@article{3f8ff7d1752d49a3845b678740ffc2be,
title = "Calculation of second order statistics of uncertain linear systems applying reduced order models",
abstract = "This contribution investigates the application of reduced order models for approximating the response of a class of uncertain linear systems. The basis associated with the reduced model is generated based on the results of a single analysis of the system plus a sensitivity analysis. The aforementioned strategy is applied in combination with control variates, thus allowing to estimate the second order statistics of the system's response. In this way, accurate estimates of these statistics can be generated with reduced numerical efforts, as a large number of samples of the system's response is evaluated with the reduced order model while only a small number of samples of the full model is required. Numerical examples comprising stochastic finite element models suggest that the proposed approach can produce estimates of the second order statistics with reduced variability.",
keywords = "Control variates, Reduced order model, Second order statistics, Stochastic finite element analysis, Uncertain linear system",
author = "Gonz{\'a}lez, {I. V.} and Valdebenito, {M. A.} and Correa, {J. I.} and Jensen, {H. A.}",
note = "Funding Information: This research is partially supported by CONICYT ( National Commission for Scientific and Technological Research ) under its program FONDECYT, grant number 1180271 , and Universidad Tecnica Federico Santa Maria under its program PAC (Programa Asistente Cientifico 2017). This support is gratefully acknowledged by the authors. In addition, the first author conducted this research with the support of CONICYT through its graduate scholarship program CONICYT-PFCHA/MagisterNacional/2017-22171799. The second author developed part of this work during a research stay at the Institute for Risk and Reliability (IRZ) of the Leibniz Universit{\"a}t Hannover, Germany, under the auspice of the Alexander von Humboldt Foundation through its program Humboldt Research Fellowship for Experienced Researchers; the support of the Humboldt Foundation and of Professor Michael Beer (director of the IRZ) is gratefully acknowledged. Publisher Copyright: {\textcopyright} 2019",
year = "2019",
month = oct,
doi = "10.1016/j.ress.2019.106514",
language = "English",
volume = "190",
journal = "Reliability Engineering and System Safety",
issn = "0951-8320",
publisher = "Elsevier Ltd.",
}