  We consider the problem of optimizing the design of a heat sink used for
cooling an insulated gate bipolar transistor (IGBT) power module. The thermal
behavior of the heat sink is originally estimated using a high-fidelity
computational fluid dynamics (CFD) simulation, which renders numerical
optimization too computationally demanding. To enable optimization studies, we
substitute the CFD simulation model with an inexpensive polynomial surrogate
model that approximates the relation between the device's design features and a
relevant thermal quantity of interest. The surrogate model of choice is a
data-driven polynomial chaos expansion (DD-PCE), which learns the
aforementioned relation by means of polynomial regression. Advantages of the
DD-PCE include its applicability in small-data regimes and its easily adaptable
model structure. To address the issue of model-form uncertainty and model
robustness in view of limited training and test data, ensembles of DD-PCEs are
generated based on data re-shuffling. Then, using the full ensemble of
surrogate models, the surrogate-based predictions are accompanied by
uncertainty metrics such as mean value and variance. Once trained and tested in
terms of accuracy and robustness, the ensemble of DD-PCE surrogates replaces
the high-fidelity simulation model in optimization algorithms aiming to
identify heat sink designs that optimize the thermal behavior of the IGBT under
geometrical and operational constraints. Optimized heat sink designs are
obtained for a computational cost much smaller than utilizing the original
model in the optimization procedure. Due to ensemble modeling, the optimization
results can also be assessed in terms of uncertainty and robustness.
Comparisons against alternative surrogate modeling techniques illustrate why
the DD-PCE should be preferred in the considered setting.
