Problems in turbomachinery computational fluid dynamics (CFD) are often characterized by nonlinear and discontinuous responses. Ensuring the reliability of uncertainty quantification (UQ) codes in such conditions, in an autonomous way, is challenging. In this work, we suggest a new approach that combines three state-of-the-art methods: multivariate Padé approximations, optimal quadrature subsampling (OQS), and statistical learning. Its main component is the generalized least-squares multivariate Padé–Legendre (PL) approximation. PL approximations are globally fitted rational functions that can accurately describe discontinuous nonlinear behavior. They need fewer model evaluations than local or adaptive methods and do not cause the Gibbs phenomenon like continuous polynomial chaos methods. A series of modifications of the Padé algorithm allows us to apply it to arbitrary input points instead of optimal quadrature locations. This property is particularly useful for industrial applications, where a database of CFD runs is already available, but not in optimal parameter locations. One drawback of the PL approximation is that it is nontrivial to ensure reliability. To improve stability, we suggest to couple it with OQS. Our reasoning is that least-squares errors, caused by an ill-conditioned design matrix, are the main source of error. Finally, we use statistical learning methods to check smoothness and convergence. The resulting method is shown to efficiently and correctly fit thousands of partly discontinuous response surfaces for an industrial film cooling and shock interaction problem using only nine CFD simulations.
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April 2018
Research-Article
Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations
Richard Ahlfeld,
Richard Ahlfeld
Uncertainty Quantification Lab,
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
e-mail: r.ahlfeld14@imperial.ac.uk
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
e-mail: r.ahlfeld14@imperial.ac.uk
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Francesco Montomoli,
Francesco Montomoli
Uncertainty Quantification Lab,
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
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Mauro Carnevale,
Mauro Carnevale
Osney Thermo-Fluids Laboratory,
Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
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Simone Salvadori
Simone Salvadori
Department of Industrial Engineering,
University of Florence,
Florence 50121, Italy
University of Florence,
Florence 50121, Italy
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Richard Ahlfeld
Uncertainty Quantification Lab,
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
e-mail: r.ahlfeld14@imperial.ac.uk
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
e-mail: r.ahlfeld14@imperial.ac.uk
Francesco Montomoli
Uncertainty Quantification Lab,
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
Department of Aeronautics Imperial
College London,
London SW7 2AZ, UK
Mauro Carnevale
Osney Thermo-Fluids Laboratory,
Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
Simone Salvadori
Department of Industrial Engineering,
University of Florence,
Florence 50121, Italy
University of Florence,
Florence 50121, Italy
1Corresponding author.
Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 12, 2017; final manuscript received October 14, 2017; published online January 23, 2018. Editor: Kenneth Hall.
J. Turbomach. Apr 2018, 140(4): 041004 (10 pages)
Published Online: January 23, 2018
Article history
Received:
May 12, 2017
Revised:
October 14, 2017
Citation
Ahlfeld, R., Montomoli, F., Carnevale, M., and Salvadori, S. (January 23, 2018). "Autonomous Uncertainty Quantification for Discontinuous Models Using Multivariate Padé Approximations." ASME. J. Turbomach. April 2018; 140(4): 041004. https://doi.org/10.1115/1.4038826
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