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Research Papers

Identifiability Analysis of Finite Element Models for Vibration Response-Based Structural Damage Detection in Elastic Beams

[+] Author and Article Information
Yuhang Liu

Department of Industrial
and Systems Engineering,
University of Wisconsin-Madison, Madison,
3255 Mechanical Engineering,
1513 University Avenue,
Madison, WI 53706
e-mail: liu427@wisc.edu

Shiyu Zhou

Department of Industrial
and Systems Engineering,
University of Wisconsin-Madison, Madison,
1513 University Avenue,
Madison, WI 53706
e-mail: shiyuzhou@wisc.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 October 25, 2015; final manuscript received June 29, 2016; published online August 19, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(12), 121006 (Aug 19, 2016) (12 pages) Paper No: DS-15-1532; doi: 10.1115/1.4034155 History: Received October 25, 2015; Revised June 29, 2016

Finite element model (FEM) is a broadly used numerical tool in structural damage detection. In such applications, damage parameters in FEM are estimated by minimizing the differences between experimental modal analysis data and the corresponding FEM model prediction. Very limited works exist on analyzing the identifiability of the FEM used in such applications. In this paper, the identifiability of FEM-based structural damage detection is investigated for undamped elastic beams. We theoretically proved that damage severity at a given location in a uniform beam is identifiable by reformulating the FEM into a linear time invariant (LTI) system. A numerical algorithm is also proposed for checking the identifiability issue of multiple damage locations. Numerical case studies are provided to validate the effectiveness and usefulness of the proposed framework.

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Figures

Grahic Jump Location
Fig. 1

An example of finite element representation of a beam structure with n elements and n+1  nodes

Grahic Jump Location
Fig. 2

Two different experimental beam setups. (a) Fixed–fixed: both ends of the beam are fixed such that the ends can no longer move or rotate. (b) Fixed-free: one end is fixed and the other one is free to move and rotate. In (a), the collocated node for excitation and measurement is at the middle of the beam and the symmetric damage locations are shaded.

Grahic Jump Location
Fig. 3

Normalized natural frequencies computed from matrix product M−1K(p, γ ) for a fixed location p=23 versus damage parameter γ in two different beam setups. (a) Fixed–fixed uniform beam, (b) fixed-free uniform beam, (c) fixed–fixed nonuniform beam, and (d) fixed-free nonuniform beam.

Grahic Jump Location
Fig. 4

The plot Sk as a function of damage locations in different boundary conditions of a uniform beam. Three different L s are used in the calculation of Sk.

Grahic Jump Location
Fig. 5

The plot Sk as a function of damage locations in different boundary conditions of a nonuniform beam. Three different L s are used in the calculation of Sk.

Grahic Jump Location
Fig. 6

The plot Sk2|k1 as a function of damage location k1 in different boundary conditions of a uniform beam. Three different L s are used in the calculation of Sk.

Grahic Jump Location
Fig. 7

The plot Sk2|k1 as a function of damage location k1 in different boundary conditions of a nonuniform beam. Three different L s are used in the calculation of Sk.

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