Multi-Fidelity Low-Rank Approximations for Uncertainty Quantification of a Supersonic Aircraft Design

Sihmehmet Yildiz, Hayriye Pehlivan Solak, Melike Nikbay*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.

Original languageEnglish
Article number250
Issue number7
Publication statusPublished - Jul 2022

Bibliographical note

Publisher Copyright:
© 2022 by the authors.


All authors would like to acknowledge the collaboration established among members of the NATO STO AVT-331 Research Task Group titled “Goal-driven, multi-fidelity approaches for military vehicle system-level design” co-chaired by Phil Beran and Matteo Diez under the framework of NATO Science and Technology Organization Applied Vehicle Technology Panel. All authors would like to thank Andrew Thelen for his support and suggestions in improving the writing of the article. M.N. would like to thank NASA Langley Research Center for distributing sBOOM sonic boom prediction code internationally for academic research. M.N. would like to acknowledge ITU Scientific Research Projects Unit for “Stochastic Design Optimization of Military Sea and Air Vehicles” Project with grant number MGA-2018-41090. First and last authors would like to express their gratitude to TUBITAK for the research grant provided under the 218M471 TUBITAK 1001 project titled as “Development of Multifidelity and Multidisciplinary Methodologies Integrating Sonic Boom, Aeroelasticity and Propulsion System for Supersonic Aircraft Design”. First and last authors authors would like to acknowledge the graduate thesis support provided by Istanbul Technical University Scientific Research Program for MYL-2019-42352 project titled as “Application of Multidisciplinary and Multifidelity Optimization Techniques for Supersonic Aircraft”.

FundersFunder number
ITU Scientific Research Projects UnitMGA-2018-41090
Istanbul Teknik ÜniversitesiMYL-2019-42352


    • high dimensional uncertainty quantification
    • low-rank approximation
    • multi-fidelity
    • supersonic
    • surrogate modelling


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