Goodlet Brent R, Bales Ben, Pollock Tresa M
Materials Department, University of California, Santa Barbara, CA 93106, USA.
The Earth Institute, Columbia University, New York, NY 10025, USA.
Ultrasonics. 2021 Aug;115:106455. doi: 10.1016/j.ultras.2021.106455. Epub 2021 Apr 24.
A novel nondestructive method for complete elastic characterization of substrate-coating bilayer specimens with distinct anisotropic layers via resonant ultrasound spectroscopy (RUS) and Bayesian inversion is developed here. Bayesian formulations of the RUS inversion problem-of quantifying elastic properties given a measured list of resonance frequencies recorded from a single, typically small, precisely fabricated, macroscopically homogeneous, linear-elastic specimen-are a recent development. Here we report the first Bayesian formulation of the bilayer problem, and through a series of practical examples, demonstrate novel parameter estimation capabilities of our open-source CmdStan-RUS code. Finding specimen geometry and the number of resonance modes used for inversion strongly govern the ability to retrieve individual elastic moduli. The concept of "invertability" is explored for a range of relevant geometries using virtual specimens that resemble experimental bilayers of plasma sprayed ceramic coatings on single crystal metallic substrates. A range of Bayesian posterior evaluation methods are addressed, particularly considering the large computational cost of the bilayer forward model. Laplace approximation methods are thus developed and implemented for bilayer geometry design space modeling and expedient estimates of parameter uncertainties. Ideal specimen design, different noise models, the influence of prior distributions, dual-likelihood fits incorporating measurements of the bare substrate, and how Bayesian RUS methods differ from traditional RUS optimization are discussed.
本文开发了一种新颖的无损方法，通过共振超声光谱（RUS）和贝叶斯反演对具有不同各向异性层的基底-涂层双层试样进行完整的弹性表征。RUS反演问题的贝叶斯公式——即给定从单个（通常较小）、精确制造、宏观均匀的线弹性试样记录的共振频率测量列表来量化弹性特性——是最近的一项进展。在这里，我们报告了双层问题的首个贝叶斯公式，并通过一系列实际示例展示了我们的开源CmdStan-RUS代码的新型参数估计能力。找到试样几何形状以及用于反演的共振模式数量对恢复各个弹性模量的能力有很大影响。使用类似于单晶金属基底上等离子体喷涂陶瓷涂层实验双层的虚拟试样，对一系列相关几何形状探讨了“可反演性”概念。讨论了一系列贝叶斯后验评估方法，特别考虑到双层正向模型的巨大计算成本。因此开发并实施了拉普拉斯近似方法，用于双层几何设计空间建模和参数不确定性的便捷估计。讨论了理想试样设计、不同噪声模型、先验分布的影响、结合裸基底测量的双似然拟合以及贝叶斯RUS方法与传统RUS优化的不同之处。
