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Efficient Bayesian inference for finite element model updating with surrogate modeling techniques

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Journal of Civil Structural Health Monitoring Aims and scope Submit manuscript

Abstract

Bayesian finite element model updating has become an important tool for structural health monitoring. However, it takes a large amount of computational cost to update the finite element model using the Bayesian inference methods. The surrogate modeling techniques have received much attention in recent years due to their ability to speed up the computation of Bayesian inference. This study introduces two new surrogate models for Bayesian inference. Specifically, the radial basis function neural networks and fully-connected neural networks are used to construct surrogate models for the intractable likelihood function, avoiding the enormous computational cost of repeatedly calling the finite element model in the Monte Carlo sampling process. A full-scale numerical simulation of a concrete frame and a six-story steel frame experiment were selected as case studies. The trained surrogate models were used for Bayesian model updating, and the updated results were compared with the results obtained directly using the finite element model evaluation. The posterior distributions of the finite element model parameters obtained using the trained surrogate models are sufficiently accurate compared to those obtained using direct finite element evaluation. In addition, using surrogate models for finite element model updating greatly reduces computational costs.

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References

  1. Shu J, Ding W, Zhang J, Lin F, Duan Y (2022) Continual-learning-based framework for structural damage recognition. Struct Control Health Monit 29(11):e3093

    Article  Google Scholar 

  2. Shu J, Zhang C, Chen X, Niu Y (2023) Model-informed deep learning strategy with vision measurement for damage identification of truss structures. Mech Syst Signal Process 196:110327

    Article  Google Scholar 

  3. Tamuly P, Chakraborty A, Das S (2021) Nonlinear finite element model updating using constrained unscented Kalman filter for condition assessment of reinforced concrete structures. J Civ Struct Heal Monit 11:1137–1154

    Article  Google Scholar 

  4. Friswell M, Mottershead JE (1995) Finite element model updating in structural dynamics. Springer, London

    Book  Google Scholar 

  5. Li D, Zhang J (2023) Finite element model updating through derivative-free optimization algorithm. Mech Syst Signal Process 185:109726

    Article  Google Scholar 

  6. Kong Q, Gu J, Xiong B, Yuan C (2023) Vision-aided three-dimensional damage quantification and finite element model geometric updating for reinforced concrete structures. Comput Aided Civ Infrastruct Eng 2023:1

    Google Scholar 

  7. Qin S, Yuan Y, Han S, Li S (2023) A novel multiobjective function for finite-element model updating of a long-span cable-stayed bridge using in situ static and dynamic measurements. J Bridg Eng 28(1):04022131

    Article  Google Scholar 

  8. Otsuki Y, Li D, Dey SS, Kurata M, Wang Y (2021) Finite element model updating of an 18-story structure using branch-and-bound algorithm with epsilon-constraint. J Civ Struct Heal Monit 11:575–592

    Article  Google Scholar 

  9. Otsuki Y, Lander P, Dong X, Wang Y (2022) Formulation and application of SMU: an open-source MATLAB package for structural model updating. Adv Struct Eng 25(4):698–715

    Article  Google Scholar 

  10. Behmanesh I, Moaveni B, Lombaert G, Papadimitriou C (2015) Hierarchical Bayesian model updating for structural identification. Mech Syst Signal Process 64:360–376

    Article  ADS  Google Scholar 

  11. Lam H-F, Yang J, Au S-K (2015) Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm. Eng Struct 102:144–155

    Article  Google Scholar 

  12. Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461

    Article  Google Scholar 

  13. Ching J, Chen Y-C (2007) Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J Eng Mech 133(7):816–832

    Article  Google Scholar 

  14. Ding Y-J, Wang Z-C, Chen G, Ren W-X, Xin Y (2022) Markov Chain Monte Carlo-based Bayesian method for nonlinear stochastic model updating. J Sound Vib 520:116595

    Article  Google Scholar 

  15. Huang Y, Beck JL, Li H (2017) Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment. Comput Methods Appl Mech Eng 318:382–411

    Article  ADS  MathSciNet  Google Scholar 

  16. Ching J, Muto M, Beck JL (2006) Structural model updating and health monitoring with incomplete modal data using Gibbs sampler. Comput Aided Civ Infrastruct Eng 21(4):242–257

    Article  Google Scholar 

  17. Su G, Peng L, Hu L (2017) A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis. Struct Saf 68:97–109

    Article  Google Scholar 

  18. Boulkaibet I, Mthembu L, Marwala T, Friswell M, Adhikari S (2017) Finite element model updating using Hamiltonian Monte Carlo techniques. Inverse Probl Sci Eng 25(7):1042–1070

    Article  MathSciNet  Google Scholar 

  19. Baisthakur S, Chakraborty A (2021) Experimental verification for load rating of steel truss bridge using an improved Hamiltonian Monte Carlo-based Bayesian model updating. J Civ Struct Heal Monit 11(4):1093–1112

    Article  Google Scholar 

  20. Duan Y et al (2011) Advanced finite element model of Tsing Ma Bridge for structural health monitoring. Int J Struct Stab Dyn 11(02):313–344

    Article  Google Scholar 

  21. Ni Y, Xia Y, Lin W, Chen W, Ko J (2012) SHM benchmark for high-rise structures: a reduced-order finite element model and field measurement data. Smart Struct Syst 10(4–5):411–426

    Article  Google Scholar 

  22. Cheng K, Lu Z, Ling C, Zhou S (2020) Surrogate-assisted global sensitivity analysis: an overview. Struct Multidiscip Optim 61:1187–1213

    Article  MathSciNet  Google Scholar 

  23. Sudret B, Marelli S, Wiart J (2017) Surrogate models for uncertainty quantification: an overview. In: 2017 11th European conference on antennas and propagation (EUCAP). IEEE, New York, pp 793–797

  24. Bichon BJ, McFarland JM, Mahadevan S (2011) Efficient surrogate models for reliability analysis of systems with multiple failure modes. Reliab Eng Syst Saf 96(10):1386–1395

    Article  Google Scholar 

  25. Forrester AI, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(1–3):50–79

    Article  Google Scholar 

  26. Li M, Wang Z (2019) Surrogate model uncertainty quantification for reliability-based design optimization. Reliab Eng Syst Saf 192:106432

    Article  Google Scholar 

  27. Dubourg V (2011) Adaptive surrogate models for reliability analysis and reliability-based design optimization. Université Blaise Pascal-Clermont-Ferrand II

  28. Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964–979

    Article  Google Scholar 

  29. Ni P, Xia Y, Li J, Hao H (2019) Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures. Mech Syst Signal Process 119:293–311

    Article  ADS  Google Scholar 

  30. Ni P, Li J, Hao H, Han Q, Du X (2021) Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling. Comput Methods Appl Mech Eng 383:113915

    Article  ADS  MathSciNet  Google Scholar 

  31. Radaideh MI, Kozlowski T (2020) Surrogate modeling of advanced computer simulations using deep Gaussian processes. Reliab Eng Syst Saf 195:106731

    Article  Google Scholar 

  32. Han Q, Ni P, Du X, Zhou H, Cheng X (2022) Computationally efficient Bayesian inference for probabilistic model updating with polynomial chaos and Gibbs sampling. Struct Control Health Monit 29(6):e2936

    Article  Google Scholar 

  33. Wan H-P, Ren W-X (2016) Stochastic model updating utilizing Bayesian approach and Gaussian process model. Mech Syst Signal Process 70:245–268

    Article  ADS  Google Scholar 

  34. Ponsi F, Bassoli E, Vincenzi L (2022) Bayesian and deterministic surrogate-assisted approaches for model updating of historical masonry towers. J Civ Struct Heal Monit 12(6):1469–1492

    Article  Google Scholar 

  35. Ni P, Han Q, Du X, Cheng X (2022) Bayesian model updating of civil structures with likelihood-free inference approach and response reconstruction technique. Mech Syst Signal Process 164:108204

    Article  Google Scholar 

  36. Ramancha MK, Vega MA, Conte JP, Todd MD, Hu Z (2022) Bayesian model updating with finite element vs. surrogate models: application to a miter gate structural system. Eng Struct 272:114901

    Article  Google Scholar 

  37. Oladyshkin S, Nowak W (2012) Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. Reliab Eng Syst Saf 106:179–190

    Article  Google Scholar 

  38. Snelson E, Ghahramani Z (2007) Local and global sparse Gaussian process approximations. In: Artificial intelligence and statistics. PMLR, pp 524–531

  39. Williams CK, Rasmussen CE (2006) Gaussian processes for machine learning, vol 3. MIT Press, Cambridge

    Google Scholar 

  40. Dadras Eslamlou A, Huang S (2022) Artificial-neural-network-based surrogate models for structural health monitoring of civil structures: a literature review. Buildings 12(12):2067

    Article  Google Scholar 

  41. Flah M, Nunez I, Ben Chaabene W, Nehdi ML (2021) Machine learning algorithms in civil structural health monitoring: a systematic review. Arch Comput Methods Eng 28:2621–2643

    Article  Google Scholar 

  42. Toh G, Park J (2020) Review of vibration-based structural health monitoring using deep learning. Appl Sci 10(5):1680

    Article  CAS  Google Scholar 

  43. Avci O, Abdeljaber O, Kiranyaz S, Hussein M, Gabbouj M, Inman DJ (2021) A review of vibration-based damage detection in civil structures: from traditional methods to machine learning and deep learning applications. Mech Syst Signal Process 147:107077

    Article  Google Scholar 

  44. Lim EA, Zainuddin Z (2008) An improved fast training algorithm for RBF networks using symmetry-based fuzzy C-means clustering. MATEMATIKA Malays J Ind Appl Math 2008:141–148

    Google Scholar 

  45. Higham CF, Higham DJ (2019) Deep learning: an introduction for applied mathematicians. SIAM Rev 61(4):860–891

    Article  MathSciNet  Google Scholar 

  46. Bansal S (2015) A new Gibbs sampling based Bayesian model updating approach using modal data from multiple setups. Int J Uncertain Quantific 5(4):1

    Article  CAS  Google Scholar 

  47. Cheung SH, Bansal S (2017) A new Gibbs sampling based algorithm for Bayesian model updating with incomplete complex modal data. Mech Syst Signal Process 92:156–172

    Article  ADS  Google Scholar 

  48. Dong X, Liu X, Wright T, Wang Y, DesRoches R (2016) Validation of wireless sensing technology densely instrumented on a full-scale concrete frame structure. In: Transforming the future of infrastructure through smarter information: proceedings of the international conference on smart infrastructure and construction, 27–29 June 2016. ICE Publishing, New York, pp 143–148

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Correspondence to Pinghe Ni.

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Li, Q., Du, X., Ni, P. et al. Efficient Bayesian inference for finite element model updating with surrogate modeling techniques. J Civil Struct Health Monit (2024). https://doi.org/10.1007/s13349-024-00768-y

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