Chen Qi, Xu Kailiang, Ta Dean
Center for Biomedical Engineering, School of Information Science and Technology, Fudan University, Shanghai 200433, China.
Center for Biomedical Engineering, School of Information Science and Technology, Fudan University, Shanghai 200433, China; Zhuhai Fudan Innovation Institute, Zhuhai 519000, China.
Ultrasonics. 2021 Aug;115:106427. doi: 10.1016/j.ultras.2021.106427. Epub 2021 Apr 16.
Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.
超声兰姆波已被广泛用于无损评估和检测。然而，从测量的导波信号反演材料特性，在多模态色散信号处理和参数估计方面仍然是一项具有挑战性的任务。本文提出了一种稳健的策略，包括多模态色散曲线的高分辨率提取和基于模型的弹性特性估计。首先，采用旋转不变技术估计信号参数（ESPRIT）来提取板中兰姆波的色散曲线。然后，利用粒子群优化（PSO）算法，通过最大化由色散方程构建的目标函数来检索最优模型参数。从而可以确定弹性特性（即各向同性板的两个独立常数和横向各向同性板的四个常数）。钢、铝和复合材料板的结果表明，估计值与参考值一致。模拟、钢、铝和复合材料实验中，由反演模型参数计算得到的估计色散曲线与理论色散曲线之间的均方根误差（RMSE）分别为0.027 rad/mm、0.032 rad/mm、0.033 rad/mm和0.102 rad/mm。厚度估计误差小于1%。所提出的基于模型的反演策略具有几个优点：（1）色散曲线的高分辨率估计允许为参数反演构建目标函数而无需寻峰过程。（2）基于ESPRIT的色散曲线提取策略在参数空间中提供了一个尖锐的目标函数。（3）使用PSO优化器解决了超声导波特性的反问题，该优化器易于实现且几乎无需调整参数。
