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

Isabela Coelho Lima, Annika Robens-Radermacher, Thomas Titscher, Daniel Kadoke, Phaedon Stelios Koutsourelakis, Jörg F. Unger

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)1189-1210
Number of pages22
JournalComputational Mechanics
Issue number6
StatePublished - Dec 2022


  • Digital twin
  • Goal-oriented
  • Proper Generalized Decomposition
  • Random field
  • Variational inference


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