Combining A Reduced Polynomial Chaos Expansion Approach with Universal Kriging for Uncertainty Quantification

Abstract

Engineering design optimization studies, based on the large number of computational fluid dynamics simulations necessary for uncertainty quantification, are computationally expensive. Polynomial chaos expansion methods have the potential to save computational costs by reducing the number of input design parameters. Kriging methods are able to accurately predict off-design values and give an estimate of their error. However, each has its limitations. In this paper, we combine a reduced dimensional polynomial chaos approach with a universal Kriging method as a new non-intrusive metamodeling method for fast uncertainty quantification and optimization in a simplified engine nacelle inlet design. Its performance is benchmarked against the reduced dimensional polynomial chaos approach and universal Kriging. Results show the reduced-polynomial-chaos-Kriging method gives more accurate results than the reduced dimensional polynomial chaos approach for nonsmooth solutions. However, the new method is highly-dependent on the experimental design. The application of a standalone Kriging method on the reduced model produced excellent stability and indicates refinement of the method is possible.

Analysis of a Polynomial Chaos-Kriging Metamodel for Uncertainty Quantification in Aerospace Applications

“…In our previous work, 1 we found that the RPC-K metamodel provides more accurate estimates for nonsmooth flows than the RPC metamodel. However, a few solutions indicated discontinuities and/or underpredicted values.…”

“…We evaluated the model in the present study on an engine nacelle inlet design case from our previous works. 1,4 This case shows the performance of the metamodel on a realistic CFD simulation with non-smooth flow behavior. The CFD simulations were solved using the CFD++ solver from Metacomp Technologies.…”

“…The adaptive RPC-K method was verified on a one-dimensional transient convection-diffusion-reaction problem. This same problem was used in our previous studies 1,4 to verify the RPC and RPC-K methods. A brief description of the problem is provided below for convenience.…”

“…Further, results along the +Y and -Z profiles are not shown as their smooth profiles do not show significant deviations among the metamodels. 1 The uncertainty quantification study aims to accurately identify the effect of flow separation on the engine's operating conditions.…”

“…These low impact design variables are then removed from the uncertainty quantification study by setting them to their mean value. In the engine nacelle inlet study used in our previous works, 1,4 we were able to reduce the number of design variables from 7 to 5. Accordingly, the number of CFD simulations is reduced from 120 to 56.…”