Skip to main content
SpringerLink
Log in

Input force estimation accounting for modeling errors and noise in responses

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Determination of forces applied on structures and machines is very important in engineering. A dynamic force estimation method based on regularized total least squares method in time domain is proposed in this paper. This method can deal with errors in both system models and measured vibration responses, the latter of which are contaminated by white noise. A numerical test is made to illustrate the effectiveness of this force estimation method, and the numerical results obtained by the proposed method are shown to be more accurate than those from the conventional regularized least squares method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Stevens, K.K.: Force identification problems–an overview, In: Proceedings of the 1987 SEM Spring Conference on Experimental Mechanics, Houston pp. 838–844 (1987)

  2. Dobson, B.J., Rider, E.: A review of the indirect calculations of excitation forces from measured structural response data. Proc. Inst. Mech. Eng. J. Mech. Eng. Sci. 204(C2), 69–75 (1990)

    Article  Google Scholar 

  3. Innoue, H., Harrigan, J.J., Reid, S.R.: Review of inverse analysis for indirect measurement of impact force. Appl. Mech. Rev. 54(6), 503–524 (2001)

    Article  Google Scholar 

  4. Nordstrom, L.J.L., Nordberg, T.P.: A critical comparison of time domain load identification methods. Proc. Sixth Int. Conf. Motion Vib. Control 2, 1151–1156 (2002)

    Google Scholar 

  5. Gunturkun, U., Reilly, J.P., Kirubarajanm, T., Debruin, H.: Recursive hidden input estimation in nonlinear dynamic systems with varying amounts of a priori knowledge. Signal Process. 99, 171–184 (2014)

    Article  Google Scholar 

  6. Sanchez, J., Benaroya, H.: Review of force reconstruction techniques. J. Sound Vib. 333(14), 2999–3018 (2014)

    Article  Google Scholar 

  7. Barlett Jr, F.D., Flannelly, W.G.: Model verification of force determination for measuring vibration loads. J. Am. Helicopter Soc. 19(4), 10–18 (1979)

    Article  Google Scholar 

  8. Hillary, B., Ewins, D.J.: The use of strain gauges in force determination and frequency response function measurements. In: Proceeding of the 2th IMACA, pp. 627–634 (1984)

  9. Starkey, J.M., Merrill, G.L.: On the ill-conditioned nature of indirect force measurement techniques. J. Modal Anal. 7, 103–108 (1989)

    Google Scholar 

  10. Martin, M.T., Doyle, J.F.: Impact force identification from wave propagation responses. Int. J. Impact Eng. 18, 65–77 (1996)

    Article  Google Scholar 

  11. Doyle, J.F.: A wavelet decomposition deconvolution method for impact force identification. Exp. Mech. 37(4), 403–408 (1997)

    Article  MathSciNet  Google Scholar 

  12. Wu, E., Yeh, J.-C., Yen, C.-S.: Identification of impact forces at multiple locations on laminated plates. AIAA J. 32, 2433–2439 (1994)

    Article  MATH  Google Scholar 

  13. Wu, E., Tsai, T.-D., Yen, C.-S.: Two methods for determining impact-force history on elastic plates. Exp. Mech. 35, 11–18 (1995)

    Article  Google Scholar 

  14. De Araujo, M., Antunes, J., Piteau, P.: Remote identification of impact forces on loosely supported tubes: part 1-basic theory and experiments. J. Sound Vib. 215(5), 1015–1041 (1998)

    Article  Google Scholar 

  15. Antunes, J., Paulino, M., Piteau, P.: Remote identification of impact forces on loosely supported tubes: part 2-complex vibro-impact motions. J. Sound Vib. 215(5), 1043–1064 (1998)

    Article  Google Scholar 

  16. Choi, K., Chang, F.K.: Identification of impact force and location using distributed sensors. AIAA J. 34(1), 136–142 (1996)

    Article  MATH  Google Scholar 

  17. Seydel, R., Chang, F.K.: Impact identification of stiffened composite panels: I. Syst. Dev. Smart Mater. Struct. 10, 354–369 (2001)

    Article  Google Scholar 

  18. Seydel, R., Chang, F.K.: Impact identification of stiffened composite panels: II. Implement. Stud. Smart Mater. Struct. 10, 370–379 (2001)

    Article  Google Scholar 

  19. Meo, M., Zumpano, G., Piggott, M., Marengo, G.: Impact identification on a sandwich plate from wave propagation responses. Compos. Struct. 71, 302–306 (2005)

    Article  Google Scholar 

  20. Gunawan, F.E., Homma, H., Kanto, Y.: Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction. J. Sound Vib. 297, 200–214 (2006)

    Article  Google Scholar 

  21. Hu, N., Fukunaga, H., Matsumoto, S., Yan, B., Peng, X.H.: An efficient approach for identifying impact force using embedded piezoelectric sensors. Int. J. Impact Eng. 34, 1258–1271 (2007)

    Article  Google Scholar 

  22. Atobe, S., Hu, N., Fukunaga, H.: Real-time impact force identification of CFRP structures using experimental transfer matrices. In: Proceedings of the 14th US-Japan Conference on Composite Materials, Dayton, p. 1058 (2010)

  23. Kammer, D.C.: Input force reconstruction using a time domain technique, AIAA Dynamics Specialists Conference, Salt Lake City, UT, pp. 21–30 (1996)

  24. Kammer, D.C., Steltzner, A.D.: Structural identification using inverse system dynamics. J. Guid. Control Dyn. 23, 819–825 (2000)

    Article  Google Scholar 

  25. Allen, M.S., Carne, T.G.: Delayed, multi-step inverse structural filter for robust force identification. Mech. Syst. Signal Process. 22, 1036–1054 (2008)

    Article  Google Scholar 

  26. Ma, C.K., Ho, C.C.: An inverse method for the estimation of input forces acting on non-linear structural systems. J. Sound Vib. 275, 953–971 (2004)

    Article  Google Scholar 

  27. Carne, T.G., Mayes, R.L., Bateman, V.I.: Force reconstruction using a sum of weighted accelerations technique. In: 10th International Modal Analysis Conference, San Diego (1992)

  28. Genaro, G., Rade, D.A.: Input force identification in the time domain. In: 16th International Modal Analysis Conference, Santa Barbara (1998)

  29. Jacquelin, E., Bennani, A., Hamelin, P.: Force reconstruction analysis and regularization of a deconvolution problem. J. Sound Vib. 265, 81–107 (2003)

    Article  Google Scholar 

  30. Zhu, X.Q., Law, S.S.: Practical aspects in moving load identification. J. Sound Vib. 258(1), 123–146 (2002)

    Article  Google Scholar 

  31. Mao, Y.M., Guo, X.L., Zhao, Y.: A state space force identification method based on Markov parameters precise computation and regularization technique. J. Sound Vib. 329, 3008–3019 (2010)

    Article  Google Scholar 

  32. Huang, C.H.: A non-linear inverse vibration problem of estimating the external forces for a system with displacement-dependent parameters. J. Sound Vib. 248(5), 798–807 (2001)

    Article  Google Scholar 

  33. Gunawan, F.E.: Levenberg-Marquardt iterative regularization for the pulse-type impact-force reconstruction. J. Sound Vib. 331, 5424–5434 (2012)

    Article  Google Scholar 

  34. Ewins, D.J.: Modal testing: theory, practice and application. Research Studies Press, London (2003)

    Google Scholar 

  35. Brownjohn, J.M.W., Pavic, A.: Experimental methods for estimating modal mass in footbridges using human-induced dynamic excitation. Eng. Struct. 29, 2833–2843 (2007)

    Article  Google Scholar 

  36. Cottin, N.: Dynamic model updating—a multiparameter eigenvalue problem. Mech. Syst. Signal Process. 15(4), 649–665 (2001)

    Article  Google Scholar 

  37. Devriendt, C., Guillaume, P.: Identification of modal parameters from transmissibility measurements. J. Sound Vib. 314, 343–356 (2008)

    Article  Google Scholar 

  38. Mottershead, J.E., Friswell, M.I.: Model updating in structural dynamics: a survey. J. Sound Vib. 167(2), 347–375 (1993)

    Article  MATH  Google Scholar 

  39. Katayama, T.: Subspace methods for system identification. Springer, New York (2005)

    Book  MATH  Google Scholar 

  40. Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C.: Past, present and future of nonlinear identification in structural dynamics. Mech. Syst. Signal Process. 20(3), 505–592 (2006)

    Article  Google Scholar 

  41. Marchesiello, S., Garibaldi, L.: A time domain approach for identifying vibrating structures by subspace methods. Mech. Syst. Signal Process. 22, 81–101 (2008)

    Article  Google Scholar 

  42. Liu, Y., Shepard Jr, W.S.: Dynamic force identification based on enhanced least squares and total least-squares in the frequency domain. J. Sound Vib. 282, 37–60 (2005)

    Article  Google Scholar 

  43. Zhang, E., Antoni, J., Feissel, P.: Bayesian force reconstruction with an uncertain model. J. Sound Vib. 331, 798–814 (2012)

    Article  Google Scholar 

  44. Trujillo, D.M.: The direct numerical integration of linear matrix differential equations using Pade approximations. Intern. J. Numer. Method Eng. 9(2), 259–270 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  45. Golub, G.H., Van Loan, C.F.: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883–893 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  46. Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  47. Hansen, P.C., O’Leary, D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14(6), 1487–1503 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  48. Golub, G.H., Hansen, P.C., Oleary, D.P.: Tikhonov regularization and total least squares. SIAM J. Matrix Anal. Appl. 21(1), 185–194 (1999). DIANNE P O’LEARY

    Article  MATH  MathSciNet  Google Scholar 

  49. Huffel, S.V., Lemmerling, P.: Total least squares and errors-in-variables modeling. Kluwer Academic Publishers, Berlin (2002)

    Book  MATH  Google Scholar 

  50. Kamm, J., Nagy, J.G.: A total least squares method for Toeplitz systems of equations. BIT 38, 560–582 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  51. Fierro, R.D., Golub, G.H., Hansen, P.C., Oleary, D.P.: Regularization by truncated total least squares. SIAM J. Sci. Comput. 18(4), 1223–1241 (1997)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The present investigation is supported by the Natural Science Foundation of China under grant 11102115.

Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Spacecraft Mechanism, Shanghai Institute of Aerospace System Engineering, Shanghai, 201109, China

    Y. M. Mao & J. F. Lin

  2. Shanghai Academic of Space Technology, Shanghai, 201109, China

    W. D. Zhang

  3. School of Engineering, University of Liverpool, Liverpool, L69 3GH, UK

    H. Ouyang

Authors
  1. Y. M. Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. D. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Ouyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. F. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. M. Mao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, Y.M., Zhang, W.D., Ouyang, H. et al. Input force estimation accounting for modeling errors and noise in responses. Arch Appl Mech 85, 909–919 (2015). https://doi.org/10.1007/s00419-015-1000-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-015-1000-0

Keywords

Search

Navigation