Damage detection in beam-like structures using static shear energy redistribution

doi:10.1007/s11709-022-0903-4

Frontiers of Structural and Civil Engineering

2022, Vol. 16

Issue (12): 1552-1564 https://doi.org/10.1007/s11709-022-0903-4

本期目录

Damage detection in beam-like structures using static shear energy redistribution

Xi PENG^1,², Qiuwei YANG^1,²(

)

¹. School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China
². Engineering Research Center of Industrial Construction in Civil Engineering of Zhejiang, Ningbo University of Technology, Ningbo 315211, China

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Abstract：

In this study, a static shear energy algorithm is presented for the damage assessment of beam-like structures. According to the energy release principle, the strain energy of a damaged element suddenly changes when structural damage occurs. Therefore, the change in the static shear energy is employed to determine the damage locations in beam-like structures. The static shear energy is derived from the spectral factorization of the elementary stiffness matrix and structural deflection variation. The advantage of using shear energy as opposed to total energy is that only a few deflection data points of the beam structure are required during the process of damage identification. Another advantage of the proposed approach is that damage detection can be performed without establishing a structural finite-element model in advance. The proposed technique is first validated using a numerical example with single, multiple, and adjacent damage scenarios. A channel steel beam and rectangular concrete beam are employed as experimental cases to further verify the proposed approach. The results of the simulation and experiment examples indicate that the proposed algorithm provides a simple and effective method for defect localization in beam-like structures.

Key words： damage detection beam structure strain energy static displacement variation energy damage index

收稿日期: 2022-06-21 出版日期: 2023-01-16

Corresponding Author(s): Qiuwei YANG

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2022, 16(12): 1552-1564.
Xi PENG, Qiuwei YANG. Damage detection in beam-like structures using static shear energy redistribution. Front. Struct. Civ. Eng., 2022, 16(12): 1552-1564.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-022-0903-4
https://academic.hep.com.cn/fsce/CN/Y2022/V16/I12/1552

Fig.1

Fig.2

Fig.3

Tab.1

Tab.2

Fig.4

Fig.5

Fig.6

Fig.7

damage case	mean of the damage indices for elements 1–9 ( $Δ Ω ¯ 1 − 9$ )	standard deviation of the damage indices for elements 1–9 ( $σ 1 − 9$ )	$Δ Ω 10 ″ − Δ Ω ¯ 1 − 9 − 3 ? σ 1 − 9$
scenario 1	0.1478	0.0423	0.0455 > 0
scenario 2	0.3468	0.0743	0.0451 > 0
scenario 3	0.5948	0.0862	0.3322 > 0
scenario 4	0.9288	0.0879	0.6326 > 0

Tab.3

damage case	mean of the damage indices for elements 11–20 ( $Δ Ω ¯ 11 − 20$ )	standard deviation of the damage indices for elements 11–20 ( $σ 11 − 20$ )	$Δ Ω 10 ″ − Δ Ω ¯ 11 − 20 − 3 ? σ 11 − 20$
scenario 1	−0.1305	0.0529	−0.053 < 0
scenario 2	−0.32	0.0783	0.164 > 0
scenario 3	−0.5355	0.0441	0.4072 > 0
scenario 4	−0.8392	0.0649	0.6771 > 0

Tab.4

damage case	mean of the damage indices for elements 1–5 ( $Δ Ω ¯ 1 − 5$ )	standard deviation of the damage indices for elements 1–5 ( $σ 1 − 5$ )	$Δ Ω 6 ″ − Δ Ω ¯ 1 − 5 − 3 ? σ 1 − 5$
case 5	0.3892	0.009	0.1512 > 0
case 6	1.3926	0.0478	0.7871 > 0

Tab.5

damage case	mean of the damage indices for elements 7–14 ( $Δ Ω ¯ 7 − 14$ )	standard deviation of the damage indices for elements 7–14 ( $σ 7 − 14$ )	$Δ Ω 6 ″ − Δ Ω ¯ 7 − 14 − 3 ? σ 7 − 14$
case 5	−0.0176	0.0558	0.0612 > 0
case 6	−0.1671	0.0867	0.3692 > 0

Tab.6

damage case	mean of the damage indices for elements 7–14 ( $Δ Ω ¯ 7 − 14$ )	standard deviation of the damage indices for elements 7–14 ( $σ 7 − 14$ )	$Δ Ω 15 ″ − Δ Ω ¯ 7 − 14 − 3 ? σ 7 − 14$
case 5	−0.0176	0.0558	0.0109 > 0
case 6	−0.1671	0.0867	0.2392 > 0

Tab.7

Fig.8

damage case	mean of the damage indices for elements 16–20 ( $Δ Ω ¯ 16 − 20$ )	standard deviation of the damage indices for elements 16–20 ( $σ 16 − 20$ )	$Δ Ω 15 ″ − Δ Ω ¯ 16 − 20 − 3 ? σ 16 − 20$
case 5	−0.3641	0.165	0.1187 > 0
case 6	−1.0845	0.0233	0.3482 > 0

Tab.8

Fig.9

number	mean of the damage indices for elements 1–11 ( $Δ Ω ¯ 1 − 11$ )	standard deviation of the damage indices for elements 1–11 ( $σ 1 − 11$ )	$Δ Ω 12 ″ − Δ Ω ¯ 1 − 11 − 3 ? σ 1 − 11$
element 12	0.3447	0.0408	0.0969 > 0

Tab.9

number	mean of the damage indices for elements 14−20 ( $Δ Ω ¯ 14 − 20$ )	standard deviation of the damage indices for elements 14−20 ( $σ 14 − 20$ )	$Δ Ω 13 ″ − Δ Ω ¯ 14 − 20 − 3 ? σ 14 − 20$
element 13	−0.5098	0.0250	0.1164 > 0

Tab.10

Tab.11

Tab.12

number	mean of the damage indices for elements 1−3 ( $Δ Ω ¯ 1 − 3$ )	standard deviation of the damage indices for elements 1−3 ( $σ 1 − 3$ )	$Δ Ω 4 ″ − Δ Ω ¯ 1 − 3 − 3 ? σ 1 − 3$
segment 4	7.0311 × 10⁻⁵	2.1264 × 10⁻⁶	8.4332 × 10⁻⁵ > 0

Tab.13

number	mean of the damage indices for elements 6–8 ( $Δ Ω ¯ 6 − 8$ )	standard deviation of the damage indices for elements 6–8 ( $σ 6 − 8$ )	$Δ Ω 5 ″ − Δ Ω ¯ 6 − 8 − 3 ? σ 6 − 8$
segment 5	−5.7556 × 10⁻⁵	4.8668 × 10⁻⁶	2.5088 × 10⁻⁵ > 0

Tab.14

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