School of Biological Science and Medical Engineering, Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, 100083, China.
Laboratoire d'Imagerie Biomédicale (LIB), Centre National de la Recherche Scientifique (CNRS), Institut National de la Santé et de la Recherche Médicale (INSERM), Sorbonne Université, 75006, Paris, France.
J Mech Behav Biomed Mater. 2021 Dec;124:104848. doi: 10.1016/j.jmbbm.2021.104848. Epub 2021 Sep 22.
Finite element method based resonant ultrasound spectroscopy (FEM-based RUS) allows elasticity measurement for a material with high quality factor (Q) and arbitrary geometry by minimizing the differences between its theoretically calculated resonant frequencies and the corresponding experimentally measured ones. As Q decreases, some experimental frequencies remain undetermined, which makes it difficult to pair the calculated and experimental frequencies and to correctly identify the elastic constants. Additional difficulty need be tackled for irregularly-shaped low-Q materials due to the adoption of time-consuming FEM, thus efficiency of the identification method needs to be focused on. To apply FEM-based RUS to low-Q materials, a new elastic constant identification method is proposed based on a differential evolution algorithm in this paper. This method can perform a global search combining with local optimizations in the elastic constant space, and improve the overall efficiency by limiting the number of the frequency calculations. By using numerical experiments, the effectiveness of the proposed method under different frequency missing situations was verified and its efficiency was measured from the required frequency calculation numbers, showing an approximate two third reduction compared with an existing method. Finally, the elastic constants of an actual irregular cortical bone-mimicking material (Q ≈ 25) were measured using the two methods, yielding consistent Young's moduli (calculated from the identified constants) with the data provided by the manufacturer and a similar improvement in computational efficiency of the proposed method.
基于有限元法的共振超声光谱学（FEM-based RUS）通过最小化理论计算的共振频率与其对应的实验测量频率之间的差异，允许对具有高质量因数（Q）和任意几何形状的材料进行弹性测量。随着 Q 值的降低，一些实验频率仍然无法确定，这使得难以对计算和实验频率进行配对，并正确识别弹性常数。由于采用了耗时的有限元法，对于形状不规则的低 Q 值材料，还需要解决额外的困难，因此需要关注识别方法的效率。为了将基于有限元法的 RUS 应用于低 Q 值材料，本文提出了一种基于差分进化算法的新的弹性常数识别方法。该方法可以在弹性常数空间中进行全局搜索，并结合局部优化，通过限制频率计算次数来提高整体效率。通过数值实验，验证了该方法在不同频率缺失情况下的有效性，并从所需的频率计算次数来衡量其效率，与现有方法相比，效率提高了约三分之二。最后，使用两种方法测量了实际的不规则皮质骨模拟材料（Q≈25）的弹性常数，从识别出的常数计算出的杨氏模量与制造商提供的数据一致，并且该方法的计算效率也得到了类似的提高。
