Time-variant spectral characteristics of nonstationary random processes: an application to structural reliability and earthquake engineering

Abstract eng:
In this paper, 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 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 closed-form solutions for the time-variant bandwidth parameter. 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.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket