Moreover, the GM‐ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses.

To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity‐augmented version of GM‐ELM.

To overcome these technical challenges and promote applications of GM‐ELM to earthquake engineering practice, an efficient GM‐ELM‐based fragility analysis method is proposed for nonstationary excitations. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. Gaussian mixture–based equivalent linearization method (GM‐ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. 445-464 SeriesĪdvances in the Astronautical Sciences, ISSN 1081-6003 139 National CategoryĪstronomy, Astrophysics and Cosmology Identifiers URN: urn:nbn:se:kth:diva-170101 ISI: 000309482700028 Scopus ID: 2-s2.0-80053418231 ISBN: 978-0-87703-565-7 (print) OAI: oai:DiVA.Gaussian mixture–based equivalent linearization method (GM‐ELM) for fragility analysis of structures under nonstationary excitations Place, publisher, year, edition, pages2011. A companion paper deals with the identification of nonlinear input-output models instead of state-space models for a bilinear system using the same interaction matrix approach. The bilinear state-space model is then extracted from the identified ELM. This relationship is used to convert the bilinear model to an Equivalent Linear Model (ELM) which can be identified by any linear identification method such as a superspace method presented here. By extending the interaction matrix formulation from linear to bilinear state-space models, the bilinear system state is expressed in terms of input-output measurements. This paper presents a method for discrete-time bilinear state-space model identification from a single set of input-output data. 445-464 Conference paper, Published paper (Refereed) Abstract ALFRIEND ASTRODYNAMICS SYMPOSIUM, 2011, p.

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