Comparison of statistical counting methods in SHM-based reliability assessment of bridges

  • Xiao Wang
  • Yi-Qing NiEmail author
  • Ke-Chang Lin
Original Paper


Structural condition assessment technology has gained widespread applications for providing desired solution to assess safety and serviceability of civil engineering structures. The structural reliability assessment which incorporates structural health monitoring (SHM) data is capable of providing authentic information about in-service performance of the instrumented structure and accommodating uncertainties in the measurement data. Because the peak values of the measurands which illustrate the critical condition/status of the structure are random in nature, it is important to adopt appropriate statistical counting methods to extract favorable peak values for reliability assessment. Several algorithms, such as the sampling method, the peak counting method, and the pointwise counting method, have been proposed for peak counting. In the present study, different statistical counting methods for the selection of peak data targeted for SHM-based reliability assessment of instrumented bridges are examined and compared, through the application of the above methods for the purpose of constructing peak-stress histograms and formulating probability density functions by use of long-term strain monitoring data from an instrumented bridge. Peak covering rate is defined to serve as a common basis for relating the amount of peak data and the control parameters for peak counting and helping determine the values of the control parameters in different statistical counting methods which ensure identical peak covering rate. The reliability indices obtained from the different statistical counting methods under the same amount of peak data are also compared.


Structural health monitoring (SHM) Structural reliability assessment Strain/stress time history Statistical counting methods Suspension bridge 



The work described in this paper was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 5224/13E), and partially by the National Science Foundation of China under Grant No. U1234201.


  1. 1.
    Estes AC (1997) A system reliability approach to the lifetime optimization of inspection and repair of highway bridges. Ph.D. Thesis, University of ColoradoGoogle Scholar
  2. 2.
    Frangopol DM, Kong JS, Gharaibeh ES (2001) Reliability-based life-cycle management of highway bridges. J Comput Civil Eng ASCE 15:27–34CrossRefGoogle Scholar
  3. 3.
    Ko JM, Ni YQ (2005) Technology developments in structural health monitoring of large-scale bridges. Eng Struct 27:1715–1725CrossRefGoogle Scholar
  4. 4.
    Lark RJ, Katja DF (2005) The use of reliability analysis to aid bridge management. Struct Eng 83:27–31Google Scholar
  5. 5.
    Catbas FN, Susoy M, Frangopol DM (2008) Structural health monitoring and reliability estimation: long span truss bridge application with environmental monitoring data. Eng Struct 30:2347–2359CrossRefGoogle Scholar
  6. 6.
    Frangopol DM, Strauss A, Kim S (2008) Bridge reliability assessment based on monitoring. J Bridge Eng ASCE 13:258–270CrossRefGoogle Scholar
  7. 7.
    Hosser D, Klinzmann C, Schnetgöke R (2008) A framework for reliability-based system assessment based on structural health monitoring. Struct Infrastruct Eng 4:271–285CrossRefGoogle Scholar
  8. 8.
    Liu M, Frangopol DM, Kim S (2009) Bridge safety evaluation based on monitored live load effects. J Bridge Eng ASCE 14:257–269CrossRefGoogle Scholar
  9. 9.
    Peil U (2005) Assessment of bridges via monitoring. Struct Infrastruct Eng 1:101–117CrossRefGoogle Scholar
  10. 10.
    Xia HW, Ni YQ, Wong KY, Ko JM (2012) Reliability-based condition assessment of in-service bridges using mixture distribution models. Comput Struct 106–107:204–213CrossRefGoogle Scholar
  11. 11.
    Frangopol DM, Strauss A, Kim S (2008) Use of monitoring extreme data for the performance prediction of structures: general approach. Eng Struct 30:3644–3653CrossRefGoogle Scholar
  12. 12.
    Messervey TB, Frangopol DM, Casciati S (2011) Application of the statistics of extremes to the reliability assessment and performance prediction of monitored highway bridges. Struct Infrastruct Eng 7:87–99CrossRefGoogle Scholar
  13. 13.
    Ni YQ, Lin KC (2013) Reliability-based condition assessment of bridge deck using long-term monitoring data. In: Chang F-K (ed) Structural health monitoring 2013: a roadmap to intelligent structures. DEStech Publications, Lancaster, pp 2736–2743Google Scholar
  14. 14.
    Frýba L (1996) Dynamics of railway bridges. Thomas Telford, New YorkCrossRefGoogle Scholar
  15. 15.
    O’Haver TC (2013) Signal processing tools: free downloadable Matlab scripts for scientists.
  16. 16.
    Ni YQ, Xia HW, Wong KY, Ko JM (2012) In-service condition assessment of bridge deck using long-term monitoring data of strain response. J Bridge Eng ASCE 17:876–885CrossRefGoogle Scholar
  17. 17.
    Bučar T, Nagode M, Fajdiga M (2004) Reliability approximation using finite Weibull mixture distributions. Rel Eng Sys Safety 84:241–251CrossRefGoogle Scholar
  18. 18.
    Ni YQ, Ye XW, Ko JM (2012) Modeling of stress spectrum using long-term monitoring data and finite mixture distributions. J Eng Mech ASCE 138:175–183CrossRefGoogle Scholar
  19. 19.
    Wong KY (2007) Design of a structural health monitoring system for long-span bridges. Struct Infrastruct Eng 3:169–185CrossRefGoogle Scholar
  20. 20.
    Ni YQ, Wong KY, Xia Y (2011) Health checks through landmark bridges to sky-high structures. Adv Struct Eng 14:103–119CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringThe Hong Kong Polytechnic UniversityKowloonHong Kong

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