Surrogate-to-code verification of a non-intrusive POD-GPR machine-learning emulator of peak thermomechanical fields, with application to a carbon-carbon aircraft brake disc
Computational Engineering, Finance, and Science
Summary
The authors present a way to check how accurate a fast, simplified model (an emulator) is when predicting maximum temperature and stress in an aircraft brake part during a tough condition. Instead of comparing to real-world data, they compare the emulator’s predictions to the known uncertainty from the detailed simulation itself. They break down the emulator’s errors into parts and show it performs as well as the detailed solver within its own limits. Additionally, they introduce methods to predict both heat and stress peaks together and to locate where these peaks happen in space. Their approach works for similar reduced models where simulation uncertainty can be estimated.
Authors
Franklin Kamche
Abstract
While non-intrusive reduced-order emulators successfully substitute for costly finite-element simulations, certification-grade applications demand a rigorous error assessment relative to the solver's own discretization uncertainty. This work introduces a verification framework designed to evaluate prediction accuracy directly against this numerical uncertainty floor, rather than physical observation. We demonstrate this approach on a carbon-carbon aircraft brake disc during a rejected take-off scenario, predicting peak temperature and peak von Mises stress fields. Operating over a fixed mesh of 60914 nodes, the emulator relies on a pipeline coupling proper orthogonal decomposition (POD) and Gaussian process regression (GPR) parameterized by 5 inputs. We formulate an algebraically exact, a posteriori error budget that isolates the emulator's signed error into distinct truncation and regression components at the extremum. This error is then evaluated against a discretization floor established via mesh-convergence studies on the peak quantities of interest. On a completely independent test set, our emulator matches the high-fidelity solver's peak values within its own discretization uncertainty for both fields, a benchmark we define as surrogate-to-code fidelity. Notably, the residual error stems primarily from linear reduction limits rather than regression inaccuracies. Beyond the main framework, we present two secondary contributions: the concurrent, non-intrusive prediction of the thermal and mechanical peaks, and a probabilistic approach to spatial zone localization for these extrema. This methodology applies to non-intrusive reduced-order models of parameterized finite-element simulations wherever a discretization-error estimate for the quantity of interest can be obtained.