Model updating using sum of squares (SOS) optimization to minimize modal dynamic residuals

TL;DR

This paper introduces a sum of squares (SOS) optimization approach for finite element model updating to effectively minimize modal dynamic residuals, improving the accuracy of structural models.

Contribution

It proposes a novel SOS-based global optimization method for FE model updating, addressing nonconvexity issues in modal residual minimization.

Findings

Validated through numerical simulation and experimental study.

Demonstrated improved model accuracy over traditional methods.

Showed effectiveness in updating a four-story shear frame structure.

Abstract

This research studies finite element (FE) model updating through sum of squares (SOS) optimization to minimize modal dynamic residuals. In the past few decades, many FE model updating algorithms have been studied to improve the similitude between a numerical model and the as-built structure. FE model updating usually requires solving nonconvex optimization problems, while most off-the-shelf optimization solvers can only find local optima. To improve the model updating performance, this paper proposes the SOS global optimization method for minimizing modal dynamic residuals of the generalized eigenvalue equations in structural dynamics. The proposed method is validated through both numerical simulation and experimental study of a four-story shear frame structure.