Abstract
An industry-ready uncertainty quantification tool chain is developed and successfully applied to both simultaneous operational and geometrical uncertainties and uncertainties resulting from manufacturing variability, which are characterized by correlations of the measured coordinates. The non-intrusive probabilistic collocation method is combined with a sparse grid approach to drastically reduce the computational cost. This is one of the key features that make UQ in industrial applications feasible. A second required element is the automatization of the entire simulation chain, from uncertainty definition, simulation setup, post-processing and in case of geometrical uncertainties, geometry modification, and re-meshing. This process is fully automated including the post-processing of the UQ simulations, which consists of output PDF reconstruction and the calculation of scaled sensitivity derivatives. This tool chain is applied to the rotor 37 configuration with imposed uncertainties, demonstrating its capability of handling many simultaneous operational and geometrical or correlated manufacturing uncertainties in turnaround times significantly below the UMRIDA quantitative objectives of less than 1000CPUh for 10 simultaneous uncertainties. It is found that a level 1 sparse grid approach is sufficient if the mean and variance of output quantities are needed and a level 2 sparse grid is sufficient for the reconstructed PDF shape for most engineering applications. For manufacturing uncertainties, it is shown that a level 1 sparse grid can be used for the propagation of manufacturing uncertainties and that a surface reconstruction accuracy of 99% seems necessary for the purpose of UQ studies on manufacturing variability.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dunham, J.: CFD Validation For Propulsion System Components, AGARD-AR-355 (1998)
Golub, G.H., Welsch, J.H.: Calculation of Gaussian quadrature rules. Math. Comput. 23, 221–230 (1969)
Loève, M.: Probability theory I. In: Graduate Texts in Mathematics, vol. 45, 4th edn. Springer, New York-Heidelberg (1977)
Loeven, G.J.A., Witteveen, J.A.S., Bijl, H.: Probabilistic collocation: an efficient non-intrusive approach for arbitrarily distributed parametric uncertainties. In: Proceedings of 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA paper 2007-317, Reno, United States (2007)
Mathelin, L., Hussaini, M.Y.: A Stochastic Collocation Algorithm for Uncertainty Analysis (2003)
Nataf, A.: Détermination des distributions de probabilités dont les marges sont données. Comptesrendus de l’académie des sciences 225, 42–43 (1962)
Nigro, R., Wunsch, D., Coussement, G., Hirsch, C.: Chapter 14—Uncertainty quantification in internal flows, STO_TR_AVT_191 (2016)
Numeca: User Manual FINETM/Turbo v11.1 (2016)
Pearson, K.: Philosophical Transactions of the royal Society of London. 8 laws variant (1895, 1901, 1915)
Putko, M.M., Newman, P.A., Taylor III, A.C., Green, L.L.: Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives. Tech. Rep. 2528, AIAA
Smolyak, S.: Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Adad. Nauk USSR B, 240–243 (1963)
Turgeon, E., Pelletier, D., Borggaard, J.: Applications of continuous sensitivity equations to flows with temperature-dependent properties. Numer. Heat Transf. 44, 611–624 (2003)
Wunsch, D., Nigro, R., Coussement, G., Hirsch C.: Quantification of combined operational and geometrical uncertainties in turbo-machinery design. In: Proceedings of the ASME GT2015, GT2015-43399 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Wunsch, D., Nigro, R., Coussement, G., Hirsch, C. (2019). Non-intrusive Probabilistic Collocation Method for Operational, Geometrical, and Manufacturing Uncertainties in Engineering Practice. In: Hirsch, C., Wunsch, D., Szumbarski, J., Łaniewski-Wołłk, Ł., Pons-Prats, J. (eds) Uncertainty Management for Robust Industrial Design in Aeronautics . Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-77767-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-77767-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77766-5
Online ISBN: 978-3-319-77767-2
eBook Packages: EngineeringEngineering (R0)