Research Papers

Sparse Sum-of-Squares Optimization for Model Updating Through Minimization of Modal Dynamic Residuals

[+] Author and Article Information
Dan Li

School of Civil and Environmental Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0355

Yang Wang

School of Civil and Environmental Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0355;
School of Electrical and Computing Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0250
e-mail: yang.wang@ce.gatech.edu

1Corresponding author.

Manuscript received September 18, 2017; final manuscript received November 25, 2018; published online January 7, 2019. Assoc. Editor: Victor Giurgiutiu.

ASME J Nondestructive Evaluation 2(1), 011005 (Jan 07, 2019) (9 pages) Paper No: NDE-17-1091; doi: 10.1115/1.4042176 History: Received September 18, 2017; Revised November 25, 2018

This research investigates the application of sum-of-squares (SOS) optimization method on finite element model updating through minimization of modal dynamic residuals. The modal dynamic residual formulation usually leads to a nonconvex polynomial optimization problem, the global optimality of which cannot be guaranteed by most off-the-shelf optimization solvers. The SOS optimization method can recast a nonconvex polynomial optimization problem into a convex semidefinite programming (SDP) problem. However, the size of the SDP problem can grow very large, sometimes with hundreds of thousands of variables. To improve the computation efficiency, this study exploits the sparsity in SOS optimization to significantly reduce the size of the SDP problem. A numerical example is provided to validate the proposed method.

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Grahic Jump Location
Fig. 1

Plane truss structure with eight nodes (16DOFs) instrumented/measured

Grahic Jump Location
Fig. 2

Optimized objective function value (i.e., optimal residual r*=fx*) for all search starting points: (a) Gauss–Newton and (b) trust-region-reflective

Grahic Jump Location
Fig. 3

Objective function value (i.e., residual r=fx) on a linesegment between a local minimum xTR* and the global minimum x*

Grahic Jump Location
Fig. 4

Plane truss structure with 8DOFs measured



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