Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

Advanced Modeling and Simulation in Engineering Sciences

Research Article

Harald Willmann¹  Wolfgang A. Wall¹  Sebastian Brandstäter²  Jonas Nitzler³ 

[1]Institute for Computational Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. München, Germany

[2]Institute for Computational Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. München, Germany

[3]Institute for Continuum and Material Mechanics, University of Technology Hamburg, Eißendorfer Str. 42, 21073, Hamburg, Germany

[4]Institute for Computational Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. München, Germany

[5]Professorship for Data-driven Materials Modeling, Technical University of Munich, Boltzmannstr. 15, 85748, Garching b. München, Germany

关键词: Bayesian calibration;    Inverse analysis;    Coupled problems;    Fluid–structure interaction;    Interface shape;    Biofilm;   

DOI  :  10.1186/s40323-022-00237-5

 received in 2022-06-09, accepted in 2022-11-28,  发布年份 2022

来源: Springer

【 摘 要 】

Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement data of material points is available. The interpretation of such a calibration problem as a statistical inference problem, in contrast to deterministic model calibration, is computationally more robust and allows the analyst to find a posterior distribution over possible solutions rather than a single point estimate. The proposed framework also enables the consideration of unavoidable uncertainties that are present in every experiment and are expected to play an important role in the model calibration process. To mitigate the computational costs of expensive forward model evaluations, we propose to learn the log-likelihood function from a controllable amount of parallel simulation runs using Gaussian process regression. We introduce and specifically study the effect of three different discrepancy measures for deformed interfaces between reference data and simulation. We show that a statistically based discrepancy measure results in the most expressive posterior distribution. We further apply the approach to numerical examples in higher model parameter dimensions and interpret the resulting posterior under uncertainty. In the examples, we investigate coupled multi-physics models of fluid–structure interaction effects in biofilms and find that the model parameters affect the results in a coupled manner.

【 授权许可】

CC BY   
© The Author(s) 2022

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