The project involves fundamental research aimed at estimating unknown geometric and material properties of layered structures through non destructive evaluation (NDE). This is achieved by sending sound waves into the system and processing the resulting data using advanced computational algorithms rooted in mathematics, mechanics and statistics. Successful completion of the project will advance the state of the art in various areas of high socioeconomic impact: (a) characterizing soil layers for accurate determination of earthquake loads on buildings and bridges, (b) NDE of laminated composites used in civil, mechanical and aerospace engineering, (c) NDE of thin films on substrates, prevalent in electronics industry and materials science, (d) NDE of pavements, the largest part of the nation's infrastructure, and (e) estimation of arterial stiffness that could lead to early diagnosis of cardiovascular diseases. Given its broad nature, the project will naturally lead to interdisciplinary training of graduate students. Further, the project will include the development of education modules for recruitment of high-school students into STEM disciplines.
When wave energy is imparted into stratified structures, it propagates along the layers in the form of guided waves that disperse and decay. The dispersion and attenuation characteristics have long been used to nondestructively estimate unknown geometric and material properties of the layered structures, using mathematical and computational algorithms classified as guided wave inversion (GWI). While it is important to quantify uncertainty in the estimated parameters, statistical approaches are rarely used in GWI due to the need for a large number of simulations requiring intense computational resources. The project is aimed at overcoming the bottleneck of computational expense leading to the development of practical probabilistic GWI techniques. The computational cost will be reduced by incorporating two newly developed techniques: (a) complex-length finite element method, based on linking the disparate ideas of finite element discretization and rational (Padé) approximants, and (b) approximate analytical differentiation of the dispersion curves that facilitate faster convergence of inverse iterations. Together, these ideas lead to orders of magnitude reduction in the computational cost. These techniques will be fully developed for complicated structures such as cylindrical waveguides with fluid-structure interaction and multidirectional acquisition, and then be incorporated into a Bayesian statistical inference framework to quantify uncertainty. The final algorithms, which will invert the experimental dispersion and attenuation curves and result in probabilistic reconstructions of stratified media, will be validated using multiple application problems.
