A surrogate model for uncertainty quantification and global sensitivity analysis of nonlinear large-scale dome structures

doi:10.1007/s11709-023-0007-9

Frontiers of Structural and Civil Engineering

2023, Vol. 17

Issue (12): 1813-1829 https://doi.org/10.1007/s11709-023-0007-9

本期目录

A surrogate model for uncertainty quantification and global sensitivity analysis of nonlinear large-scale dome structures

Huidong ZHANG^1,²(

), Yafei SONG¹, Xinqun ZHU³, Yaqiang ZHANG¹, Hui WANG¹, Yingjun GAO¹

¹. School of Civil Engineering, Tianjin Chengjian University, Tianjin 300384, China
². Tianjin Key Laboratory of Civil Building Protection and Reinforcement, Tianjin 300384, China
³. School of Civil and Environmental Engineering, University of Technology Sydney, Sydney NSW 2007, Australia

全文: PDF(11422 KB) HTML

Abstract：

Full-scale dome structures intrinsically have numerous sources of irreducible aleatoric uncertainties. A large-scale numerical simulation of the dome structure is required to quantify the effects of these sources on the dynamic performance of the structure using the finite element method (FEM). To reduce the heavy computational burden, a surrogate model of a dome structure was constructed to solve this problem. The dynamic global sensitivity of elastic and elastoplastic structures was analyzed in the uncertainty quantification framework using fully quantitative variance- and distribution-based methods through the surrogate model. The model considered the predominant sources of uncertainty that have a significant influence on the performance of the dome structure. The effects of the variables on the structural performance indicators were quantified using the sensitivity index values of the different performance states. Finally, the effects of the sample size and correlation function on the accuracy of the surrogate model as well as the effects of the surrogate accuracy and failure probability on the sensitivity index values are discussed. The results show that surrogate modeling has high computational efficiency and acceptable accuracy in the uncertainty quantification of large-scale structures subjected to earthquakes in comparison to the conventional FEM.

Key words： large-scale dome structure surrogate model global sensitivity analysis uncertainty quantification structural performance

收稿日期: 2023-01-06 出版日期: 2024-02-05

Corresponding Author(s): Huidong ZHANG

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2023, 17(12): 1813-1829.
Huidong ZHANG, Yafei SONG, Xinqun ZHU, Yaqiang ZHANG, Hui WANG, Yingjun GAO. A surrogate model for uncertainty quantification and global sensitivity analysis of nonlinear large-scale dome structures. Front. Struct. Civ. Eng., 2023, 17(12): 1813-1829.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-023-0007-9
https://academic.hep.com.cn/fsce/CN/Y2023/V17/I12/1813

Fig.1

index	theoretical value	variance-based	distribution-based
$S 1$	0.3139	0.3139	0.5124 (1)
$S 2$	0.4425	0.4426	0.4201 (2)
$S 3$	0	0	0.2286 (3)
$S T 1$	0.5575 (1)	0.5574 (1)	–
$S T 2$	0.4425 (2)	0.4426 (2)	–
$S T 3$	0.2437 (3)	0.2435 (3)	–

Tab.1

Fig.2

Fig.3

variable	mean (μ)	Sd (σ)	bound	distribution
elastic modulus, E (Pa)	$2.06 × 1011$	$0.05 × μ$	${μ ? σ, μ + σ}$	$X ～ N o r m (μ, σ$ )
yield strength, $f y$ (Pa)	$345 × 106$	$0.05 × μ$
strain-hardening ratio, $b$	0.015	$0.05 × μ$
wall thickness of the member, $t w$ (m)	0.01	$0.05 × μ$
node load, $N l$ (kg)	9471.0	$0.1 × μ$
damping ratio, $ξ$	0.02	0.3 × μ

Tab.2

Tab.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Fig.22

1	H D Zhang, X Q Zhu, S Yao. Nonlinear dynamic analysis method for large-scale single-layer lattice domes with uncertain-but-bounded parameters. Engineering Structures, 2020, 203: 109780 https://doi.org/10.1016/j.engstruct.2019.109780
2	H D Zhang, X Q Zhu, X Liang, F Y Guo. Stochastic uncertainty quantification of seismic performance of complex large-scale structures using response spectrum method. Engineering Structures, 2021, 235: 112096 https://doi.org/10.1016/j.engstruct.2021.112096
3	B Bhattacharyya. Global sensitivity analysis: A bayesian learning based polynomial chaos approach. Journal of Computational Physics, 2020, 415: 109539 https://doi.org/10.1016/j.jcp.2020.109539
4	P Wei, Z Lu, X Yuan. Monte Carlo simulation for moment-independent sensitivity analysis. Reliability Engineering & System Safety, 2013, 110: 60–67 https://doi.org/10.1016/j.ress.2012.09.005
5	H V Gupta, S Razavi. Revisiting the basis of sensitivity analysis for dynamical earth system models. Water Resources Research, 2018, 54(11): 8692–8717 https://doi.org/10.1029/2018WR022668
6	D Partington, M J Knowling, C T Simmons, P G Cook, Y Xie, T Iwanaga, C Bouchez. Worth of hydraulic and water chemistry observation data in terms of the reliability of surface water-groundwater exchange flux predictions under varied flow conditions. Journal of Hydrology, 2020, 590: 125441 https://doi.org/10.1016/j.jhydrol.2020.125441
7	I M Sobol, S Tarantola, D Gatelli, S S Kucherenko, W Mauntz. Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering & System Safety, 2007, 92(7): 957–960 https://doi.org/10.1016/j.ress.2006.07.001
8	S TarantolaN GiglioliJ JesinghausA Saltelli. Can global sensitivity analysis steer the implementation of models for environmental assessments and decision-making? Stochastic Environmental Research and Risk Assessment, 2002, 16(1): 63–76
9	S Razavi, A Jakeman, A Saltelli, C Prieur, B Iooss, E Borgonovo, E Plischke, S Lo Piano, T Iwanaga, W Becker, S Tarantola, J H A Guillaume, J Jakeman, H Gupta, N Melillo, G Rabitti, V Chabridon, Q Duan, X Sun, S Smith, R Sheikholeslami, N Hosseini, M Asadzadeh, A Puy, S Kucherenko, H R Maier. The future of sensitivity analysis: An essential discipline for systems modeling and policy support. Environmental Modelling & Software, 2021, 137: 104954 https://doi.org/10.1016/j.envsoft.2020.104954
10	N A Nariman, R R Hussain, I I Mohammad, P Karampour. Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action. Frontiers of Structural and Civil Engineering, 2019, 13(6): 1289–1300 https://doi.org/10.1007/s11709-019-0548-0
11	M Zoutat, S M Elachachi, M Mekki, M Hamane. Global sensitivity analysis of soil structure interaction system using N2-SSI method. European Journal of Environmental and Civil Engineering, 2018, 22(2): 192–211 https://doi.org/10.1080/19648189.2016.1185970
12	M Menz, S Dubreuil, J Morio, C Gogu, N Bartoli, M Chiron. Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes. Structural Safety, 2021, 93: 102116 https://doi.org/10.1016/j.strusafe.2021.102116
13	K C Zhang, Z Z Lu, D Q Wu, Y L Zhang. Analytical variance based global sensitivity analysis for models with correlated variables. Applied Mathematical Modelling, 2017, 45: 748–767 https://doi.org/10.1016/j.apm.2016.12.036
14	M M Javidan, J K Kim. Variance-based global sensitivity analysis for fuzzy random structural systems. Computer-Aided Civil and Infrastructure Engineering, 2019, 34(7): 602–615 https://doi.org/10.1111/mice.12436
15	S R Arwade, M Moradi, A Louhghalam. Variance decomposition and global sensitivity for structural systems. Engineering Structures, 2010, 32(1): 1–10 https://doi.org/10.1016/j.engstruct.2009.08.011
16	G Boscato, S Russo, R Ceravolo, L Z Fragonara. Global sensitivity-based model updating for heritage structures. Computer-Aided Civil and Infrastructure Engineering, 2015, 30(8): 620–635 https://doi.org/10.1111/mice.12138
17	X F Zhang, M D Pandey. An effective approximation for variance-based global sensitivity analysis. Reliability Engineering & System Safety, 2014, 121: 164–174 https://doi.org/10.1016/j.ress.2013.07.010
18	S Cucurachi, E Borgonovo, R Heijungs. A protocol for the global sensitivity analysis of impact assessment models in life cycle assessment. Risk Analysis, 2016, 36(2): 357–377 https://doi.org/10.1111/risa.12443
19	G Baroni, T Francke. An effective strategy for combining variance- and distribution-based global sensitivity analysis. Environmental Modelling & Software, 2020, 134: 104851 https://doi.org/10.1016/j.envsoft.2020.104851
20	P F Wei, Y Y Wang, C H Tang. Time-variant global reliability sensitivity analysis of structures with both input random variables and stochastic processes. Structural and Multidisciplinary Optimization, 2017, 55(5): 1883–1898 https://doi.org/10.1007/s00158-016-1598-8
21	P Ni, Y Xia, J Li, H Hao. Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures. Mechanical Systems and Signal Processing, 2019, 119: 293–311 https://doi.org/10.1016/j.ymssp.2018.09.029
22	P H Ni, J Li, H Hao, H Y Zhou. Reliability based design optimization of bridges considering bridge−vehicle interaction by Kriging surrogate model. Engineering Structures, 2021, 246: 112989 https://doi.org/10.1016/j.engstruct.2021.112989
23	P H Ni, J Li, H Hao, Q Han, X L Du. Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling. Computer Methods in Applied Mechanics and Engineering, 2021, 383: 113915 https://doi.org/10.1016/j.cma.2021.113915
24	Z X Yuan, P Liang, T Silva, K Yu, J E Mottershead. Parameter selection for model updating with global sensitivity analysis. Mechanical Systems and Signal Processing, 2019, 115: 483–496 https://doi.org/10.1016/j.ymssp.2018.05.048
25	H P Wan, Y Q Ni. An efficient approach for dynamic global sensitivity analysis of stochastic train-track-bridge system. Mechanical Systems and Signal Processing, 2019, 117: 843–861 https://doi.org/10.1016/j.ymssp.2018.08.018
26	A Amini, A Abdollahi, M A Hariri-Ardebili, U Lall. Copula-based reliability and sensitivity analysis of aging dams: Adaptive Kriging and polynomial chaos Kriging methods. Applied Soft Computing, 2021, 109: 107524 https://doi.org/10.1016/j.asoc.2021.107524
27	J H Xian, C Su, B F Jr Spencer. Stochastic sensitivity analysis of energy-dissipating structures with nonlinear viscous dampers by efficient equivalent linearization technique based on explicit time-domain method. Probabilistic Engineering Mechanics, 2020, 61: 103080 https://doi.org/10.1016/j.probengmech.2020.103080
28	R V Vazna, M Zarrin. Sensitivity analysis of double layer diamatic dome space structure collapse behavior. Engineering Structures, 2020, 212: 110511 https://doi.org/10.1016/j.engstruct.2020.110511
29	H P Wan, W X Ren. Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel. Journal of Structural Engineering, 2015, 141(6): 04014164 https://doi.org/10.1061/(ASCE)ST.1943-541X.0001108
30	Q Q Sun, D Dias. Global sensitivity analysis of probabilistic tunnel seismic deformations using sparse polynomial chaos expansions. Soil Dynamics and Earthquake Engineering, 2021, 141: 106470 https://doi.org/10.1016/j.soildyn.2020.106470
31	N Vu-Bac, M Silani, T Lahmer, X Zhuang, T Rabczuk. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535 https://doi.org/10.1016/j.commatsci.2014.04.066
32	R Tuo, W J Wang. Kriging prediction with isotropic Matérn correlations: Robustness and experimental designs. Journal of Machine Learning Research, 2020, 21(1): 7604–7641
33	N Vu-Bac, T Lahmer, Y Zhang, X Zhuang, T Rabczuk. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95 https://doi.org/10.1016/j.compositesb.2013.11.014
34	B Liu, N Vu-Bac, X Zhuang, T Rabczuk. Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites. Mechanics of Materials, 2020, 142: 103280 https://doi.org/10.1016/j.mechmat.2019.103280
35	S N Xiao, Z Z Lu. Structural reliability sensitivity analysis based on classification of model output. Aerospace Science and Technology, 2017, 71: 52–61 https://doi.org/10.1016/j.ast.2017.09.009
36	D Fenwick, C Scheidt, J Caers. Quantifying asymmetric parameter interactions in sensitivity analysis: Application to reservoir modeling. Mathematical Geosciences, 2014, 46(4): 493–511 https://doi.org/10.1007/s11004-014-9530-5
37	S J Sheather, M C Jones. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B. Methodological, 1991, 53(3): 683–690 https://doi.org/10.1111/j.2517-6161.1991.tb01857.x
38	A Marrel, B Iooss, B Laurent, O Roustant. Calculations of sobol indices for the Gaussian process metamodel. Reliability Engineering & System Safety, 2009, 94(3): 742–751 https://doi.org/10.1016/j.ress.2008.07.008
39	B Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 2008, 93(7): 964–979 https://doi.org/10.1016/j.ress.2007.04.002
40	T T Liu, Z He, Y Yang. Vertical earthquake vulnerability of long-span spherical lattice shells with low rise-span ratios. Engineering Structures, 2020, 207: 110181 https://doi.org/10.1016/j.engstruct.2020.110181
41	M K Kaul. Stochastic characterization of earthquakes through their response spectrum. Earthquake Engineering & Structural Dynamics, 1978, 6(5): 497–509 https://doi.org/10.1002/eqe.4290060506
42	R Scanlan, K Sachs. Earthquake time histories and response spectra. Journal of the Engineering Mechanics Division, 1974, 100(4): 635–655 https://doi.org/10.1061/JMCEA3.0001911
43	K A Bani-Hani, A I Malkawi. A multi-step approach to generate response-spectrum-compatible artificial earthquake accelerograms. Soil Dynamics and Earthquake Engineering, 2017, 97: 117–132 https://doi.org/10.1016/j.soildyn.2017.03.012

Viewed

Full text

Abstract

Cited

Shared

Discussed