Model reduction by CPOD and Kriging
Résumé
This paper proposes a novel approach for multiobjective optimization when the criteria of interest rely on a
functional output from an expensive-to-evaluate numerical
simulator. More specifically, the proposed method is developed in the frame of an automotive application. The aim of
this application is to design the shape of an intake port in
order to maximize the mass flow (denoted by Q) and the
tumble (denoted by T ), which both depend on a 3D velocity field obtained by numerical flow simulation. Since the
considered flow simulator is time-consuming, using regular multi-objective genetic algorithms (MOGA) directly on
integral quantities depending on the simulator output is prohibitive. Three different Reduced Order Models (ROMs)
are presented. The first one consists in directly Kriging
the integral quantities Q and T on the basis of the outputs
computed at an initial design of experiments, and basing
the optimization search on the sequentially obtained couples of response surfaces. The other methods explored in
the present work consist in building a parametrized representation of the whole velocity field by different variants
of the Proper Orthogonal Decomposition (POD). Instead
of directly Kriging Q and T at un-sampled locations, the
proposed technique is hence to proceed in two steps: first
approximate the functional outcome by Kriging the POD
coefficients, and then compute the integral quantities Q and
T associated with the approximate 3D field. However, such
an approach induces new difficulties since the truncated
POD does not preserve the global (integrated) quantities,
and that surrogate-based MOGA with this kind of POD
are therefore likely to fail locating the (Q, T )-Pareto front
accurately. This is what motivates to propose an original
constrained POD method (called CPOD) meant to overcome
the bias created by the truncation made in regular POD.
More precisely, this means modifying the way of calculating the POD coefficients by imposing the integral quantities
Q and T based on the truncated POD to match with the
actual Q and T values obtained by flow simulation at the
design of experiments. A detailed comparison of the Pareto
sets obtained from the three ROMs demonstrates the interest
of the CPOD approach.