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Dölz, J., Harbrecht, H., Jerez-Hanckes, C., & Multerer M. (2022). Isogeometric multilevel quadrature for forward and inverse random acoustic scattering. Comput. Methods in Appl. Mech. Eng., 388, 114242.
Abstract: We study the numerical solution of forward and inverse time-harmonic acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that it suffices to know the deformation field’s expectation and covariance at the scatterer’s boundary to model the surface’s Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered wave’s expectation and variance. By computing the wave’s Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problems validate the proposed approach.
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Zhao, W. H., Yang, L. C., Dang, C., Rocchetta, R., Valdebenito, M., & Moens, D. (2022). Enriching stochastic model updating metrics: An efficient Bayesian approach using Bray-Curtis distance and an adaptive binning algorithm. Mech. Syst. Sig. Process., 171, 108889.
Abstract: In practical engineering, experimental data is not fully in line with the true system response due to various uncertain factors, e.g., parameter imprecision, model uncertainty, and measurement errors. In the presence of mixed sources of aleatory and epistemic uncertainty, stochastic model updating is a powerful tool for model validation and parameter calibration. This paper in-vestigates the use of Bray-Curtis (B-C) distance in stochastic model updating and proposes a Bayesian approach addressing a scenario where the dataset contains multiple outliers. In the proposed method, a B-C distance-based uncertainty quantification metric is employed, that re-wards models for which the discrepancy between observations and simulated samples is small while penalizing those which exhibit large differences. To improve the computational efficiency, an adaptive binning algorithm is developed and embedded into the Bayesian approximate computation framework. The merit of this algorithm is that the number of bins is automatically selected according to the difference between the experimental data and the simulated data. The effectiveness and efficiency of the proposed method is verified via two numerical cases and an engineering case from the NASA 2020 UQ challenge. Both static and dynamic cases with explicit and implicit propagation models are considered.
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