Power module heat sink design optimization with ensembles of data-driven polynomial chaos surrogate models

Abstract

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.