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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (4) : 965-980     https://doi.org/10.1007/s11709-019-0530-x
RESEARCH ARTICLE
Finite element model updating of a large structure using multi-setup stochastic subspace identification method and bees optimization algorithm
Reza KHADEMI-ZAHEDI1(), Pouyan ALIMOURI2
1. Institute of Structural Mechanics, Bauhaus-Universit?t Weimar, Weimar 99423, Germany
2. Mechanical Engineering Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran
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Abstract

In the present contribution, operational modal analysis in conjunction with bees optimization algorithm are utilized to update the finite element model of a solar power plant structure. The physical parameters which required to be updated are uncertain parameters including geometry, material properties and boundary conditions of the aforementioned structure. To determine these uncertain parameters, local and global sensitivity analyses are performed to increase the solution accuracy. An objective function is determined using the sum of the squared errors between the natural frequencies calculated by finite element method and operational modal analysis, which is optimized using bees optimization algorithm. The natural frequencies of the solar power plant structure are estimated by multi-setup stochastic subspace identification method which is considered as a strong and efficient method in operational modal analysis. The proposed algorithm is efficiently implemented on the solar power plant structure located in Shahid Chamran university of Ahvaz, Iran, to update parameters of its finite element model. Moreover, computed natural frequencies by numerical method are compared with those of the operational modal analysis. The results indicate that, bees optimization algorithm leads accurate results with fast convergence.

Keywords operational modal analysis      solar power plant structure      multi-setup stochastic subspace      bees optimization algorithm      sensitivity analysis     
Corresponding Authors: Reza KHADEMI-ZAHEDI   
Just Accepted Date: 18 March 2019   Online First Date: 16 May 2019    Issue Date: 10 July 2019
 Cite this article:   
Reza KHADEMI-ZAHEDI,Pouyan ALIMOURI. Finite element model updating of a large structure using multi-setup stochastic subspace identification method and bees optimization algorithm[J]. Front. Struct. Civ. Eng., 2019, 13(4): 965-980.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0530-x
http://journal.hep.com.cn/fsce/EN/Y2019/V13/I4/965
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Reza KHADEMI-ZAHEDI
Pouyan ALIMOURI
Fig.1  Present research procedure
Fig.2  Finite element model of solar structure
frequency finite element method (rad/s)
first 39.630
second 43.439
third 49.423
fourth 64.252
fifth 72.118
Tab.1  Solar structure frequencies obtained by finite element method
Fig.3  Five first mode shapes of solar structure. (a) First mode shape; (b) second mode shape; (c) third mode shape; (d) fourth mode shape; (e) fifth mode shape
item parameter symbol (unit) lower limit upper limit
1 legs density rl (kg/m3) 7400 8000
2 legs Young’s modulus El (Gpa) 180 210
3 legs Poisson’s ratio nl ([]) 0.1 0.3
4 legs length Ll (mm) 1800 2200
5 legs thickness tl (mm) 1 4
6 legs cross- section area Al (mm2) 9 25
7 deck members density rd (kg/m3) 7400 8000
8 deck members Young’s modulus Ed (Gpa) 180 210
9 deck members Poisson’s ratio nd ([]) 0.1 0.3
10 deck members thickness td (mm) 1 4
11 deck members cross- section area Ad (mm2) 1 9
12 stair members density rb (kg/m3) 7400 8000
13 stair members Young’s modulus Eb (Gpa) 180 210
14 stair members Poisson’s ratio nb ([]) 0.1 0.3
15 stair members thickness tb (mm) 1 3
16 stair members cross- section area Ab (mm2) 1 4
17 solar panel density rs (kg/m3) 1500 3000
18 solar panels Young’s modulus Es (Gpa) 60 90
19 solar panels Poisson’s ratio ns ([]) 0.1 0.3
20 solar panels thickness ts (mm) 30 100
21 sign boards density rsi (kg/m3) 1800 2200
22 sign boards Young’s modulus Esi (Gpa) 30 50
23 sign boards Poisson’s ratio nsi ([]) 0.1 0.3
24 sign boards thickness tsi (mm) 10 40
25 transformer 1 mass M1(kg) 10 20
26 transformer 2 mass M2(kg) 20 50
27 transformer 3 mass M3(kg) 10 20
28 transformer 4 mass M4(kg) 20 50
29 transformer 5 mass M5(kg) 10 20
Tab.2  Investigated parameters for sensitivity analysis of the structure
Fig.4  Results obtained from local sensitivity index
Fig.5  Results obtained from GSI
item parameter symbol (unit)
1 legs density rl (kg/m3)
2 legs Young’s modulus El (Gpa)
3 legs length Ll (mm)
4 legs thickness tl (mm)
5 legs cross- section area Al (mm2)
6 deck members density rd (kg/m3)
7 deck members Young’s modulus Ed (Gpa)
8 deck members thickness td (mm)
9 deck members cross-section area Ad (mm2)
10 solar panel density rs (kg/m3)
11 solar panel Young’s modulus Es (Gpa)
12 solar panel thickness ts (mm)
Tab.3  Sensitive parameters of the solar structure
Fig.6  Reference sensors positions
Fig.7  (a) Method of mounting accelerometers to the structure; (b) experimental tests equipment; (c) general view of the experiment
Fig.8  Sample of acceleration diagram corresponding to solar structure under random excitation
Fig.9  Multi-setup SSI technique algorithm
Fig.10  Stabilization diagram for multi-setup SSI technique in y direction
Fig.11  Five first mode shapes obtained from multi-setup SSI method. (a) First mode shape; (b) second mode shape; (c) third mode shape; (d) fourth mode shape; (e) fifth mode shape
item frequency (rad/s) relative error
1 34.470 14.970%
2 37.178 16.841%
3 42.606 16.000%
4 56.027 14.680%
5 62.593 15.217%
Tab.4  Natural frequencies calculated by SSI method and their relative error compared with finite element method
Fig.12  Flowchart of bees optimization algorithm
Fig.13  Convergence diagram of bees’ optimization algorithm
analysis type value
number of calculated objective functions 47000
neighborhood radius 0.01
Nt1 30
Nt2 20
nt1 15
nt2 10
Nt 100
Tab.5  Control parameters of bees’ optimization algorithm
item natural frequencies of updated finite elemenrt model relative error
1 34.485 0.043%
2 37.193 0.040%
3 42.645 0.091%
4 56.074 0.084%
5 62.554 0.062%
Tab.6  The comparison of natural frequencies (rad/s) obtained from structure finite elemenrt model updating method and their relative errors
item symbol (unit) parameter value
1 rl (kg/m3) 7760
2 El (Gpa) 191
3 Ll (mm) 2103
4 tl (mm) 3.6
5 Al (mm2) 21.16
6 rd (kg/m3) 7561
7 Ed (Gpa) 198
8 td (mm) 1.85
9 Ad (mm2) 4.41
10 rs (kg/m3) 2300
11 Es (Gpa) 73
12 ts (mm) 63
Tab.7  Optimized parameters of the solar structure
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