An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

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• 作者：P. S. B. Nigro ; M. Anndif ; Y. Teixeira ; P. M. Pimenta…
• 关键词：Model order reduction ; PSS ; Ritz vector ; Nonlinear dynamic analysis ; Galerkin projection ; Adaptive strategy
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：57
• 期：4
• 页码：537-554
• 全文大小：4,239 KB
• 参考文献：1.Campello EMB, Pimenta PM, Wriggers P (2003) A triangular finite shell element based on a fully nonlinear shell formulation. Comput Mech 31:505–518CrossRef MATH
  2.Pimenta PM, Wriggers P, Campello EMB (2004) A fully nonlinear multi-parameter shell model with thickness variation and a triangular shell finite element. Comput Mech 34:181–193CrossRef MATH
  3.Ladevèze P, Passieux J-C, Néron D (2010) The LATIN multiscale computational method and the proper generalized decomposition. Comput Methods Appl Mech Eng 199:1287–1296MathSciNet CrossRef MATH
  4.Chinesta F, Ammar A, Cueto E (2010) Recent Advances and New Challenges in the Use of the proper generalized decomposition for solving multidimensional models. Arch Comput Methods Eng 17:327–350MathSciNet CrossRef MATH
  5.Anttonen SR, King P, Beran P (2003) POD-based reduced-order models with deforming grids. Math Comput Model 38:41–62MathSciNet CrossRef MATH
  6.Anttonen JSR, King PI, Beran P (2005) Application of multi-POD to a pitching and plunging airfoil. Math Comput Model 42:245–259MathSciNet CrossRef MATH
  7.Braconnier T et al (2010) Towards an adaptive POD/SVD surrogate model for aeronautic design. Comput Fluids 40:195–209MathSciNet CrossRef MATH
  8.Bui-Thanh T, Damodaran M, Willcox K (2004) Aerodynamic sata reconstruction and inverse design using proper orthogonal decomposition. AIAA J 42:1505–1516CrossRef
  9.Gurka R, Liberzon A, Hetsroni G (2006) POD of vorticity fields: a method for spatial characterization of coherent structures. Heat Fluid Flow 27:416–423CrossRef
  10.Kerschen G, Golinval C (2002) Physical interpretation of the proper orthogonal modes using the singular value decomposition. J Sound Vib 249:849–865MathSciNet CrossRef MATH
  11.Lenaerts V, Kerschen G (2001) Proper orthogonal decomposition for model updating of non-linear mechanical systems. Mech Syst Signal Process 15:31–43CrossRef
  12.Tadmor G et al. (2008) Fast approximated POD for a Flat Plate Benchmark with a time varying angle of attack. 4th Flow Control Conference, Seattle
  13.Kemper J (2011) Long-time behavior of the proper orthogonal decomposition method. Numer Linear Algebra Appl 19:842–868MathSciNet CrossRef MATH
  14.Kerfriden Gosselet, Adhikari S, Bordas S (2010) Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Comp Methods Appl Mech Eng 200:850–866MathSciNet CrossRef MATH
  15.Ryckelynck D (2005) A priori hyperreduction method: an adaptive approach. J Comput Phys 202:346–366CrossRef MATH
  16.Carlberg K (2015) Adaptive h-refinement for reduced-order models. Int J Numer Methods Eng 102:1192–1210MathSciNet CrossRef
  17.Zahr MJ, Farhat C (2015) rogressive construction of a parametric reduced-order model for PDE-constrained optimization. Int J Numer Methods Eng 102:1111–1135MathSciNet CrossRef
  18.Amsallem D, Farhat C (2012) Stabilization of projection-based reduced-order models. Int J Numer Methods Eng 91:358–377MathSciNet CrossRef MATH
  19.Carlberg K, Farhat C (2009) An Adaptive POD-Krylov reduced-order model for structural optimization. 8th World Congress on Structural and Multidisciplinary Optimization, Lisbon
  20.Carlberg K, Bou-Mosleh C, Farhat C (2010) Efficient nonlinear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations. Int J Numer Methods Eng 86:155–181MathSciNet CrossRef MATH
  21.Spiess H, Wriggers P (2005) Reduction methods for FE analysis in nonlinear structural dynamics. PAMM 5:135–136CrossRef
  22.Krysl P, Lall S, Marsden JE (2001) Dimensional model reduction in non-linear finite element dynamics of solid and structures. Int J Numer Methods Eng 51:479–504MathSciNet CrossRef MATH
  23.Uzunoglu B, Fletcher SJ, Zupanski M, Navon IM (2007) Adaptive ensemble reduction and inflation. Q J R Meteorol Soc 133:1281–1294CrossRef
  24.Gosselet P, Rey C (2003) On a selective reuse of Krylov subspaces in Newton–Krylov approaches for nonlinear elasticity. In: Fourteenth international conference on domain decomposition methods, Cocoyoc
  25.Demmel J (1997) Applied numerical linear algebra, 1st edn. SIAM, PhiladelphiaCrossRef MATH
  26.Golub GH, Van Loan CF (1996) Matrix Computations, 3rd edn. The Johns Hopkins Press Ltd., LondonMATH
  27.Hendrix EMT, Tóth BG (2010) Introduction to nonlinear and global optimization. Springer, New YorkCrossRef MATH
  28.Bartholomew-Biggs M (2008) Nonlinear optimization with engineering applications. Springer, New YorkCrossRef MATH
  29.Wriggers P (2008) Nonlinear finite element methods. Springer, BerlinMATH
  
• 作者单位：P. S. B. Nigro (1) (2)
  M. Anndif (2)
  Y. Teixeira (1)
  P. M. Pimenta (1)
  P. Wriggers (2)
  
  1. Department of Structural and Geotechnical Engineering, Polytechnic School at University of São Paulo, Av. Prof. Almeida Prado 83, São Paulo, 05508-010, Brazil
  2. Institute of Continuum Mechanics, Leibniz University Hannover, Appelstraße 11, 30167, Hannover, Germany
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).