Application of a Bayesian hierarchical model to system identification of structural parameters

  • Shinyoung Kwag
  • Bu Seog JuEmail author
Original Article


System identification (SI) is a key step in the process of evaluating the status or condition of physical structures and of devising a scheme to sustain their structural integrity. SI is typically carried out by updating the current structural parameters used in a computational model based on the measured responses of the structure. In the deterministic approach, SI has been conducted by minimizing the error between calculated responses (using the computational model) and measured responses. However, this brought about unexpected numerical issues such as the ill-posedness of the inverse problem, which likely results in non-uniqueness of the solutions or non-stability of the optimization operation. To address this issue, Bayesian updating enhanced with an advanced modeling technique such as a Bayesian network (BN) was introduced. However, it remained challenging to construct the quantitative relations between structural parameters and responses (which are placed in conditional probability tables: CPTs) in a BN setting. Therefore, this paper presented a novel approach for conducting the SI of structural parameters using a Bayesian hierarchical model (BHM) technique. Specifically, the BHM was integrated into the Bayesian updating framework instead of utilizing a BN. The primary advantage of the proposed approach is that it enables use of the existing relations between structural parameters and responses. This can save the computational effort needed to construct CPTs to relate the parameter and response nodes. The proposed approach was applied to two experimental structures and a realistic soil-slope structure. The results showed that the proposed SI approach provided good agreement with actual measurements and also gave relatively robust estimation results compared to the traditional approach of maximum likelihood estimation. Hence, the proposed approach is expected to be utilized to address SI problems for complex structural systems and its computational model when integrated with a statistical regression approach or with various machine learning algorithms.


Bayesian updating Bayesian hierarchical model System identification Measurement MCMC sampling 



This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science, and ICT) (NRF-2017M2A8A4015290 and NRF-2017R1C1B1002855). These supports are gratefully acknowledged.


  1. 1.
    Farrar CR, Worden K (2012) Structural health monitoring: a machine learning perspective. Wiley, New YorkCrossRefGoogle Scholar
  2. 2.
    Annamdas VGM, Bhalla S, Soh CK (2017) Applications of structural health monitoring technology in Asia. Struct Health Monit 16(3):324–346CrossRefGoogle Scholar
  3. 3.
    Nelles O (2013) Nonlinear system identification: from classical approaches to neural networks and fuzzy models. Springer, BerlinzbMATHGoogle Scholar
  4. 4.
    Ladeveze P, Rougeot P (1997) New advances on a posteriori error on constitutive relation in FE analysis. Comput Methods Appl Mech Eng 150(1–4):239–249CrossRefzbMATHGoogle Scholar
  5. 5.
    Louf F, Charbonnel PE, Ladeveze P, Gratien C (2008) An updating method for structural dynamics models with unknown excitations. J Phys Conf Ser 135(1):12065 (IOP Publishing) CrossRefGoogle Scholar
  6. 6.
    Weaver J (2015) The self-optimizing inverse methodology for material parameter identification and distributed damage detection. Ph.D. dissertation, The University of Akron, USGoogle Scholar
  7. 7.
    Thoft-Christensen P, Murotsu Y (2012) Application of structural systems reliability theory. Springer, BerlinzbMATHGoogle Scholar
  8. 8.
    Benjamin JR, Cornell CA (1970) Probability. Statistics, and decision for civil engineers. McGraw-Hill, New YorkGoogle Scholar
  9. 9.
    Ang AHS, Tang WH (1984) Probability concepts in engineering planning and design. Wiley, New YorkGoogle Scholar
  10. 10.
    Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461CrossRefGoogle Scholar
  11. 11.
    Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277CrossRefGoogle Scholar
  12. 12.
    Straub D, Papaioannou I (2014) Bayesian updating with structural reliability methods. J Eng Mech 141(3):04014134CrossRefGoogle Scholar
  13. 13.
    Beven K (2010) Environmental modelling: an uncertain future?. CRC Press, Boca RatonGoogle Scholar
  14. 14.
    Weber P, Medina-Oliva G, Simon C, Iung B (2012) Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas. Eng Appl Artif Intell 25(4):671–682CrossRefGoogle Scholar
  15. 15.
    Bensi M, Kiureghian AD, Straub D (2014) Framework for post-earthquake risk assessment and decision making for infrastructure systems. ASCE-ASME J Risk Uncertain Eng Syst Part A: Civil Eng 1(1):04014003CrossRefGoogle Scholar
  16. 16.
    Kwag S, Gupta A (2016) Bayesian network technique in probabilistic risk assessment for multiple hazards. In: Proceedings of 24th International Conference on Nuclear Engineering (ICONE 24), 26–30 June 2016, Charlotte, NC, USGoogle Scholar
  17. 17.
    Kwag S, Gupta A (2017) Probabilistic risk assessment framework for structural systems under multiple hazards using Bayesian statistics. Nucl Eng Des 315:20–34CrossRefGoogle Scholar
  18. 18.
    Kwag S, Oh J, Lee JM, Ryu JS (2017) Bayesian-based seismic margin assessment approach: application to research reactor system. Earthq Struct. 12(6):653–663Google Scholar
  19. 19.
    Kwag S, Gupta A, Dinh N (2018) Probabilistic risk assessment based model validation method using Bayesian network. Reliab Eng Syst Saf 169:380–393CrossRefGoogle Scholar
  20. 20.
    Kwag S, Oh J, Lee JM (2018) Application of Bayesian statistics to seismic probabilistic safety assessment for research reactor. Nucl Eng Des 328:166–181CrossRefGoogle Scholar
  21. 21.
    Kwag S, Oh J (2019) Development of network-based probabilistic safety assessment: a tool for risk analyst for nuclear facilities. Prog Nucl Energy 110:178–190CrossRefGoogle Scholar
  22. 22.
    Richard B, Adelaide L, Cremona C, Orcesi A (2012) A methodology for robust updating of nonlinear structural models. Eng Struct 41:356–372CrossRefGoogle Scholar
  23. 23.
    Ma Y, Wang L, Zhang J, Xiang Y, Liu Y (2014) Bridge remaining strength prediction integrated with Bayesian network and In situ load testing. J Bridg Eng 19(10):04014037CrossRefGoogle Scholar
  24. 24.
    Lee SH, Song J (2016) Bayesian-network-based system identification of spatial distribution of structural parameters. Eng Struct 127:260–277CrossRefGoogle Scholar
  25. 25.
    Gelman A, Carlin JB, Stern HS, Rubin DB (2014) Bayesian data analysis (vol 2). Chapman and Hall/CRC, Boca RatonzbMATHGoogle Scholar
  26. 26.
    Bolstad WM, Curran JM (2016) Introduction to Bayesian statistics. Wiley, New YorkGoogle Scholar
  27. 27.
    Kruschke J (2014) Doing Bayesian data analysis: a tutorial with R, JAGS, and Stan. Academic Press, New YorkzbMATHGoogle Scholar
  28. 28.
    Plummer M (2013) rjags: Bayesian graphical models using MCMC. R package version, 3Google Scholar
  29. 29.
    Wartman J, Seed RB, Bray JD (2005) Shaking table modeling of seismically induced deformations in slopes. J Geotech Geoenviron Eng 131(5):610–622CrossRefGoogle Scholar
  30. 30.
    Wilson RC, Keefer DK (1983) Dynamic analysis of a slope failure from the 6 August 1979 Coyote Lake, California, earthquake. Bull Seismol Soc Am 73(3):863–877Google Scholar
  31. 31.
    Newmark NM (1965) Effects of earthquakes on dams and embankments. Geotechnique 15(2):139–160CrossRefGoogle Scholar
  32. 32.
    Jibson RW (2011) Methods for assessing the stability of slopes during earthquakes—a retrospective. Eng Geol 122(1):43–50CrossRefGoogle Scholar
  33. 33.
    Jibson RW (2007) Regression models for estimating coseismic landslide displacement. Eng Geol 91(2):209–218CrossRefGoogle Scholar
  34. 34.
    Ambraseys NN, Menu JM (1988) Earthquake-induced ground displacements. Earthq Eng Struct Dyn 16(7):985–1006CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Korea Atomic Energy Research InstituteDaejeonSouth Korea
  2. 2.Department of Civil EngineeringKyungHee UniversityYongin-siSouth Korea

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