Bulletin of Earthquake Engineering

, Volume 17, Issue 2, pp 681–706 | Cite as

A posteriori optimal intensity measures for probabilistic seismic demand modeling

  • Ao Du
  • Jamie E. PadgettEmail author
  • Abdollah Shafieezadeh
Original Research


A probabilistic seismic demand modeling approach with the optimal intensity measure (IM) parameters determined a posteriori (POS-PSDM) is employed to examine and compare the full potential of the explanatory power of different IM formulations. A total of six IM formulations adopting the optimal IM parameters determined a posteriori (i.e. POS-IMs) are studied, including two spectral IMs with the optimal period T*, two fractional order IMs with the optimal fractional order α*, as well as two spectral IMs with the optimal period T* and the optimal damping ratio ζ*. A comprehensive IM comparative study is conducted based on hysteretic single-degree-of-freedom systems, considering a wide range of structural parameters. The POS-IMs manifest substantially improved performance (i.e. efficiency and sufficiency) compared with their conventional counterparts, revealing the value of adopting this POS-PSDM approach to ensure the PSDM predictive performance. In particular, the spectral acceleration at the optimal period and damping ratio, Sa(T*,ζ*), which is introduced as an IM candidate for the first time, not only consistently demonstrates superior explanatory power but also exhibits fairly good hazard computability. The POS-PSDM approach in conjunction with Sa(T*,ζ*) exhibits good potential in further improving the accuracy and reliability of probabilistic seismic risk assessment with negligible increase in computation cost.


Probabilistic seismic demand modeling A posteriori optimal intensity measure parameter determination Higher-damped spectral acceleration Fractional order calculus Intensity measure comparison 



The insightful and helpful reviews of this manuscript from two anonymous reviewers are gratefully appreciated. The authors would like to acknowledge the support for this research by the National Science Foundation (NSF) through Grants CMMI-1462177 and CMMI-1462183. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would also like to acknowledge the computational facilities provided by the Data Analysis and Visualization Cyberinfrastructure under NSF Grant OCI-0959097, the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award under NSF Grant CNS-1338099 and Rice University.

Supplementary material

10518_2018_484_MOESM1_ESM.docx (24 kb)
Supplementary material 1 (DOCX 23 kb)


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Ao Du
    • 1
  • Jamie E. Padgett
    • 1
    Email author
  • Abdollah Shafieezadeh
    • 2
  1. 1.Department of Civil and Environmental EngineeringRice UniversityHoustonUSA
  2. 2.Department of Civil, Environmental and Geodetic EngineeringThe Ohio State UniversityColumbusUSA

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