Abstract
This paper proposes a multi-level Bayesian calibration approach that fuses information from heterogeneous sources and accounts for uncertainties in modeling and measurements for time-dependent multi-component systems. The developed methodology has two elements: quantifying the uncertainty at component and system levels, by fusing all available information, and corrected model prediction. A multi-level Bayesian calibration approach is developed to estimate component-level and system-level parameters using measurement data that are obtained at different time instances for different system components. Such heterogeneous data are consumed in a sequential manner, and an iterative strategy is developed to calibrate the parameters at the two levels. This calibration strategy is implemented for two scenarios: offline and online. The offline calibration uses data that is collected over all the time-steps, whereas online calibration is performed in real-time as new measurements are obtained at each time-step. Analysis models and observation data for the thermo-mechanical behavior of gas turbine engine rotor blades are used to analyze the effectiveness of the proposed approach.
Keywords:
information fusion,
Bayesian statistics,
model calibration,
uncertainty quantification,
Bayesian network,
artificial intelligence,
big data and analytics,
data-driven engineering,
inverse methods for engineering applications,
machine learning for engineering applications,
model-based systems engineering,
multi-physics modeling and simulation,
physics-based simulations
References
1.
VanDerHorn
, E.
, and Mahadevan
, S.
, 2018
, “Bayesian Model Updating With Summarized Statistical and Reliability Data
,” Reliab. Eng. Syst. Saf.
, 172
, pp. 12
–24
. 2.
Karve
, P. M.
, Guo
, Y.
, Kapusuzoglu
, B.
, Mahadevan
, S.
, and Haile
, M. A.
, 2020
, “Digital Twin Approach for Damage-Tolerant Mission Planning Under Uncertainty
,” Eng. Fract. Mech.
, 225
, p. 106766
. 3.
Viana
, F. A.
, and Subramaniyan
, A. K.
, 2021
, “A Survey of Bayesian Calibration and Physics-Informed Neural Networks in Scientific Modeling
,” Arch. Comput. Methods Eng.
, 28
(5
), pp. 3801
–3830
. 4.
DeCarlo
, E. C.
, Smarslok
, B. P.
, and Mahadevan
, S.
, 2016
, “Segmented Bayesian Calibration of Multidisciplinary Models
,” AIAA J.
, 54
(12
), pp. 3727
–3741
. 5.
Nannapaneni
, S.
, and Mahadevan
, S.
, 2016
, “Manufacturing Process Evaluation Under Uncertainty: A Hierarchical Bayesian Network Approach
,” IDETC-CIE, Vol. Volume 1B: 36th Computers and Information in Engineering Conference
, Charlotte, NC
, Aug. 21–24
, ASME
, p. V01BT02A026
.6.
Rebba
, R.
, and Mahadevan
, S.
, 2006
, “Model Predictive Capability Assessment Under Uncertainty
,” AIAA J.
, 44
(10
), pp. 2376
–2384
. 7.
Mahadevan
, S.
, Zhang
, R.
, and Smith
, N.
, 2001
, “Bayesian Networks for System Reliability Reassessment
,” Struct. Saf.
, 23
(3
), pp. 231
–251
. 8.
Kennedy
, M. C.
, and O’Hagan
, A.
, 2001
, “Bayesian Calibration of Computer Models
,” J. R. Stat. Soc.: Ser. B (Stat. Methodol.)
, 63
(3
), pp. 425
–464
. 9.
Ling
, Y.
, Mullins
, J.
, and Mahadevan
, S.
, 2014
, “Selection of Model Discrepancy Priors in Bayesian Calibration
,” J. Comput. Phys.
, 276
, pp. 665
–680
. 10.
Sankararaman
, S.
, and Mahadevan
, S.
, 2015
, “Integration of Model Verification, Validation, and Calibration for Uncertainty Quantification in Engineering Systems
,” Reliab. Eng. Syst. Saf.
, 138
, pp. 194
–209
. 11.
Li
, C.
, and Mahadevan
, S.
, 2016
, “Role of Calibration, Validation, and Relevance in Multi-Level Uncertainty Integration
,” Reliab. Eng. Syst. Saf.
, 148
, pp. 32
–43
. 12.
Behmanesh
, I.
, Moaveni
, B.
, Lombaert
, G.
, and Papadimitriou
, C.
, 2015
, “Hierarchical Bayesian Model Updating for Structural Identification
,” Mech. Syst. Signal Process.
, 64
, pp. 360
–376
. 13.
Nagel
, J. B.
, and Sudret
, B.
, 2015
, “Bayesian Multilevel Model Calibration for Inverse Problems Under Uncertainty With Perfect Data
,” J. Aerosp. Inf. Syst.
, 12
(1
), pp. 97
–113
.14.
Nagel
, J. B.
, and Sudret
, B.
, 2016
, “A Unified Framework for Multilevel Uncertainty Quantification in Bayesian Inverse Problems
,” Probab. Eng. Mech.
, 43
, pp. 68
–84
. 15.
Jia
, X.
, Sedehi
, O.
, Papadimitriou
, C.
, Katafygiotis
, L. S.
, and Moaveni
, B.
, 2022
, “Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics Using Modal Features
,” Mech. Syst. Signal Process.
, 170
, p. 108784
. 16.
Sedehi
, O.
, Papadimitriou
, C.
, and Katafygiotis
, L. S.
, 2019
, “Probabilistic Hierarchical Bayesian Framework for Time-Domain Model Updating and Robust Predictions
,” Mech. Syst. Signal Process.
, 123
, pp. 648
–673
. 17.
Sedehi
, O.
, Katafygiotis
, L. S.
, and Papadimitriou
, C.
, 2020
, “Hierarchical Bayesian Operational Modal Analysis: Theory and Computations
,” Mech. Syst. Signal Process.
, 140
, p. 106663
. 18.
Song
, M.
, Behmanesh
, I.
, Moaveni
, B.
, and Papadimitriou
, C.
, 2020
, “Accounting for Modeling Errors and Inherent Structural Variability Through a Hierarchical Bayesian Model Updating Approach: An Overview
,” Sensors
, 20
(14
), p. 3874
. 19.
Mullins
, J.
, and Mahadevan
, S.
, 2016
, “Bayesian Uncertainty Integration for Model Calibration, Validation, and Prediction
,” ASME J. Verif. Valid. Uncertain. Quantif.
, 1
(1
), p. 011006
.20.
DeCarlo
, E. C.
, Smarslok
, B. P.
, and Mahadevan
, S.
, 2018
, “Quantifying Model Discrepancy in Time-Dependent, Coupled Analyses
,” AIAA J.
, 56
(6
), pp. 2403
–2411
. 21.
Pearl
, J.
, 1988
, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
, Morgan Kaufmann Publishers Inc.
, San Francisco, CA
.22.
Hastings
, W. K.
, 1970
, “Monte Carlo Sampling Methods Using Markov Chains and Their Applications
,” Biometrika
, 57
(1
), pp. 97
–109
. 23.
Del Moral
, P.
, Doucet
, A.
, and Jasra
, A.
, 2006
, “Sequential Monte Carlo Samplers
,” J. R. Stat. Soc.: Ser. B (Stat. Methodol.)
, 68
(3
), pp. 411
–436
. 24.
Fearnhead
, P.
, 2004
, “Particle Filters for Mixture Models With an Unknown Number of Components
,” Stat. Comput.
, 14
(1
), pp. 11
–21
. 25.
Dempster
, A. P.
, Laird
, N. M.
, and Rubin
, D. B.
, 1977
, “Maximum Likelihood From Incomplete Data Via the EM Algorithm
,” J. R. Stat. Soc.: Ser. B (Methodol.)
, 39
(1
), pp. 1
–22
.26.
Xiu
, D.
, and Karniadakis
, G. E.
, 2002
, “The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,” SIAM J. Sci. Comput.
, 24
(2
), pp. 619
–644
. 27.
Rasmussen
, C. E.
, 2004
, Gaussian Processes in Machine Learning
, Springer
, Berlin
, pp. 63
–71
.28.
Geurts
, P.
, Ernst
, D.
, and Wehenkel
, L.
, 2006
, “Extremely Randomized Trees
,” Mach. Learn.
, 63
(1
), pp. 3
–42
. 29.
Ke
, G.
, Meng
, Q.
, Finley
, T.
, Wang
, T.
, Chen
, W.
, Ma
, W.
, Ye
, Q.
, and Liu
, T.-Y.
, 2017
, “Lightgbm: A Highly Efficient Gradient Boosting Decision Tree,” Advances in Neural Information Processing Systems
, Guyon
, I.
, Luxburg
, U. V.
, Bengio
, S.
, Wallach
, H.
, Fergus
, R.
, Vishwanathan
, S.
, and Garnett
, R.
, eds, Vol. 30
, Curran Associates, Inc.
, Long Beach, CA
, pp. 3149
–3157
.30.
Chen
, T.
, and Guestrin
, C.
, 2016
, “Xgboost: A Scalable Tree Boosting System
,” Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16
, San Francisco, CA
, Aug. 13–17
, Association for Computing Machinery
, pp. 785
–794
.31.
Prokhorenkova
, L.
, Gusev
, G.
, Vorobev
, A.
, Dorogush
, A. V.
, and Gulin
, A.
, 2018
, “Catboost: Unbiased Boosting With Categorical Features,” Advances in Neural Information Processing Systems
, Bengio
, S.
, Wallach
, H.
, Larochelle
, H.
, Grauman
, K.
, Cesa-Bianchi
, N.
, and Garnett
, R.
, eds., Vol. 31
, Curran Associates, Inc
., Montreal, Canada.32.
Franklin
, J.
, 2005
, “The Elements of Statistical Learning: Data Mining, Inference and Prediction
,” Math. Intelligencer
, 27
(2
), pp. 83
–85
. 33.
Halko
, N.
, Martinsson
, P.-G.
, and Tropp
, J. A.
, 2011
, “Finding Structure With Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
,” SIAM Rev.
, 53
(2
), pp. 217
–288
. 34.
Kapusuzoglu
, B.
, Guo
, Y.
, Mahadevan
, S.
, Matsumoto
, S.
, Yoshitomo
, M.
, Taba
, S.
, and Watanabe
, D.
, 2022
, “Dimension Reduction for Efficient Surrogate Modeling in High-Dimensional Applications
,” AIAA SCITECH 2022 Forum
, San Diego, CA
, Jan. 3–7
, p. 1440
.35.
Morris
, M. D.
, and Mitchell
, T. J.
, 1995
, “Exploratory Designs for Computational Experiments
,” J. Stat. Plann. Inference
, 43
(3
), pp. 381
–402
. 36.
Arendt
, P. D.
, Apley
, D. W.
, and Chen
, W.
, 2012
, “Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability
,” ASME J. Mech. Des.
, 134
(10
), p. 100908
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