DOI QR코드

DOI QR Code

Quantity vs. Quality in the Model Order Reduction (MOR) of a Linear System

  • Received : 2013.03.13
  • Accepted : 2013.05.04
  • Published : 2014.01.25

Abstract

The goal of any Model Order Reduction (MOR) technique is to build a model of order lower than the one of the real model, so that the computational effort is reduced, and the ability to estimate the input-output mapping of the original system is preserved in an important region of the input space. Actually, since only a subset of the input space is of interest, the matching is required only in this subset of the input space. In this contribution, the consequences on the achieved accuracy of adopting different reduction technique patterns is discussed mainly with reference to a linear case study.

Keywords

References

  1. Benjeddou, A. (2009), "New insights in piezoelectric free-vibrations using simplified modeling and analyses" , Smart Struct. Syst., 5(6), 591-612. https://doi.org/10.12989/sss.2009.5.6.591
  2. Carlberg, K., Bou Mosleh, C. and Farhat, C. (2011), "Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations", Int. J. Numer. Method., 86(2),155-181. https://doi.org/10.1002/nme.3050
  3. Casciati, F., Casciati, S., Faravelli, L. and Franchinotti, M. (2012), "Model order reduction vs. structural control", Proceedings of the ACMA2012, Fez (Marocco).
  4. Casciati, S. (2008), "Stiffness identification and damage localization via differential evolution algorithms", Struct.Control Health Monit., 15(3), 436-449. https://doi.org/10.1002/stc.236
  5. Casciati, S. (2010), "Response surface models to detect and localize distributed cracks in a complex continuum", J. Eng. Mech. - ASCE, 136(9), 1131-1142. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000148
  6. Casciati, S. and Al-Saleh, R. (2010), "Dynamic behavior of a masonry civic belfry under operational conditions", Acta Mech., 215( 1-4), 211-224. https://doi.org/10.1007/s00707-010-0343-4
  7. Casciati, S. and Borja, R.L. (2004), "Dynamic FE analysis of south memnon colossus including 3D soil-foundation-structure interaction", Comput. Struct., 82(20-21), 1719-1736. https://doi.org/10.1016/j.compstruc.2004.02.026
  8. Casciati, S. and Osman, A. (2005), "Damage assessment and retrofit study for the luxor memnon colossi", Struct.Control Health Monit., 12(2), 139-156. https://doi.org/10.1002/stc.53
  9. Chinestaa, F., Ammarb, A., Leyguea, A. and Keuningsc, R. (2011), "An overview of the proper generalized decomposition with applications in computational rheology", J. Non-Newton. Fluid., 166(11), 578-592. https://doi.org/10.1016/j.jnnfm.2010.12.012
  10. Craig, R.J. (1987), "A review of time-domain and frequency domain component mode synthesis methods", Int. J. Anal. Exp. Modal Anal., 2(2), 59-72.
  11. Hurty, W.C., Collins, J.D. and Hart, G.C. (1971), "Dynamic analysis of large structures by modal synthesis techniques", Comput. Struct., 1(4), 535-563. https://doi.org/10.1016/0045-7949(71)90029-0
  12. Kaczmarek, J. (2010), "Collection of dynamical systems with dimensional reduction as a multiscale method of modelling for mechanics of materials", Interact. Multiscale Mech., 3(1), 1-22. https://doi.org/10.12989/imm.2010.3.1.001
  13. MacNeal, R.H. (1971), "A hybrid method of component mode synthesis", Comput. Struct., 1(4), 581-601. https://doi.org/10.1016/0045-7949(71)90031-9
  14. Ni, Y.Q., Xia, Y., Lin, W., Chen, W.H. and Ko, J.M. (2012), "SHM benchmark for high-rise structures: a reduced-order finite element model and field measurement data", Smart Struct. Syst., 10(4), 411-426. https://doi.org/10.12989/sss.2012.10.4_5.411
  15. MSC (2013), http://www.mscsoftware.com.
  16. Ohtori, Y., Christenson, R.E. and Spencer, B.F. (2004), "Benchmark control problems for seismically excited nonlinear buildings", J. Eng. Mech. - ASCE., 130, 366-376. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:4(366)
  17. Preumont, A. and Seto, K. (2008), Active control of structures, John Wiley & Sons, Chichester.
  18. Schilders, W.H.A., van der Vorst, H.A. and Rommes, J. (2008), Model order reduction: theory, research aspects and applications, Springer, Berlin.
  19. SDTools (2012), Structural dynamics toolbox, User's Guide on December 5, 2012.

Cited by

  1. Krylov subspace-based model order reduction for Campbell diagram analysis of large-scale rotordynamic systems vol.50, pp.1, 2014, https://doi.org/10.12989/sem.2014.50.1.019
  2. Applications of noise barriers with a slanted flat-tip jagged cantilever for noise attenuation on a construction site 2018, https://doi.org/10.1177/1077546317747779
  3. A European Association for the Control of Structures joint perspective. Recent studies in civil structural control across Europe vol.21, pp.12, 2014, https://doi.org/10.1002/stc.1652
  4. Designing the control law on reduced-order models of large structural systems vol.23, pp.4, 2016, https://doi.org/10.1002/stc.1805
  5. Nonparametric identification of structural modifications in Laplace domain vol.85, 2017, https://doi.org/10.1016/j.ymssp.2016.09.018
  6. Dynamic transient analysis of systems with material nonlinearity: a model order reduction approach vol.18, pp.1, 2016, https://doi.org/10.12989/sss.2016.18.1.001
  7. Multilevel reduced-order computational model in structural dynamics for the low- and medium-frequency ranges vol.160, 2015, https://doi.org/10.1016/j.compstruc.2015.08.007
  8. Swing Story–Lateral Force Resisting System Connected with Dampers: Novel Seismic Vibration Control System for Building Structures vol.144, pp.2, 2018, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001390
  9. Multilevel model reduction for uncertainty quantification in computational structural dynamics vol.59, pp.2, 2017, https://doi.org/10.1007/s00466-016-1348-1
  10. Sensor placement driven by a model order reduction (MOR) reasoning vol.13, pp.3, 2014, https://doi.org/10.12989/sss.2014.13.3.343
  11. An improved substructural damage detection approach of shear structure based on ARMAX model residual vol.23, pp.2, 2016, https://doi.org/10.1002/stc.1766
  12. A finite-element based damage detection technique for nonlinear reinforced concrete structures vol.22, pp.10, 2015, https://doi.org/10.1002/stc.1736
  13. Component Mode Synthesis Order-Reduction for Dynamic Analysis of Structure Modeled With NURBS Finite Element vol.138, pp.2, 2016, https://doi.org/10.1115/1.4032516
  14. Improving the dynamic performance of base-isolated structures via tuned mass damper and inerter devices: A comparative study vol.25, pp.10, 2018, https://doi.org/10.1002/stc.2234
  15. Toward a paradigm for civil structural control vol.14, pp.5, 2014, https://doi.org/10.12989/sss.2014.14.5.981
  16. Model Reduction of Nonlinear Systems by Trajectory Piecewise Linear Based on Output-Weighting Models: A Balanced-Truncation Methodology vol.42, pp.2, 2018, https://doi.org/10.1007/s40998-018-0058-4
  17. A parametric reduced-order model using substructural mode selections and interpolation vol.212, pp.None, 2014, https://doi.org/10.1016/j.compstruc.2018.10.018
  18. Substructural damage detection in shear structures via ARMAX model and optimal subpattern assignment distance vol.191, pp.None, 2014, https://doi.org/10.1016/j.engstruct.2019.04.084