Structural Damage Detection with Lamb Waves Based on Time-Domain Convolution and Smoothing Methods

Problem Description:

It's one of the two final projects of the course Statistics Learning. The students need to choose one topic based on their research direction and solve the problem with the methods of statistics learning.

My topic is to detect the structural damage with lamb waves. There are two core problems in this topic: how to separate the multi-mode signal into single modes and how to localize the damage structure. A better performance is expected with the help of the statistics learning methods.

The Solution:

In the previous project, the multi-mode signal separation problem was tackled by the frequency-wavenumber analysis and special clustering algorithm, and the localization of the damage was done by estimating the signal amplitude distribution based on the finite element model. However, the multi-mode signal separation part in the previous work had a huge computation cost, which made it hard to be used in practice.

Here I used a time-domain method to solve this problem, as shown in Figure 1, with a small computation cost: Firstly, the wavelet smoothing was utilized to eliminate the random noise in the raw signal. Then we convolute the output of wavelet smoothing with the excitation signal, a complete lamb wave. Due to the similarity of the excitation signal and the dispersive signal, the convolution signal would reach its peaks when the excitation signal was shifted to the position of the single-mode components. The positions of single-mode components could be obtained by detecting the peaks in the convolution result. At last, the amplitude of each components was estimated as a least square error problem. The local linear regression method aims at reducing the effect of the noise because the single-mode components were sparse in time domain. In Figure 2, the reconstruction signals (green/red) and the raw signal (blue) were matched well.

In the localization section, I employed the A0-mode amplitudes in all the sensor nodes as predictors of the signal amplitude distribution in the 2-D plate. In the previous research, we declared that the model-based methods had better accuracy than response-based ones. Here I compared the FEM-based algorithm, one model-based method proposed in the previous work, with two smoothing methods learnt from Statistics Learning, cubic smoothing and cubic spline smoothing. In Figure 3, we could see that the FEM model had no obvious advantages visually compared with the cubic smoothing method in the current damage situation. In addition, the damage center estimated by cubic spline smoothing was closest to the real position, although the distribution (Fig 3.(d)) wasn't quite similar to the real one (Fig 3.(a)). Hence, the two response-based methods actually had their own advantages compared with the FEM method.

More details about this work is available in the project report below.