Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2021 Feb 3;21(4):1029.
doi: 10.3390/s21041029.

A Step-by-Step Damage Identification Method Based on Frequency Response Function and Cross Signature Assurance Criterion

Jiawang Zhan  1 , Fei Zhang  1 , Mohammad Siahkouhi  1
Affiliations

A Step-by-Step Damage Identification Method Based on Frequency Response Function and Cross Signature Assurance Criterion

Jiawang Zhan et al. Sensors (Basel). .

Abstract

This paper aims to present a method for quantitative damage identification of a simply supported beam, which integrates the frequency response function (FRF) and model updating. The objective function is established using the cross-signature assurance criterion (CSAC) indices of the FRFs between the measurement points and the natural frequency. The CSAC index in the frequency range between the first two frequencies is found to be sensitive to damage. The proposed identification procedure is tried to identify the single and multiple damages. To verify the effectiveness of the method, numerical simulation and laboratory testing were conducted on some model steel beams with simulated damage by cross-cut sections, and the identification results were compared with the real ones. The analysis results show that the proposed damage evaluation method is insensitive to the systematic test errors and is able to locate and quantify the damage within the beam structures step by step.

Keywords: cross-signature assurance criterion (CSAC); damage identification; frequency response function (FRF); model updating; simply supported beam; structural health monitoring.

PubMed Disclaimer

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
A simply supported beam under external loading.
Figure 2
Figure 2
Schematic layout of cross-signature assurance criterion (CSAC) indices between adjacent points.
Figure 3
Figure 3
Flowchart of the step-by-step damage identification method.
Figure 4
Figure 4
Finite element model of the simply supported steel beam.
Figure 5
Figure 5
Frequency response function (FRF) spectrum comparison between undamaged and damaged conditions, Case 3; (a) measurement points 2, 3 and (b) measurement points 5, 6.
Figure 6
Figure 6
Comparison of damage cases with respect to different frequency ranges; (a) frequency range 1; (b) frequency range 2; (c) frequency range 3; and (d) frequency range 4.
Figure 7
Figure 7
Damage identification results under different cases; (a) Case 1, (b) Case 2, (c) Case 3, and (d) Case 4.
Figure 8
Figure 8
(a) Iteration numbers of Case 2 for the convergence and comparison of the acceleration FRF curves before and after model updating; (b) Case 3, and (c) Case 4.
Figure 8
Figure 8
(a) Iteration numbers of Case 2 for the convergence and comparison of the acceleration FRF curves before and after model updating; (b) Case 3, and (c) Case 4.
Figure 9
Figure 9
Identification results of double damage with 5% noise.
Figure 10
Figure 10
The first layout of the load, beam elements, and sensors (a) with a gradual subdivision of elements as (b–d), respectively.
Figure 11
Figure 11
Identified values of damage in each element based on Figure 10; (a) damage indices of Figure 10a, (b) damage indices of Figure 10b, and (c) damage indices of Figure 10c.
Figure 12
Figure 12
Damage identification results after adjusting of measurement points.
Figure 13
Figure 13
Schematic drawing of the simply supported steel beam (mm).
Figure 14
Figure 14
(a) Configuration of accelerometers on the beam, (b) fixed end of the beam, (c) roller end of the beam, (d) impact hammer, and (e) damage simulation on the beam (Case 1).
Figure 15
Figure 15
Time history of impact force.
Figure 16
Figure 16
FRF spectrum of the undamaged beam in measurement Point 6.
Figure 17
Figure 17
First layout of load, elements, and sensors; (a) with the gradual subdivision of elements as (b,c).
Figure 18
Figure 18
FRF spectrum of measurement Point 6 between the undamaged and damaged beam (Case 1).
Figure 19
Figure 19
Identified values of damage (a) damage indices for Figure 17a, (b) damage indices for Figure 17b, and (c) damage indices for Figure 17c.
Figure 20
Figure 20
FRF spectrum of measurement Point 6 between the undamaged and damaged beam (Case 2).
Figure 21
Figure 21
Identified values of damages in each element based on Figure 10. (a) damage indices of Figure 10a, (b) damage indices of Figure 10b, and (c) damage indices of Figure 10c.
Figure 22
Figure 22
Damage indices of Figure 10d.
Figure 23
Figure 23
Damage indices versus the number of iterations.
See this image and copyright information in PMC

References

    1. Oskoui E.A., Taylor T., Ansari F. Method and monitoring approach for distributed detection of damage in multi-span continuous bridges. Eng. Struct. 2019;189:385–395. doi: 10.1016/j.engstruct.2019.02.037. - DOI
    1. Locke W., Sybrandt J., Redmond L., Safro I., Atamturktur S. Using drive-by health monitoring to detect bridge damage considering environmental and operational effects. J. Sound Vib. 2020;468:115088. doi: 10.1016/j.jsv.2019.115088. - DOI
    1. Zhou C., Wu Y., Cui G., Zhang A., Gao Y., Wang X., Ouyang J., Sun H., Liang Y., Liu Z., et al. Comprehensive measurement techniques and multi-index correlative evaluation approach for structural health monitoring of highway bridges. Measurement. 2020;152:107360. doi: 10.1016/j.measurement.2019.107360. - DOI
    1. Zhu X., Cao M., Ostachowicz W., Xu W. Damage Identification in Bridges by Processing Dynamic Responses to Moving Loads: Features and Evaluation. Sensors. 2019;19:463. doi: 10.3390/s19030463. - DOI - PMC - PubMed
    1. Yin T., Jiang Q., Yuen K. Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique. Eng. Struct. 2017;132:260–277. doi: 10.1016/j.engstruct.2016.11.035. - DOI

LinkOut - more resources