A bi-level meta-modeling approach for structural optimization using modified POD bases and Diffuse Approximation

Authors:
Balaji Raghavan;Mohamed Hamdaoui;Manyu Xiao;Piotr Breitkopf;Pierre Villon
Affiliations:
Laboratoire Roberval UMR 7337 CNRS, Labex MS2T, Compiegne 60200, France;Laboratoire Roberval UMR 7337 CNRS, Labex MS2T, Compiegne 60200, France;Laboratoire Roberval UMR 7337 CNRS, Labex MS2T, Compiegne 60200, France and Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, Shaanxi, People's Republic of Ch ...;Laboratoire Roberval UMR 7337 CNRS, Labex MS2T, Compiegne 60200, France;Laboratoire Roberval UMR 7337 CNRS, Labex MS2T, Compiegne 60200, France
Venue:
Computers and Structures
Year:
2013

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Abstract

Managing computational effort (CPU time, memory, interfacing) is a major issue in design optimization, due to the cost of the high fidelity numerical simulations (finite elements, finite volumes, etc.) involved. In order to decrease the overall cost of the optimization process, reduced-order models such as Proper Orthogonal Decomposition (POD) are an economical and efficient option. However, truncating the POD basis yields an error in the calculation of the global values used as performance objectives and constraints which in turn affects the optimization results. This paper proposes novel constrained versions of Proper Orthogonal Decomposition that produce an alternative orthonormal basis, which is then successfully applied first to a 1D test-case with a quadratic constraint and next to an industrial example with both linear and quadratic constraints: the multi-objective shape optimization of an air-conditioning duct.