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Research Papers

# Measurements Selection for Bias Reduction in Structural Damage Identification

[+] Author and Article Information
Yuhang Liu

Department of Industrial and
Systems Engineering,
3255 Mechanical Engineering,
1513 University Ave.,
e-mail: liu427@wisc.edu

Shiyu Zhou

Department of Industrial and
Systems Engineering,
1513 University Ave.,
e-mail: shiyuzhou@wisc.edu

Yong Chen

Department of Industrial and Systems Engineering,
University of Iowa,
Iowa City, IA 52242
e-mail: yong-chen@uiowa.edu

Jiong Tang

Department of Mechanical Engineering,
University of Connecticut,
Storrs, Storrs, CT 06269
e-mail: jtang@engr.uconn.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 3, 2018; final manuscript received September 10, 2018; published online October 31, 2018. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 141(3), 031003 (Oct 31, 2018) (14 pages) Paper No: DS-18-1005; doi: 10.1115/1.4041505 History: Received January 03, 2018; Revised September 10, 2018

## Abstract

Linearization of the eigenvalue problem has been widely used in vibration-based damage detection utilizing the change of natural frequencies. However, the linearization method introduces bias in the estimation of damage parameters. Moreover, the commonly employed regularization method may render the estimation different from the true underlying solution. These issues may cause wrong estimation in the damage severities and even wrong damage locations. Limited work has been done to address these issues. It is found that particular combinations of natural frequencies will result in less biased estimation using linearization approach. In this paper, we propose a measurement selection algorithm to select an optimal set of natural frequencies for vibration-based damage identification. The proposed algorithm adopts $L1$-norm regularization with iterative matrix randomization for estimation of damage parameters. The selection is based on the estimated bias using the least square method. Comprehensive case analyses are conducted to validate the effectiveness of the method.

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Topics: Algorithms , Damage

## References

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## Figures

Fig. 1

The fixed-free beam for the simulation. There are total 20 elements in the beam.

Fig. 2

The bias of the estimated damages for different combinations of natural frequencies

Fig. 3

Damage parameter histogram of 20 elements with Algorithm 1. True damages of each element are labeled using dashed lines.

Fig. 4

Damage parameter histogram of 20 elements after Algorithm 2. True damages of each element are labeled using dashed lines.

Fig. 5

Plots of b̂k and dk for k=8,9,…,127

Fig. 6

Comparison of damage parameter estimation using different approaches

Fig. 7

Damage parameter histogram of 20 elements after Algorithm 2. True damages of each element are labeled using dashed lines.

Fig. 8

Plots of b̂k and Δα̂(k)−Δαtruth2 for k=29,30,…,127

Fig. 9

Comparison of damage parameter estimation using different approaches

Fig. 10

Accuracy of damage location identification by Algorithm 2 under random noise scenarios

Fig. 11

Δα̂ for each iteration q by Algorithm 2. The x-axis is 200 elements and the y-axis is Δα̂. The dashed lines are the underlying damage for elements 40 and 170.

Fig. 12

A small mass is attached on the middle of the beam to mimic the stiffness reduction with an accelerometer located near one end of the beam

Fig. 13

Accuracy of linear approximation in natural frequencies

Fig. 14

Damage parameter histogram of 20 elements after Algorithm 2. True damages of each element are labeled using dashed lines.

Fig. 15

Plots of b̂k with Δα̂(k)−Δαtruth2 for k=29,30,…,127 with severe damage

## Errata

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