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

Abstract

Reliable verification and evaluation of the mechanical properties of an assembled layered composite ensemble are critical for industrially relevant applications, but 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 2 of the prediction variance introduced by the use of a surrogate model are 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.

Sampling methods for solving Bayesian model updating problems: A tutorial

“…It is also noteworthy that by adopting the Uniform distribution as the prior, the posterior would simply be proportional to the likelihood function. Some recent research works which adopted the Uniform prior in its Bayesian model updating set-up include: estimating model parameters used to model a bolted structure [45]; structural parameters of a composite structure [46]; crack parameters of a beam structure [47]; stiffness and mass parameters of a DLR-AIRMOD structure [48]; and stiffness parameters of a cantilever beam [49].…”

A homogenisation scheme for ultrasonic Lamb wave dispersion in textile composites through multiscale wave and finite element modelling

“…[27][28][29][30][31]33 Bayesian inverse algorithms and neural network techniques are also used as inversion procedures. 35,36 Balasubramaniam and Rao 27 were the first to employ GAs for inverting unidirectional composite material elastic moduli with significant success. The advantage of GAs over other search algorithms is that GAs do not need an initial guess but rather a valid search space; GAs are also robust and avoid entrapment at local minima.…”

“…Bulk 24–28 and Lamb 28–34 wave data are both of interest, and many different optimisation algorithms have been put to use in that context, such as the least‐square method, 24–26 simulated annealing, 34 or Genetic Algorithms (GAs) 27–31,33 . Bayesian inverse algorithms and neural network techniques are also used as inversion procedures 35,36 . Balasubramaniam and Rao 27 were the first to employ GAs for inverting unidirectional composite material elastic moduli with significant success.…”

Reconstruction of Material Stiffness Properties From Dispersion Relations Using Genetic Algorithms

“…Different inversion procedures have been used to identify the elastic constants of composite plates [12,19,20,21]. Balasubramaniam [19] was the first to employ genetic algorithms (GAs) for inverting unidirectional composite material elastic moduli with significant success.…”

“…Neural network techniques have also been applied in solving inverse problems [12,20]. More recently, a Bayesian identification technique based on finite element modelling and the properties of propagating waves in multilayered structures is proposed, which overcomes the limitations of ill-conditioning and non-uniqueness associated with the conventional approaches [21]. Considering the advantages of GAs, GAs are adopted in this paper.…”