PSI - Issue 80

Guangxiao Zou et al. / Procedia Structural Integrity 80 (2026) 93–104 Author name / Structural Integrity Procedia 00 (2023) 000–000

101

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A circular array of twelve piezoelectric transducers was surface-mounted on the plate to generate and record the Lamb wave signals. The origin (0, 0) was defined as the lower-left corner of the plate. The coordinates for each sensor in the array are detailed below:

Table 1. Coordinates of the piezoelectric transducers. Sensor # X(mm) Y(mm)

Sensor #

X(mm)

Y(mm)

Sensor #

X(mm)

Y(mm)

1 2 3 4

270 261 235 200

200 235 261 270

5 6 7 8

165 139 130 139

261 235 200 165

9

165 200 235 261

139 130 139 165

10 11 12

In sequence, each transducer acts as a transmitter while the other N − 1 transducers record the resulting guided waves. Although this process generates 132 total waveforms, only one signal from each unique transmitter-receiver pair needs to be used, resulting in 66 signals. Damage was simulated by applying a small amount of putty with a 15 mm radius to the surface of the plate. This acts as a local mass that scatters the incident Lamb waves. The coordinates for the simulated damage cases are shown inTable 2.

Table 2. Coordinates of the simulated damage cases. Damage Case

X-coordinate (mm)

Y-coordinate (mm)

Damage 1 Damage 2

235 200

200 200

3.2. Experimental results

A critical issue in the implementation of MVDR imaging is that the spatiotemporal correlation matrix, R xy , is often ill-posed. This makes its inversion, a necessary step for calculating the weight vector in Eq. (16), numerically unstable. To address this, a regularization technique known as diagonal loading is employed:

R − 1 xy = ( R xy + f λ 1 I ) − 1

(26)

where λ 1 refers to the largest eigenvalue of R xy , and f denotes a scaling factor applied to determine the degree of diagonal loading. The determination of f is crucial for achieving high-quality imaging. The figures in Fig(2) show howdi ff erent values of f influence the image quality, and it can be seen from Fig. (2)(c) that f = 0 . 001 provides the best imaging quality. Hence, this value is adopted in the present work. Figures (3), (4), and (5) present the imaging results for the two damage locations. The DAS method produces images with poor spatial resolution and a high level of artifacts, which makes it di ffi cult to reliably localize the true damage. In contrast, MVDR imaging provides significantly better results by successfully suppressing these artifacts and improving both the accuracy and resolution of the damage indication. However, the MUSIC imaging algorithm fails to correctly localize the damage in this case. This failure is due to a violation of the algorithm’s core assumption: the orthogonality between the signal and noise subspaces. In the eigen decomposition process, the eigenvectors that are supposed to form the noise subspace appear to be correlated with the signal. This suggests that the noise eigenvectors still contain significant signal components, which invalidates the orthogonality assumption and causes the method to fail.