Koopman-Based Approach to Nonintrusive Projection-Based Reduced-Order Modeling with Black-Box High-Fidelity Models

This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models governing nonlinear static parametric systems. The methodology specifically addres...

[1]  Earl H. Dowell,et al.  Mach Number Influence on Reduced-Order Models of Inviscid Potential Flows in Turbomachinery , 2002 .

[2]  K. Willcox,et al.  Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis , 2009 .

[3]  K. Willcox,et al.  Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition , 2004 .

[4]  Massimo Gennaretti,et al.  Multiblade Reduced-Order Aerodynamics for State-Space Aeroelastic Modeling of Rotors , 2012 .

[5]  Ionel M. Navon,et al.  Reduced‐order modeling based on POD of a parabolized Navier–Stokes equation model I: forward model , 2012 .

[6]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[7]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[8]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[9]  Charbel Farhat,et al.  Adaptation of Aeroelastic Reduced-Order Models and Application to an F-16 Configuration , 2007 .

[10]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[11]  Karen Willcox,et al.  Parametric reduced-order models for probabilistic analysis of unsteady aerodynamic applications , 2007 .

[12]  Jentung Ku,et al.  Projection-Based Reduced-Order Modeling for Spacecraft Thermal Analysis , 2015 .

[13]  Bogdan I. Epureanu,et al.  A parametric analysis of reduced order models of viscous flows in turbomachinery , 2003 .

[14]  Clarence W. Rowley,et al.  A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition , 2014, Journal of Nonlinear Science.

[15]  K. Schittkowski NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[16]  David J. Lucia,et al.  Reduced order modeling of a two-dimensional flow with moving shocks , 2003 .

[17]  C. Pain,et al.  Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation , 2015 .

[18]  Dimitri N. Mavris,et al.  A Methodology for Projection-Based Model Reduction with Black-Box High-Fidelity Models , 2017, 1709.08713.

[19]  A. Chatterjee An introduction to the proper orthogonal decomposition , 2000 .

[20]  Bryan Glaz,et al.  Reduced-Order Nonlinear Unsteady Aerodynamic Modeling Using a Surrogate-Based Recurrence Framework , 2010 .

[21]  Paul G. A. Cizmas,et al.  Reduced-Order Modeling of Unsteady Viscous Flow in a Compressor Cascade , 1998 .

[22]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[23]  Carlos E. S. Cesnik,et al.  Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation , 2010 .

[24]  B. O. Koopman,et al.  Hamiltonian Systems and Transformation in Hilbert Space. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Steven L. Brunton,et al.  On dynamic mode decomposition: Theory and applications , 2013, 1312.0041.

[26]  M. Fossati Evaluation of aerodynamic loads via reduced order methodology , 2015 .

[27]  Layne T. Watson,et al.  Efficient global optimization algorithm assisted by multiple surrogate techniques , 2012, Journal of Global Optimization.

[28]  Shih-Ping Han A globally convergent method for nonlinear programming , 1975 .

[29]  David J. Lucia,et al.  Domain Decomposition for Reduced-Order Modeling of a Flow with Moving Shocks , 2002 .

[30]  Benjamin Peherstorfer,et al.  Dynamic data-driven reduced-order models , 2015 .

[31]  Carlos E. S. Cesnik,et al.  Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes , 2014 .

[32]  Moti Karpel,et al.  Reduced-order models for integrated aeroservoelastic optimization , 1999 .

[33]  Ionel M. Navon,et al.  Non-intrusive reduced order modelling of the Navier-Stokes equations , 2015 .

[34]  C. Farhat,et al.  Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity , 2008 .

[35]  Steven L. Brunton,et al.  Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control , 2015, PloS one.

[36]  Juan J. Alonso,et al.  Airfoil design optimization using reduced order models based on proper orthogonal decomposition , 2000 .

[37]  R. D. Firouz-Abadi,et al.  Reduced-order aerodynamic model for aeroelastic analysis of complex configurations in incompressible flow , 2007 .

[38]  Earl H. Dowell,et al.  Three-Dimensional Transonic Aeroelasticity Using Proper Orthogonal Decomposition-Based Reduced-Order Models , 2001 .

[39]  Francis Y. Enomoto,et al.  THE CGNS SYSTEM , 1998 .

[40]  Hossein Haj-Hariri,et al.  Reduced-Order Modeling of a Heaving Airfoil , 2005 .

[41]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[42]  Massimo Gennaretti,et al.  Time-dependent coefficient reduced-order model for unsteady aerodynamics of proprotors , 2005 .

[43]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[44]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[45]  David J. Lucia,et al.  Projection methods for reduced order models of compressible flows , 2003 .