Skip to main content
SpringerLink
Log in

Identification of the nonlinear seismic response of buildings by a combined Stockwell Transform and deconvolution interferometry approach

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

Abstract

In presence of soil–structure interaction (SSI), changes in dynamic properties of the system can be related to nonlinearities in both the structural and soil response. Identifying the nonlinearities related to non-stationary phenomena due to structural damage is an important issue for damage detection and localization. In this study, a novel approach is proposed to identify the non-linear structural response of an instrumented building in presence of SSI. Considering the advantages provided by the use of the time–frequency representation to explore the time-variant behavior of the system, and the direct evaluation of the shear wave velocity by the use of the deconvolution interferometry to decouple structural response from soil response, a combined Stockwell Transform and deconvolution interferometry approach is presented. The combined approach is applied to a selected data set of a well-documented building, the Jalapa building, whose nonlinear response was already investigated with other methods. This offers the possibility to validate the results obtained by the proposed approach. Jalapa building is a reinforced concrete structure, located on soft clay in Mexico City. Both SSI effects and structural and nonstructural damage affected the building response during earthquakes in the 1990s. The building was retrofitted twice during its lifetime. The data of three events are considered when investigating the changes in dynamic properties of the structure due to damage and retrofitting. The results allow us to detect the different phases of non-linear structural response in a reasonable agreement with the documented status of the building after each event.

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

Similar content being viewed by others

References

  • Addison PS (2002) The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. IOP Publishing, Bristol

    Book  Google Scholar 

  • Askari R, Siahkoohi HR (2007) Ground roll attenuation using the S and x-f-k transforms. Geophys Prospect 55:1–10

    Article  Google Scholar 

  • Bertero M, Boccacci P (1998) Introduction to inverse problems in imaging. IOP Publishing, Bristol

    Book  Google Scholar 

  • Bindi D, Petrovic B, Karapetrou S, Manakou M, Boxberger T, Raptakis D, Pitilakis D, Parolai S (2014) Seismic response of an 8-story RC-building from ambient vibration analysis. Bull Earthq Eng 13:2095–2120

    Article  Google Scholar 

  • Boutin C, Hans S, Ibraim E (2005) Roussillon P (2005) In situ experiments and seismic analysis of existing buildings. Part II: seismic integrity threshold. Earthq Eng Struct Dyn 34:1531–1546

    Article  Google Scholar 

  • Bradford SC, Yang J, Heaton T (2006) Variations in the dynamic properties of structures: the Wigner–Ville distribution. In: Proceedings of the 8th US national conference on earthquake engineering. San Francisco

  • Cardenas M, Bard PY, Gueguen, P, Chavez-Garcia FJ (2000) Soil–structure interaction in Mexico City. Wave field radiated away from Jalapa Building: data and modeling. In: Proceedings of 12th world conference on earthquake engineering, Auckland, January 30—Friday 4

  • Céspedes I, Huang Y, Ophir J, Spratt S (1995) Methods for estimation of subsample time delays of digitized echo signals. Ultrason Imaging 17:142–171

    Article  Google Scholar 

  • Cheng MH, Heaton TH (2015) Simulating building motion using ratios of the building’s natural frequencies and a timoshenko beam model. Earthq Spectra 31(1):403–420

    Article  Google Scholar 

  • Chopra AK (1996) Modal analysis of linear dynamic systems: physical interpretation. J Struct Eng 122:517–527

    Article  Google Scholar 

  • Cohen L (1989) Time-frequency distributions—a review. Proc IEEE 77(7):941–981

    Article  Google Scholar 

  • Daubechies I (1992) Ten lectures on wavelet, Society for Industrial and Applied Mathematics. ISBN 0898712742

  • Dehghani MJ (2009) Comparison of S-transform and wavelet transform in power quality analysis. World Acad Sci Eng Technol 50:395–398

    Google Scholar 

  • Ditommaso R, Ponzo FC (2015) Automatic evaluation of the fundamental frequency variations and related damping factor of reinforced concrete framed structures using the Short Time Impulse Response Function (STIRF). Eng Struct 82:104–112

    Article  Google Scholar 

  • Ditommaso R, Mucciarelli M, Ponzo FC (2012) Analysis of non-stationary structural systems by using a band-variable filter. Bull Earthq Eng 10:895–911

    Article  Google Scholar 

  • Ebrahimian M, Todorovska MI (2014) Wave propagation in a Timoshenko beam building model. J Eng Mech 140(5):04014018

    Article  Google Scholar 

  • Ebrahimian M, Todorovska MI (2015) Structural system identification of buildings by a wave method based on a non uniform timoshenko beam model. J Eng Mech 141:1–11

    Article  Google Scholar 

  • Ebrahimian M, Rahmani M, Todorovska MI (2014) Nonparametric estimation of wave dispersion in high-rise buildings by seismic interferometry. Earthquake Eng Struct Dynam 43:2361–2375

    Article  Google Scholar 

  • Futterman WI (1962) Dispersive body waves. J Geophys Res 67(13):5279–5291

    Article  Google Scholar 

  • Gabor D (1946) Theory of communications. J Inst Elect Eng 93:429–457

    Google Scholar 

  • Ivanovic SS, Trifunac MD, Todorovska MD (2001) On identification of damage in structures via wave travel times. In: Erdik M, Celebi M, Mihailov V, Apaydin N (eds) Strong motion instrumentation for civil engineering structures, NATO Science Series (Series E: Applied Sciences), vol 373. pp 447–467

  • Kanai K (1965)Some new problems of seismic vibrations of a structure. In: Proceedings of the 3rd world conference on earthquake engineering, Auckland and Wellington, New Zealand

  • Kaya Y, Kocakaplan S, Şafak E (2015) System identification and model calibration of multi-story buildings through estimation of vibration time histories at non-instrumented floors. Bull Earthq Eng 13(11):3301–3323

    Article  Google Scholar 

  • Kohler MD, Davis PM, Safak E (2005) Earthquake and ambient vibration monitoring of the steel frame UCLA factor building. Earthq Spectra 21(3):715

    Article  Google Scholar 

  • Kohler MD, Heaton TH, Bradford SC (2007) Propagating waves in the steel, moment-frame factor building recorded during earthquakes. Bull Seismol Soc Am 97:13341345

    Article  Google Scholar 

  • Li Y, Mau ST (1991) A case study of Mimo system identification applied to building seismic records. Earthq Eng Struct Dyn 20:1045–1064

    Article  Google Scholar 

  • Luco JE (1980) Soil–structure interaction and identification of structural models. Proceedings of 2nd ASCE conference on civil engineering and nuclear power, Knoxville, Tennessee; vol 3, no 10, pp 10.1–10.30

  • Mallat S (1998) A wavelet tour of signal processing. Academic, New York

    Google Scholar 

  • Meli R, Faccioli E, Murià-Vila D, Quaas R, Paolucci R (1998) A study of site effects and seismic response of an instrumented building in Mexico City. J Earthq Eng 2:89–111

    Google Scholar 

  • Michel C, Guéguen P (2010) Time–frequency analysis of small frequency variations in civil engineering structures under weak and strong motions using a reassignment method. Struct Health Monit 9(2):159–171

    Article  Google Scholar 

  • Michel C, Guéguen P (2017) Interpretation of the velocity measured in buildings by seismic interferometry based on Timoshenko beam theory under weak and moderate motion. Soil Dyn Earthq Eng 104:131–142

    Article  Google Scholar 

  • Michel C, Gueguen P, Lestuzi P (2011) Observed non-linear soil–structure interaction from low amplitude earthquakes and forced-vibration recordings, in Proceedings, 8th international conference on structural Dynamics, EURODYN 2011, Leuven, Belgium, 4–6 July 2011

  • Miranda E, Taghavi S (2005) Approximate floor acceleration demands in multistory buildings. I: formulation. J Struct Eng 13:203–211

    Article  Google Scholar 

  • Mucciarelli M, Masi A, Gallipoli MR, Harabaglia P, Vona M, Ponzo F, Dolce M (2004) Analysis of RC building dynamic response and soil-building resonance based on data recorded during a damaging earthquake (Molise, Italy, 2002). Bull Seismol Soc Am 94:1943–1953

    Article  Google Scholar 

  • Murià-Vila D (2007) Experienciamexicanasobre la respuestasísmica de edificiosinstrumentados, III Coloquio de Ingreso a la Academia. Academía de Ingeniería, México

    Google Scholar 

  • Murià-Vila D, Rodriguez G, Zapata A, Toro AM (2001) Seismic response of a twice-retrofitted building. ISET J Earthq Technol 38:67–92

    Google Scholar 

  • Murià-Vila D, Taborda R, Zapata-Escobar A (2004) Soil–structure interaction effects in two instrumented tall buildings. In: 13th world conference on earthquake engineering, Vancouver, BC, August 1–6, paper no. 1911

  • Murià-Vila D, Aldama BD, Loera S (2010) Structural warning for instrumented buildings. In: Proceedings of the 14th European conference on earthquake engineering, Ohrid, Macedonia, September 2010

  • Nakata N, Snieder R, Kuroda S, Ito S, Aizawa T, Kunimi T (2013) Monitoring a building using deconvolution interferometry, I: earthquake-data analysis. Bull Seismol Soc Am 103:1662–1678

    Article  Google Scholar 

  • Nakata N, Tanaka W, Oda Y (2015) Damage detection of a building caused by the 2011 Tohoku-Oki Earthquake with Seismic Interferometry. Bull Seismol Soc Am 105:2411–2419

    Article  Google Scholar 

  • Ordaz M, Faccioli E (1994) Site response analysis in the Valley of Mexico: selection of input motion and extent of non-linear soil behavior. Earthq Eng Struct Dyn 23:895–908

    Article  Google Scholar 

  • Paolucci R (1993) Soil–structure interaction effects on an instrumented building in Mexico City. Eur Earthq Eng VII(3):33–44

  • Parolai S (2009) Denoising of seismograms using the S transform. Bull Seismol Soc Am 99:226–234

    Article  Google Scholar 

  • Petrovic B, Parolai S (2016) Joint deconvolution of building and downhole strong-motion recordings: evidence for the seismic wavefield being radiated back into the shallow geological layers. Bull Seismol Soc Am 106:1720–1732

    Article  Google Scholar 

  • Petrovic B, Dikmen SU, Parolai S (2017a) Real data and numerical simulations-based approaches for estimating the dynamic characteristics of a tunnel formwork building. Bull Earthquake Eng. https://doi.org/10.1007/s10518-017-0250-3

  • Petrovic B, Parolai S, Pianese G, Dikmen SU, Moldobekov B, Orunbaev S, Paolucci R (2017b) Joint deconvolution of building and downhole recordings: an application to three test cases. Bull Earthq Eng (submitted for publication)

  • Picozzi M, Parolai S, Mucciarelli M, Milkereit C, Bindi D, Ditommaso R, Vona M, Gallipoli MR, Zschau J (2011) Interferometric analysis of strong ground motion for structural health monitoring: the example of the L’Aquila, Italy, seismic sequence of 2009. Bull Seismol Soc Am 101:635–651

    Article  Google Scholar 

  • Pinnegar CR, Eaton DE (2003) Application of the S-transform to prestack noise attenuation filtering. J Geophys Res 108(B9):2422

    Article  Google Scholar 

  • Ponzo FC, Ditommaso R, Auletta G, De Muro A (2013) Damage detection on reinforced concrete framed structures using a band-variable filter. Research and applications in structural engineering, Mechanics and computation. In: Proceedings of the 5th international conference on structural engineering, mechanics and computation, SEMC 2013, pp 2303–2307

  • Prieto GA, Lawrence JF, Chung AI, Kohler MD (2010) Impulse response of civil structures from ambient noise analysis. Bull Seismol Soc Am 100:2322–2328

    Article  Google Scholar 

  • Puglia R, Ditommaso R, Pacor F, Mucciarelli M, Luzi L, Bianca M (2011) Frequency variation in site as observed from strong motion data of the L’Aquila (2009) seismic sequence. Bull Earthq Eng 9:869–892

    Article  Google Scholar 

  • Rahmani M, Todorovska MI (2013) 1D system identification of buildings from earthquake response by seismic interferometry with waveform inversion of impulse responses—method and application to Millikan Library. Soil Dyn Earthq Eng 47:157–174

    Article  Google Scholar 

  • Rahmani M, Ebrahimian M, Todorovska MI (2014) Wave dispersion in high-rise buildings due to soil–structure interaction. Earthq Eng Struct Dyn 44:317–323

    Article  Google Scholar 

  • Rahmani M, Ebrahimian M, Todorovska MI (2015) Time-wave velocity analysis for early earthquake damage detection in buildings: application to a damaged full-scale RC building. Earthq Eng Struct Dyn 44:619–636

    Article  Google Scholar 

  • Safak E (1989) Wave propagation formulation of seismic response of multi-story buildings. J Struct Eng ASCE 125(4):426–437

    Article  Google Scholar 

  • Schimmel M, Gallart J (2005) The inverse S transform with windows of arbitrary and varying shape. IEEE Trans Signal Proc 53:4417–4422

    Article  Google Scholar 

  • Simon C, Ventosa S, Schimmel M, Heldring A, Dañobeitia JJ, Gallart J, Manuel A (2007) The S-transform and its inverses: side effects of discretizing and filtering. IEEE Trans Signal Process 55:4928–4937

    Article  Google Scholar 

  • Snieder R, Safak E (2006) Extracting the building response using seismic interferometry: theory and application to the Millikan Library in Pasadena, California. Bull Seismol Soc Am 96:586–598

    Article  Google Scholar 

  • Stockwell RG, Mansinha L, Lowe RP (1996) Localization of the complex spectrum: the S transform. IEEE Trans Signal Process 44:998–1001

    Article  Google Scholar 

  • Tamim NSM, Ghani F (2010) Techniques for optimization in time delay estimation from cross correlation function. Int J Eng Technol 10(2):69–75

    Google Scholar 

  • Tikhonov AN, Arsenin VY (1977) Solution of ill-posed problems. Wiston/Wiley, Washington

    Google Scholar 

  • Timoshenko S (1937) Vibration problems in engineering, 2nd edn. Van Nostrand, Princeton, NJ

  • Todorovska MI (2009a) Seismic interferometry of a soil–structure interaction model with coupled horizontal and rocking response. Bull Seismol Soc Am 99:611–625

    Article  Google Scholar 

  • Todorovska MI (2009b) Soil–structure system identification of Millikan Library North–South response during four earthquakes (1970–2002): what caused the observed wandering of the system frequencies? Bull Seismol Soc Am 99:626–635

    Article  Google Scholar 

  • Todorovska MI, Rahmani M (2013) System identification of buildings by wave travel time analysis and layered shear beam models—spatial resolution and accuracy. Struct Control Heal Monit 20:686–702

    Article  Google Scholar 

  • Todorovska MI, Trifunac MD (2007) Earthquake damage detection in the Imperial county services building I: the data and time–frequency analysis. Soil Dyn Earthq Eng 27:564–576

    Article  Google Scholar 

  • Todorovska MI, Trifunac MD (2008a) Earthquake damage detection in the imperial county services building III: analysis of wave travel times via impulse response function. Soil Dyn Earthq Eng 28:387–404

    Article  Google Scholar 

  • Todorovska MI, Trifunac MD (2008b) Impulse response analysis of the Van Nuys 7-storey hotel during 11 earthquakes and earthquake damage detection. Struct Control Health Monit 15:90–116

    Article  Google Scholar 

  • Trifunac MD, Ivanović SS, Todorovska MD (2001) Apparent periods of a building. II: time-frequency analysis. J Struct Eng 127(5):527–537

    Article  Google Scholar 

  • Trifunac MD, Ivanovic SS, Todorovska MI (2003) Wave propagation in a seven-story reinforced concrete building. Part III: damage detection via changes in wavenumbers. Soil Dyn Earth Eng 23:65–75

    Article  Google Scholar 

  • Trifunac MD, Todorovska MI, Manić MI, Bulajić B (2008) Variability of the fixed-base and soil–structure system frequencies of a building—the case of Borik-2 building. Structural Control Health Monit 17:120–151

    Article  Google Scholar 

  • Ville J (1948) Theorieet applications de la notion de signal analytique. Cableset Transm 2A:61

    Google Scholar 

  • Wen W, Kalkan E (2017) System Identification based on deconvolution and cross correlation: an application to a 20-story Instrumented Building in Anchorage. Alaska, Bull Seismol Soc Am, p 107

    Google Scholar 

  • Wigner E (1932) On the quantum correction for thermodynamic equilibrium. Phys Rev 40:749–759

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank Murià-Vila for taking care of the Jalapa accelerograph network and for sharing the data set, from 1996 onwards, with us. Kevin Fleming kindly revised our English. The authors thank the anonymous reviewers and the Editor for their comments, which helped improve this paper.

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Giovanna Pianese & Roberto Paolucci

  2. Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Potsdam, Germany

    Bojana Petrovic & Stefano Parolai

Authors
  1. Giovanna Pianese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bojana Petrovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefano Parolai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roberto Paolucci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanna Pianese.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pianese, G., Petrovic, B., Parolai, S. et al. Identification of the nonlinear seismic response of buildings by a combined Stockwell Transform and deconvolution interferometry approach. Bull Earthquake Eng 16, 3103–3126 (2018). https://doi.org/10.1007/s10518-018-0307-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-018-0307-y

Keywords

Search

Navigation