基于能量最小化原理的弹性波CT成像频域有限元反演算法

FEM Inversion Algorithm in Frequency Domain for ElasticWave CT Based on Energy Minimization Principles

摘要:

在材料和模型实验中，试样内部位移场的精确量测对于加载过程中试样力学性质的研究有着十分重要的意义。提出基于能量最小化原理的弹性波CT成像频域有限元反演算法，并在波动方程的基础上通过有限元数值实验，利用估计位移场和实际位移场的偏差，得出包括密度ρ和拉梅常数λ在内的单元材料参数的更新梯度，进一步经过若干次正负反馈的迭代，实现试样参数的反演。该算法避开已有方法中求解参数更新梯度Jacobi矩阵的过程，计算效率得到极大的提高。计算结果表明，在已知位移场的情况下，迭代更新λ的效率和准确性较高；在已知部分节点实际位移的情况下，参数迭代效率与观测网格密度正相关。

Abstract:

In element and model tests, high-accuracy measurement for the internal displacement field of a sample is crucial in investigating the mechanical property of the material under loading. In this study, a frequency-domain finite element method based on the energy minimization principle is developed for elastic wave CT. Through solving the wave equation numerically, the displacement fields are estimated and then compared with their actual values. Thus, the renewal gradients of the parameters of every element are obtained, including the density (ρ) and the Lame constant (λ). Furthermore, the distribution of density (ρ) and the Lame constant (λ) can be acquired upon several iterations. The new method can avoid solving the Jacobi matrix, leading to a great improvement in calculation efficiency. In addition, the numerical inversion iteration of the Lame constant (λ) shows high efficiency and accuracy when the whole displacement field is known, and the efficiency and accuracy gradually decrease with an increased number of unknown displacement nodes.