Structural Engineering and Mechanics

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Double 𝑙1 regularization for moving force identification using response spectrum-based weighted dictionary

  • Yuandong Lei (MOE Key laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University) ;
  • Bohao Xu (MOE Key laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University) ;
  • Ling Yu (MOE Key laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University)
  • Received : 2024.03.13
  • Accepted : 2024.07.06
  • Published : 2024.07.25
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Abstract

Sparse regularization methods have proven effective in addressing the ill-posed equations encountered in moving force identification (MFI). However, the complexity of vehicle loads is often ignored in existing studies aiming at enhancing MFI accuracy. To tackle this issue, a double 𝑙1 regularization method is proposed for MFI based on a response spectrum-based weighted dictionary in this study. Firstly, the relationship between vehicle-induced responses and moving vehicle loads (MVL) is established. The structural responses are then expanded in the frequency domain to obtain the prior knowledge related to MVL and to further construct a response spectrum-based weighted dictionary for MFI with a higher accuracy. Secondly, with the utilization of this weighted dictionary, a double 𝑙1 regularization framework is presented for identifying the static and dynamic components of MVL by the alternating direction method of multipliers (ADMM) method successively. To assess the performance of the proposed method, two different types of MVL, such as composed of trigonometric functions and driven from a 1/4 bridge-vehicle model, are adopted to conduct numerical simulations. Furthermore, a series of MFI experimental verifications are carried out in laboratory. The results shows that the proposed method's higher accuracy and strong robustness to noises compared with other traditional regularization methods.

Keywords

Acknowledgement

This work was jointly sponsored by the National Natural Science Foundation of China under grant numbers 52178290 and 51678278.

References

  1. Bao, Y.Q., Li, H., Chen, Z.C., Zhang, F.J. and Guo, A.X. (2016), "Sparse l1 optimization-based identification approach for the distribution of moving heavy vehicle loads on cable-stayed bridges", Struct. Control Hlth. Monit., 23(1), 144-155. https://doi.org/10.1002/stc.1763.
  2. Chen, Z. and Yu, L. (2014), "Identification of dynamic axle loads on a bridge based on truncated generalized singular value decomposition", J. Vib. Shock., 33(10), 97-100.
  3. Chen, Z.W., Zhao, L., Zhang, J., Cai, Q.L., Li, J. and Zhu, S.Y. (2021), "Damage quantification of beam structures using deflection influence line changes and sparse regularization", Adv. Struct. Eng., 24(9), 1997-2010. https://doi.org/10.1177/1369433221992482.
  4. Chung, M. and Renaut, R.A. (2023), "A variable projection method for large-scale inverse problems with ℓ1 regularization", Appl. Numer. Math., 192, 297-318. https://doi.org/10.1016/j.apnum.2023.06.015.
  5. Cooley, J.W. and Tukey, J.W. (1965), "An algorithm for the machine calculation of complex fourier series", Math. Comput., 19(90), 297-301.
  6. Deng, L. and Cai, C.S. (2009), "Identification of parameters of vehicles moving on bridges", Eng. Struct., 31(10), 2474-2485. https://doi.org/10.1016/j.engstruct.2009.06.005.
  7. He, W.Y., Wang, Y. and Ren, W.X. (2020), "Dynamic force identification based on composite trigonometric wavelet shape function", Mech. Syst. Signal Pr., 141, 106493. https://doi.org/10.1016/j.ymssp.2019.106493.
  8. Hou, R.G., Xia, Y., Bao, Y.Q. and Zhou, X.Q. (2018), "Selection of regularization parameter for l1-regularized damage detection", J. Sound Vib., 423, 141-160. https://doi.org/10.1016/j.jsv.2018.02.064.
  9. Huang, P.M., Wang, J.F., Han, W.S. and Yuan, Y.G. (2022), "Study on impact factors of small- and medium-span bridges under the special-purpose vehicle load", Struct., 43, 606-620. https://doi.org/10.1016/j.istruc.2022.06.077.
  10. Jeong, B., Kim, T. and Lee, U. (2018), "Vibration analysis of a multi-span beam subjected to a moving point force using spectral element method", Struct. Eng. Mech., 65(3), 263-274. https://doi.org/10.12989/sem.2018.65.3.263.
  11. Law, S.S., Chan, T.H.T. and Zeng, Q.H. (1997), "Moving force identification: a time domain method", J. Sound Vib., 201(1), 1-22. https://doi.org/10.1006/jsvi.1996.0774.
  12. Law, S.S., Chan, T.H.T., Zhu, Q.X. and Zeng, Q.H. (2001), "Regularization in moving force identification", J. Eng Mech., 127(2), 136-148. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:2(136).
  13. Li, J.H., Zhang, H.T. and Chen, S.S. (2020), "Investigation of axle-span ratio and moving load speed affecting bridge extreme response using a moving load amplitude spectrum method", Struct., 28, 2633-2645. https://doi.org/10.1016/j.istruc.2020.10.034.
  14. Li, J.T., Zhu, X.Q. and Guo, J. (2022), "Bridge modal identification based on successive variational mode decomposition using a moving test vehicle", Adv. Struct. Eng., 25(11), 2284-2300. https://doi.org/10.1177/13694332221092678.
  15. Liang, Y., Hou, Z.L. and Yu, L. (2023), "An improved block orthogonal matching pursuit for moving force identification using block-sparse compressed sensing", Measure., 222, 113632. https://doi.org/10.1016/j.measurement.2023.113632.
  16. Liu, H.L., Luo, Z.W. and Yu, L. (2021), "A semi-convex function for both constant and time-varying moving force identification", Mech. Syst. Signal Pr., 146, 107062. https://doi.org/10.1016/j.ymssp.2020.107062.
  17. Liu, H.L., Yu, L., Luo, Z.W. and Pan, C.D. (2020), "Compressed sensing for moving force identification using redundant dictionaries", Mech. Syst. Signal Pr., 138, 106535. https://doi.org/10.1016/j.ymssp.2019.106535.
  18. Liu, J. and Li, K. (2021), "Sparse identification of time-space coupled distributed dynamic load", Mech. Syst. Signal Pr., 148, 107177. https://doi.org/10.1016/j.ymssp.2020.107177.
  19. Liu, Y.K., Wang, W., Deng, L., Dai, J.J. and He, W. (2022), "Identification of vehicle axle loads based on visual measurement", Meas. Sci. Technol., 33(10), 105902. https://doi.org/10.1088/1361-6501/ac7d99.
  20. Lydon, M., Taylor, S.E., Robinson, D., Mufti, A. and Brien, E.J.O. (2016), "Recent developments in bridge weigh in motion (BWIM)", J. Civil Struct. Hlth. Monit., 6(1), 69-81. https://doi.org/10.1007/s13349-015-0119-6.
  21. Pan, C.D., Yu, L., Liu, H.L., Chen, Z.P. and Luo, W.F. (2018), "Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization", Mech. Syst. Signal Pr., 98, 32-49. https://doi.org/10.1016/j.ymssp.2017.04.032.
  22. Qiao, B.J., Ao, C.Y., Mao, Z. and Chen, X.F. (2020), "Nonconvex sparse regularization for impact force identification", J. Sound Vib., 477, 115311. https://doi.org/10.1016/j.jsv.2020.115311.
  23. Qiao, B.J., Zhang, X.W., Wang, C.X., Zhang, H. and Chen, X.F. (2016), "Sparse regularization for force identification using dictionaries", J. Sound Vib., 368, 71-86. https://doi.org/10.1016/j.jsv.2016.01.030.
  24. Salawu, O.S. and Williams, C. (1995), "Review of full-scale dynamic testing of bridge structures", Eng. Struct., 17(2), 113-121. https://doi.org/10.1016/0141-0296(95)92642-L.
  25. Sun, Z., Siringoringo, D.M. and Fujino, Y. (2021), "Load-carrying capacity evaluation of girder bridge using moving vehicle", Eng. Struct., 229, 111645. https://doi.org/10.1016/j.engstruct.2020.111645.
  26. Talaei, S., Zhu, X.Q., Li, J.C., Yu, Y. and Chan, T.H.T. (2023), "Transfer learning based bridge damage detection: Leveraging time-frequency features", Struct., 57, 105052. https://doi.org/10.1016/j.istruc.2023.105052.
  27. Wahlberg, B., Boyd, S., Annergren, M. and Wang, Y. (2012), "An admm algorithm for a class of total variation regularized estimation problems", IFAC Proc., 45(16), 83-88. https://doi.org/10.3182/20120711-3-BE-2027.00310.
  28. Xu, B.H. and Yu, L. (2023), "A novel regularized adaptive matching pursuit for moving force identification using multiple criteria and prior knowledge", Int. J. Struct. Stab. Dyn., 23(10), 2350117. https://doi.org/10.1142/s0219455423501171.
  29. Xu, B.H., Chen, Y.H. and Yu, L. (2023), "Identification of moving vehicle loads using instantaneous vision-based vehicle spatiotemporal information and improved time domain method", Int. J. Struct. Stab. Dyn., 24(14), 2450163. https://doi.org/10.1142/S0219455424501633.
  30. Yang, Y.B., Chen, J. and Xu, H. (2024), "Normalized formula for removing damping effect in recovering bridge mode shapes using a moving and a stationary vehicle", J. Sound Vib., 573, 118219. https://doi.org/10.1016/j.jsv.2023.118219.
  31. Yang, Y.B., Zhang, B., Wang, T.Y., Xu, H. and Wu, Y.T. (2019), "Two-axle test vehicle for bridges: Theory and applications", Int. J. Mech. Sci., 152, 51-62. https://doi.org/10.1016/j.ijmecsci.2018.12.043.
  32. Zhang, L.Q., Liang, Y. and Yu, L. (2022), "Moving force identification based on group lasso and compressed sensing", Int. J. Struct. Stab. Dyn., 22(15), 2250170. https://doi.org/10.1142/s021945542250170x.
  33. Zhang, Y.F. and Zhu, J.S. (2021), "Damage identification for bridge structures based on correlation of the bridge dynamic responses under vehicle load", Struct., 33, 68-76. https://doi.org/10.1016/j.istruc.2021.04.022.
  34. Zhang, Z.H., He, W.Y. and Ren, W.X. (2022), "Moving force identification based on learning dictionary with double sparsity", Mech. Syst. Signal Pr., 170, 108811. https://doi.org/10.1016/j.ymssp.2022.108811.
  35. Zhong, J.W., Liu, H.L. and Yu, L. (2019), "Sparse regularization for traffic load monitoring using bridge response measurements", Measure., 131, 173-182. https://doi.org/10.1016/j.measurement.2018.07.044.
  36. Zhou, X.H. and Zhang, X.G. (2019), "Thoughts on the development of bridge technology in China", Eng., 5(6), 1120-1130. https://doi.org/10.1016/j.eng.2019.10.001.
  37. Zhou, X.Y., He, W., Zeng, Y.X. and Zhang, Y.H. (2022), "A semi-analytical method for moving force identification of bridge structures based on the discrete cosine transform and FEM", Mech. Syst. Signal Pr., 180, 109444. https://doi.org/10.1016/j.ymssp.2022.109444.
  38. Zhu, H., Mao, L., Weng, S. and Xia, Y. (2015), "Structural damage and force identification under moving load", Struct. Eng. Mech., 53(2), 261-276. https://doi.org/10.12989/sem.2015.53.2.261.
  39. Zhu, X.Q., Law, S.S. and Bu, J.Q. (2006), "A state space formulation for moving loads identification", J. Vib. Acoust., 128(4), 509-520. https://doi.org/10.1115/1.2202149.