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1. Topological acoustic sensing for defect localization in heterogeneous plate structures using Lamb waves

   https://doi.org/10.1117/12.3049106  

   Zhang, Guangdong; Kundu, Tribikram; Deymier, Pierre A; Runge, Keith (May 2025, SPIE)

   Rizzo, Piervincenzo; Su, Zhongqing; Ricci, Fabrizio; Peters, Kara J (Ed.)

   Defect localization in homogeneous plate structures is relatively easy with various well-established acoustics-based techniques. However, localizing defects in heterogeneous structures can be challenging due to complicated reflection, refraction and scattering patterns arising from heterogeneous boundaries during wave propagations. This work introduces a topological acoustic (TA) sensing technique for localizing defects in heterogeneous plate structures. The geometric phase change – index (GPC-I) derived from TA sensing is used to detect perturbations caused by defects along the sensing paths between transmitters and receivers. The proposed method identifies the largest GPC-I values for various sensing paths. A higher GPC-I value on a sensing path implies a higher probability of having a defect on that path. A maximum peak value dependent threshold in GPC-I plots (GPC-I vs. sensor sites) is defined to identify and filter out those unreliable sensing paths in the proposed localization method. Finite element based numerical analysis in Abaqus/CAE software verifies the effectiveness of the proposed method. The commonly used methods using velocity differences (VD) and amplitude ratios (AR) are also tried out for defect localization for comparison. The performance comparison of the localization results using GPC-I, VD, and AR reveal that the GPC-I based technique is the most effective technique for defect localization. 

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2. Defect localization in heterogeneous plate structures using the geometric phase change – index of Lamb waves

   https://doi.org/10.1016/j.ultras.2025.107654  

   Zhang, Guangdong; Kundu, Tribikram; Deymier, Pierre A; Runge, Keith (August 2025, Ultrasonics)

   Defect localization in homogeneous structures using ultrasonic waves is relatively easy to implement. However, locating defects in heterogeneous structures made of different materials can be challenging. This is because complicated reflections, refractions and scatterings occur when ultrasonic waves pass through the interfaces between two dissimilar materials of the heterogeneous structures. To address this issue, a localization methodology based on geometric phase change – index (GPC-I), derived from topological acoustic (TA) sensing, is proposed to adapt to the complicated scenarios when defects are present in heterogeneous plate structures. The GPC-I is adopted as the damage index (DI) to present the possibility of defects appearing on different acoustic sensing paths. A maximum peak value-dependent threshold in GPC-I plots (GPC-I vs. sensor sites) is defined to filter out unreliable sensing paths resulting from the heterogeneity. Different sensing modes (I and II) are combined to comprehensively provide a more reliable and accurate localization framework. Numerical modeling carried out by Abaqus/CAE software verifies the proposed GPC-I based localization technique. Comparison results among GPC-I and other two commonly used acoustic parameters—wave velocity differences (VD) and amplitude ratio (AR) (or wave attenuation) show that the GPC-I has superiority with higher sensitivity and stability for defect localization. This work can provide promising guidance for localizing defects in complex heterogeneous plate structures used in real-world engineering applications. 

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3. A Comparative Study of Geometric Phase Change- and Sideband Peak Count-Based Techniques for Monitoring Damage Growth and Material Nonlinearity

   https://doi.org/10.3390/s24206552  

   Zhang, Guangdong; Kundu, Tribikram; Deymier, Pierre A; Runge, Keith (October 2024, Sensors)

   This work presents numerical modeling-based investigations for detecting and monitoring damage growth and material nonlinearity in plate structures using topological acoustic (TA) and sideband peak count (SPC)-based sensing techniques. The nonlinear ultrasonic SPC-based technique (SPC-index or SPC-I) has shown its effectiveness in monitoring damage growth affecting various engineering materials. However, the new acoustic parameter, “geometric phase change (GPC)” and GPC-index (or GPC-I), derived from the TA sensing technique adopted for monitoring damage growth or material nonlinearity has not been reported yet. The damage growth modeling is carried out by the peri-ultrasound technique to simulate nonlinear interactions between elastic waves and damages (cracks). For damage growth with a purely linear response and for the nonlinearity arising from only the nonlinear stress–strain relationship of the material, the numerical analysis is conducted by the finite element method (FEM) in the Abaqus/CAE 2021 software. In both numerical modeling scenarios, the SPC- and GPC-based techniques are adopted to capture and compare those responses. The computed results show that, from a purely linear scattering response in FEM modeling, the GPC-I can effectively detect the existence of damage but cannot monitor damage growth since the linear scattering differences are small when crack thickness increases. The SPC-I does not show any change when a nonlinear response is not generated. However, the nonlinear response from the damage growth can be efficiently modeled by the nonlocal peri-ultrasound technique. Both the GPC-I and SPC-I techniques can clearly show the damage evolution process if the frequencies are properly chosen. This investigation also shows that the GPC-I indicator has the capability to distinguish nonlinear materials from linear materials while the SPC-I is found to be more effective in distinguishing between different types of nonlinear materials. This work can reveal the mechanism of GPC-I for capturing linear and nonlinear responses, and thus can provide guidance in structural health monitoring (SHM). 

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4. Monitoring defects in plates using topological acoustic sensing and sideband peak counting

   https://doi.org/10.1016/j.ultras.2025.107568  

   Ho, I-Ting; Muralidharan, Krishna; Runge, Keith; Hernandez_Granados, Araceli; Kundu, Tribikram; Deymier, Pierre A (May 2025, Ultrasonics)

   We demonstrate an integrated non-destructive inspection methodology that employs the nonlinear ultrasonics-based sideband peak counting (SPC) technique in conjunction with topological acoustics (TA) sensing to comprehensively characterize the acoustic response of steel plates that contain differing levels of damage. By combining the SPC technique and TA, increased sensitivity to defect/damage detection as well as the ability to spatially resolve the presence of defects was successfully established. Towards this end, using a Rockwell hardness indenter, steel plates were subject to one, three and five centrally located indentations respectively. The acoustic response of the plate as a function of number of indentations was examined at a frequency range between 50 kHz and 800 kHz, from which the change in a global geometric phase was valuated. Here, geometric phase is a measure of the topological acoustic field response to the spatial locations of the indentations within the steel plates. The global geometric phase unambiguously showed an increase with increasing number of indentations. In addition, spatial variations in a ‘local’ geometric phase as well as spatial variations in the PC index (SPC-I) were also determined. Spatial variations in both the local geometric phase as well as the SPC-I were particularly significant across the indentations for frequencies below 300 kHz, and by combining the respective spatial variations in the SPC-I and geometric phase, the locations of the indentations were accurately identified. The developed SPC-TA nondestructive method represents a promising technique for detecting and evaluating defects in structural materials. 

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5. Diagnostic imaging for damage detection in plates based on topological acoustic (TA) sensing technique

   https://doi.org/10.1016/j.ultras.2025.107750  

   Hu, Bo; Kundu, Tribikram; Deymier, Pierre A; Runge, Keith (December 2025, Ultrasonics)

   Traditional structural damage detection methods in aerospace applications face challenges in accuracy and sensitivity, often necessitating multiple sensors to evaluate various measurement paths between the reference and defective states. However, the recently developed topological acoustic (TA) sensing technique can capture shifts in the geometric phase of an acoustic field, enabling the detection of even minor perturbations in the supporting medium. In this study, a diagnostic imaging method for damage detection in plate structures based on the TA sensing technique is presented. The method extracts the geometric phase shift index (GPS-I) from the Lamb wave response signals to indicate the location of the damage. Using Abaqus/CAE, a finite element model of the plate was established to simulate the Lamb wave response signals, which were then used to validate the feasibility of the proposed method. The results indicate that this technique enables rapid and precise identification of damage and its location within the plate structure, requiring response signals from only a few points on the damaged plate, and it is reference-free. 

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