Structural Engineering and Mechanics

  • 제88권4호
  • /
  • Pages.301-309
  • /
  • 2023
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new conjugate gradient method for dynamic load identification of airfoil structure with randomness

  • Lin J. Wang (Hubei Key Laboratory of Hydroelectric Machinery Design and Maintenance, College of Mechanical and Power Engineering, China Three Gorges University) ;
  • Jia H. Li (Hubei Key Laboratory of Hydroelectric Machinery Design and Maintenance, College of Mechanical and Power Engineering, China Three Gorges University) ;
  • You X. Xie (College of Science Technology, China Three Gorges University)
  • 투고 : 2023.05.09
  • 심사 : 2023.10.27
  • 발행 : 2023.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a new modified conjugate gradient (MCG) method is presented which is based on a new gradient regularizer, and this method is used to identify the dynamic load on airfoil structure without and with considering random structure parameters. First of all, the newly proposed algorithm is proved to be efficient and convergent through the rigorous mathematics theory and the numerical results of determinate dynamic load identification. Secondly, using the perturbation method, we transform uncertain inverse problem about force reconstruction into determinate load identification problem. Lastly, the statistical characteristics of identified load are evaluated by statistical methods. Especially, this newly proposed approach has successfully solved determinate and uncertain inverse problems about dynamic load identification. Numerical simulations validate that the newly developed method in this paper is feasible and stable in solving load identification problems without and with considering random structure parameters. Additionally, it also shows that most of the observation error of the proposed algorithm in solving dynamic load identification of deterministic and random structure is respectively within 11.13%, 20%.

키워드

과제정보

This work is supported by the National Natural Science Foundation of China (11202116).

참고문헌

  1. Callahan, J.O. and Piergentili, F. (1994), "Force estimation using operational data", Proceeding of Eighth International Modal Analysis Conference, 1586-1592.
  2. Fuhry, M. and Reichel, L. (2012), "A new Tikhonov regularization method", Numer. Algorith., 59, 433-445. https://doi.org/10.1007/s11075-011-9498-x.
  3. Gunawan, F.E., Homma, H. and Kanto, Y. (2006), "Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction", J. Sound Vib., 297(1-2), 200-214. https://doi.org/10.1016/j.jsv.2006.03.036.
  4. Jacquelin, E., Bennani, A. and Hamelin, P. (2003), "Force reconstruction: Analysis and regularization of a deconvolution problem", J. Sound Vib., 265(1), 81-107. https://doi.org/10.1016/S0022-460X(02)01441-4.
  5. Jia, Y., Yang, Z.C., Guo, N. and Wang, L. (2015), "Random dynamic load identification based on error analysis and weighted total least squares method", J. Sound Vib., 358, 111-123. https://doi.org/10.1016/j.jsv.2015.07.035.
  6. Jiang, J.H., Ding, M. and Li, J. (2021), "A novel time-domain dynamic load identification numerical algorithm for continuous systems", Mech. Syst. Signal Pr., 160, 107881. https://doi.org/10.1016/j.ymssp.2021.107881.
  7. Jiang, J.H., Tang, H.Z., Mohamed, M.S., Luo, S.Y. and Chen, J.D. (2020), "Augmented tikhonov regularization method for dynamic load identification", Appl. Sci-Basel., 10, 6348. https://doi.org/10.3390/app10186348.
  8. Law, S.S., Bu, J.Q., Zhu, X.Q. and Chan, S.L. (2004), "Vehicle axle loads identification using finite element method", Eng. Struct., 26(8), 1143-1153. https://doi.org/10.1016/j.engstruct.2004.03.017.
  9. Law, S.S., Bu, J.Q., Zhu, X.Q. and Chan, S.L. (2004), "Vehicle axle loads identification using finite element method", Eng. Struct., 26, 1143-1153. https://doi.org/10.1016/j.engstruct.2004.03.017.
  10. Li, K., Liu, J., Han, X., Jiang, C., Zhang, D.Q. (2017), "Distributed dynamic load identification based on shape function method and polynomial selection technique", Invers. Prob. Sci. Eng., 25(9), 1323-1342. https://doi.org/10.1080/17415977.2016.1255740.
  11. Li, Y.X., Wang, X.Y., Xia, Y. and Sun, L.M. (2023), "Sparse Bayesian technique for load identification and full response reconstruction", J. Sound Vib., 553, 117669. https://doi.org/10.1016/j.jsv.2023.117669.
  12. Lindfield, G. and Penny, J. (1995), Numerical Method using MATLAB, Ellis Horwood Limit, London.
  13. Ling, Y. and Tommy, C.T.H. (2002), "Moving force identification from bending moment responses of bridge", Struct. Eng. Mech., 14(2), 151-170. https://doi.org/10.12989/sem.2002.14.2.151.
  14. Ling, Y., Tommy, H.T.C. and Zhu, J.H. (2008), "A MOM-based algorithm for moving force identification: Part I. Theory and numerical simulation", Struct. Eng. Mech., 29(2), 135-154. https://doi.org/10.12989/sem.2008.29.2.135.
  15. Liu, J., Han, X., Jiang, C. and Ning, H.M. (2011), "Dynamic load identification for uncertain structures based on interval analysis and regulation method", Int. J. Comput. Meth., 8, 667-683. https://doi.org/10.1142/S0219876211002757.
  16. Liu, J., Meng, X.H., Jiang, C., Han, X. and Zhang, D.Q. (2016), "Time-domain Galerkin method for dynamic load identification", Int. J. Numer. Meth. Eng., 105, 620-640. https://doi.org/10.1002/nme.4991
  17. Liu, J., Meng, X.H., Zhang, D.Q., Jiang, C. and Han, X. (2017), "An efficient method to reduce ill-posedness for structural dynamic load identification", Mech. Syst. Signal. Pr., 95, 273-285. https://doi.org/10.1016/j.ymssp.2017.03.039.
  18. Liu, J., Sun, X.S., Han, X., Jiang, C. and Yu, D.J. (2014), "A novel computational inverse technique for load identification using the shape function method of moving least square fitting", Comput. Struct., 144, 127-137. https://doi.org/10.1016/j.compstruc.2014.08.002.
  19. Liu, J., Sun, X.S., Han, X., Jiang, C. and Yu, D.J. (2015), "Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method", Mech. Syst. Signal Pr., 56-57, 35-54. https://doi.org/10.1016/j.ymssp.2014.10.008.
  20. Liu, Y. and Wang, L. (2023), "A two-step weighting regularization method for stochastic excitation identification under multi-source uncertainties based on response superposition-decomposition principle", Mech. Syst. Signal Pr., 182, 109565. https://doi.org/10.1016/j.ymssp.2022.109565.
  21. Mao, Y.M., Guo, X.L. and Zhao, Y. (2010), "A state space force identification method based on Markov parameters precise computation and regularization technique", J. Sound Vib., 329(15), 3008-3019. https://doi.org/10.1016/j.jsv.2010.02.012.
  22. Ory, H., Glaser, H. and Holzdeppe, D. (1986), "Quality of modal analysis and reconstruction of forcing functions based on measured output data", Proceedings of the 4th International Modal Analysis Conference, Los Angeles, 850-857.
  23. Qin, Y.T., Zhang, F. and Chen, G.P. (2007), "A frequency method for two dimensional distributed load identification", J. Vib. Eng., 20, 512-518.
  24. Sas, P., Snoeys, R. and Desanghere, G. (1982), "Prediction of the accoustic intensity based on structural deformations", CIRP Ann-Manuf. Techn., 31(1), 263-268. https://doi.org/10.1016/S0007-8506(07)63310-1.
  25. Sun, X.S., Liu, J., Han, X., Jiang, C. and Chen, R. (2014), "A new improved regularization method for dynamic load identification", Invers. Prob. Sci. Eng., 22, 1062-1076. https://doi.org/10.1080/17415977.2013.854353.
  26. Tang, X.J. (1987), "Dynamic load identification by time domain method", J. Dalian Inst. Technol., 26(4), 21-27. (in Chinese)
  27. Turco, E. (1998), "Load distribution modelling for pin-jointed trusses by an inverse approach", Comput. Meth. Appl. Mech. Eng., 165, 291-333. https://doi.org/10.1016/S0045-7825(98)80013-3.
  28. Turco, E. (2005), "A strategy to identify exciting forces acting on structures", Int. J. Numer. Meth. Eng., 64, 1483-1508. https://doi.org/10.1002/nme.1418.
  29. Turco, E. (2005), "Is the statistical approach suitable for identifying actions on structures", Comput. Struct., 83, 2112-2120. https://doi.org/10.1016/j.compstruc.2005.03.006.
  30. Wang, L.J., Deng, Q.C. and Xie, Y.X. (2017), "A new conjugate gradient algorithm for solving dynamic load identification", Struct. Eng. Mech., 64(2), 271-278. https://doi.org/10.12989/sem.2017.64.2.271.
  31. Wang, L.J., Han, X. and Xie, Y.X. (2012), "A new conjugate gradient method for solving multi-source dynamic load identification problem", Int. J. Mech. Mater. Des., 9(3), 191-197. https://doi.org/10.1007/s10999-012-9208-4.
  32. Wang, L.J., Han, X., Liu, J., He, X.Q. and Huang, F. (2011), "A new regularization method and application to dynamic load identification problems", Invers. Prob. Sci. Eng., 19(6), 765-776. https://doi.org/10.1080/17415977.2010.531468.
  33. Wang, L.J., Liu, J.W., Xie, Y.X. and Gu, Y.T. (2018), "A new regularization method for the dynamic load identification of stochastic structures", Comput. Math. Appl., 76, 741-759. https://doi.org/10.1016/j.camwa.2018.05.013.
  34. Wang, L.J., Peng, Y.L., Xie, Y.X., Chen, B.J. and Du, Y.X. (2021), "A new iteration regularization method for dynamic load identification of stochastic structures", Mech. Syst. Signal Pr., 156, 107586. https://doi.org/10.1016/j.ymssp.2020.107586.
  35. Wang, L.J., Xu, L., Xie, Y.X., Du, Y.X. and Han, X. (2019), "A new hybrid conjugate gradient method for dynamic force reconstruction", Adv. Mech. Eng., 11(1), 1-21. https://doi.org/10.1177/1687814018822360.
  36. Xiang, Z., Chan, T., Thambiratnam, D. and Nguyen, A. (2015), "Prestress force and moving load identification on prestressed concrete beam based on virtual distortion method", Proceedings of the 2015 World Congress on Advances in Structural Engineering and Mechanics (ASEM15), 1-13.
  37. Yang, H.G., Jiang, J.H., Chen, G.P. and Zhao, J.M. (2023), "Dynamic load identification based on deep convolution neural network", Mech. Syst. Signal Pr., 185, 109757. https://doi.org/10.1016/j.ymssp.2022.109757.
  38. Zhang, B., Zhang, J.F. and Wu, Z.J. (2008), "A load reconstruction model for advanced grid-stiffened composite plates", Compos. Struct., 82, 600-608. https://doi.org/10.1016/j.compstruct.2007.02.010.
  39. Zhang, F. and Zhu, D.M. (1996), "A new theoretical study of dynamic laod identification based on generalized polynomial expansion", J. Nanjing Univ. Aeronaut. Astronaut., 28(6), 755-760. (in Chinese)
  40. Zhang, F., Qin, Y.T. and Deng, J.H. (2006), "Research of identification technology of dynamic load distributed on the structure", J. Vib. Eng., 19, 81-85.
  41. Zhao, Z.Y. and Meng, Z.H. (2011), "A modified Tikhonov regularization method for a backward heat equation", Invers. Prob. Sci. Eng., 19, 1175-1182. https://doi.org/10.1080/17415977.2011.605885.
  42. Zhu, T., Xiao, S.N. and Yang, G.W. (2014), "Force identification in time domain based on dynamic programming", Appl. Math. Comput., 235, 226-234. https://doi.org/10.1016/j.amc.2014.03.008.
  43. Zhu, X.Q. and Law, S.S. (2001), "Orthogonal function in moving force identification on a continuous beam", J. Sound Vib., 245, 329-345. https://doi.org/10.1006/jsvi.2001.3577