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Reliability assessment and data inversion using a surrogate model of wave propagation in functionally graded materials. (English) Zbl 1461.62177

Summary: In this paper, we assess the reliability of explicit formulas introduced by P. C. Vinh et al. [Wave Motion 54, 134–144 (2015; Zbl 1454.74068)] to compute the propagation of one-component waves through a stack of homogeneous layers, inserted between two half-planes, as a surrogate model of wave propagation in functionally graded materials (FGM). Afterwards, we use the model reliability assessment as diagnostics prior to solving the associated inverse problem. We have used both the Legendre continuous nodal Galerkin method with Gauss-Lobatto quadratures (LCNG) and the Thomson-Haskell (TH) method as reference approaches to approximate the solution of the continuous problem. Consequently, we have compared computationally the output of the surrogate model, the TM method and the LCNG method through sensitivity analysis; and secondly, we have used the surrogate model and the Bayesian inferential framework to estimate the FGM shear modulus given measurements of the amplitude of the reflected wave. We have found that if we know the structure of noise in the data and the signal to noise ratio, then we can reliably infer the FGM shear modulus.

MSC:

62N05 Reliability and life testing
62F15 Bayesian inference
74J10 Bulk waves in solid mechanics

Citations:

Zbl 1454.74068

Software:

corner.py
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Full Text: DOI

References:

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