TY - JOUR

T1 - Application of a Reduced Order Model for Fuzzy Analysis of Linear Static Systems

AU - Valdebenito, Marcos A.

AU - Jensen, Héctor A.

AU - Wei, Pengfei

AU - Beer, Michael

AU - Beck, André T.

N1 - Funding Information: This research is partially supported by ANID (National Agency for Research and Development, Chile) under its program FONDE-CYT, Grant Nos. 1180271 and 1200087, and ANID+FAPESP (São Paulo State Foundation for Research, Brazil), Grant No. 2019/13080-9. The first author developed part of this work during a research stay at the Institute for Risk and Reliability (IRZ) of the Leibniz Universit€at Hannover, Germany. Both the first and third authors conducted this research under the auspice of the Alexander von Humboldt Foundation. This support is gratefully acknowledged by the authors.

PY - 2021/6

Y1 - 2021/6

N2 - This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying a-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is constructed by means of a single analysis of the system plus a sensitivity analysis. This reduced basis is enriched as the a-level optimization strategy progresses in order to protect the quality of the approximations provided by the reduced order model. A numerical example shows that with the proposed strategy, it is possible to produce an accurate estimate of the membership function of the response of the system with a limited number of full system analyses.

AB - This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying a-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is constructed by means of a single analysis of the system plus a sensitivity analysis. This reduced basis is enriched as the a-level optimization strategy progresses in order to protect the quality of the approximations provided by the reduced order model. A numerical example shows that with the proposed strategy, it is possible to produce an accurate estimate of the membership function of the response of the system with a limited number of full system analyses.

UR - http://www.scopus.com/inward/record.url?scp=85126837107&partnerID=8YFLogxK

U2 - 10.1115/1.4050159

DO - 10.1115/1.4050159

M3 - Article

VL - 7

JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

SN - 2332-9017

IS - 2

M1 - 020904

ER -