Optimization under uncertainties is achieving more and more agreement in the industrial design community. In fact, most of the industrial processes are permeated by uncertainties, including for instance dimensional tolerances and fluctuations in the operating conditions. These uncertainties are commonly transferred to the performance of the system, which cannot be determined by a single value, but rather by a statistical distribution of results. To deal with industrial problems characterized by a large number of uncertainties and expensive simulation time, it is particularly important to develop methodologies to obtain accurate results, and rely on a reduced number of sample evaluations at the same time. In this paper two different methodologies, applied to aeronautical test cases, are presented. The first one takes advantage of multi-fidelity metamodels, consisting of combining few high-fidelity simulations (HF) with low-fidelity ones (LF), to evaluate the propagation of the uncertainties using Cokriging algorithm. The method is particularly efficient for large number of uncertainties since it provides quite a linear correlation of the samples with the uncertainties number, while other methods, such as the ones based on Polynomial Chaos Expansion, may require at least a quadratic correlation. The second methodology is instead based on the UQ application of Reduced Order Models (ROM), that define an equivalent CFD model in function of a given set of parameters, by interpolating a sampling series of CFD snapshots. Surrogate models like Deep Learning can be used for the interpolation, or as alternative POD (ProperOrthogonal Decomposition) methods which are instead based on the interpolation of a reduced number of modes (the principal components). In both cases, the ROM model can be used to instantly evaluate a Monte C arlo DOE at the variation of the uncertain parameters, allowing the computation of the uncertainty propagation of the vectorial field of interest.
Uncertainty Quantification Based on Multi-fidelity Metamodels and Reduced Order Models
Alberto Clarich
;Carlo Poloni;
2026-01-01
Abstract
Optimization under uncertainties is achieving more and more agreement in the industrial design community. In fact, most of the industrial processes are permeated by uncertainties, including for instance dimensional tolerances and fluctuations in the operating conditions. These uncertainties are commonly transferred to the performance of the system, which cannot be determined by a single value, but rather by a statistical distribution of results. To deal with industrial problems characterized by a large number of uncertainties and expensive simulation time, it is particularly important to develop methodologies to obtain accurate results, and rely on a reduced number of sample evaluations at the same time. In this paper two different methodologies, applied to aeronautical test cases, are presented. The first one takes advantage of multi-fidelity metamodels, consisting of combining few high-fidelity simulations (HF) with low-fidelity ones (LF), to evaluate the propagation of the uncertainties using Cokriging algorithm. The method is particularly efficient for large number of uncertainties since it provides quite a linear correlation of the samples with the uncertainties number, while other methods, such as the ones based on Polynomial Chaos Expansion, may require at least a quadratic correlation. The second methodology is instead based on the UQ application of Reduced Order Models (ROM), that define an equivalent CFD model in function of a given set of parameters, by interpolating a sampling series of CFD snapshots. Surrogate models like Deep Learning can be used for the interpolation, or as alternative POD (ProperOrthogonal Decomposition) methods which are instead based on the interpolation of a reduced number of modes (the principal components). In both cases, the ROM model can be used to instantly evaluate a Monte C arlo DOE at the variation of the uncertain parameters, allowing the computation of the uncertainty propagation of the vectorial field of interest.Pubblicazioni consigliate
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