skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Constrained reduced-order models based on proper orthogonal decomposition

Abstract

A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The ^ 7 Karush–Kuhn–Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user8 defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the 9 first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. It was shown that the ROM and C-ROM 10 produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.

Authors:
 [1];  [2];  [3];  [1];  [1];  [1]
  1. Florida Intl Univ., Miami, FL (United States)
  2. Texas A & M Univ., College Station, TX (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Texas A & M Univ., College Station, TX (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Florida Intl Univ., Miami, FL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1369450
Alternate Identifier(s):
OSTI ID: 1397433; OSTI ID: 1410456
Report Number(s):
SAND-2017-3244J
Journal ID: ISSN 0045-7825; 652058
Grant/Contract Number:  
AC04-94AL85000; FE0023114; FIU/ARC
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 321; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; proper orthogonal decomposition; reduced-order modeling; Karush–Kuhn–Tucker; multiphase flows; computational fluid dynamics; fluidized beds; 97 MATHEMATICS AND COMPUTING

Citation Formats

Reddy, Sohail R., Freno, Brian Andrew, Cizmas, Paul G. A., Gokaltun, Seckin, McDaniel, Dwayne, and Dulikravich, George S.. Constrained reduced-order models based on proper orthogonal decomposition. United States: N. p., 2017. Web. https://doi.org/10.1016/j.cma.2017.03.038.
Reddy, Sohail R., Freno, Brian Andrew, Cizmas, Paul G. A., Gokaltun, Seckin, McDaniel, Dwayne, & Dulikravich, George S.. Constrained reduced-order models based on proper orthogonal decomposition. United States. https://doi.org/10.1016/j.cma.2017.03.038
Reddy, Sohail R., Freno, Brian Andrew, Cizmas, Paul G. A., Gokaltun, Seckin, McDaniel, Dwayne, and Dulikravich, George S.. Sun . "Constrained reduced-order models based on proper orthogonal decomposition". United States. https://doi.org/10.1016/j.cma.2017.03.038. https://www.osti.gov/servlets/purl/1369450.
@article{osti_1369450,
title = {Constrained reduced-order models based on proper orthogonal decomposition},
author = {Reddy, Sohail R. and Freno, Brian Andrew and Cizmas, Paul G. A. and Gokaltun, Seckin and McDaniel, Dwayne and Dulikravich, George S.},
abstractNote = {A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The ^ 7 Karush–Kuhn–Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user8 defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the 9 first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. It was shown that the ROM and C-ROM 10 produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.},
doi = {10.1016/j.cma.2017.03.038},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 321,
place = {United States},
year = {2017},
month = {4}
}

Journal Article:

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control
journal, September 2013


Passive reduced-order modeling of electromagnetic systems
journal, February 1999

  • Cangellaris, Andreas C.; Zhao, Li
  • Computer Methods in Applied Mechanics and Engineering, Vol. 169, Issue 3-4
  • DOI: 10.1016/S0045-7825(98)00162-5

A Survey of Model Reduction by Balanced Truncation and Some New Results
journal, May 2004


A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
journal, February 2003

  • Rewienski, M.; White, J.
  • IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, Issue 2
  • DOI: 10.1109/TCAD.2002.806601

Reduced-order modeling - New approaches for computational physics
conference, August 2001

  • Beran, Philip; Silva, Walter
  • 39th Aerospace Sciences Meeting and Exhibit
  • DOI: 10.2514/6.2001-853

Reduced-order modeling: new approaches for computational physics
journal, February 2004


Existence Results for a Nonlinear Semipositone Telegraph System with Repulsive Weak Singular Forces
journal, January 2011

  • Wang, Fanglei; Wang, Yunhai; An, Yukun
  • Mathematical Problems in Engineering, Vol. 2011
  • DOI: 10.1155/2011/610812

A reduced-order model for a bubbling fluidized bed based on proper orthogonal decomposition
journal, December 2005


Reduced-order finite difference extrapolation model based on proper orthogonal decomposition for two-dimensional shallow water equations including sediment concentration
journal, September 2015

  • Luo, Zhendong; Gao, Junqiang; Xie, Zhenghui
  • Journal of Mathematical Analysis and Applications, Vol. 429, Issue 2
  • DOI: 10.1016/j.jmaa.2015.04.024

Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity
journal, July 2008

  • Amsallem, David; Farhat, Charbel
  • AIAA Journal, Vol. 46, Issue 7
  • DOI: 10.2514/1.35374

Using proper orthogonal decomposition to model off-reference flow conditions
journal, September 2013


On the use of sensitivity analysis in model reduction to predict flows for varying inflow conditions
journal, January 2011

  • Hay, Alexander; Akhtar, Imran; Borggaard, Jeff T.
  • International Journal for Numerical Methods in Fluids, Vol. 68, Issue 1
  • DOI: 10.1002/fld.2512

Highly efficient optimization mesh movement method based on proper orthogonal decomposition: OPTIMIZATION MESH MOVEMENT METHOD BASED ON POD
journal, December 2010

  • Bogaers, A. E. J.; Kok, S.; Malan, A. G.
  • International Journal for Numerical Methods in Engineering, Vol. 86, Issue 8
  • DOI: 10.1002/nme.3080

A proper orthogonal decomposition method for nonlinear flows with deforming meshes
journal, December 2014


The use of dynamic basis functions in proper orthogonal decomposition
journal, April 2015


Acceleration techniques for reduced-order models based on proper orthogonal decomposition
journal, August 2008

  • Cizmas, Paul G. A.; Richardson, Brian R.; Brenner, Thomas A.
  • Journal of Computational Physics, Vol. 227, Issue 16
  • DOI: 10.1016/j.jcp.2008.04.036

A reduced-order model for heat transfer in multiphase flow and practical aspects of the proper orthogonal decomposition
journal, August 2012


Augmented proper orthogonal decomposition for problems with moving discontinuities
journal, October 2010


A method to generate computationally efficient reduced order models
journal, July 2009

  • Alonso, D.; Velazquez, A.; Vega, J. M.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 33-36
  • DOI: 10.1016/j.cma.2009.03.012

Turbulence and the dynamics of coherent structures. I. Coherent structures
journal, January 1987

  • Sirovich, Lawrence
  • Quarterly of Applied Mathematics, Vol. 45, Issue 3
  • DOI: 10.1090/qam/910462

    Works referencing / citing this record:

    A spectral method for solving heat and moisture transfer through consolidated porous media
    journal, December 2018

    • Gasparin, Suelen; Dutykh, Denys; Mendes, Nathan
    • International Journal for Numerical Methods in Engineering, Vol. 117, Issue 11
    • DOI: 10.1002/nme.5994

    Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model
    journal, April 2018

    • Gasparin, Suelen; Berger, Julien; Dutykh, Denys
    • Journal of Building Performance Simulation, Vol. 12, Issue 1
    • DOI: 10.1080/19401493.2018.1458905