Probabilistic Guided Wave Inversion for Nondestructive Characterization of Stratified Media

该项目涉及基础研究，旨在通过无损评估(NDE)来估计层状结构的未知几何和材料特性。这是通过向系统发送声波，并使用植根于数学、力学和统计学的高级计算算法处理产生的数据来实现的。该项目的成功完成将推动各个具有高度社会经济影响的领域的最先进水平：(A)用于准确确定建筑物和桥梁上的地震荷载的土层的特性，(B)用于土木、机械和航空航天工程的层叠复合材料的无损检测，(C)在电子工业和材料科学中普遍存在的衬底薄膜的无损检测，(D)国家基础设施的最大部分--人行道的无损检测，以及(E)可能导致早期诊断心血管疾病的动脉僵硬的估计。鉴于其广泛的性质，该项目自然会导致研究生的跨学科培训。此外，该项目将包括为招收高中生进入STEM学科开发教育模块。当波能被赋予分层结构时，它以导波的形式沿着层传播，导波弥散和衰减。长期以来，频散和衰减特性一直被用来无损地估计层状结构的未知几何和材料特性，使用的数学和计算算法被归类为导波反演(GWI)。虽然量化估计参数中的不确定性很重要，但统计方法很少在GWI中使用，因为需要大量的模拟，需要大量的计算资源。该项目的目的是克服导致发展实用概率GWI技术的计算费用的瓶颈。通过结合两种新开发的技术将降低计算成本：(A)基于有限元离散和有理(Padé)近似的不同思想的复数长度有限元方法，以及(B)有助于逆迭代更快收敛的色散曲线的近似解析微分。总而言之，这些想法导致了计算成本的数量级减少。这些技术将被充分开发用于复杂结构，如具有流固耦合和多向捕获的圆柱形波导，然后被纳入贝叶斯统计推理框架，以量化不确定性。最终的算法将反演实验的色散和衰减曲线，并导致层状介质的概率重建，将通过多个应用问题进行验证。

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.