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Research Papers

Multi-Objective Model Updating Optimization Considering Orthogonality

[+] Author and Article Information
Braden T. Warwick

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: braden.warwick@queensu.ca

Il Yong Kim

Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: kimiy@queensu.ca

Chris K. Mechefske

Professor
Department of Mechanical and
Materials Engineering,
Queen's University,
Kingston, ON K7L 2V9, Canada
e-mail: chris.mechefske@queensu.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 22, 2018; final manuscript received February 28, 2019; published online April 8, 2019. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 14(6), 061009 (Apr 08, 2019) (11 pages) Paper No: CND-18-1525; doi: 10.1115/1.4043086 History: Received November 22, 2018; Revised February 28, 2019

The coordinate orthogonality check (CORTHOG) and multi-objective optimization considering pseudo-orthogonality as an objective function are introduced to overcome several limitations present in current model updating methods. It was observed that the use of the CORTHOG to remove four inaccurate degrees-of-freedom (DOF) was able to increase the orthogonality between mode shape vectors. The multi-objective model updating process generated a Pareto front with 38 unique optimal solutions. Four critical points were identified along the Pareto front, of which decreased the natural frequency error by greater than 2.84% and further increased the orthogonality between mode shape vectors. Therefore, it has been demonstrated that both steps of the methodology are critical to significantly reduce the overall errors of the system and to generate a finite element (FE) model that best describes physical reality. Additionally, the methodology introduced in this work generated a feasible computational runtime allowing for it to be easily adapted to widespread applications.

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Figures

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Fig. 1

Visual representation of the crowding distance for solution x with respect to objectives 1 and 2 (based off Fig. 2(b) in Ref. [20])

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Fig. 2

Experimental setup as used by Warwick et al. [40,41]

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Fig. 3

CORTHOG of the original data set

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Fig. 4

(a) Original POC [40] and (b) post-CORTHOG POC

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Fig. 5

Bend angles of the optimal solutions along the Pareto front

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Fig. 6

Pareto front of optimal solutions

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Fig. 7

Natural frequency correlation for solutions: (a) B1, (b) B2, (c) B3, and (d) B4

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Fig. 8

POC for solutions: (a) B1, (b) B2, (c) B3, and (d) B4

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