Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; Geraci, Gianluca; Eldred, Michael S.; Vane, Zachary P.; Lacaze, Guilhem; Oefelein, Joseph C.; Najm, Habib N.

doi:10.2514/1.J056278

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

Journal Article · Fri Feb 09 00:00:00 EST 2018 · AIAA Journal

DOI:https://doi.org/10.2514/1.J056278· OSTI ID:1431213

Huan, Xun ^[1]; Safta, Cosmin ^[1]; Sargsyan, Khachik ^[1]; Geraci, Gianluca ^[2]; Eldred, Michael S. ^[2]; Vane, Zachary P. ^[1]; Lacaze, Guilhem ^[1]; Oefelein, Joseph C. ^[1]; Najm, Habib N. ^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. In conclusion, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: Defense Advanced Research Projects Agency (DARPA); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1431213

Alternate ID(s):: OSTI ID: 1429819

Report Number(s):: SAND--2018-1603J; 661557

Journal Information:: AIAA Journal, Journal Name: AIAA Journal Journal Issue: 3 Vol. 56; ISSN 0001-1452

Publisher:: AIAACopyright Statement

Country of Publication:: United States

Language:: English

References (46)

For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution Donoho, David L. Communications on Pure and Applied Mathematics, Vol. 59, Issue 6, p. 797-829 https://doi.org/10.1002/cpa.20132	journal	January 2006
On the Statistical Calibration of Physical Models: STATISTICAL CALIBRATION OF PHYSICAL MODELS Sargsyan, K.; Najm, H. N.; Ghanem, R. International Journal of Chemical Kinetics, Vol. 47, Issue 4 https://doi.org/10.1002/kin.20906	journal	February 2015
The Elements of Statistical Learning Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome Springer Series in Statistics https://doi.org/10.1007/978-0-387-84858-7	book	January 2009
Stochastic Finite Elements: A Spectral Approach Ghanem, Roger G.; Spanos, Pol D. Springer New York, NY https://doi.org/10.1007/978-1-4612-3094-6	book	January 1991
Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics Le Maître, O. P.; Knio, Omar M. Scientific Computation https://doi.org/10.1007/978-90-481-3520-2	book	January 2010
Dimension?Adaptive Tensor?Product Quadrature Gerstner, T.; Griebel, M. Computing, Vol. 71, Issue 1 https://doi.org/10.1007/s00607-003-0015-5	journal	August 2003
Making best use of model evaluations to compute sensitivity indices Saltelli, Andrea Computer Physics Communications, Vol. 145, Issue 2 https://doi.org/10.1016/S0010-4655(02)00280-1	journal	May 2002
Analysis of variance designs for model output Jansen, Michiel J. W. Computer Physics Communications, Vol. 117, Issue 1-2 https://doi.org/10.1016/S0010-4655(98)00154-4	journal	March 1999
Theorems and examples on high dimensional model representation Sobol', I. M. Reliability Engineering & System Safety, Vol. 79, Issue 2 https://doi.org/10.1016/S0951-8320(02)00229-6	journal	February 2003
Validating predictions of unobserved quantities Oliver, Todd A.; Terejanu, Gabriel; Simmons, Christopher S. Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.08.023	journal	January 2015
Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index Saltelli, Andrea; Annoni, Paola; Azzini, Ivano Computer Physics Communications, Vol. 181, Issue 2 https://doi.org/10.1016/j.cpc.2009.09.018	journal	February 2010
Sparse Legendre expansions via ℓ1-minimization Rauhut, Holger; Ward, Rachel Journal of Approximation Theory, Vol. 164, Issue 5 https://doi.org/10.1016/j.jat.2012.01.008	journal	May 2012
A weighted -minimization approach for sparse polynomial chaos expansions Peng, Ji; Hampton, Jerrad; Doostan, Alireza Journal of Computational Physics, Vol. 267 https://doi.org/10.1016/j.jcp.2014.02.024	journal	June 2014
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies Hampton, Jerrad; Doostan, Alireza Journal of Computational Physics, Vol. 280 https://doi.org/10.1016/j.jcp.2014.09.019	journal	January 2015
Enhancing ℓ 1 -minimization estimates of polynomial chaos expansions using basis selection Jakeman, J. D.; Eldred, M. S.; Sargsyan, K. Journal of Computational Physics, Vol. 289 https://doi.org/10.1016/j.jcp.2015.02.025	journal	May 2015
Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet Constantine, P. G.; Emory, M.; Larsson, J. Journal of Computational Physics, Vol. 302 https://doi.org/10.1016/j.jcp.2015.09.001	journal	December 2015
Large eddy simulation of turbulent combustion processes in propulsion and power systems Oefelein, Joseph C. Progress in Aerospace Sciences, Vol. 42, Issue 1 https://doi.org/10.1016/j.paerosci.2006.02.001	journal	January 2006
Hypersonics into the 21st century: A perspective on AFOSR-sponsored research in aerothermodynamics Schmisseur, John D. Progress in Aerospace Sciences, Vol. 72 https://doi.org/10.1016/j.paerosci.2014.09.009	journal	January 2015
Large eddy simulation of swirling particle-laden flow in a model axisymmetric combustor Oefelein, Joseph C.; Sankaran, Vaidyanathan; Drozda, Tomasz G. Proceedings of the Combustion Institute, Vol. 31, Issue 2 https://doi.org/10.1016/j.proci.2006.08.017	journal	January 2007
Analysis of high-pressure Diesel fuel injection processes using LES with real-fluid thermodynamics and transport Lacaze, Guilhem; Misdariis, Antony; Ruiz, Anthony Proceedings of the Combustion Institute, Vol. 35, Issue 2 https://doi.org/10.1016/j.proci.2014.06.072	journal	January 2015
On the convergence of generalized polynomial chaos expansions Ernst, Oliver G.; Mugler, Antje; Starkloff, Hans-Jörg ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, Issue 2 https://doi.org/10.1051/m2an/2011045	journal	October 2011
Idealized gas turbine combustor for performance research and validation of large eddy simulations Williams, Timothy C.; Schefer, Robert W.; Oefelein, Joseph C. Review of Scientific Instruments, Vol. 78, Issue 3 https://doi.org/10.1063/1.2712936	journal	March 2007
A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output Saltelli, A.; Tarantola, S.; Chan, K. P. -S. Technometrics, Vol. 41, Issue 1 https://doi.org/10.1080/00401706.1999.10485594	journal	February 1999
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems Figueiredo, MÁrio A. T.; Nowak, Robert D.; Wright, Stephen J. IEEE Journal of Selected Topics in Signal Processing, Vol. 1, Issue 4 https://doi.org/10.1109/JSTSP.2007.910281	journal	December 2007
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information Candes, E.J.; Romberg, J.; Tao, T. IEEE Transactions on Information Theory, Vol. 52, Issue 2, p. 489-509 https://doi.org/10.1109/TIT.2005.862083	journal	February 2006
Compressed sensing Donoho, D. L. IEEE Transactions on Information Theory, Vol. 52, Issue 4 https://doi.org/10.1109/TIT.2006.871582	journal	April 2006
Bayesian calibration of computer models Kennedy, Marc C.; O'Hagan, Anthony Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3 https://doi.org/10.1111/1467-9868.00294	journal	August 2001
Sparse Approximate Solutions to Linear Systems Natarajan, B. K. SIAM Journal on Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S0097539792240406	journal	April 1995
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics Najm, Habib N. Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165248	journal	January 2009
General state space Markov chains and MCMC algorithms Roberts, Gareth O.; Rosenthal, Jeffrey S. Probability Surveys, Vol. 1, Issue 0 https://doi.org/10.1214/154957804100000024	journal	January 2004
Multilevel Monte Carlo Path Simulation Giles, Michael B. Operations Research, Vol. 56, Issue 3 https://doi.org/10.1287/opre.1070.0496	journal	June 2008
Dimensionality Reduction for Complex Models via Bayesian Compressive Sensing Sargsyan, Khachik; Safta, Cosmin; Najm, Habib N. International Journal for Uncertainty Quantification, Vol. 4, Issue 1 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2013006821	journal	January 2014
An Adaptive Metropolis Algorithm Haario, Heikki; Saksman, Eero; Tamminen, Johanna Bernoulli, Vol. 7, Issue 2 https://doi.org/10.2307/3318737	journal	April 2001
Toward Validation of Large Eddy Simulation for Turbulent Combustion Oefelein, Joseph C.; Schefer, Robert W.; Barlow, Robert S. AIAA Journal, Vol. 44, Issue 3 https://doi.org/10.2514/1.16425	journal	March 2006
Hypersonic International Flight Research and Experimentation (HIFiRE) Fundamental Science and Technology Development Strategy Dolvin, Douglas 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference https://doi.org/10.2514/6.2008-2581	conference	June 2012
The HIFiRE Flight 2 Experiment: An Overview and Status Update Jackson, Kevin; Gruber, Mark; Barhorst, Todd 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit https://doi.org/10.2514/6.2009-5029	conference	June 2012
Hypersonic International Flight Research and Experimentation Technology Development and Flight Certification Strategy Dolvin, Douglas 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference https://doi.org/10.2514/6.2009-7228	conference	June 2012
HIFiRE Flight 2 Project Overview and Status Update 2011 Jackson, Kevin; Gruber, Mark; Buccellato, Salvatore 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference https://doi.org/10.2514/6.2011-2202	conference	June 2012
Combustor Operability and Performance Verification for HIFiRE Flight 2 Storch, Andrea; Bynum, Michael; Liu, Jiwen 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference https://doi.org/10.2514/6.2011-2249	conference	June 2012
Uncertainty quantification and error estimation in scramjet simulation Witteveen, Jeroen; Duraisamy, Karthik; Iaccarino, Gianluca 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference https://doi.org/10.2514/6.2011-2283	conference	June 2012
Multifidelity Uncertainty Quantification Using Non-Intrusive Polynomial Chaos and Stochastic Collocation Ng, Leo Wai-Tsun; Eldred, Michael 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference<BR>20th AIAA/ASME/AHS Adaptive Structures Conference<BR>14th AIAA https://doi.org/10.2514/6.2012-1852	conference	June 2012
Large Eddy Simulation of the HIFiRE Direct Connect Rig Scramjet Combustor Lacaze, Guilhem; Vane, Zachary; Oefelein, Joseph C. 55th AIAA Aerospace Sciences Meeting https://doi.org/10.2514/6.2017-0142	conference	January 2017
A multifidelity multilevel Monte Carlo method for uncertainty propagation in aerospace applications Geraci, Gianluca; Eldred, Michael S.; Iaccarino, Gianluca 19th AIAA Non-Deterministic Approaches Conference https://doi.org/10.2514/6.2017-1951	conference	January 2017
Detailed Modeling and Simulation of High-Pressure Fuel Injection Processes in Diesel Engines Oefelein, Joseph; Dahms, Rainer; Lacaze, Guilhem SAE International Journal of Engines, Vol. 5, Issue 3 https://doi.org/10.4271/2012-01-1258	journal	January 2012
Effects of Real-Fluid Thermodynamics on High-Pressure Fuel Injection Processes Oefelein, Joseph; Lacaze, Guilhem; Dahms, Rainer SAE International Journal of Engines, Vol. 7, Issue 3 https://doi.org/10.4271/2014-01-1429	journal	April 2014