Identifying Local Reductions to Mass and Stiffness with Incomplete Modal Information, Sparsity, and Nonnegative Constraints
Publication: Journal of Engineering Mechanics
Volume 148, Issue 12
Abstract
The -norm regularized inverse methods have been suggested as a means to quantify and localize spatially sparse damage from a set of identified natural frequencies. Thus far, damage has been interpreted as changes in stiffness without any appreciable associated changes in mass. In seeking to generalize -norm-based inverse methods to encompass damage that produces significant changes in both mass and stiffness, this paper finds that sparsity is too weak a prior to uniquely solve the associated underdetermined inverse problem. However, when damage is defined by local reductions to stiffness and mass, then the addition of a nonnegative constraint when combined with sparsity can yield physically meaningful solutions. This work proposes a two-step model-updating method to obtain sparse and nonnegative solutions. The findings and proposed method were verified using two numerical models: a shear beam and a four-level plane frame. The proposed methodology was experimentally validated using vibration data taken from a four-level bolted steel frame subjected to multiple damage scenarios.
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Data Availability Statement
The experimental data used to support the findings of this study and the MATLAB code used to implement the proposed methods are available from the corresponding author upon reasonable request.
Acknowledgments
The first author is partially funded by the National Science Foundation Research Award DGE-1144388. The second author is partially funded by the National Science Foundation Research Award CMMI-1453502. The support is gratefully acknowledged.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 27, 2019
Accepted: Jan 13, 2022
Published online: Sep 26, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 26, 2023
ASCE Technical Topics:
- Analysis (by type)
- Beams
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Frames
- Methodology (by type)
- Models (by type)
- Motion (dynamics)
- Natural frequency
- Numerical methods
- Numerical models
- Oscillations
- Research methods (by type)
- Solid mechanics
- Spatial analysis
- Spatial data
- Steel frames
- Stiffening
- Structural behavior
- Structural engineering
- Structural members
- Structural systems
- Verification
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