Bayesian inference for random field parameters with a goal-oriented quality control of the PGD forward model’s accuracy

Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future of monitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally c...

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Bibliographic Details
Published in:	Computational mechanics Vol. 70; no. 6; pp. 1189 - 1210
Main Authors:	Coelho Lima, Isabela, Robens-Radermacher, Annika, Titscher, Thomas, Kadoke, Daniel, Koutsourelakis, Phaedon-Stelios, Unger, Jörg F.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2022 Springer Springer Nature B.V
Subjects:	Accuracy Bayesian analysis Classical and Continuum Physics Computational Science and Engineering Damage detection Digital twins Divergence Engineering Fields (mathematics) Model accuracy Numerical models Original Paper Parameter identification Probability density functions Quality control Reduced order models Statistical inference Stochastic models Stochastic processes Theoretical and Applied Mechanics Twins Proper Generalized Decomposition Random field Variational inference Digital twin Goal-oriented
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Summary:	Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future of monitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results.
ISSN:	0178-7675 1432-0924
DOI:	10.1007/s00466-022-02214-6