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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (1) : 92-108     https://doi.org/10.1007/s11709-016-0379-1
RESEARCH ARTICLE
A combination of damage locating vector method (DLV) and differential evolution algorithm (DE) for structural damage assessment
T. NGUYEN-THOI1,3(), A. TRAN-VIET2,3, N. NGUYEN-MINH1,3, T. VO-DUY1,3, V. HO-HUU1,3
1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Hochiminh City, Vietnam
3. Faculty of Civil Engineering, Ton Duc Thang University, Hochiminh City, Vietnam
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Abstract

In this study, a two-stage method is presented for identifying multiple damage scenarios. In the first stage, the damage locating vector (DLV) method using normalized cumulative energy (nce) is employed for damage localization in structures. In the second stage, the differential evolution algorithm (DE) is used for damage severity of the structures. In addition, in the second stage, a modification of an available objective function is made for handing the issue of symmetric structures. To verify the effectiveness of the present technique, numerical examples of a 72-bar space truss and a one-span steel portal frame are considered. In addition, the effect of noise on the performance of the identification results is also investigated. The numerical results show that the proposed combination gives good assessment of damage location and extent for multiple structural damage cases.

Keywords damage assessment      damage locating vector method (DLV)      differential evolution (DE)      multiple damage location assurance criterion (MDLAC)      mode shape error function     
Corresponding Author(s): T. NGUYEN-THOI   
Online First Date: 13 April 2017    Issue Date: 08 March 2018
 Cite this article:   
T. NGUYEN-THOI,A. TRAN-VIET,N. NGUYEN-MINH, et al. A combination of damage locating vector method (DLV) and differential evolution algorithm (DE) for structural damage assessment[J]. Front. Struct. Civ. Eng., 2018, 12(1): 92-108.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-016-0379-1
http://journal.hep.com.cn/fsce/EN/Y2018/V12/I1/92
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T. NGUYEN-THOI
A. TRAN-VIET
N. NGUYEN-MINH
T. VO-DUY
V. HO-HUU
Fig.1  A flow chart for implementation of differential evolution algorithm
parameter DE PSO
mutation strategy DE / Rand / 1
crossover scheme binomial
population size (NP) 20 (two damaged elements)
30 (three damaged elements)
20 (two damaged elements)
30 (three damaged elements)
mutation constant (F) 0.5
crossover constant (CR) 1.0
maximum number of iterations 200 200
cognitive parameters (C1) - 1.49
social parameters (C2) - 1.49
inertia range - [0.1,1.1]
tolerance 1e-5 1e-5
Tab.1  Parameters of the DE and PSO algorithms
property/unit value
E (Young’s modulus)/(N·m–2) 6.98e+10
ρ (mass density)/(kg·m–3) 2770
add mass/kg 2270
Tab.2  Material properties of the 72-bar space truss
element group cross – sectional area element group cross – sectional area
1–4 2.854 37–40 16.328
5–12 8.301 41–48 8.299
13–16 0.645 49–52 0.645
17–18 0.645 53–54 0.645
19–22 8.202 55–58 15.048
23–30 7.043 59–66 8.268
31–34 0.645 67–70 0.645
35–36 0.645 71–72 0.645
Tab.3  Cross-sectional areas (cm2) for 16 element groups of the 72-bar space truss
Case 1 case 2
element No. extent (%) element No. extent (%)
7 10 11 10
9 30 22 20
52 25
Tab.4  Two damage cases for the 72-bar space truss
mode Kaveh and Zolghadr [50] undamaged model
(present)
damaged model (present)
case 1 case 2
1 4.000 4.0003 3.9798 3.9702
2 4.000 4.0003 3.9949 3.9977
3 6.004 6.0002 5.9532 5.9904
4 6.2491 6.2496 6.2425 6.2306
5 8.9726 8.9728 8.9080 8.9378
Tab.5  First five frequencies (Hz) of the 72-bar space truss for undamaged and damaged structures
DE PSO
No. damaged element and damage extent No. of
iterations
damaged element and damage extent No. of
iterations
7 9 7 9
1 10 30 46 10 30 53
2 10 30 44 10 30 70
3 10 30 48 10 30 55
4 10 30 42 10 30 60
5 10 30 44 10 30 47
6 10 30 48 10 30 50
7 10 30 51 10 30 63
8 10 30 44 10 30 56
9 10 30 41 10 30 58
10 10 30 49 10 30 53
average 10 30 45.7 10 30 56.5
Tab.6  Damage severity assessment results of the DE and PSO for case 1 of the 72-bar space truss
DE PSO
No. damaged element and damage extent No. of iterations damaged element and damage extent No. of iterations
7 9 7 9
1 30.02 10.02 30 30.00 10.00 47
2 30.02 10.00 27 10.00 30.00 33
3 9.95 29.93 38 10.00 30.00 42
4 30.02 10.00 43 30.00 10.00 37
5 10.06 30.08 29 10.02 30.01 38
6 30.06 10.03 40 30.00 10.01 33
7 9.93 29.97 32 10.00 30.00 36
8 29.94 9.95 31 10.06 30.08 50
9 10.00 30.00 42 10.00 30.00 34
10 10.09 30.06 26 10.00 30.00 34
average 20.01 20.00 33.8 16.01 24.01 38.4
Tab.7  Damage severity assessment results using the MDLAC function for case 1 of the 72-bar space truss
Fig.2  A sketch of a 72-bar space truss
Fig.3  nce for all elements of the 72-bar space truss for case 1 where elements 7 and 9 are damaged
Fig.4  Convergence history of the DE and PSO for damage severity estimation in case 1 of the 72-bar space truss. (a) DE; (b) PSO
DE PSO
No. damaged element and damage extent No. of
iterations
damaged element and damage extent No. of
iterations
11 22 52 11 22 52
1 10 20 25 79 10 20 25 93
2 10 20 25 77 10 20 25 78
3 10 20 25 75 10 20 25 109
4 10 20 25 71 10 20 25 98
5 10 20 25 77 10 20 25 93
6 10 20 25 79 10 20 25 93
7 10 20 25 64 10 20 25 96
8 10 20 25 78 10 20 25 60
9 10 20 25 77 10 20 25 83
10 10 20 25 76 10 20 25 121
average 10 20 25 75.3 10 20 25 92.4
Tab.8  Damage severity assessment results of the DE and PSO for case 2 of the 72-bar space truss
Fig.5  nce of all elements of the 72-bar space truss for case 2 where elements 11, 22 and 52 are damaged
Fig.6  nce of all elements of the 72-bar space truss for case 2 where elements 11, 22 and 52 are damaged
Fig.7  Convergence history of the DE and PSO for damage severity estimation in case 2 of 72-bar space truss. (a) DE; (b) PSO
case 1 case 2
element No. extent (%) element No. extent (%)
4 15 4 25
25 25 19 10
25 20
Tab.9  Two damage cases for the one-span steel portal frame
mode Hao and Xia [39] undamaged model
(present)
damaged model (present)
case 1 case 2
1 4.69 4.69 4.68 4.67
2 18.22 18.23 18.16 18.16
3 28.93 28.95 28.59 28.54
4 31.48 31.49 31.24 31.20
5 64.53 64.57 64.19 63.92
Tab.10  First five frequencies (Hz) of the one-span steel portal frame for undamaged and damaged structures
Fig.8  A sketch of a one-span steel portal frame
refined mesh 1
(mesh size of 60)
refined mesh 2
(mesh size of 90)
element No. extent (%) element No. extent (%)
7 15 10 15
8 15 11 15
49 25 22 15
50 25 73 25
74 25
75 25
Tab.11  Damage cases of refined meshes for the one-span steel portal frame
DE PSO
No. damaged element and damage extent No. of
iterations
damaged element and damage extent No. of
iterations
4 25 4 25
1 15 20 49 15 20 63
2 15 20 51 15 20 63
3 15 20 48 15 20 51
4 15 20 43 15 20 58
5 15 20 52 15 20 47
6 15 20 47 15 20 63
7 15 20 43 15 20 62
8 15 20 52 15 20 52
9 15 20 47 15 20 52
10 15 20 46 15 20 46
average 15 20 47.8 15 20 55.7
Tab.12  Damage severity assessment results of the DE and PSO for case 1 of the one-span steel portal frame
Fig.9  nce for all elements of the one-span steel portal frame for case 1 where elements 4 and 25 are damaged
Fig.10  nce for all elements of the one-span steel portal frame for case 1 with various meshes. (a) Initial mesh; (b) refined mesh 1; (c) refined mesh 2
Fig.11  Convergence history of the DE and PSO for damage severity estimation in case 1 of the one-span steel portal frame. (a) DE; (b) PSO
DE PSO
No. damaged element and damage extent No. of
iterations
damaged element and damage extent No. of
iterations
4 19 25 4 19 25
1 25 10 20 59 25 10 20 83
2 25 10 20 69 25 10 20 69
3 24.94 10.87 20 58 25 10 20 63
4 25 10 20 60 25 10 20 73
5 25 10 20 60 25 10 20 67
6 25 10 20 59 25 10 20 64
7 25 10 20 74 25 10 20 66
8 25.07 10.28 20 58 25 10 20 78
9 25 10 20 53 25 10 20 67
10 25 9.98 20 61 25 10 20 72
average 25 10.11 20 59 25 10 20 70.2
Tab.13  Damage severity assessment results of the DE and PSO for case 2 of the one-span steel portal frame
Fig.12  nce of all element of the one-span steel portal frame for case 2 where elements 4, 19 and 25 are damaged
Fig.13  Convergence history of optimization algorithms for damage severity estimation in case 2 of the one-span steel portal frame. (a) DE; (b) PSO
DE PSO No. of iterations
No. damaged element and damage extent No. of iterations damaged element and damage extent
7 9 7 9
1 10.03 30.05 35 10.01 30.03 48
2 10.03 30.05 35 10.01 30.03 42
3 10.03 30.05 39 10.01 30.03 42
4 10.03 30.05 39 10.01 30.03 42
5 10.32 30.52 62 10.01 30.03 45
6 10.03 30.05 42 10.01 30.03 42
7 10.03 30.05 41 10.01 30.03 52
8 10.03 30.05 35 10.01 30.03 59
9 10.03 30.05 36 10.01 30.03 55
10 10.03 30.05 38 10.01 30.03 42
average 10.06 30.10 40.2 10.01 30.03 46.9
Tab.14  Damage severity assessment results of the DE and PSO for case 1 of the 72-bar space truss with considering measurement noise (1% for frequency and 5% for mode shape)
Fig.14  nce for all elements of the 72-bar space truss for case 1 under effect of noise (ηf = 1%, ηφ = 3%)
Fig.15  nce for all elements of the 72-bar space truss for case 1 under effect of noise (ηf = 1%, ηφ = 5%)
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