Earthquake Engineering and Engineering Vibration

, Volume 17, Issue 4, pp 805–820 | Cite as

Restoring force correction based on online discrete tangent stiffness estimation method for real-time hybrid simulation

  • Liang Huang
  • Tong GuoEmail author
  • Cheng Chen
  • Menghui Chen


In real-time hybrid simulation (RTHS), it is difficult if not impossible to completely erase the error in restoring force due to actuator response delay using existing displacement-based compensation methods. This paper proposes a new force correction method based on online discrete tangent stiffness estimation (online DTSE) to provide accurate online estimation of the instantaneous stiffness of the physical substructure. Following the discrete curve parameter recognition theory, the online DTSE method estimates the instantaneous stiffness mainly through adaptively building a fuzzy segment with the latest measurements, constructing several strict bounding lines of the segment and calculating the slope of the strict bounding lines, which significantly improves the calculation efficiency and accuracy for the instantaneous stiffness estimation. The results of both computational simulation and real-time hybrid simulation show that: (1) the online DTSE method has high calculation efficiency, of which the relatively short computation time will not interrupt RTHS; and (2) the online DTSE method provides better estimation for the instantaneous stiffness, compared with other existing estimation methods. Due to the quick and accurate estimation of instantaneous stiffness, the online DTSE method therefore provides a promising technique to correct restoring forces in RTHS.


online discrete tangent stiffness estimation restoring force correction fuzzy segment parameter updating real-time hybrid simulation 


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Liang Huang
    • 1
  • Tong Guo
    • 2
    Email author
  • Cheng Chen
    • 3
  • Menghui Chen
    • 1
  1. 1.School of Civil EngineeringSoutheast UniversityNanjingChina
  2. 2.Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of EducationSoutheast UniversityNanjingP.R. China
  3. 3.School of EngineeringSan Francisco State UniversitySan FranciscoUSA

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