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SCIENCE CHINA Technological Sciences, Volume 60 , Issue 8 : 1188-1196(2017) https://doi.org/10.1007/s11431-016-0786-7

A Fourier spectrum-based strain energy damage detection method for beam-like structures in noisy conditions

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  • ReceivedOct 20, 2016
  • AcceptedJan 9, 2017
  • PublishedFeb 14, 2017

Abstract

In this paper, the Fourier spectrum-based strain energy damage detection method for beam-like structures is proposed based on the discrete Fourier transform. The classical strain energy damage detection method localizes damage by the comparison of the strain energy between the intact and inspected structures. The evaluation of the 2nd-order derivative term in the strain energy plays a crucial part in the comparison. The classical methods are mostly based on a numerical derivative estimation for this term. The numerical derivative, however, introduces additional disturbances into damage indications. To address this problem, a discrete Fourier transform-based strain energy is proposed with the emphasis of enhancing the performance in noisy condition. The validations conducted on the simulated and experimental data show that the developed method is effective enough for composite beam damage detection in noisy environments.


Funded by

National Natural Science Foundation of China(51405369 ,&, 51421004)

National Key Basic Research Program of China(2015CB057400)

National Natural Science Foundation of Shaanxi Province(2016JQ5049)

and the Postdoctoral Science Foundation of Shaanxi Province. Special acknowledgements should be addressed to Prof. A. Katunin

who shared the benchmark in the website.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51405369 & 51421004), the National Key Basic Research Program of China (Grant No. 2015CB057400), the National Natural Science Foundation of Shaanxi Province (Grant No. 2016JQ5049), and the Postdoctoral Science Foundation of Shaanxi Province. Special acknowledgements should be addressed to Prof. A. Katunin, who shared the benchmark in the website.


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  • Figure 1

    The differences between the ND-based and the DFT-based estimations for spatial derivatives.

  • Figure 2

    (Color online) Comparison of different window functions.

  • Figure 3

    k-domain filtering flowchart.

  • Figure 4

    (Color online) The DIs for the single-crack 1st–3rd order mode shapes (from left to right). (a) Based on the ND-SE; (b) based on the DFT-SE.

  • Figure 5

    (Color online) The DIs for the multiple-crack 1st–3rd order mode shapes (from left to right). (a) Based on the ND-SE; (b) based on the DFT-SE.

  • Figure 6

    (Color online) The noise immunity test via case #A3 at noise levels SNR=60, 50, 40 dB (from left to right). (a) DIs based on the ND-SE; (b) DIs based on the DFT-SE.

  • Figure 7

    (Color online) The noise immunity test via case #A4 at noise levels SNR=60, 50, 40 dB (from left to right). (a) DIs based on the ND-SE; (b) DIs based on the DFT-SE.

  • Figure 8

    (Color online) Comparison of node density effects. (a) DI based on the ND-SE; (b) DI based on the DFT-SE. The corresponding number of nodes: 300, 150, 50, 30 (from left to right) for each row.

  • Figure 9

    (Color online) Damage localization for single-crack structure. (a) ND-SE based DIs for the 1st–4th mode shapes; (b) DFT-SE based DIs for the 1st–4th mode shapes.

  • Figure 10

    (Color online) Damage localization for multiple-crack structure. (a) ND-SE based DIs of the 1st–3rd mode shapes; (b) DFT-SE based DIs of the 1st–3rd mode shapes.

  • Table 1   Damage scenarios used in simulations

    Case

    Mode

    Lc (mm)

    d (mm)

    SNR (dB)

    #A1

    1st–3rd

    300

    4

    0

    #A2

    1st–3rd

    200, 300

    4, 4

    0

    #A3

    1st

    200

    4

    40, 50, 60

    #A4

    1st

    200, 300

    4, 4

    40, 50, 60

  • Table 2   Damage scenarios in experiments

    Data name

    Lc (mm)

    Mode shape

    Res01

    1st–4th

    Res05

    150

    1st–4th

    Belka1

    50,119

    1st–3rd

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