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Computational Methods in Stochastic Dynamics pp 67–88Cite as

Use of Time-Variant Spectral Characteristics of Nonstationary Random Processes in the First-Passage Problem for Earthquake Engineering Applications

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 22))

Abstract

In this work, the spectral characteristics of non-stationary random processes are applied to the time-variant first-passage problem in structural reliability. The first-passage problem consists in computing the probability of a response quantity exceeding a deterministic threshold in a given interval of time when the parameters defining the structural system and/or the loading are random quantities. The Vanmarcke and modified Vanmarcke approximations of the failure probability are expressed herein as integrals in time of the closed-forms of the corresponding hazard functions. These closed-forms refer to linear elastic systems subjected to a time-modulated coloured noise base excitation and are obtained using the corresponding closed-form solutions for the time-variant bandwidth parameter of the system response processes. These approximate solutions to the first-passage problem are compared with the classical Poisson approximation and Monte Carlo simulation results for an idealized linear elastic model of a three-story one-bay shear-type steel building. The retrofit of this benchmark structure with viscous dampers is also considered, allowing (1) to illustrate the use of the newly available closed-form approximations of the failure probability for non-classically damped linear elastic systems and (2) to show an example of practical use in structural engineering of the presented analytical derivations. The earthquake base excitation is modelled as a filtered white noise process defined by the well-known Kanai-Tajimi equation and time-modulated by the widely-used Shinozuka and Sato modulating function. The failure condition is expressed in terms of interstory drifts outcrossing specified deterministic thresholds. The results presented in this study show that the two Vanmarcke approximations can improve considerably the estimates of the failure probability for the first-passage problem when compared with the simpler Poisson approximation.

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Acknowledgements

Support of this research by the LSU Council on Research through the 2008 Summer Stipend Program and the Louisiana Board of Regents through the Pilot Funding for New Research (Pfund) Program of the National Science Foundation (NSF) Experimental Program to Stimulate Competitive Research (EPSCoR) under Award No. NSF(2008)-PFUND86 is gratefully acknowledged. Any opinions, findings, conclusions and/or recommendations expressed in this material are those of the author and do not necessarily reflect those of the sponsors.

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  1. Louisiana State University and A&M College, 3531 Patrick F. Taylor Hall, Baton Rouge, 70803, LA, USA

    Michele Barbato

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  1. Michele Barbato
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Correspondence to Michele Barbato .

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Editors and Affiliations

  1. Inst. Structural Analysis &, Seismic Research, National Technical Univ. Athen, Iroon Polytechniou Str. 9, Athens, 157 80, Greece

    Manolis Papadrakakis

  2. , Intitute of Structural Analysis and Seis, National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    George Stefanou

  3. , Institute of Structural Analysis and Se, National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    Vissarion Papadopoulos

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Barbato, M. (2011). Use of Time-Variant Spectral Characteristics of Nonstationary Random Processes in the First-Passage Problem for Earthquake Engineering Applications. In: Papadrakakis, M., Stefanou, G., Papadopoulos, V. (eds) Computational Methods in Stochastic Dynamics. Computational Methods in Applied Sciences, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9987-7_4

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  • DOI: https://doi.org/10.1007/978-90-481-9987-7_4

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