Recent technological advances have led to the development of layered and intricate structures that have widely found applications in aerospace, automotive, construction and energy sectors. As such, the development of strict quality control and nondestructive evaluation procedures to ensure that the characteristics of the employed layers match the requirements has been a natural target in the field of composites. At present, experimental testing is expected to play important roles in detecting or updating the mechanical properties of structures, assessing system conditions and reconciling numerical predictions. In this context, inverse techniques in the time domain, frequency domain or time-frequency domain ought to be used to extract the information about the behavior of a structure directly from experimental data. Past research proposed the application of deterministic wave propagation techniques. These have, however, been overtaken by the recently proposed Bayesian statistical approaches coupled with modern signal processing techniques.
Multinational collaboration between Professor Wang-Ji Yan and Dr. Ka-Veng Yuen at University of Macau in China together with Dr. Dimitrios Chronopoulos and Dr. Sergio Cantero-Chinchilla at The University of Nottingham in England and Professor Costas Papadimitriou at the University of Thessaly in Greece, proposed to develop a fast Bayesian inference scheme based on multifrequency single shot measurements of wave propagation characteristics, to overcome the limitations of ill-conditioning and non-uniqueness associated with the conventional approaches. Their work has been recently published in the top journal, Mechanical Systems and Signal Processing.
In their approach, a Transitional Markov chain Monte Carlo (TMCMC) algorithm was employed for the sampling process. A Wave and Finite Element (WFE)-assisted metamodeling scheme in lieu of expensive-to-evaluate explicit FE analysis was 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 was 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 was also properly taken into account when estimating the posterior probability distribution of the parameters by TMCMC. Lastly, a numerical study as well as an experimental study were conducted to verify the computational efficiency and accuracy of the proposed methodology.
The authors reported that the TMCMC algorithm in conjunction with the WFE forward solver-aided metamodeling could sample the posterior probability density function of the updated parameters at a very reasonable cost. More so, the researchers reported that the practically unlimited and user-selected excitation frequencies, as well as wave dispersiveness could effectively increase the number of identifiable parameters through inverse wave modelling, resulting in a significant increase of the method’s robustness and applicability in a broadband frequency sense.
In summary, the study demonstrated the successful development and application of a Bayesian identification technique based on FE modelling and the properties of propagating waves in multilayered structures. The principal contribution was the development of a robust numerical nondestructive testing procedure for recovering effective and local structural parameters of layered composites through a WFE-aided metamodeling. In a statement to Advances in Engineering, the authors mentioned that their approach was 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.
Wang-Ji Yan, Dimitrios Chronopoulos, Sergio Cantero-Chinchilla, Ka-Veng Yuen, Costas Papadimitriou. 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. Mechanical Systems and Signal Processing, volume 143 (2020) 106802.