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logo SMC logo SMC  OPTI logo SMC  OPTI  MOOUU Design under uncertainty
   
Contact Jérémy Lebon, Rajan Filomeno Coelho
   
Keywords multicriteria optimization, evolutionary algorithms, optimization under uncertainty, polynomial chaos expansion, stochastic metamodels, truss structures
   
Collaborations
  • Prof. P. Breitkopf, Prof. P. Villon, Laboratoire Roberval (UTC-CNRS, UMR 6253), Université de Technologie de Compiègne, France
   
Design under uncertainty In many engineering fields, finding the best solutions of a given problem with regards to some contradictory requirements on the solution (for example minimizing the mass of a truss and maximizing its strength under some dimensional restrictions) is a nearly daily common decision making problem. The fundamental question is then: what is the best compromise solution among the possible solutions? Multicriteria optimization is a method which aims at giving to the design engineer detailed information on the body of performances of the range of possible solutions considering the choice criteria (Pareto optimization).

Moreover, other aspects such as uncertainties on the design parameters, material characteristics and loadings of the structure are worth of attention. A small variation of the design parameters could lead to a solution which does not respect the constraints of the problem anymore, i.e. an unsatisfactory solution. To avoid this situation, two approaches have been developed:

  • the first one is called RDO (Robust Design Optimization) : this is a deterministic method which takes into account of the sensibility of the parameter during the optimization process;
  • the second method is called RBDO (Reliability Based Design Optimization) : it uses the probability distribution of each conception variable to build a global reliability index of the structure.

From the point of view of the design engineer, the second approach presents the advantages to give more information about the collapsing risk of the structure, and so helps him to master it more precisely. But this approach is very demanding in computing resources. That why some appreciative methods (FORM, SORM) has been developed in order to compute the reliability index more easily. A particular attention to the computation costs will be given along this research. Therefore, a metamodeling approach will be developed based on non-intrusive Stochastic Finite Elements.

To summarize, our current research is concerned with:

  • the development of reliability-based formulations adapted to multiobjective evolutionary optimization;
  • the development of stochastic surrogate models based on polynomial chaos expansion and general metamodels (kriging);
  • the validation on several applications, especially civil engineering and building structures (e.g. trusses and beam-column structures).
     
Support
  • This project is funded by a Brains (Back) to Brussels project entitled "Optimisation multicritère avec prise en compte des incertitudes (en variables continues et discrètes) appliquée aux constructions".
     
Selected publications
  • [1] J Lebon, G Le Quilliec, P Breitkopf, R Filomeno Coelho, P Villon. A two-pronged approach for springback variability assessment using sparse polynomial chaos expansion and multi-level simulations. International Journal of Material Forming, 2013. Published online.
  • [2] R Filomeno Coelho. Co-evolutionary optimization for multi-objective design under uncertainty. Journal of Mechanical Design, 135(2):021006, 2013.
  • [3] R Filomeno Coelho, J Lebon, and Ph Bouillard. Hierarchical stochastic metamodels based on moving least squares and polynomial chaos expansion–Application to the multiobjective reliability-based optimization of 3D truss structures. Structural and Multidisciplinary Optimization, 43(5):707–729, 2011.