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Frontiers of Structural and Civil Engineering

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ISSN 2095-2449(Online)

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Front. Struct. Civ. Eng.    2024, Vol. 18 Issue (7) : 1066-1083    https://doi.org/10.1007/s11709-024-1084-0
Design parameter optimization method for a prestressed steel structure driven by multi-factor coupling
Guo-Liang SHI1,2, Zhan-Sheng LIU1,2(), De-Chun LU1,2, Qing-Wen ZHANG1,2, Majid DEZHKAM1,2, Ze-Qiang WANG3
1. Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100124, China
2. The Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China
3. Beijing Building Construction Research Institute Co., Ltd., Beijing 100039, China
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Abstract

To achieve efficient structural design, it is crucial to reduce the cost of materials while ensuring structural safety. This study proposes an optimization method for design parameters (DPs) in a prestressed steel structure driven by multi-factor coupling. To accomplish this, a numerical proxy model of prestressed steel structures is established with integration of DPs and mechanical parameters (MPs). A data association-parameter analysis-optimization selection system is established. A correlation between DPs and MPs is established using a back propagation (BP) neural network. This correlation provides samples for parameter analysis and optimization selection. MPs are used to characterize the safety of the structure. Based on the safety grade analysis, the key DPs that affect the mechanical properties of the structure are obtained. A mapping function is created to match the MPs and the key DPs. The optimal structural DPs are obtained by setting structural materials as the optimization objective and safety energy as the constraint condition. The theoretical model is applied to an 80-m-span gymnasium and verified with a scale test physical model. The MPs obtained using the proposed method are in good agreement with the experimental results. Compared with the traditional design method, the design cycle can be shortened by more than 90%. Driven by the optimal selection method, a saving of more than 20% can be achieved through reduction of structural material quantities. Moreover, the cross-sectional dimensions of radial cables have a substantial influence on vertical displacement. The initial tension and cross-sectional size of the upper radial cable exhibit the most pronounced impact on the stress distribution in that cable. The initial tension and cross-sectional size of the lower radial cable hold the greatest sway over the stress distribution in that cable.
Keywords structure design      association relationship      performance analysis      optimum selection      experimental verification     
Corresponding Author(s): Zhan-Sheng LIU   
Just Accepted Date: 11 June 2024   Online First Date: 04 July 2024    Issue Date: 06 August 2024
 Cite this article:   
Guo-Liang SHI,Zhan-Sheng LIU,De-Chun LU, et al. Design parameter optimization method for a prestressed steel structure driven by multi-factor coupling[J]. Front. Struct. Civ. Eng., 2024, 18(7): 1066-1083.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-024-1084-0
https://academic.hep.com.cn/fsce/EN/Y2024/V18/I7/1066
Fig.1  Multi-factor coupling driven parameter optimization architecture.
Fig.2  A diagram of neural network structure.
Fig.3  The process of establishing parameter association relationship.
Fig.4  The structure’s mechanical performance analysis process.
Fig.5  GA-based optimum selection of structure DPs.
Fig.6  Structure style of the gymnasium (① upper radial cable, ② lower radial cable, ③ inner vertical cable, ④ outer vertical cable, ⑤ upper inner ring beam, ⑥ lower inner ring beam, ⑦ flying column, ⑧ outer ring beam, ⑨ outer column).
Parameter type Value
Cable number 10, 12
Upper radial cable diameter (mm) 60, 70, 80, 90, 100
Lower radial cable diameter (mm) 60, 70, 80, 90, 100
Vertical cable diameter (mm) 30, 40, 50
Initial tension of upper radial cable (kN) 800, 850, 900, 950, 1000
Initial tension of lower radial cable (kN) 800, 850, 900, 950, 1000
Initial tension of vertical cable (kN) 200, 250, 300
Tab.1  A table of values assigned to DPs
Fig.7  Impacts of different numbers of hidden layer neurons on the iteration number.
Fig.8  Comparison between vertical displacement of model output and vertical displacement of FEM analysis (partial sample).
Fig.9  Comparison between upper radial cable stress of model output and that of FEM analysis (partial sample).
Fig.10  Comparison of lower radial cable stress from model output and lower radial cable stress from FEM analysis (partial sample).
Limiting condition Loading condition number Loading condition
Ultimate limit state Loading Condition 1 1.3 × (constant load + prestress) + 1.5 × live load
Loading Condition 2 1.3 × (constant load + prestress) + 1.5 × wind load
Serviceability limit state Loading Condition 3 1.0 × (constant load + prestress) + 1.0 × live load
Loading Condition 4 1.0 × (constant load + prestress) + 1.0 × wind load
Tab.2  Load combination cases
Fig.11  Comparison of vertical displacement obtained by the model with that of FEM analysis (partial samples): (a) comparison under the action of Loading Condition 1; (b) comparison under the action of Loading Condition 3.
Fig.12  Comparison of upper radial cable stress obtained by the model with that of FEM analysis (partial samples): (a) comparison under the action of Loading Condition 1; (b) comparison under the action of Loading Condition 3.
Fig.13  Comparison of lower radial cable stress obtained by the model with that of FEM analysis (partial samples): (a) comparison under the action of Loading Condition 1; (b) comparison under the action of Loading Condition 3.
Parameter type Structural safety rating Parameter range
Vertical displacement A [?212.5 mm, ?150 mm)
B [?275 mm, ?212.5 mm)
C [?337.5 mm, ?275 mm)
D [?400 mm, ?337.5 mm]
Upper radial cable stress A [200 MPa,275 MPa)
B [275 MPa,350 MPa)
C [350 MPa,425 MPa)
D [425 MPa,500 MPa]
Lower radial cable stress A [0 MPa,50 MPa)
B [50 MPa,100 MPa)
C [100 MPa,150 MPa)
D [150 MPa,200 MPa]
Tab.3  Classification of MPs
Fig.14  Influence degrees of DPs on MPs.
DP Value range
Upper radial cable diameter [60 mm,100 mm]
Lower radial cable diameter [60 mm,100 mm]
Constructional cable diameter [30 mm,50 mm]
Tab.4  Optimal selection range of DPs
Fig.15  Relationship between MPs and key DPs: (a) relationship between DPs and vertical displacement; (b) relationship between DPs and upper radial cable stress; (c) relationship between DPs and lower radial cable stress.
MP Intercept Upper radial cable diameter Lower radial cable diameter Constructional cable diameter Goodness of fit
Vertical displacement ?381.09728 2.75068 ?0.1041 ?1.10263 0.97502
Upper radial cable stress 858.4 ?8.036 ?0.424 3.52 0.96778
Lower radial cable stress 188.00533 1.38867 ?2.7194 ?0.3613 0.97216
Tab.5  The properties and goodness of fit for MPs and DPs
Fig.16  Parameter optimization process driven by GA.
Cable type Diameter of section (mm) Corresponding initial tension (kN)
Upper radial cable 70 850
Lower radial cable 60 800
Constructional cable 30 200
Tab.6  DPs corresponding to the optimum solution
MP Vertical displacement (mm) Upper radial cable stress (MPa) Lower radial cable stress (MPa)
FEM analysis result ?228.2 378.1 121.9
Correlation fitting results ?227.6 376.0 125.7
Tab.7  MPs corresponding to the optimum solution
Fig.17  Test model and load arrangement.
Fig.18  Comparison between fitted and measured values of MPs: (a) cable force comparison; (b) node displacement comparison.
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