Abstract
In this paper, a structural identification problem considering modeling uncertainty is investigated, which not only needs to identify the unknown parameters of mechanical structure, but also accurately quantifies the influence of stochastic modeling uncertainty on the unknown structural parameters. As a typical inverse problem, the solving of structural stochastic identification faces the double nesting of uncertainty propagation analysis and inverse calculations. In order to overcome this difficult, a novel uncertain inverse method based on sparse grid and similar system analysis is proposed. Firstly, this structural stochastic identification problem is decomposed into several deterministic inverse problems by sparse grid technique. Since the small variations of uncertain variables at any two adjacent sparse grid nodes, the corresponding two systems at sparse grid nodes are similar. Thus, by adequately utilizing this similarity, the similar system analysis strategy is innovatively developed, which reduces these time-consuming deterministic inverse problems into only one deterministic optimization inverse and a few forward problem calculations. Therefore, the inverse efficiency is significantly improved. Subsequently, the statistical moments and the probability density functions of the unknown structural parameters will be identified by utilizing the deterministic inverse results and their concentrated probabilities at the sparse grid nodes. Finally, the practicability of uncertain inverse method will be illustrated by four examples.
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References
Barzdajn B (2014) Maximum entropy distribution under moments and quantiles constraints. Measurement 57:102–107. https://doi.org/10.1016/j.measurement.2014.07.012
Bao N, Wang C (2015) A Monte Carlo simulation based inverse propagation method for stochastic model updating. Mech Syst Signal Proc 60–61:928–944. https://doi.org/10.1016/j.ymssp.2015.01.011
Behmanesh I, Moaveni B, Lombaert G, Papadimitriou C (2015) Hierarchical Bayesian model updating for structural identification. Mech Syst Signal Proc 64:360–376. https://doi.org/10.1016/j.ymssp.2015.03.026
Bilionis I, Zabaras N (2013) Solution of inverse problems with limited forward solver evaluations: a Bayesian perspective. Inverse Probl 30:015004. https://doi.org/10.1088/0266-5611/30/1/015004
Bocciarelli M, Bolzon G, Maier G (2005) Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping. Mech Mater 37(8):855–868. https://doi.org/10.1016/j.mechmat.2004.09.001
Bruyère J, Dantan JY, Bigot R, Martin P (2007) Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation. Mech Mach Theory 42:1326–1351. https://doi.org/10.1016/j.mechmachtheory.2006.11.003
Bureerat S, Pholdee N (2018) Inverse problem based differential evolution for efficient structural health monitoring of trusses. Appl Soft Comput 66:462–472. https://doi.org/10.1016/j.asoc.2018.02.046
Cao L, Liu J, Jiang C, Wu Z, Zhang Z (2020) Evidence-based structural uncertainty quantification by dimension reduction decomposition and marginal interval analysis. J Mech Des 142(5):051701. https://doi.org/10.1115/1.4044915
Cao L, Liu J, Meng X, Zhao Y, Yu Z (2021) Inverse uncertainty quantification for imprecise structure based on evidence theory and similar system analysis. Struct Multidisc Optim 64:2183–2198. https://doi.org/10.1007/s00158-021-02974-4
Chatzi EN, Smyth AW, Masri SF (2010) Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty. Struct Saf 32(5):326–337. https://doi.org/10.1016/j.strusafe.2010.03.008
Du X (2013) Inverse simulation under uncertainty by optimization. J Comput Inf Sci Eng 13:021005. https://doi.org/10.1115/1.4023859
Engen M, Hendriks MAN, Köhler J, Øverli JA, Åldstedt E (2017) A quantification of the modelling uncertainty of non-linear finite element analyses of large concrete structures. Struct Saf 64:1–8. https://doi.org/10.1016/j.strusafe.2016.08.003
Faes M, Cerneels J, Vandepitte D, Moens D (2017) Identification and quantification of multivariate interval uncertainty in finite element models. Comput Methods Appl Mech Eng 315:896–920. https://doi.org/10.1016/j.cma.2016.11.023
Fang SE, Zhang QH, Ren WX (2014) Parameter variability estimation using stochastic response surface model updating. Mech Syst Signal Proc 49:249–263. https://doi.org/10.1016/j.ymssp.2014.04.017
Fonseca JR, Friswell MI, Mottershead JE, Lees AW (2005) Uncertainty identification by the maximum likelihood method. J Sound Vib 288:587–599. https://doi.org/10.1016/j.jsv.2005.07.006
Goodfellow RC, Dimitrakopoulos R (2016) Global optimization of open pit mining complexes with uncertainty. Appl Soft Comput 40:292–304. https://doi.org/10.1016/j.asoc.2015.11.038
Jie Z, Richards CM (2007) Parameter identification of analytical and experimental rubber isolators represented by Maxwell models. Mech Syst Signal Proc 21(7):2814–2832. https://doi.org/10.1016/j.ymssp.2007.02.007
Kitahara M, Bi S, Broggi M, Beer M (2022) Nonparametric Bayesian stochastic model updating with hybrid uncertainties. Mech Syst Signal Proc 163:108195. https://doi.org/10.1016/j.ymssp.2021.108195
Knabe T, Datcheva M, Lahmer T, Cotecchia F, Schanz T (2013) Identification of constitutive parameters of soil using an optimization strategy and statistical analysis. Comput Geotech 49:143–157. https://doi.org/10.1016/j.compgeo.2012.10.002
Lee G, Kim W, Oh H, Youn B, Kim N (2019a) Review of statistical model calibration and validation—from the perspective of uncertainty structures. Struct Multidisc Optim 60:1619–1644. https://doi.org/10.1016/j.cma.2012.06.017
Lee G, Son H, Youn BD (2019b) Sequential optimization and uncertainty propagation method for efficient optimization-based model calibration. Struct Multidisc Optim 60(4):1355–1372. https://doi.org/10.1007/s00158-019-02351-2
Liu GR, Han X (2003) Computational inverse techniques in nondestructive evaluation. CRC Press, Boca Raton. https://doi.org/10.1016/B978-075067883-4/50000-0
Liu J, Sun X, Han X, Jiang C, Yu D (2015) Dynamic load identification for stochastic structures based on gegenbauer polynomial approximation and regularization method. Mech Syst Signal Proc 56–57:35–54. https://doi.org/10.1016/j.ymssp.2014.10.008
Liu J, Hu Y, Xu C, Jiang C, Han X (2016) Probability assessments of identified parameters for stochastic structures using point estimation method. Reliab Eng Syst Saf 156:51–58. https://doi.org/10.1016/j.ress.2016.07.021
Liu J, Meng X, Xu C, Zhang D, Jiang C (2018) Forward and inverse structural uncertainty propagations under stochastic variables with arbitrary probability distributions. Comput Meth Appl Mech Eng 342:287–320. https://doi.org/10.1016/j.cma.2018.07.035
Lu ZR, Liu JK (2011) Identification of both structural damages in bridge deck and vehicular parameters using measured dynamic responses. Comput Struct 89(13–14):1397–1405. https://doi.org/10.1016/j.compstruc.2011.03.008
Ma X, Zabaras N (2009) An efficient bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method. Inverse Probl 25:035013. https://doi.org/10.1088/0266-5611/25/3/035013
Marzouk Y, Xiu D (2009) A stochastic collocation approach to bayesian inference in inverse problems. Commun Comput Phys 6:826–847. https://doi.org/10.4208/cicp.2009.v6.p826
Meggitt JWR, Moorhouse AT, Elliott AS (2019) A covariance based framework for the propagation of uncertainty through inverse problems with an application to force identification. Mech Syst Signal Proc 124:275–297. https://doi.org/10.1016/j.ymssp.2018.11.038
Rodríguez JI, Thompson DC, Ayers PW, Köster AM (2008) Numerical integration of exchange-correlation energies and potentials using transformed sparse grids. J Chem Phys 128:240. https://doi.org/10.1063/1.2931563
Savvas D, Papaioannou I, Stefanou G (2020) Bayesian identification and model comparison for random property fields derived from material microstructure. Comput Methods Appl Mech Eng 365:113026. https://doi.org/10.1016/j.cma.2020.113026
Schobi R, Sudret B (2019) Global sensitivity analysis in the context of imprecise probabilities (p-boxes) using sparse polynomial chaos expansions. Reliab Eng Syst Saf 187:129–141. https://doi.org/10.1016/j.ress.2018.11.021
Soize C (2011) A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension. Comput Meth Appl Mech Eng 200:3083–3099. https://doi.org/10.1016/j.cma.2011.07.005
Tran A, Mitchell JA, Swiler LP, Wildey T (2020) An active learning high-throughput microstructure calibration framework for solving inverse structure–process problems in materials informatics. Acta Mater 194:80–92. https://doi.org/10.1016/j.actamat.2020.04.054
Wang Z, Broccardo M (2020) A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis. Struct Saf 84:101937. https://doi.org/10.1016/j.strusafe.2020.101937
Wang J, Zabaras N (2004) A bayesian inference approach to the inverse heat conduction problem. Int J Heat Mass Transf 47(17–18):3927–3941. https://doi.org/10.1016/j.ijheatmasstransfer.2004.02.028
Widany KU, Mahnken R (2012) Adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements. Comput Methods Appl Mech Eng 245–246:117–131
Xiong F, Greene S, Chen W, Xiong Y, Yang S (2010) A new sparse grid based method for uncertainty propagation. Struct Multidisc Optim 41:335–349. https://doi.org/10.1115/detc2009-87430
Xu ZD, Cao YH, Zhao M (2012) Parameter identification of tailplane iced aircraft based on maximum likelihood method. Appl Mech Mater 192:57–62. https://doi.org/10.4028/www.scientific.net/amm.192.57
Yang L, Bi S, Faes MGR, Broggi M, Beer M (2022) Bayesian inversion for imprecise probabilistic models using a novel entropy-based uncertainty quantification metric. Mech Syst Signal Proc 162:107954. https://doi.org/10.1016/j.ymssp.2021.107954
Zhang D, Han X, Jiang C, Liu J, Li Q (2017) Time-dependent reliability analysis through response surface method. J Mechl Des 139(4):041404. https://doi.org/10.1115/1.4035860
Zhao M, Yan W, Yuen KV, Beer M (2021) Non-probabilistic uncertainty quantification for dynamic characterization functions using complex ratio interval arithmetic operation of multidimensional parallelepiped model. Mech Syst Signal Proc 156:107559. https://doi.org/10.1016/j.ymssp.2020.107559
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 51975199) and the Changsha Municipal Natural Science Foundation (Grant No. kq2014050).
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Cao, L., Liu, J., Hu, Y. et al. Structural stochastic identification considering modeling uncertainty through sparse grid and similar system analysis. Struct Multidisc Optim 65, 219 (2022). https://doi.org/10.1007/s00158-022-03316-8
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DOI: https://doi.org/10.1007/s00158-022-03316-8