A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography

Abstract

SUMMARY The present paper proposes a novel Bayesian, a computational strategy in the context of model‐based inverse problems in elastostatics. On one hand, we attempt to provide probabilistic estimates of the material properties and their spatial variability that account for the various sources of uncertainty. On the other hand, we attempt to address the question of model fidelity in relation to the experimental reality and particularly in the context of the material constitutive law adopted. This is especially important in biomedical settings when the inferred material properties will be used to make decisions/diagnoses. We propose an expanded parametrization that enables the quantification of model discrepancies in addition to the constitutive parameters. We propose scalable computational strategies for carrying out inference and learning tasks and demonstrate their effectiveness in numerical examples with noiseless and noisy synthetic data. Copyright © 2012 John Wiley & Sons, Ltd.

Beyond Black-Boxes in Bayesian Inverse Problems and Model Validation: Applications in Solid Mechanics of Elastography

“…The present paper extends previous work [63] towards developing a novel modeling framework and a set of scalable algorithms that will address the two main challenges in model calibration and validation in PDE-based models, i.e. a) the significant computational cost in problems with an expensive, black-box forward model, and b) the quantification of structural, model uncertainty and its effect on model calibration and predictive estimates.…”

“…However, this explicit additive term may violate physical constraints (e.g. conservation of mass, energy), can get entangled with the measurement error, is not physically interpretable and cumbersome or impractical to infer when it depends on a large number of input parameters [5,7,63,91,96].…”

Constitutive model error and uncertainty quantification

“…In this paper, we introduced an effective quantification of model fidelity with an intrusive Bayesian framework to quantify constitutive model error. Based on recent work [9], we opened the classical black-box forward problem to assess the model fidelity in a physical context. In addition, we added a consistent normalization term, which allows for more flexible prior assumptions.…”

Bayesian inference to identify parameters in viscoelasticity

“…For two decades afterwards, BI was not used for material parameter identification. When the developments started again, it was amongst others used for the identification of elastic constants from dynamic responses (Alvin 1997;Beck and Katafygiotis 1998;Marwala and Sibusiso 2005;Daghia et al 2007;Abhinav and Manohar 2015), the elastic constants of composite and laminate plates (Lai and Ip 1996;Daghia et al 2007;Nichols et al 2010;Gogu et al 2013) and spatially varying elastic constants (Koutsourelakis 2012). An introduction to identify Young's moduli using BI is presented in Gogu et al (2010).…”