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Research on structural damage identification of bridge engineering based on dynamic parameters

Qianxue Liang

Qianxue Liang

Guangxi Transportation Science & Technology Group Co., LtdNanning, China
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Liang, Qianxue
  
19 mar 2025
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Pubblicato online: 19 mar 2025
Ricevuto: 24 ott 2024
Accettato: 07 feb 2025
DOI: https://doi.org/10.2478/amns-2025-0483
Parole chiave
© 2025 Qianxue Liang, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

RBF neural network structure
RBF neural network structure

Figure 2.

Basic steps of structural damage identification based on neural network
Basic steps of structural damage identification based on neural network

Figure 3.

Analysis diagram of training results
Analysis diagram of training results

Figure 4.

Analysis Diagram of Training Process
Analysis Diagram of Training Process

Figure 5.

Analysis diagram of training results
Analysis diagram of training results

Figure 6.

Analysis diagram of training results
Analysis diagram of training results

Figure 7.

Analysis diagram of training results
Analysis diagram of training results

Figure 8.

Parameter sensitivity analysis
Parameter sensitivity analysis

Figure 9.

Analysis diagram of training results
Analysis diagram of training results

Bridge damage condition

Operating condition Degree of damage Damage position
1 15 Unit 14
2 30 Unit 14
3 45 Unit 14
4 15 Unit 6, Unit23
5 15, 30 Unit 6, Unit23
6 15, 30, 45 Unit 6, 14, 23

Curvature frequency combination test set input

Fifth curvature Sixth curvature Seventhr curvature Fifth frequency Sixth frequency Seventh frequency
5.63E-13 8.75E-09 -2.33E-08 0.03247178 0.03428187 0.08173032
6.38E-13 8.75E-09 -2.33E-08 0.03246915 0.0342769 0.08172591
7.29E-13 8.75E-09 -2.33E-08 0.03246527 0.03426931 0.08171919
8.37E-13 1.46E-08 -2.33E-08 0.03245865 0.0342561 0.08170754
6.15E-13 8.75E-09 -2.33E-08 0.03247241 0.0342852 0.08173421
7.50E-13 8.75E-09 -2.33E-08 0.03247052 0.03428417 0.0817341
9.12E-13 1.46E-08 -2.33E-08 0.03246779 0.03428294 0.081734
1.16E-12 1.46E-08 -2.33E-08 0.03246338 0.03428143 0.08173379

Neural network training results

Operating condition Damage position Target output Training output
1 6, 14, 23 0, 0.15, 0 0.0019, 0.1566, 0.0021
2 6, 14, 23 0, 0.30, 0 0.0033, 0.3083, 0.0028
3 6, 14, 23 0, 0.45, 0 0.0028, 0.4574, 0.0026
4 6, 14, 23 0.15, 0, 0.15 0.1557, 0.0016, 0.1562
5 6, 14, 23 0.15, 0, 0.3 0.1533, 0.0036, 0.3061
6 6, 14, 23 0.3, 0.3, 0.45 0.3022, 0.3068, 0.4571

Unit 6 damage operating condition output error

Damage operating condition Target output Training output Error Error ratio
4 0.15 0.1562 0.0062 4.13%
5 0.3 0.3061 0.0061 2.03%
6 0.45 0.4571 0.0071 1.58%

Training results of arch bridge model

Degree of damage Tag value Actual output
0.25 0 0
0.35 1 1
0.45 2 2
0.55 3 3
0.65 4 4
0.25 0 0
0.35 1 2
0.45 2 2
0.55 3 3
0.65 4 4

Parameter correction

Bridge model Elastic modulus E (MPa) Density p (kg/m3)
Prefix 3.54*104 2558
Corrected 3.87*104 2506

Training results

Degree of damage Tag value Actual output
0.25 0 1
0.35 1 1
0.45 2 2
0.55 3 2
0.65 4 4
0.25 0 0
0.35 1 1
0.45 2 2
0.55 3 3
0.65 4 4

First ten order frequencies of arch bridge

First order Second order Third order Fourth order Fifth order
0 2.45E-06 1.51E-05 4.04E-05 0.03247
9.45E-08 2.61E-06 1.54E-05 4.10E-05 0.03247
5.57E-07 2.51E-06 1.58E-05 4.18E-05 0.03247
0 2.58E-06 1.63E-05 4.28E-05 0.03246
5.78E-07 2.67E-06 1.72E-05 4.48E-05 0.03245
4.94E-07 2.45E-06 1.51E-05 4.01E-05 0.03247
4.10E-07 2.52E-06 1.65E-05 4.15E-05 0.03246
2.84E-07 2.71E-06 1.75E-05 4.31E-05 0.03246
0.03428 0.08173 0.08853 0.13198 0.23312
0.03428 0.08173 0.08848 0.13192 0.23312
0.03427 0.08172 0.08842 0.13183 0.23311
0.03426 0.08171 0.08834 0.13169 0.23309

Label value and actual output value comparison

Degree of damage Tag value Actual output
0.25 0 0
0.35 1 1
0.45 2 2
0.55 3 3
0.65 4 4
0.25 0 0
0.35 1 1
0.45 2 2
0.55 3 3
0.65 4 4

Corrected and measured frequency

Test span Exponent Vibration frequency (Hz) Frequency error (Fc-Fe/Fe/Fe)/Fe Damping ratio(%)
Measured Fe Computed Fc
Span 3 1 3.759 3.569 5.05% 3.268
2 12.668 12.531 1.08%

Test set of curvature input items

Fifth Sixth seventh Eighth Ninth Tenth
5.63E-13 8.75E-09 -2.33E-08 -1.72E-08 1.92E-12 7.32E-11
6.38E-13 8.75E-09 -2.33E-08 -1.95E-08 1.92E-12 7.38E-11
7.29E-13 8.75E-09 -2.33E-08 -1.95E-08 1.95E-12 7.50E-11
8.37E-13 1.46E-08 -2.33E-08 -1.92E-08 1.95E-12 7.58E-11
6.15E-13 8.75E-09 -2.33E-08 -1.81E-08 1.87E-12 7.35E-11
7.50E-13 8.75E-09 -2.33E-08 -1.77E-08 1.92E-12 7.43E-11
9.12E-13 1.46E-08 -2.33E-08 -1.81E-08 1.90E-12 7.55E-11
1.16E-12 1.46E-08 -2.33E-08 -1.84E-08 1.95E-12 7.70E-11
5.51E-13 8.75E-09 -2.33E-08 -1.77E-08 1.84E-12 7.20E-11
6.10E-13 8.75E-09 -2.33E-08 -1.81E-08 1.84E-12 7.27E-11

Input vectors of frequency combination test set

A B C D E F
0.032431 0.807294 0.996617 0.946447 0.131961 0.10116
0.032428 0.807298 0.996617 9.597352 0.131895 0.101218
0.032423 0.807306 0.996616 9.603805 0.131794 0.101306
0.032416 0.807319 0.996615 9.612078 0.131618 0.101466
0.032432 0.807289 0.996616 9.619341 0.131951 0.101164
0.03243 0.80729 0.996615 9.59507 0.13188 0.101222
0.032427 0.807293 0.996614 9.599349 0.131781 0.101306
0.032422 0.807294 0.996612 9.60444 0.131621 0.101449
0.032432 0.807289 0.996617 9.607996 0.131934 0.101161
0.03243 0.80729 0.996616 9.590933 0.13185 0.101218

Fixed and measured frequency

Test span Exponent Vibration frequency (Hz) Frequency error (Fc-Fe/Fe/Fe)/Fe Damping ratio(%)
Measured Fe Computed Fc
Span 3 1 3.759 3.427581 8.82% 3.268
2 12.668 12.066219 4.75%
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