Skip to main content
SpringerLink
Log in

Strategy for the selection of input ground motion for inelastic structural response analysis based on naïve Bayesian classifier

  • Original Research Paper
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

An application of the naïve Bayesian classifier for selecting strong motion data in terms of the deformation probably induced on a given structural system is presented. The main differences between the proposed method and the “standard” procedure based on the inference of a polynomial relationship between a single intensity measure and the engineering demand parameter are: the discrete description of the engineering demand parameter; the use of an array of intensity measures; the combination of the information issued from the training phase via a Bayesian formulation. Six non-linear structural systems with initial fundamental frequency of 1, 2 and 5 Hz and with different strength reduction factors are modelled. Their behaviour is described using the Takeda hysteretic model and the engineering demand parameter is expressed as the relative drift. A database of 6,373 strong motion records is built from worldwide catalogues and is described by a set of “classical” intensity measures; it constitutes the “training dataset” used to feed the Bayesian classifier. The structural system response is reduced to a description of three possible classes: elastic, if the induced drift is lower than the yield displacement; plastic, if the drift ranges between the yield and the ultimate drift values; fragile if the drift reaches the ultimate drift. The goal is to evaluate the conditional probability of observing a given status of the system as a function of the intensity measure array. To validate the presented methodology and evaluate its prediction capability, a blind test on a second dataset, completely disjointed from the training one, composed of 7,000 waveforms recorded in Japan, is performed. The Japanese data are classed using the probability distribution functions derived on the first data set. It is shown that, by combining several intensity measures through the likelihood product, a stable result is obtained whereby most of the data (\(>\)75 %) are well classed. The degree of correlation between the intensity measure and the engineering demand parameter controls the reliability of the probability curves associated to each intensity measure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Abrahamson NA (1992) Non-stationary spectral matching. Seismol Res Lett 63(1):30

    Google Scholar 

  • Al Atik L, Abrahamson NA (2010) An improved method for nonstationary spectral matching. Earthq Spectra 26(3):601–617. doi:10.1193/1.3459159

    Article  Google Scholar 

  • Allahabadi R, Powell GH (1988) DRAIN-2DX user guide. Report No. UCB/EERC-88/06. Berkeley Earthquake Engineering Research Centre, University of California

  • Ambraseys N, Smit P, Douglas J, Margaris B, Sigbjornsson R, Olafsson S, Suhadolc P, Costa G (2004) Internet site for European strong-motion data. Bollettino Geofisica Teorica e Applicata 45:113–129

    Google Scholar 

  • Asgarian B, Nojoumi RM, Alanjari P (2012) Performance-based evaluation of tall building using advanced intensity measures (case study: 30-story steel structure with frame-tube system). Struct Des Tall Spec Build 23(2):81–93, 10. doi:10.1002/tal.2013

  • Bommer JJ, Martinez-Pereira A (2000) The effective duration of earthquake strong motion. J Earthquake Eng 3:127–172. doi:10.1142/S1363246999000077

    Google Scholar 

  • Brune JN (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. J Geophys Res 75(26):4997–5009. doi:10.1029/JB075i026p04997

    Article  Google Scholar 

  • Chapmann MC (1999) On the use of elastic input energy for seismic hazard analysis. Earthq Spectra 15(4):607–635. doi:10.1193/1.1586064

    Article  Google Scholar 

  • Chopra AK (2011) Dynamics of structures. Prentice-Hall International Series in Civil Engineering and Engineering Mechanics. ISBN-13:978–0132858038

  • Cosenza E, Manfredi G (2000) Damage index and damage measures. Prog Struct Eng Mater 2(1):50–59. doi:10.1002/(SICI)1528-2716(200001/03)2:1<50::AID-PSE7>3.0CO;2-S()

  • De Biasio M, Grange S, Dufour F, Allain F, Petre-Lazar I (2014) A simple and efficient intensity measure to account for nonlinear structural behavior. Earthq Spectra 30(4):1403–1426

  • Federal Emergency Management Agency FEMA (2003) HAZUS-MH MR1 advances engineering building module technical and user’s manual. Department of Homeland Security Emergency Preparedness and Response Directorate, Washington

  • Gasparini DA, Vanmarke EH (1976) Simulated earthquake motions compatible with prescribed response spectra. MIT civil engineering research report R76–4. Massachusetts Institute of Technology, Cambridge

  • Giovenale P, Cornell A, Esteva L (2004) Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses. Earthq Eng Struc 3:951–979. doi:10.1002/eqe.386

    Article  Google Scholar 

  • Grant D, Diaferia R (2012) Assessing adequacy of spectrum-matched ground motion for response history analysis. Earthq Eng Struct 42(9):1265–1280. doi:10.1002/eqe.2270

    Article  Google Scholar 

  • Hancock J, Bommer JJ (2006) A state of knowledge review of the influence of strong-motion duration on structural damage. Earthq Spectra 22:827–845. doi:10.1193/1.2220576

    Article  Google Scholar 

  • Hogg D (2008) Data analysis recipes: choosing the binning for a histogram. Cornell University Library. arXiv:0807.4820

  • Hunter JD (2007) Matplotlib: A 2D graphics environment. Comput Sci Eng 9:90–95

    Article  Google Scholar 

  • Jayaram N, Mollaioli F, Bazzurro P, De Sortis A, Bruno S (2010) Prediction of structural response of reinforced concrete frames subjected to earthquake ground motions. In: 9th US National and 10th Canadian conference of earthquake engineering, pp 428–437, Toronto, Canada

  • Katona TJ, Tóth L (2013) Damages indicators for post-earthquake condition assessment. Acta Geodaetica et Geophysica Hungarica 48(3):333–345. doi:10.1007/s40328-013-0021-9

    Article  Google Scholar 

  • Katsanos EI, Sextos AG, Manolis GD (2009) Selection of earthquake ground motion records: a state-of-the-art review from a structural engineering perspective. Soil Dyn Earthq Eng 30:157–169. doi:10.1016/j.soildyn.2009.10.005

    Article  Google Scholar 

  • Kostov MK (2005) Site specific estimation of cumulative absolute velocity. In: 18th international conference on structural mechanics in reactor technology (SMiRT 18), SMiRT 18–K03\_4, Bejing, China

  • Kuehn NM, Scherbaum F (2010) A naïve Bayesian classifier for intensities using peak ground velocity and acceleration. Bull Seismol Soc Am 100:3278–3283. doi:10.1785/0120100082

    Article  Google Scholar 

  • Kuehn NM, Riggelsen C, Sherbaum F (2011) Modeling the joint probability of earthquake, site and ground-motion parameters using Bayesian networks. Bull Seismol Soc Am 101:235–249. doi:10.1785/0120100080

    Article  Google Scholar 

  • Laurendedau A, Cotton F, Bonilla LF (2012) Nonstationary simulation of strong ground motion time histories: application to the K-Net Japanese database. In: 15th World conference on earthquake engineering, Lisbon, Portugal

  • Lestuzzi P, Badoux M (2008) Génie Parasismique, 2nd edn. Presses polytechniques et universitaires romandes, Lausanne, Swiss

    Google Scholar 

  • Lestuzzi P, Schawab P, Koller M, Lacave C (2004) How to choose earthquake recordings for non-linear seismic analysis of structures. In: Proceedings of 13th world conference on earthquake engineering, Vancouver, British Columbia, Canada

  • Luco N, Bazzurro P (2007) Does amplitude scaling of ground motion records result in biased nonlinear structural drift response? Earthq Eng Struct 36(13):1813–1835. doi:10.1002/eqe.695

    Article  Google Scholar 

  • Luco N, Cornell A (2007) Structure-Specific scalar intensity measures for near-source and ordinary earthquake ground motions. Earthq Spectra 23(2):357–392. doi:10.1193/1.2723158

    Article  Google Scholar 

  • Luco N, Manuel L, Baldava S, Bazzurro P (2005) Correlation of damage of steel moment resisting frames to a vector-valued set of ground motion parameters. In: Proceedings of 9th international conference on structural safety and reliability, Rome, Italy

  • Lucchini A, Mollaioli F, Monti G (2011) Intensity measures for response prediction of a torsional building subjected to bi-directional earthquake ground motion. Bull Earthq Eng 9(5):1499–1518. doi:10.1007/s10518-011-9258-2

    Article  Google Scholar 

  • Mollaioli F, Luchini A, Cheng Y, Monti G (2013) Intensity measures for the seismic response prediction of base-isolated buildings. Bull Earthq Eng 11:1841–1866. doi:10.1007/s10518-013-9431-x

    Article  Google Scholar 

  • NEHRP Consultants Joint Venture (2011) Selecting and scaling earthquake ground motions for performing response-history analyses. www.nehrp.gov/pdf/nistgcr11-917-15.pdf

  • Pousse G, Bonila LF, Cotton F, Margerin L (2006) Nonstationary stochastic simulation of strong ground motion time histories including natural variability: application to the K-Net Japanese database. Bull Seismol Soc Am 96(6):2103–2117. doi:10.1785/0120050134

    Article  Google Scholar 

  • Preumont A (1984) The generation of spectrum compatible accelerograms for the design of nuclear power plants. Earthq Eng Struct 12(4):481–497. doi:10.1002/eqe.4290120405

    Article  Google Scholar 

  • Silva WJ, Lee L (1987) WES RASCAL code for synthesizing earthquake ground motions. State-of-the-art for assessing earthquake hazard in the United States. Report 24. U.S. Army Engineers Waterways Experiment Station, Misc. Paper S-73-1

  • Song SG, Dalguer LA, Mai PM (2014) Pseudo-dynamic source modelling with 1-point and 2-points statistics of earthquake source parameters. Geophys J Int 196:1770–1786. doi:10.1093/gji/ggt479

    Article  Google Scholar 

  • Takeda T, Sozen MA, Nielsen NN (1970) Reinforced concrete response to simulated earthquakes. J Struct Div ASCE 96(12):2557–2573

    Google Scholar 

  • Wasserman L (2004) All of statistics. A coincise course in statistical inference. Springer, New York

    Google Scholar 

  • Yamamoto Y, Baker J (2011) Stochastic model for earthquake ground motion using wavelet packets. In: 11th international conference on applications of statistics and probability in civil engineering, Zurich, Switzerland

  • Yakut A, Yilmaz H (2008) Correlation of deformation demands with ground motion intensity. J Struct Eng 134(12):1818–1828. doi:10.1061/(ASCE)0733-9445(2008)134:12(1818)

    Article  Google Scholar 

Download references

Acknowledgments

This work would not have been possible without the huge work made by people working at CESMD, RAP, ITACA, K-Net, KiK-Net, GNS, IGN databases, the authors are deeply thankfully for their continuous efforts in ensuring data collection and distribution. The authors also thank Prof Pierino Lestuzzi for distributing his research codes through his personal web-page. This work benefits of fruitful discussions with O. Scotti, C. Satriano, F. Lopez-Caballero and I. Zenter. Maria Lancieri thanks O. Zagordi for his valuable help in developing the naïve Bayesian classifier. The figures have been plotted using Matplotlib (Hunter 2007). The work has-been partially found by the “Group d’intérêt scientifique du Réseau Accélérométrique Permanent” (GIS-RAP).

Author information

Authors and Affiliations

  1. PRP-DGE/SCAN/BERSSIN, Institut de Radioprotection et Sûreté Nucléaire, Bp 17, 92262, Fontenay aux Roses CEDEX, France

    M. Lancieri, M. Renault & D. Baumont

  2. DEN/DANS/DM2S, Comissariat à l’énergie atomique, Centre de Saclay, 91191, Gif sur Yvette, France

    C. Berge-Thierry

  3. ISTerre-IFSTTAR, Université Joseph Fourier, 1/CNRS/IFSTTAR, BP 53, 38041, Grenoble cedex 9, France

    P. Gueguen & M. Perrault

Authors
  1. M. Lancieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Renault
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Berge-Thierry
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Gueguen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. D. Baumont
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Perrault
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Lancieri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lancieri, M., Renault, M., Berge-Thierry, C. et al. Strategy for the selection of input ground motion for inelastic structural response analysis based on naïve Bayesian classifier. Bull Earthquake Eng 13, 2517–2546 (2015). https://doi.org/10.1007/s10518-015-9728-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-015-9728-z

Keywords

Search

Navigation