Structural Engineering and Mechanics

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Anti-sparse representation for structural model updating using l∞ norm regularization

  • Luo, Ziwei (MOE Key Laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University) ;
  • Yu, Ling (MOE Key Laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University) ;
  • Liu, Huanlin (MOE Key Laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University) ;
  • Chen, Zexiang (MOE Key Laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University)
  • Received : 2020.02.14
  • Accepted : 2020.04.18
  • Published : 2020.08.25
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Abstract

Finite element (FE) model based structural damage detection (SDD) methods play vital roles in effectively locating and quantifying structural damages. Among these methods, structural model updating should be conducted before SDD to obtain benchmark models of real structures. However, the characteristics of updating parameters are not reasonably considered in existing studies. Inspired by the l∞ norm regularization, a novel anti-sparse representation method is proposed for structural model updating in this study. Based on sensitivity analysis, both frequencies and mode shapes are used to define an objective function at first. Then, by adding l∞ norm penalty, an optimization problem is established for structural model updating. As a result, the optimization problem can be solved by the fast iterative shrinkage thresholding algorithm (FISTA). Moreover, comparative studies with classical regularization strategy, i.e. the l2 norm regularization method, are conducted as well. To intuitively illustrate the effectiveness of the proposed method, a 2-DOF spring-mass model is taken as an example in numerical simulations. The updating results show that the proposed method has a good robustness to measurement noises. Finally, to further verify the applicability of the proposed method, a six-storey aluminum alloy frame is designed and fabricated in laboratory. The added mass on each storey is taken as updating parameter. The updating results provide a good agreement with the true values, which indicates that the proposed method can effectively update the model parameters with a high accuracy.

Keywords

Acknowledgement

This work is jointly supported by the National Natural Science Foundation of China with Grant Numbers 51678278 and 51278226.

References

  1. Arora, V. (2014), "FE model updating method incorporating damping matrices for structural dynamic modifications", Struct. Eng. Mech., 52(2), 261-274. https://doi.org/10.12989/sem.2014.52.2.261.
  2. Avitabile, P. (2010), "Can the shaker stinger have any effect on the frequency response measurements?", Exp. Tech., 34(3), 11-12. https://doi.org/10.1111/j.1747-1567.2010.00636.x.
  3. Batou, A. (2019), "A sensitivity-based one-parameter-at-a-time model updating method", Mech. Syst. Signal Process., 122, 247-255. https://doi.org/10.1016/j.ymssp.2018.12.025.
  4. Behmanesh, I., Yousefianmoghadam, S., Nozari, A., Moaveni, B. and Stavridis, A. (2018), "Uncertainty quantification and propagation in dynamic models using ambient vibration measurements, application to a 10-story building", Mech. Syst. Signal Process., 107, 502-514. https://doi.org/10.1016/j.ymssp.2018.01.033.
  5. Cadzow, J. (1971), "Algorithm for the minimum-effort problem", IEEE Trans. Automat. Contr., 16(1), 60-63. https://doi.org/10.1109/TAC.1971.1099634.
  6. Cao, Z., Fei, Q., Jiang, D., Wu, S. and Fan, Z. (2019), "Model updating of a stitched sandwich panel based on multistage parameter selection", Math. Probl. Eng., 1584953. https://doi.org/10.1155/2019/1584953.
  7. Chen, H.P. and Maung, T.S. (2014), "Regularized finite element model updating using measured incomplete modal data", J. Sound Vib., 333(21), 5566-5582. https://doi.org/10.1016/j.jsv.2014.05.051.
  8. Chen, Z. P. and Yu, L. (2017), "A novel PSO-based algorithm for structural damage detection using Bayesian multi-sample objective function", Struct. Eng. Mech., 63(6), 825-835. https://doi.org/10.12989/sem.2017.63.6.825.
  9. Deo, A.S. and Walker, I.D. (1997), "Minimum effort inverse kinematics for redundant manipulators", IEEE Trans. Robot. Automat., 13(5), 767-775. https://doi.org/10.1109/70.631238.
  10. Ding, Z., Li, J. and Hao, H. (2019), "Structural damage identification using improved Jaya algorithm based on sparse regularization and Bayesian inference", Mech. Syst. Signal Process., 132, 211-231. https://doi.org/10.1016/j.ymssp.2019.06.029.
  11. Elvira, C., Chainais, P. and Dobigeon, N. (2016), "Democratic prior for anti-sparse coding", 2016 IEEE Statistical Signal Processing Workshop, Palma, Spain, June. https://doi.org/10.1109/SSP.2016.7551813.
  12. Elvira, C., Chainais, P. and Dobigeon, N. (2017), "Bayesian anti-sparse coding", IEEE Trans. Signal Process., 65, 1660-1672. https://doi.org/10.1109/TSP.2016.2645543.
  13. Esfandiari, A., Chaei, M. G. and Rofooei, F. R. (2018), "A structural model updating method using incomplete power spectral density function and modal data", Struct. Eng. Mech., 68(1), 39-51. https://doi.org/10.12989/sem.2018.68.1.039.
  14. Fan, X., Li, J., Hao, H. and Ma, S. (2018), "Identification of minor structural damage based on electromechanical impedance sensitivity and sparse regularization", J. Aerosp. Eng., 31(5), 1-14. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000892.
  15. Friswell, M.I., Mottershead, J.E. and Ahmadian, H. (2001), "Finite-element model updating using experimental test data: parametrization and regularization", Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 359(1778), 169-186. https://doi.org/10.1098/rsta.2000.0719.
  16. Fuchs, J.J. (2011), "Spread representations", 2011 Conference Record of the Forty-Fifth Asilomar Conference on Signals, Systems and Computers, Pacific grove, USA, November.
  17. Goksu, C., Inci, P., Demir, U., Yazgan, U. and Ilki, A. (2017), "Field testing of substandard RC buildings through forced vibration tests", Bull. Earthq. Eng., 15(8), 3245-3263. https://doi.org/10.1007/s10518-015-9799-x.
  18. Hansen, P.C., Nagy, J.G. and O'leary, D.P. (2007), "Deblurring im-ages: matrices, spectra, and filtering", J. Electron. Imaging., 17, 019901. https://doi.org/10.1117/1.2900557.
  19. Ha, T., Kim, J., Cho, B.H., Kim, D.J., Jung, J.E., Shin, S.H. and Kim, H. (2017), "Finite element model updating of multi-span greenhouses based on ambient vibration measurements", Biosyst. Eng., 161, 145-156. https://doi.org/10.1016/j.biosystemseng.2017.06.019.
  20. Hou, R., Xia, Y. and Zhou, X. (2018), "Structural damage detection based on l1 regularization using natural frequencies and mode shapes", Struct. Control Heal. Monit., 25(3), e2017. https://doi.org/10.1002/stc.2107.
  21. Hua, X.G., Ni, Y.Q. and Ko, J.M. (2009), "Adaptive regularization parameter optimization in output-error-based finite element model updating", Mech. Syst. Signal Process., 23(3), 563-579. https://doi.org/10.1016/j.ymssp.2008.05.002.
  22. Hua, X.G., Ni, Y.Q., Chen, Z.Q. and He, X.H. (2011), "Monte Carlo study of the effect of measurement noise in model updating with regularization", J. Eng. Mech., 138(1), 71-81. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000308.
  23. Jegou, H., Furon, T. and Fuchs, J.J. (2012), "Anti-sparse coding for approximate nearest neighbor search", 2012 IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, Japan, March. https://doi.org/10.1109/ICASSP.2012.6288307.
  24. Khademi-Zahedi, R. and Alimouri, P. (2019), "Finite element model updating of a large structure using multi-setup stochastic subspace identification method and bees optimization algorithm", Front. Struct. Civ. Eng., 13(4), 965-980. https://doi.org/10.1007/s11709-019-0530-x.
  25. Lakshmi, K. (2019), "Multi constrained optimization combining ARMAX with differential search for damage assessment", Struct. Eng. Mech., 72(6), 689. http://dx.doi.org/10.12989/.2019.72.6.689.
  26. Li, J., Hao, H. and Lo, J.V. (2015), "Structural damage identification with power spectral density transmissibility: numerical and experimental studies", Smart Struct. Syst., 15(1), 15-40. http://dx.doi.org/10.12989/sss.2015.15.1.015.
  27. Link, M. (1999), "Updating of analytical models-review of numerical procedures and application aspects", Structural Dynamics Forum SD2000, Baldock, UK, April.
  28. Mangasarian, O.L. and Recht, B. (2011), "Probability of unique integer solution to a system of linear equations", Eur. J. Oper. Res., 214(1), 27-30. https://doi.org/10.1016/j.ejor.2011.04.010.
  29. Mares, C., Friswell, M.I. and Mottershead, J.E. (2002), "Model updating using robust estimation", Mech. Syst. Signal Process., 16(1), 169-183. https://doi.org/10.1006/mssp.2000.1375.
  30. Pan, C.D., Yu, L. and Liu, H.L. (2017), "Identification of moving vehicle forces on bridge structures via moving average Tikhonov regularization", Smart Mater. Struct., 26(8), 085041. https://doi.org/10.1088/1361-665X/aa7a48.
  31. Pedram, M. and Esfandiari, A. (2019), "Mitigating the effect of incomplete measurement in sensitivity-based FE model updating by enhanced transfer function", Iran. J. Sci. Technol-Trans. Civ. Eng., 43(1), 467-486. https://doi.org/10.1007/s40996-018-0180-6.
  32. Shen, X. and Gu, Y. (2015), "Anti-sparse representation for continuous function by dual atomic norm with application in OFDM", 2015 IEEE Global Conference on Signal and Information Processing, Orlando, USA, December. https://doi.org/10.1109/GlobalSIP.2015.7418199.
  33. Studer, C., Yin, W. and Baraniuk, R.G. (2012), "Signal representations with minimum $l_{\infty}$-norm", 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Illinois, USA, October. https://doi.org/10.1109/Allerton.2012.6483364.
  34. Toh, K. C. and Yun, S. (2010), "An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems", Pac. J. Optim., 6(3), 615-640. https://doi.org/10.1007/s12532-014-0069-8.
  35. Vahidi, M., Vahdani, S., Rahimian, M., Jamshidi, N. and Kanee, A. T. (2019), "Evolutionary-base finite element model updating and damage detection using modal testing results", Struct. Eng. Mech., 70(3), 339-350. https://doi.org/10.12989/sem.2019.70.3.339.
  36. Wang, J. and Yang, Q.S. (2012), "Modified Tikhonov regularization in model updating for damage identification", Struct. Eng. Mech., 44(5), 585-600. http://dx.doi.org/10.12989/sem.2012.44.5.585.
  37. Xu, Z.B., Guo, H.L., Wang, Y. and Zhang, H. (2012), "Representative of $L_{1/2}$ regularization among $L_q$ (0 < q ${\leq}$ 1) regularizations: an experimental study based on phase diagram", Acta Autom. Sin., 38(7), 1225-1228. https://doi.org/10.1016/S1874-1029(11)60293-0.
  38. Zhang, C.D. and Xu, Y.L. (2016), "Comparative studies on damage identification with Tikhonov regularization and sparse regularization", Struct. Control Heal. Monit., 23(3), 560-579. https://doi.org/10.1002/stc.1785.
  39. Zhang, J., Wu, D.J., Li, Q. and Zhang, Y. (2019), "Experimental and numerical investigation of track-bridge interaction for a long-span bridge", Struct. Eng. Mech., 70(6), 723-735. https://doi.org/10.12989/sem.2019.70.6.723.
  40. Zhang, K. and Guo, X.H. (2016), "Adaptive Tikhonov regularization for simultaneous identification of structural parameters and input", 2016 International Conference on Material Science and Civil Engineering, Guilin, China, August. https://doi.org/10.12783/dtmse/msce2016/10511.