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

Marcos A. Valdebenito; Hector A. Jensen; Pengfei Wei; Michael Beer; Andre T. Beck

doi:10.1115/1.4050159

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

Marcos A. Valdebenito, Hector A. Jensen, Pengfei Wei, Michael Beer, Andre T. Beck

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Article number	020904
Journal	ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
Volume	7
Issue number	2
DOIs	https://doi.org/10.1115/1.4050159
State	Published - Jun 2021
Externally published	Yes

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title = "Application of a Reduced Order Model for Fuzzy Analysis of Linear Static Systems",

abstract = "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.",

author = "Valdebenito, {Marcos A.} and Jensen, {Hector A.} and Pengfei Wei and Michael Beer and Beck, {Andre T.}",

note = "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 (S{\~a}o 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. Publisher Copyright: Copyright VC 2021 by ASME",

year = "2021",

month = jun,

doi = "10.1115/1.4050159",

language = "English",

volume = "7",

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

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

AU - Valdebenito, Marcos A.

AU - Jensen, Hector A.

AU - Wei, Pengfei

AU - Beer, Michael

AU - Beck, Andre 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. Publisher Copyright: Copyright VC 2021 by ASME

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.

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

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