Model Updating of Nonproportionally Damped Structural Systems Using an Adapted Complex Sum-of-Squares Optimization Algorithm
Publication: Journal of Engineering Mechanics
Volume 149, Issue 8
Abstract
Various model updating approaches relying on solving nonconvex optimization problems have been developed; however, few of them can reach the global optimum. To obtain the global optimum, the real sum-of-squares optimization algorithm (SOSOA) was proposed to minimize the modal dynamic residuals of proportionally damped structural systems by recasting the nonconvex optimization into a convex optimization. However, this algorithm becomes inefficient for model updating of nonproportionally damped systems with complex-valued eigenvalues and eigvenvectors. This study proposes a model updating approach that exploits and adapts a complex SOSOA to minimize the modal dynamic residuals of nonproportionally damped systems. Numerical considerations unique to using the adapted complex SOSOA to update medium- or large-scale structural models are discussed. Finite-element models of three nonproportionally damped structures—including a base-isolated shear building, a frame building implemented with a tuned mass damper, and a frame building implemented with buckling-restrained braces—are updated to demonstrate that the adapted complex SOSOA finds the global optimum while being orders of magnitude more computationally efficient and far less demanding of computer memory than the real SOSOA.
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Data Availability Statement
Some data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including the codes for updating the finite-element model in the first and third numerical examples.
Acknowledgments
The authors gratefully acknowledge Dr. Erik A. Johnson and Dr. Mahmoud Kamalzare for kindly providing the finite-element model of the 99-DOF superstructure in the second numerical example.
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© 2023 American Society of Civil Engineers.
History
Received: Sep 4, 2022
Accepted: Feb 18, 2023
Published online: May 17, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 17, 2023
ASCE Technical Topics:
- Algorithms
- Buildings
- Computer models
- Continuum mechanics
- Damping
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Mathematics
- Methodology (by type)
- Models (by type)
- Numerical methods
- Optimization models
- Solid mechanics
- Structural dynamics
- Structural engineering
- Structural models
- Structural systems
- Structures (by type)
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