PSI - Issue 80

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

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ability of Lamb waves to propagate over long distances with minimal attenuation, their high velocity, and their pro nounced sensitivity to both surface and internal defects make them an ideal tool for rapidly monitoring large composite structures Dafydd and Sharif Khodaei (2020); Su et al. (2006). A standard approach for a Lamb wave Structural Health Monitoring (SHM) system utilizes an array of piezoelectric transducers distributed across the structure. The process typically involves one transducer exciting the structure with a given waveform, which then travels through the material and interact with any defects or boundaries. The other transducers in the array act as sensors, recording the propagating wave. The recorded sensor data are then processed by various algorithms to generate an image that maps the location and severity of the damage. Of the various algorithms, the most well-known and conceptually straightforward is the Delay-and-Sum (DAS) method, first applied to Lamb wave SHM by Wang et al. (2004).As its name implies, the algorithm functions by back-propagating the scattered signals to each point in the region of interest and then simply summing them. While its low computational complexity has led to widespread use, the DAS method has limited performance: As the recorded signals invariably become a complex mixture of overlapping reflections. These echoes arise not only from potential damage but also from numerous geometric features like boundaries, edges Ahmad and Gabbert (2012). Consequently, it often produces images with poor resolution (characterized by a large spot size) and high levels of background noise and artifacts. To address the limitations of Delay-and-Sum imaging, more advanced algorithms have been developed to improve imaging fidelity. Techniques such as Minimum Variance Distortionless Response (MVDR) and Multiple Signal Clas sification (MUSIC) aim to suppress artifacts and enhance spatial resolution.Originally developed for estimating the direction-of-arrival (DOA) of incoming waves, these algorithms were subsequently adapted for a wide range of appli cation domains, including radar positioning, biomedical imaging, and seismic exploration. More recently, they have been successfully applied to the field of Lamb wave imaging, where they have demonstrated promising results.For example, Li et al. (2025) proposed an improved MVDR imaging method to handle the coherent damage-scattered sig nals by reconstructing the signal covariance matrix using a weighted least squares approach. In another example, Yang et al. (2022) improved the MUSIC algorithm (calling it Am-MUSIC) so it works better with sparse sensor networks. This paper presents a comparative study of the DAS, MVDR, and MUSIC imaging algorithms. The performance of each method is evaluated for damage detection in a quasi-isotropic composite plate. This work details the principles of each technique, explain how MVDR and MUSIC improve upon the foundational DAS method, and highlight their key di ff erences. Despite their distinct theoretical foundations, all three algorithms share a common reliance on back propagated signals to form an image.Recognizing that these advanced techniques originate from the field of DOA estimation suggests that further progress in creating more robust and accurate damage imaging methods can be made by adapting other state-of-the-art DOA algorithms.

2. Methodology

2.1. Lamb wave scattering

Since the selected imaging methods all rely on signals scattered by damage, it is essential to first understand how they behave in propagation and how to extract these signals from the raw measurements. This paper focuses on quasi-isotropic composite laminates, which allows us to approximate Lamb wave propaga tion as isotropic. Although Lamb waves have multiple modes, techniques such as frequency tuning is used to excite just a single zero-order mode. By assuming the propagation of a single Lamb wave mode with a known phase veloc ity, c p ( ω ), it is possible to model the far-field wave from a point source. Therefore, for any given excitation x ( t ), the resulting waveform measured after a travel distance d can be mathematically expressed in frequency domain, as:

d d ref

i ω d cp ( ω )

) − 1 / 2 X ( ω )exp −

U ( ω ) = (

(1)