variance reduction by multi-level sampling is applied to the estimation of flood risks on the Garonne via TELEMAC-2D. Secondly, a reliability method involving the use of multi-fidelity surrogate models (active learning) is studied and tested on the probability of failure of the flow around a strut-braced aircraft. Finally, a decoupled RBDO approach combining Bayesian optimization and multi-fidelity surrogate models is developed. It is based on the construction of databases in an augmented space and the aggregation of information sources. This methodology is applied to the aerospace context, with launch vehicle optimization under uncertainty.

Jury

Didier LUCOR	CNRS/LISN	Reviewer
Christophette BLANCHET-SCALLIET	CNRS/ICJ	Reviewer
Didier LEMOSSE	LMN	Reviewer
Matthias DE LOZZO	IRT Saint Exupéry	Examiner
Olivier THUAL	IMFT	Examiner
Mathieu BALESDENT	ONERA	Co-PhD supervisor