Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear finite element model updating with a decentralized approach

  • Ni, P.H. (Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology) ;
  • Ye, X.W. (Department of Civil Engineering, Zhejiang University)
  • Received : 2019.05.16
  • Accepted : 2019.08.01
  • Published : 2019.12.25
⟨ Previous Next ⟩

Abstract

Traditional damage detection methods for nonlinear structures are often based on simplified models, such as the mass-spring-damper and shear-building models, which are insufficient for predicting the vibration responses of a real structure. Conventional global nonlinear finite element model updating methods are computationally intensive and time consuming. Thus, they cannot be applied to practical structures. A decentralized approach for identifying the nonlinear material parameters is proposed in this study. With this technique, a structure is divided into several small zones on the basis of its structural configuration. The unknown material parameters and measured vibration responses are then divided into several subsets accordingly. The structural parameters of each subset are then updated using the vibration responses of the subset with the Newton-successive-over-relaxation (SOR) method. A reinforced concrete and steel frame structure subjected to earthquake loading is used to verify the effectiveness and accuracy of the proposed method. The parameters in the material constitutive model, such as compressive strength, initial tangent stiffness and yielding stress, are identified accurately and efficiently compared with the global nonlinear model updating approach.

Keywords

Acknowledgement

Supported by : National Science Foundation of China, Zhejiang Provincial Natural Science Foundation of China, Central Universities of China

References

  1. Asgarieh, E., Moaveni, B. and Stavridis, A. (2014), "Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake", J. Sound. Vib., 333(23), 6057-6073. DOI:10.1016/j.jsv.2014.04.064.
  2. Astroza, R., Ebrahimian, H. and Conte, J.P. (2014), "Material parameter identification in distributed plasticity FE models of frame-type structures using nonlinear stochastic filtering", J. Eng. Mech., 141(5), 04014149. DOI:10.1061/(ASCE)EM.1943-7889.0000851.
  3. Astroza, R., Ebrahimian, H., Li, Y. and Conte, J.P. (2017), "Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures", Mech. Syst. Signal. Pr., 93, 661-687. DOI:10.1016/j.ymssp.2017.01.040.
  4. Barbato, M. and Conte, J.P. (2006), "Finite element structural response sensitivity and reliability analyses using smooth versus non-smooth material constitutive models", Inter. J. Reliab. Safe., 1(1-2), 3-39. DOI: 10.1504/IJRS.2006.010688.
  5. Conte, J.P. (2001), "Finite element response sensitivity analysis in earthquake engineering", Earthquake Engineering Frontiers in the New Millennium, pp.395-401.
  6. Conte, J., Vijalapura, P. and Meghella, M. (2003), "Consistent finite-element response sensitivity analysis", J. Eng. Mech., 129(12), 1380-1393. DOI: 10.1061/(ASCE)0733-9399(2003)129:12(1380).
  7. Chen, G., Yang, X., Ying, X. and Nanni, A. (2006), "Damage detection of concrete beams using nonlinear features of forced vibration", Struct. Health. Monit., 5(2), 125-141. DOI:10.1177/1475921706057985.
  8. Charalampakis, A. and Koumousis, V. (2008), "Identification of Bouc-Wen hysteretic systems by a hybrid evolutionary algorithm", J. Sound. Vib., 314(3), 571-585. DOI:10.1016/j.jsv.2008.01.018.
  9. Chatzi, E.N. and Smyth, A.W. (2009), "The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing", Struct. Control. Health., 16(1), 99-123. DOI: 10.1002/stc.290.
  10. Ebrahimian, H., Astroza, R. and Conte, J.P. (2015), "Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method", Earthq. Eng. Struct., 44(10), 1495-1522. DOI:10.1002/eqe.2532.
  11. Ebrahimian, H., Astroza, R., Conte, J.P. and de Callafon, R.A. (2017), "Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation", Mech. Syst. Signal. Pr., 84, 194-222. DOI:10.1016/j.ymssp.2016.02.002.
  12. Ebrahimian, H., Astroza, R., Conte, J.P. and Papadimitriou, C. (2018), "Bayesian optimal estimation for output-only nonlinear system and damage identification of civil structures", Struct. Control. Health., 25(4), e2128. DOI: 10.1002/stc.2128.
  13. Friswell, M. and Mottershead, J.E. (2013), Finite Element Model Updating in Structural Dynamics., Springer Science & Business Media.
  14. Gu, Q., Conte, J.P., Elgamal, A. and Yang, Z. (2009), "Finite element response sensitivity analysis of multi-yield-surface J2 plasticity model by direct differentiation method", Comput. Method Appl. M., 198(30-32), 2272-2285. DOI:10.1016/j.cma.2009.02.030.
  15. Hsieh, C. and Arora, J. (1984), "Design sensitivity analysis and optimization of dynamic response", Comput. Method Appl. M., 43(2), 195-219. DOI: 10.1016/0045-7825(84)90005-7.
  16. Haukaas, T. and Der Kiureghian, A. (2004), Finite Element Reliability and Sensitivity Methods for Performance-based Earthquake Engineering, Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley.
  17. He, J., Xu, B. and Masri, S.F. (2012), "Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations", Nonlinear Dynam., 69(1-2), 231-245. DOI: 10.1007/s11071-011-0260-7.
  18. Kleiber, M., Tran, D.H., Antùnez, H. and Kowalczyk, P. (1997), Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations., John Wiley, Chichester, England.
  19. Kim, J. and Lynch, J.P. (2011), "Autonomous decentralized system identification by Markov parameter estimation using distributed smart wireless sensor networks", J. Eng. Mech., 138(5), 478-490. DOI: 10.1061/(ASCE)EM.1943-7889.0000359.
  20. Kiran, R., Li, L. and Khandelwal, K. (2016), "Complex perturbation method for sensitivity analysis of nonlinear trusses", J. Struct. Eng., 143(1), 04016154. DOI:10.1061/(ASCE)ST.1943-541X.0001619.
  21. Lei, Y. and Wu, Y. (2011). "Non-parametric identification of structural nonlinearity with limited input and output measurements", Adv. Mater. Res., 243: 5403-5407. DOI:10.4028/www.scientific.net/AMR.243-249.5403.
  22. Lei, Y., Wu, D. and Liu, L. (2013), "A decentralized structural control algorithm with application to the benchmark control problem for seismically excited buildings", Struct. Control. Health., 20(9), 1211-1225. DOI: 10.1002/stc.1529.
  23. Law, S.S., Ni, P.H. and Li, J. (2014), "Parallel decentralized damage detection of a structure with subsets of parameters", AIAA. J., 52(3), 650-656. DOI: 10.2514/1.J051716.
  24. Li, Y., Astroza, R., Conte, J.P. and Soto, P. (2017), "Nonlinear FE model updating and reconstruction of the response of an instrumented seismic isolated bridge to the 2010 Maule Chile earthquake", Earthq. Eng. Struct., 46(15), 2699-2716. DOI:10.1002/eqe.2925.
  25. Lu, Z.R. and Law, S.S. (2007), "Features of dynamic response sensitivity and its application in damage detection", J. Sound. Vib., 303(1-2), 305-329. DOI: 10.1016/j.jsv.2007.01.021.
  26. McKenna, F. (2011), "OpenSees: a framework for earthquake engineering simulation", Comput. Sci. Eng., 13(4), 58-66. DOI:10.1109/MCSE.2011.66.
  27. Ni, P., Xia, Y., Law, S. S. and Zhu, S. (2014), "Structural damage detection using auto/cross-correlation functions under multiple unknown excitations", Int. J. Struct. Stab. Dy., 14(5). DOI:10.1142/S0219455414400069.
  28. Ni, P., Xia, Y., Li, J. and Hao, H. (2018), "Improved decentralized structural identification with output-only measurements", Measurement, 122, 597-610. DOI:10.1016/j.measurement.2017.09.029.
  29. Ortega, J.M. and Rheinboldt, W.C. (1970), Iterative Solution of Nonlinear Equations in Several Variables., SIAM. DOI:10.1016/C2013-0-11263-9.
  30. Prawin, J., Rao, A. and Mohan, R. (2018), "Detection of nonlinear structural behavior using time-frequency and multivariate analysis", Smart Struct. Syst., 22(6), 711-725. https://doi.org/10.12989/sss.2018.22.6.711.
  31. Smyth, A., Masri, S., Chassiakos, A. and Caughey, T. (1999), "On-line parametric identification of MDOF nonlinear hysteretic systems", J. Eng. Mech., 125(2), 133-142. DOI:10.1061/(ASCE)0733-9399(1999)125:2(133).
  32. Taucer, F., Spacone, E. and Filippou, F.C. (1991), A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures., Berkekey, California: Earthquake Engineering Research Center, College of Engineering, University of California.
  33. Ting, J.A., Mistry, M., Peters, J., Schaal, S. and Nakanishi, J. (2006), "A Bayesian approach to nonlinear parameter identification for rigid body dynamics", In Robotics: Science and Systems (pp. 32-39). DOI: 10.15607/RSS.2006.II.032.
  34. Xu, B., Wu, Z. and Yokoyama, K. (2003), "Neural networks for decentralized control of cable-stayed bridge", J. Bridge Eng., 8(4), 229-236. DOI: 10.1061/(ASCE)1084-0702(2003)8:4(229).
  35. Xu, B., He, J. and Masri, S.F. (2012), "Data-based identification of nonlinear restoring force under spatially incomplete excitations with power series polynomial model", Nonlinear Dynam., 67(3), 2063-2080. DOI: 10.1007/s11071-011-0129-9.
  36. Yuen, K.V. and Beck, J.L. (2003), "Updating properties of nonlinear dynamical systems with uncertain input", J. Eng. Mech., 129(1), 9-20. DOI:10.1061/(ASCE)0733-9399(2003)129:1(9).
  37. Ye, X.W., Ni, Y.Q., Wai, T.T., Wong, K.Y., Zhang, X.M. and Xu, F. (2013), "A vision-based system for dynamic displacement measurement of long-span bridges: algorithm and verification", Smart Struct Syst., 12(3-4), 363-379. https://doi.org/10.12989/sss.2013.12.3_4.363.
  38. Ye, X.W., Yi, T.H., Wen, C. and Su, Y.H. (2015), "Reliabilitybased assessment of steel bridge deck using a mesh-insensitive structural stress method", Smart Struct Syst., 16(2), 367-382. https://doi.org/10.12989/sss.2015.16.2.367.
  39. Ye, X.W., Dong, C.Z. and Liu, T. (2016a), "Force monitoring of steel cables using vision-based sensing technology:methodology and experimental verification", Smart Struct Syst., 18(3), 585-599. https://doi.org/10.12989/sss.2016.18.3.585.
  40. Ye, X.W., Dong, C.Z. and Liu, T. (2016b), "Image-based structural dynamic displacement measurement using different multi-object tracking algorithms", Smart Struct Syst., 17(6), 935-956. https://doi.org/10.12989/sss.2016.17.6.935.
  41. Zhang, Y. and Der Kiureghian, A. (1993), "Dynamic response sensitivity of inelastic structures", Comput. Method Appl. M., 108(1), 23-36. DOI:10.1016/0045-7825(93)90151-M.
  42. Zona, A., Barbato, M. and Conte, J.P. (2005), "Finite element response sensitivity analysis of steel-concrete composite beams with deformable shear connection", J. Eng. Mech., 131(11), 1126-1139. DOI: 10.1061/(ASCE)0733-9399(2005)131:11(1126).