Chang, Q., Zhou, C. C., Valdebenito, M. A., Liu, H. W., & Yue, Z. F. (2022). A novel sensitivity index for analyzing the response of numerical models with interval inputs. Comput. Methods in Appl. Mech. Eng., 400, 115509.
Abstract: This study proposes a novel sensitivity index to provide essential insights into numerical models whose inputs are characterized by intervals. Based on the interval model and its normalized form, the interval processes are introduced to define a new sensitivity index. The index can represent the individual or joint influence of the interval inputs on the output of a considered model. A double-loop strategy, based on global metamodeling and optimization, is established to calculate the index. Subsequently, the proposed index is theoretically compared with two other existing indices, and it is experimentally applied to three numerical examples and a practical engineering problem of a honeycomb sandwich radome. The results indicate that the proposed index is an effective tool for interval sensitivity analysis.
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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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