2019
Journal article
Open Access
Finite element model updating for structural applications
Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.
Finite elements Computational Mathematics 74S04 Lanczo FOS: Mathematics Lanczos 70J10 Trust-region Eigenvalue optimization Mathematics - Numerical Analysis 65L60 15A22 Numerical Analysis (math.NA) 65F18 Applied Mathematics Model updating Finite element
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown material parameters (such as mass density and Young's modulus) of the materials and/or the boundary conditions, which are often known only approximately. In particular, this is the case when considering historical buildings. The straightforward application of a general-purpose optimizer can be impractical, given the large size of the model involved. In the paper, we show that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, form the basis for a reliable and efficient specialized algorithm. We describe an optimization strategy based on this approach, and we provide numerical experiments that confirm its effectiveness and accuracy.
Source: Journal of computational and applied mathematics 370 (2019). doi:10.1016/j.cam.2019.112675
Publisher: Koninklijke Vlaamse Ingenieursvereniging, Amsterdam , Belgio
[1] A. Agarwal and L. T. Biegler, A trust-region framework for constrained optimization using reduced order modeling, Optimization and Engineering, 14 (2013), pp. 3{35.
[2] N. Alexandrov and J. E. Dennis, Multilevel algorithms for nonlinear optmization, Optimal design and control, (1995), pp. 1{22.
[3] D. Amsallem, M. Zahr, Y. Choi, and C. Farhat, Design optimization using hyper-reduced-order models, Structural and Multidisciplinary Optimization, 51 (2015), pp. 919{940.
[4] T. Aoki, D. Sabia, D. Rivella, and T. Komiyama, Structural characterization of a stone arch bridge by experimental tests and numerical model updating, International Journal of Architectural Heritage, 1 (2007), pp. 227{250.
[5] A. S. Araujo, P. B. Lourenco, D. V. Oliveira, and J. C. Leite, Seismic assessment of st. james church by means of pushover analysis: before and after the new zealand earthquake, The Open Civil Engineering Journal, 6 (2012), pp. 160{172.
[6] R. Azzara, G. De Roeck, E. Reynders, M. Girardi, C. Padovani, and D. Pellegrini, Assessment of the dynamic behaviour of an ancient masonry tower in lucca via ambient vibrations, in Proceedings of the 10th international conference on the Analysis of Historican Contructions-SAHC 2016, CRC Press, 2016, pp. 669{675.
[7] R. M. Azzara, G. De Roeck, M. Girardi, C. Padovani, D. Pellegrini, and E. Reynders, The in uence of environmental parameters on the dynamic behaviour of the san frediano bell tower in lucca, Engineering Structures, 156 (2018), pp. 175{187.
[8] Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Applied numerical mathematics, 43 (2002), pp. 9{44.
[9] K.-J. Bathe and E. L. Wilson, Numerical methods in nite element analysis, vol. 197, Prentice-Hall Englewood Cli s, NJ, 1976.
[10] P. Benner, S. Gugercin, and K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM review, 57 (2015), pp. 483{531.
[11] V. Binante, M. Girardi, C. Padovani, G. Pasquinelli, D. Pellegrini, M. Porcelli, and L. Robol, Nosa-itaca 1.1 documentation, 2017.
[12] A. Cabboi, C. Gentile, and A. Saisi, From continuous vibration monitoring to fem-based damage assessment: Application on a stone-masonry tower, Construction and Building Materials, 156 (2017), pp. 252{265.
[13] R. Ceravolo, G. Pistone, L. Z. Fragonara, S. Massetto, and G. Abbiati, Vibration-based monitoring and diagnosis of cultural heritage: a methodological discussion in three examples, International Journal of Architectural Heritage, 10 (2016), pp. 375{395.
[14] J. C. Chen and J. A. Garba, Analytical model improvement using modal test results, AIAA journal, 18 (1980), pp. 684{690.
[15] V. Compan, P. Pachon, M. Camara, P. B. Lourenco, and A. Saez, Structural safety assessment of geometrically complex masonry vaults by non-linear analysis. the chapel of the wurzburg residence (germany), Engineering Structures, 140 (2017), pp. 1{13.
[16] A. R. Conn, N. I. Gould, and P. L. Toint, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM journal on numerical analysis, 25 (1988), pp. 433{460.
[17] A. R. Conn, N. I. Gould, and P. L. Toint, Trust region methods, SIAM, 2000.
[18] Demmel, Applied numerical linear algebra, (1997).
[19] B. M. Douglas and W. H. Reid, Dynamic tests and system identi cation of bridges, Journal of the Structural Division, 108 (1982).
[20] Y. S. Erdogan, Discrete and continuous nite element models and their calibration via vibration and material tests for the seismic assessment of masonry structures, International Journal of Architectural Heritage, (2017).
[21] L. Z. Fragonara, G. Boscato, R. Ceravolo, S. Russo, S. Ientile, M. L. Pecorelli, and A. Quattrone, Dynamic investigation on the mirandola bell tower in post-earthquake scenarios, Bulletin of Earthquake Engineering, 15 (2017), pp. 313{337.
[22] M. Friswell and J. E. Mottershead, Finite element model updating in structural dynamics, vol. 38, Springer Science & Business Media, 2013.
[23] C. Gentile and A. Saisi, Ambient vibration testing of historic masonry towers for structural identi cation and damage assessment, Construction and Building Materials, 21 (2007), pp. 1311{1321.
[24] M. Girardi, C. Padovani, D. Pellegrini, and L. Robol, NOSA-ITACA: a free FE program for historic masonry buildings, in CORASS 2017, 2017, pp. {.
[25] A. A. Giunta and M. S. Eldred, Implementation of a trust region model management strategy in the dakota optimization toolkit, in Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, 2000.
[26] T. Kato, Perturbation theory for linear operators, vol. 132, Springer Science & Business Media, 2013.
[27] T. Kocaturk, Y. Erdogan, C. Demir, A. Gokce, S. Ulukaya, and N. Yuzer, Investigation of existing damage mechanism and retro tting of skeuophylakion under seismic loads, Engineering Structures, 137 (2017), pp. 125{144.
[28] R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK users' guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, SIAM, 1998.
[29] T. Marwala, Finite element model updating using computational intelligence techniques: applications to structural dynamics, Springer Science & Business Media, 2010.
[30] M. O'Connell, M. E. Kilmer, E. de Sturler, and S. Gugercin, Computing reduced order models via inner-outer krylov recycling in di use optical tomography, SIAM Journal on Scienti c Computing, 39 (2017), pp. B272{B297.
[31] M. L. Parks, E. De Sturler, G. Mackey, D. D. Johnson, and S. Maiti, Recycling krylov subspaces for sequences of linear systems, SIAM Journal on Scienti c Computing, 28 (2006), pp. 1651{1674.
[32] D. Pellegrini, M. Girardi, C. Padovani, and R. Azzara, A new numerical procedure for assessing the dynamic behaviour of ancient masonry towers, in Proceedings of the 6th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - COMPDYN 2017, 2017, pp. {.
[33] V. Perez-Gracia, D. Di Capua, O. Caselles, F. Rial, H. Lorenzo, R. Gonzalez-Drigo, and J. Armesto, Characterization of a romanesque bridge in galicia (spain), International Journal of Architectural Heritage, 5 (2011), pp. 251{263.
[34] M. Porcelli, On the convergence of an inexact gauss{newton trust-region method for nonlinear least-squares problems with simple bounds, Optimization Letters, 7 (2013), pp. 447{465.
[35] M. Porcelli, V. Binante, M. Girardi, C. Padovani, and G. Pasquinelli, A solution procedure for constrained eigenvalue problems and its application within the structural nite-element code nosa-itaca, Calcolo, 52 (2015), pp. 167{186.
[36] E. Qian, M. Grepl, K. Veroy, and K. Willcox, A certi ed trust region reduced basis approach to PDEconstrained optimization, SIAM Journal on Scienti c Computing, 39 (2017), pp. S434{S460.
[37] L. F. Ramos, M. Alaboz, R. Aguilar, and P. B. Lourenco, Dynamic identi cation and fe updating of s. torcato church, portugal, in Dynamics of Civil Structures, Volume 4, Springer, 2011, pp. 71{80.
[38] L. F. Ramos, L. Marques, P. B. Lourenco, G. De Roeck, A. Campos-Costa, and J. Roque, Monitoring historical masonry structures with operational modal analysis: two case studies, Mechanical systems and signal processing, 24 (2010), pp. 1291{1305.
[39] Y. Saad, Iterative methods for sparse linear systems, SIAM, 2003.
[40] E. Simoen, G. De Roeck, and G. Lombaert, Dealing with uncertainty in model updating for damage assessment: A review, Mechanical Systems and Signal Processing, 56 (2015), pp. 123{149.
[41] K. M. Soodhalter, D. B. Szyld, and F. Xue, Krylov subspace recycling for sequences of shifted linear systems, Applied Numerical Mathematics, 81 (2014), pp. 105{118.
[42] J.-g. Sun, Multiple eigenvalue sensitivity analysis, Linear algebra and its applications, 137 (1990), pp. 183{211.
[43] A. Teughels and G. De Roeck, Damage detection and parameter identi cation by nite element model updating, Revue europeenne de genie civil, 9 (2005), pp. 109{158.
[44] W. Torres, J. L. Almazan, C. Sandoval, and R. Boroschek, Operational modal analysis and fe model updating of the metropolitan cathedral of santiago, chile, Engineering Structures, 143 (2017), pp. 169{188.
[45] Y. Yue and K. Meerbergen, Accelerating optimization of parametric linear systems by model order reduction, SIAM Journal on Optimization, 23 (2013), pp. 1344{1370.
[46] M. J. Zahr and C. Farhat, Progressive construction of a parametric reduced-order model for PDE-constrained optimization, International Journal for Numerical Methods in Engineering, 102 (2015), pp. 1111{1135.
[2] N. Alexandrov and J. E. Dennis, Multilevel algorithms for nonlinear optmization, Optimal design and control, (1995), pp. 1{22.
[3] D. Amsallem, M. Zahr, Y. Choi, and C. Farhat, Design optimization using hyper-reduced-order models, Structural and Multidisciplinary Optimization, 51 (2015), pp. 919{940.
[4] T. Aoki, D. Sabia, D. Rivella, and T. Komiyama, Structural characterization of a stone arch bridge by experimental tests and numerical model updating, International Journal of Architectural Heritage, 1 (2007), pp. 227{250.
[5] A. S. Araujo, P. B. Lourenco, D. V. Oliveira, and J. C. Leite, Seismic assessment of st. james church by means of pushover analysis: before and after the new zealand earthquake, The Open Civil Engineering Journal, 6 (2012), pp. 160{172.
[6] R. Azzara, G. De Roeck, E. Reynders, M. Girardi, C. Padovani, and D. Pellegrini, Assessment of the dynamic behaviour of an ancient masonry tower in lucca via ambient vibrations, in Proceedings of the 10th international conference on the Analysis of Historican Contructions-SAHC 2016, CRC Press, 2016, pp. 669{675.
[7] R. M. Azzara, G. De Roeck, M. Girardi, C. Padovani, D. Pellegrini, and E. Reynders, The in uence of environmental parameters on the dynamic behaviour of the san frediano bell tower in lucca, Engineering Structures, 156 (2018), pp. 175{187.
[8] Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Applied numerical mathematics, 43 (2002), pp. 9{44.
[9] K.-J. Bathe and E. L. Wilson, Numerical methods in nite element analysis, vol. 197, Prentice-Hall Englewood Cli s, NJ, 1976.
[10] P. Benner, S. Gugercin, and K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM review, 57 (2015), pp. 483{531.
[11] V. Binante, M. Girardi, C. Padovani, G. Pasquinelli, D. Pellegrini, M. Porcelli, and L. Robol, Nosa-itaca 1.1 documentation, 2017.
[12] A. Cabboi, C. Gentile, and A. Saisi, From continuous vibration monitoring to fem-based damage assessment: Application on a stone-masonry tower, Construction and Building Materials, 156 (2017), pp. 252{265.
[13] R. Ceravolo, G. Pistone, L. Z. Fragonara, S. Massetto, and G. Abbiati, Vibration-based monitoring and diagnosis of cultural heritage: a methodological discussion in three examples, International Journal of Architectural Heritage, 10 (2016), pp. 375{395.
[14] J. C. Chen and J. A. Garba, Analytical model improvement using modal test results, AIAA journal, 18 (1980), pp. 684{690.
[15] V. Compan, P. Pachon, M. Camara, P. B. Lourenco, and A. Saez, Structural safety assessment of geometrically complex masonry vaults by non-linear analysis. the chapel of the wurzburg residence (germany), Engineering Structures, 140 (2017), pp. 1{13.
[16] A. R. Conn, N. I. Gould, and P. L. Toint, Global convergence of a class of trust region algorithms for optimization with simple bounds, SIAM journal on numerical analysis, 25 (1988), pp. 433{460.
[17] A. R. Conn, N. I. Gould, and P. L. Toint, Trust region methods, SIAM, 2000.
[18] Demmel, Applied numerical linear algebra, (1997).
[19] B. M. Douglas and W. H. Reid, Dynamic tests and system identi cation of bridges, Journal of the Structural Division, 108 (1982).
[20] Y. S. Erdogan, Discrete and continuous nite element models and their calibration via vibration and material tests for the seismic assessment of masonry structures, International Journal of Architectural Heritage, (2017).
[21] L. Z. Fragonara, G. Boscato, R. Ceravolo, S. Russo, S. Ientile, M. L. Pecorelli, and A. Quattrone, Dynamic investigation on the mirandola bell tower in post-earthquake scenarios, Bulletin of Earthquake Engineering, 15 (2017), pp. 313{337.
[22] M. Friswell and J. E. Mottershead, Finite element model updating in structural dynamics, vol. 38, Springer Science & Business Media, 2013.
[23] C. Gentile and A. Saisi, Ambient vibration testing of historic masonry towers for structural identi cation and damage assessment, Construction and Building Materials, 21 (2007), pp. 1311{1321.
[24] M. Girardi, C. Padovani, D. Pellegrini, and L. Robol, NOSA-ITACA: a free FE program for historic masonry buildings, in CORASS 2017, 2017, pp. {.
[25] A. A. Giunta and M. S. Eldred, Implementation of a trust region model management strategy in the dakota optimization toolkit, in Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, 2000.
[26] T. Kato, Perturbation theory for linear operators, vol. 132, Springer Science & Business Media, 2013.
[27] T. Kocaturk, Y. Erdogan, C. Demir, A. Gokce, S. Ulukaya, and N. Yuzer, Investigation of existing damage mechanism and retro tting of skeuophylakion under seismic loads, Engineering Structures, 137 (2017), pp. 125{144.
[28] R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK users' guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, SIAM, 1998.
[29] T. Marwala, Finite element model updating using computational intelligence techniques: applications to structural dynamics, Springer Science & Business Media, 2010.
[30] M. O'Connell, M. E. Kilmer, E. de Sturler, and S. Gugercin, Computing reduced order models via inner-outer krylov recycling in di use optical tomography, SIAM Journal on Scienti c Computing, 39 (2017), pp. B272{B297.
[31] M. L. Parks, E. De Sturler, G. Mackey, D. D. Johnson, and S. Maiti, Recycling krylov subspaces for sequences of linear systems, SIAM Journal on Scienti c Computing, 28 (2006), pp. 1651{1674.
[32] D. Pellegrini, M. Girardi, C. Padovani, and R. Azzara, A new numerical procedure for assessing the dynamic behaviour of ancient masonry towers, in Proceedings of the 6th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - COMPDYN 2017, 2017, pp. {.
[33] V. Perez-Gracia, D. Di Capua, O. Caselles, F. Rial, H. Lorenzo, R. Gonzalez-Drigo, and J. Armesto, Characterization of a romanesque bridge in galicia (spain), International Journal of Architectural Heritage, 5 (2011), pp. 251{263.
[34] M. Porcelli, On the convergence of an inexact gauss{newton trust-region method for nonlinear least-squares problems with simple bounds, Optimization Letters, 7 (2013), pp. 447{465.
[35] M. Porcelli, V. Binante, M. Girardi, C. Padovani, and G. Pasquinelli, A solution procedure for constrained eigenvalue problems and its application within the structural nite-element code nosa-itaca, Calcolo, 52 (2015), pp. 167{186.
[36] E. Qian, M. Grepl, K. Veroy, and K. Willcox, A certi ed trust region reduced basis approach to PDEconstrained optimization, SIAM Journal on Scienti c Computing, 39 (2017), pp. S434{S460.
[37] L. F. Ramos, M. Alaboz, R. Aguilar, and P. B. Lourenco, Dynamic identi cation and fe updating of s. torcato church, portugal, in Dynamics of Civil Structures, Volume 4, Springer, 2011, pp. 71{80.
[38] L. F. Ramos, L. Marques, P. B. Lourenco, G. De Roeck, A. Campos-Costa, and J. Roque, Monitoring historical masonry structures with operational modal analysis: two case studies, Mechanical systems and signal processing, 24 (2010), pp. 1291{1305.
[39] Y. Saad, Iterative methods for sparse linear systems, SIAM, 2003.
[40] E. Simoen, G. De Roeck, and G. Lombaert, Dealing with uncertainty in model updating for damage assessment: A review, Mechanical Systems and Signal Processing, 56 (2015), pp. 123{149.
[41] K. M. Soodhalter, D. B. Szyld, and F. Xue, Krylov subspace recycling for sequences of shifted linear systems, Applied Numerical Mathematics, 81 (2014), pp. 105{118.
[42] J.-g. Sun, Multiple eigenvalue sensitivity analysis, Linear algebra and its applications, 137 (1990), pp. 183{211.
[43] A. Teughels and G. De Roeck, Damage detection and parameter identi cation by nite element model updating, Revue europeenne de genie civil, 9 (2005), pp. 109{158.
[44] W. Torres, J. L. Almazan, C. Sandoval, and R. Boroschek, Operational modal analysis and fe model updating of the metropolitan cathedral of santiago, chile, Engineering Structures, 143 (2017), pp. 169{188.
[45] Y. Yue and K. Meerbergen, Accelerating optimization of parametric linear systems by model order reduction, SIAM Journal on Optimization, 23 (2013), pp. 1344{1370.
[46] M. J. Zahr and C. Farhat, Progressive construction of a parametric reduced-order model for PDE-constrained optimization, International Journal for Numerical Methods in Engineering, 102 (2015), pp. 1111{1135.
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BibTeX entry
@article{oai:it.cnr:prodotti:415504,
title = {Finite element model updating for structural applications},
author = {Girardi M. and Padovani C. and Pellegrini D. and Porcelli M. and Robol L.},
publisher = {Koninklijke Vlaamse Ingenieursvereniging, Amsterdam , Belgio},
doi = {10.1016/j.cam.2019.112675 and 10.48550/arxiv.1801.09122},
journal = {Journal of computational and applied mathematics},
volume = {370},
year = {2019}
}
0000-0002-7358-5607
