A fast Bayesian inference scheme for identification of local structural properties of layered composites based on wave and finite element-assisted metamodeling strategy and ultrasound measurements. (September 2020) - Yan, Wang-Ji; Chronopoulos, Dimitrios; Cantero-Chinchilla, Sergio; Yuen, Ka-Veng; Papadimitriou, Costas
Highlights: A fast Bayesian approach is proposed to recover the mechanical properties of layered composites. An ultrafast WFE forward solver is presented for quantifying wave characteristics. WFE-assisted metamodeling scheme can overcome the computational challenges of likelihood evaluations and TMCMC sampling. The uncertainty of the prediction variance introduced by the surrogate model are properly accommodated. The computational efficiency and accuracy are verified by an experimental study. Abstract: Reliable verification and evaluation of the mechanical properties of a layered composite ensemble are critical for industrially relevant applications, however it still remains an open engineering challenge. In this study, a fast Bayesian inference scheme based on multi-frequency single shot measurements of wave propagation characteristics is developed to overcome the limitations of ill-conditioning and non-uniqueness associated with the conventional approaches. A Transitional Markov chain Monte Carlo (TMCMC) algorithm is employed for the sampling process. A Wave and Finite Element (WFE)-assisted metamodeling scheme in lieu of expensive-to-evaluate explicit FE analysis is proposed to cope with the high computational cost involved in TMCMC sampling. For this, the Kriging predictor providing a surrogate mapping between the probability spaces of the model predictions for the wave characteristics and the mechanical properties in the likelihood evaluations is established based on the training outputs computed using a WFE forward solver, coupling periodic structure theory to conventional FE. The valuable uncertainty information of the prediction variance introduced by the use of a surrogate model is also properly taken into account when estimating the parameters' posterior probability distribution by TMCMC. A numerical study as well as an experimental study are conducted to verify the computational efficiency and accuracy of the proposed methodology. Results show that the TMCMC algorithm in conjunction with the WFE forward solver-aided metamodeling can sample the posterior Probability Density Function (PDF) of the updated parameters at a very reasonable cost. This approach is capable of quantifying the uncertainties of recovered independent characteristics for each layer of the composite structure under investigation through fast and inexpensive experimental measurements on localized portions of the structure.