Experimental Mechanics

, Volume 49, Issue 5, pp 743–746 | Cite as

Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm

  • C. W. Rowley
  • E. J. OBrien
  • A. GonzalezEmail author
  • A. Žnidarič


Bridge weigh-in-motion systems are based on the measurement of strain on a bridge and the use of the measurements to estimate the static weights of passing traffic loads. Traditionally, commercial systems employ a static algorithm and use the bridge influence line to infer static axle weights. This paper describes the experimental testing of an algorithm based on moving force identification theory. In this approach the bridge is dynamically modeled using the finite element method and an eigenvalue reduction technique is employed to reduce the dimension of the system. The inverse problem of finding the applied forces from measured responses is then formulated as a least squares problem with Tikhonov regularization. The optimal regularization parameter is solved using the L-curve method. Finally, the static axle loads, impact factors and truck frequencies are obtained from a complete time history of the identified moving forces.


Bridge Weigh-in-motion Force identification Regularization Dynamic programming Traffic loads 



The authors would like to express their gratitude for the financial support received from the European 6th Framework Project ARCHES towards this investigation.


  1. 1.
    Moses F (1979) Weigh-in-motion system using instrumented bridges. J Transp Eng 105TE3:233–249MathSciNetGoogle Scholar
  2. 2.
    OBrien EJ, Žnidarič A, Dempsey A (1999) Comparison of two independently developed bridge weigh-in-motion systems. Heavy vehicle systems. Int J Veh Des 61/4:147–162Google Scholar
  3. 3.
    González A, Rowley CW, OBrien EJ (2008) A general solution to the identification of vehicle interaction forces. Int J Numer Methods Eng 753:335–354. doi: 10.1002/nme.2262 CrossRefGoogle Scholar
  4. 4.
    Rowley CW OBrien EJ, Gonzalez A (2006) Moving force identification algorithm for two-span continuous bridges using an eigenvalue reduction technique. In: Topping BHV, Montero G, Montenegro R (eds) Proceedings of the Eighth International Conference on Computational Structures Technology, Civil-Comp Press, Stirlingshire, UK, paper 142Google Scholar
  5. 5.
    Rowley CW (2007) Moving force identification of axle forces on bridges. Ph.D. thesis, Department of Civil Engineering, University College Dublin, IrelandGoogle Scholar
  6. 6.
    Law SS, Fang YL (2001) Moving force identification: optimal state estimation approach. J Sound Vib 2392:233–254. doi: 10.1006/jsvi.2000.3118 CrossRefGoogle Scholar
  7. 7.
    Trujillo DM (1975) Application of dynamic programming to the general inverse problem. Int J Numer Methods Eng 12:613–624. doi: 10.1002/nme.1620120406 CrossRefMathSciNetGoogle Scholar
  8. 8.
    Trujillo DM, Busby HR (1997) Practical inverse analysis engineering. CRC, New YorkzbMATHGoogle Scholar
  9. 9.
    Busby HR, Trujillo DM (1995) Optimal regularization of an inverse dynamics problem. Comput Struct 63:243–248. doi: 10.1016/S0045-7949(96)00340-9 CrossRefGoogle Scholar
  10. 10.
    Busby HR, Trujillo DM (1986) Solution of an inverse dynamics problem using an eigenvalue reduction technique. Comput Struct 25:109–117. doi: 10.1016/0045-7949(87)90222-7 CrossRefGoogle Scholar
  11. 11.
    Adams R, Doyle JF (2002) Multiple force identification for complex structures. Exp Mech 421:25–36. doi: 10.1007/BF02411048 CrossRefGoogle Scholar
  12. 12.
    Tikhonov AN, Arsenin VY (1997) Solutions of ill-posed problems. Wiley, New YorkGoogle Scholar
  13. 13.
    Zhu XQ, Law SS (2002) Moving loads identification through regularization. J Eng Mech 1289:989–1000. doi: 10.1061/(ASCE)0733-9399(2002)128:9(989) CrossRefGoogle Scholar
  14. 14.
    Law SS, Chan THT, Zhu XQ, Zeng QH (2001) Regularization in moving force identification. J Eng Mech 1272:136–148. doi: 10.1061/(ASCE)0733-9399(2001)127:2(136) CrossRefGoogle Scholar
  15. 15.
    Lawson CL, Hanson RJ (1974) Solving least squares problems. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  16. 16.
    Hansen PC (1992) Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev 344:561–580. doi: 10.1137/1034115 zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Hansen PC (1994) Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer Algorithms 6:1–35. doi: 10.1007/BF02149761 zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hansen PC (1998) Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. SIAM Monographs on Mathematical Modelling and Computation, PhiladelphiaGoogle Scholar
  19. 19.
    Žnidarič A, Lavrič I, Kalin J (2002) The next generation of bridge weigh-in-motion systems. In: Jacob B, OBrien EJ (eds) Proceedings of the Third International Conference on Weigh-in-Motion Systems (ICWIM3), Orlando, USA, 13–15 May, pp 231–239Google Scholar
  20. 20.
    Bogner FK, Fox RL, Schmit LA (1965) The generation of interelement-compatible stiffness and mass matrices by the use of interpolation formulae. In: Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics, Air Force Institute of Technology, Wright Patterson Airforce Base, Ohio, OctoberGoogle Scholar
  21. 21.
    Logan DL (2000) A first course in the finite element method, 3rd edn. Brooks/Cole Thomson Learning, WadsworthGoogle Scholar
  22. 22.
    Przemineiecki JS (1968) Theory of matrix structural analysis, 1st edn. McGraw-Hill, New YorkGoogle Scholar
  23. 23.
    Chan THT, Yung TH (2003) A theoretical study of force identification using an existing prestressed concrete bridge. Engineering Structures 23:1529–1537Google Scholar
  24. 24.
    OECD (1997) Dynamic interaction of heavy vehicles with roads and bridge. Final report of the Committee, DIVINE Project, Ottawa, Canada, JuneGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2008

Authors and Affiliations

  • C. W. Rowley
    • 1
  • E. J. OBrien
    • 2
  • A. Gonzalez
    • 2
    Email author
  • A. Žnidarič
    • 3
  1. 1.Bridges, Buro Happold Ltd.LondonUK
  2. 2.School of Architecture, Landscape and Civil EngineeringUniversity College DublinDublin 4Ireland
  3. 3.Slovenian National Building and Civil Engineering InstituteLjubljanaSlovenia

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