Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes

Song, M.; Renson, L.; Moaveni, B.; Kerschen, Gaëtan

doi:10.1016/j.ymssp.2021.108337

Article (Scientific journals)

Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes

Song, M.; Renson, L.; Moaveni, B. et al.

2022 • In Mechanical Systems and Signal Processing, 165

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/296118

DOI
10.1016/j.ymssp.2021.108337

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Keywords :

Bayesian inference; Control-based continuation; Model class selection; Nonlinear model updating; Nonlinear normal modes; Nonlinear system identification; Uncertainty quantification and propagation; Elastic moduli; Engines; Inference engines; Nonlinear systems; Uncertainty analysis; Bayesian model updating; Class selections; Engine structure; Nonlinear systems identification; Bayesian networks

Abstract :

[en] This paper presents a Bayesian model updating and model class selection approach based on nonlinear normal modes (NNMs). The performance of the proposed approach is demonstrated on a conceptually simple wing-engine structure. Control-based continuation is exploited to measure experimentally the NNMs of the structure by tracking the phase quadrature condition between the structural response and single input excitation. A two-phase Bayesian model updating framework is implemented to estimate the joint posterior distribution of unknown model parameters: (1) at phase I, the effective Young's modulus of a detailed linear finite element model and its estimation uncertainty are inferred from the data; (2) at phase II, a reduced-order model is obtained from the updated linear model using Craig-Bampton method, and coefficient parameters of structural nonlinearities are updated using the measured NNMs. Five different model classes representing different nonlinear functions are investigated, and their Bayesian evidence are compared to reveal the most plausible model. The obtained model is used to predict NNMs by propagating uncertainties of parameters and error function. Good agreement is observed between model-predicted and experimentally identified NNMs, which verifies the effectiveness of the proposed approach for nonlinear model updating and model class selection. © 2021 Elsevier Ltd

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Song, M.; Dept. of Civil and Environmental Engineering, Tufts University, Medford, MA, United States

Renson, L.; Dept. of Mechanical Engineering, Imperial College London, London, UK, United Kingdom

Moaveni, B.; Dept. of Civil and Environmental Engineering, Tufts University, Medford, MA, United States

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes

Publication date :

2022

Journal title :

Mechanical Systems and Signal Processing

ISSN :

0888-3270

eISSN :

1096-1216

Publisher :

Academic Press

Volume :

165

Peer reviewed :

Peer Reviewed verified by ORBi

Funding text :

The authors acknowledge partial support of this study by the National Science Foundation Grant number 1903972. L. Renson acknowledges the financial support of the Royal Academy of Engineering, Research Fellowship #RF1516/15/11. The opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily represent the views of the sponsors and organizations involved in this project.

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Bibliography

Friswell, M., Mottershead, J.E., Finite element model updating in structural dynamics. 2013, Springer Science & Business Media.
Zhang, Q.W., Chang, T.Y.P., Chang, C.C., Finite-element model updating for the Kap Shui Mun cable-stayed bridge. J. Bridge Eng. 6:4 (2001), 285–293.
Brownjohn, J.M.W., Moyo, P., Omenzetter, P., Lu, Y., Assessment of highway bridge upgrading by dynamic testing and finite-element model updating. J. Bridge Eng. 8:3 (2003), 162–172.
Teughels, A., De Roeck, G., Structural damage identification of the highway bridge Z24 by FE model updating. J. Sound Vib. 278:3 (2004), 589–610.
Jaishi, B., Kim, H.-J., Kim, M.K., Ren, W.-X., Lee, S.-H., Finite element model updating of concrete-filled steel tubular arch bridge under operational condition using modal flexibility. Mech. Syst. Sig. Process. 21:6 (2007), 2406–2426.
Reynders, E., Roeck, G.D., Gundes Bakir, P., Sauvage, C., Damage identification on the Tilff Bridge by vibration monitoring using optical fiber strain sensors. J. Eng. Mech. 133:2 (2007), 185–193.
Fang, S.-E., Perera, R., De Roeck, G., Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization. J. Sound Vib. 313:3–5 (2008), 544–559.
Moaveni, B., Stavridis, A., Lombaert, G., Conte, J.P., Shing, P.B., Finite-element model updating for assessment of progressive damage in a 3-story infilled RC frame. J. Struct. Eng. 139:10 (2013), 1665–1674.
Song, M., Yousefianmoghadam, S., Mohammadi, M.-E., Moaveni, B., Stavridis, A., Wood, R.L., An application of finite element model updating for damage assessment of a two-story reinforced concrete building and comparison with lidar. Struct. Health Monitoring 17:5 (2018), 1129–1150.
Beck, J.L., Katafygiotis, L.S., Updating models and their uncertainties. I: Bayesian statistical framework. J. Eng. Mech. 124:4 (1998), 455–461.
Yuen, K.-V., Beck, J.L., Au, S.K., Structural damage detection and assessment by adaptive Markov chain Monte Carlo simulation. Struct. Control Health Monit. 11:4 (2004), 327–347.
Ching, J., Beck, J.L., New Bayesian model updating algorithm applied to a structural health monitoring benchmark. Struct. Health Monitoring 3:4 (2004), 313–332.
Muto, M., Beck, J.L., Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J. Vib. Control 14:1–2 (2008), 7–34.
Simoen, E., De Roeck, G., Lombaert, G., Dealing with uncertainty in model updating for damage assessment: a review. Mech. Syst. Sig. Process. 56-57 (2015), 123–149.
Sevieri, G., Andreini, M., De Falco, A., Matthies, H.G., Concrete gravity dams model parameters updating using static measurements. Eng. Struct., 196, 2019, 109231.
Ntotsios, E., Papadimitriou, C., Panetsos, P., Karaiskos, G., Perros, K., Perdikaris, P.C., Bridge health monitoring system based on vibration measurements. Bull. Earthq. Eng., 7(2), 2009, 469.
Lam, H.-F., Yang, J., Au, S.-K., Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm. Eng. Struct. 102 (2015), 144–155.
Behmanesh, I., Moaveni, B., Probabilistic identification of simulated damage on the Dowling Hall footbridge through Bayesian finite element model updating. Struct. Control Health Monit. 22:3 (2015), 463–483.
Behmanesh, I., Moaveni, B., Accounting for environmental variability, modeling errors, and parameter estimation uncertainties in structural identification. J. Sound Vib. 374 (2016), 92–110.
Sedehi, O., Papadimitriou, C., Katafygiotis, L.S., Probabilistic hierarchical Bayesian framework for time-domain model updating and robust predictions. Mech. Syst. Sig. Process. 123 (2019), 648–673.
Song, M., Moaveni, B., Papadimitriou, C., Stavridis, A., Accounting for amplitude of excitation in model updating through a hierarchical Bayesian approach: application to a two-story reinforced concrete building. Mech. Syst. Sig. Process. 123 (2019), 68–83.
Song, M., Behmanesh, I., Moaveni, B., Papadimitriou, C., Accounting for modeling errors and inherent structural variability through a hierarchical Bayesian model updating approach: an overview. Sensors, 20(14), 2020, 3874.
Asgarieh, E., Moaveni, B., Stavridis, A., Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake. J. Sound Vib. 333:23 (2014), 6057–6073.
Asgarieh, E., Moaveni, B., Barbosa, A.R., Chatzi, E., Nonlinear model calibration of a shear wall building using time and frequency data features. Mech. Syst. Sig. Process. 85 (2017), 236–251.
Chatzi, E.N., Smyth, A.W., The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing. Structural Control and Health Monitoring: The Official Journal of the International Association for Structural Control and Monitoring and of the European Association for the Control of Structures 16:1 (2009), 99–123.
Astroza, R., Alessandri, A., Effects of model uncertainty in nonlinear structural finite element model updating by numerical simulation of building structures. Struct. Control Health Monit., 26(3), 2019, e2297.
Song, M., Astroza, R., Ebrahimian, H., Moaveni, B., Papadimitriou, C., Adaptive Kalman filters for nonlinear finite element model updating. Mech. Syst. Sig. Process., 143, 2020, 106837.
A. Vakakis, Non-linear normal modes (NNMs) and their applications in vibration theory: an overview, 1997.
Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F., Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech. Syst. Sig. Process. 23:1 (2009), 170–194.
R. Rosenberg, The normal modes of nonlinear n-degree-of-freedom systems, 1962.
Avramov, K.V., Mikhlin, Y.V., Review of applications of nonlinear normal modes for vibrating mechanical systems. Appl. Mech. Rev., 65(2), 2013.
Kuether, R.J., Renson, L., Detroux, T., Grappasonni, C., Kerschen, G., Allen, M.S., Nonlinear normal modes, modal interactions and isolated resonance curves. J. Sound Vib. 351 (2015), 299–310.
Renson, L., Noël, J.P., Kerschen, G., Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes. Nonlinear Dyn. 79:2 (2015), 1293–1309.
Noël, J.-P., Renson, L., Grappasonni, C., Kerschen, G., Identification of nonlinear normal modes of engineering structures under broadband forcing. Mech. Syst. Sig. Process. 74 (2016), 95–110.
Peeters, M., Kerschen, G., Golinval, J.C., Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech. Syst. Sig. Process. 25:4 (2011), 1227–1247.
Renson, L., Gonzalez-Buelga, A., Barton, D.A.W., Neild, S.A., Robust identification of backbone curves using control-based continuation. J. Sound Vib. 367 (2016), 145–158.
Peter, S., Leine, R.I., Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation. Mech. Syst. Sig. Process. 96 (2017), 139–158.
Renson, L., Hill, T., Ehrhardt, D., Barton, D., Neild, S., Force appropriation of nonlinear structures. Proc. Royal Soc. A: Math. Phys. Eng. Sci., 474(2214), 2018, 20170880.
Detroux, T., Renson, L., Masset, L., Kerschen, G., The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput. Methods Appl. Mech. Eng. 296 (2015), 18–38.
Renson, L., Kerschen, G., Cochelin, B., Numerical computation of nonlinear normal modes in mechanical engineering. J. Sound Vib. 364 (2016), 177–206.
Peter, S., Grundler, A., Reuss, P., Gaul, L., Leine, R.I., Towards finite element model updating based on nonlinear normal modes. Nonlinear Dynamics, 2016, Springer, 209–217.
Hill, T.L., Green, P.L., Cammarano, A., Neild, S.A., Fast Bayesian identification of a class of elastic weakly nonlinear systems using backbone curves. J. Sound Vib. 360 (2016), 156–170.
Song, M., Renson, L., Noël, J.P., Moaveni, B., Kerschen, G., Bayesian model updating of nonlinear systems using nonlinear normal modes. Struct. Control Health Monit., 2018, e2258.
Grappasonni, C., Noël, J.-P., Kerschen, G., Subspace and nonlinear-normal-modes-based identification of a beam with softening-hardening behaviour. Nonlinear Dynamics, 2014, Springer, 55–68.
Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.-C., Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Sig. Process. 20:3 (2006), 505–592.
W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, 1970.
Haario, H., Saksman, E., Tamminen, J., An adaptive Metropolis algorithm. Bernoulli 7:2 (2001), 223–242.
Ching, J., Chen, Y.-C., Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133:7 (2007), 816–832.
Chib, S., Jeliazkov, I., Marginal likelihood from the Metropolis-Hastings output. J. Am. Stat. Assoc. 96:453 (2001), 270–281.
delli Carri, A., Weekes, B., Di Maio, D., Ewins, D.J., Extending modal testing technology for model validation of engineering structures with sparse nonlinearities: a first case study. Mech. Syst. Sig. Process. 84 (2017), 97–115.
Abaqus 6.14. Dassault Systemes.
Craig, R.R. Jr, Bampton, M.C., Coupling of substructures for dynamic analyses. AIAA J. 6:7 (1968), 1313–1319.
Peter, S., Scheel, M., Krack, M., Leine, R.I., Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes. Mech. Syst. Sig. Process. 101 (2018), 498–515.
Sieber, J., Krauskopf, B., Control based bifurcation analysis for experiments. Nonlinear Dyn. 51:3 (2008), 365–377.
Barton, D.A., Mann, B.P., Burrow, S.G., Control-based continuation for investigating nonlinear experiments. J. Vib. Control 18:4 (2012), 509–520.
Renson, L., Barton, D.A., Neild, S.A., Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation. Int. J. Bifurcation Chaos, 27(01), 2017, 1730002.
Renson, L., Sieber, J., Barton, D.A.W., Shaw, A.D., Neild, S.A., Numerical continuation in nonlinear experiments using local Gaussian process regression. Nonlinear Dyn. 98:4 (2019), 2811–2826.
Bureau, E., Schilder, F., Ferreira Santos, I., Juel Thomsen, J., Starke, J., Experimental bifurcation analysis of an impact oscillator—tuning a non-invasive control scheme. J. Sound Vib. 332:22 (2013), 5883–5897.
Renson, L., Shaw, A.D., Barton, D.A.W., Neild, S.A., Application of control-based continuation to a nonlinear structure with harmonically coupled modes. Mech. Syst. Sig. Process. 120 (2019), 449–464.
Roberts, G.O., Rosenthal, J.S., Optimal scaling for various Metropolis-Hastings algorithms. Statistical science 16:4 (2001), 351–367.
Mottershead, J.E., Link, M., Friswell, M.I., The sensitivity method in finite element model updating: a tutorial. Mech. Syst. Sig. Process. 25:7 (2011), 2275–2296.
Platten, M.F., Wright, J.R., Cooper, J.E., Dimitriadis, G., Identification of a nonlinear wing structure using an extended modal model. Journal of Aircraft 46:5 (2009), 1614–1626.
Londoño, J.M., Cooper, J.E., Neild, S.A., Identification of systems containing nonlinear stiffnesses using backbone curves. Mech. Syst. Sig. Process. 84 (2017), 116–135.