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1. Monitoring damage growth and topographical changes in plate structures using sideband peak count-index and topological acoustic sensing techniques

   https://doi.org/10.1016/j.ultras.2024.107354  

   Zhang, Guangdong; Deymier, Pierre A; Runge, Keith; Kundu, Tribikram (May 2024, Ultrasonics)

   Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count – index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are investigated. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures. 

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2. 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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3. Numerical modeling with experimental verification investigating the effects of nonlinearities on the sideband peak count-index technique and topological acoustic sensing

   https://doi.org/10.1117/12.3010021  

   Zhang, Guangdong; Hu, Bo; Alnuaimi, Hamad; Amjad, Umar; Deymier, Pierre A; Runge, Keith; Kundu, Tribikram (May 2024, SPIE)

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

   A newly developed Nonlinear Ultrasonic (NLU) technique called sideband peak count-index (or SPC-I) measures the degree of nonlinearity in materials by counting the sideband peaks above a moving threshold line – larger the SPC-I value, higher is the material nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness in Structural Health Monitoring (SHM) applications. However, the effects of different types of nonlinear phenomenon on the sideband peak generation is yet to be investigated in depth. This work addresses this knowledge gap and investigates the effects of different types of nonlinearity on the SPC-I technique. Three types of nonlinearities (material nonlinearity, structural nonlinearity and contact nonlinearity) are investigated separately through numerical modeling. Numerical modeling results show that the sideband peak values do not increase proportional to the input signal strength thus indicating nonlinear response, and different types of nonlinearities affect the SPC-I measurements differently. For the experimental verification a composite plate with impact-induced damage is considered for investigating the material nonlinearity and structural nonlinearity while a linear elastic aluminum plate is used to examine the contact nonlinearity between the transducers and the plate. The trends observed in the experimental observations matched the numerical model predictions. Monitoring damage growth in topographical structures – formed by inserting different materials in a matrix material is also investigated. In addition to the SPC-I technique an emerging acoustic parameter – “geometric phase change” based on the topological acoustics is also adopted for sensing damage growth in the topographical structures. The performance of SPC-I and topological acoustic sensing techniques as well as the Spectral Amplitude Difference (SAD) parameter for sensing the damage growth in topographical structures are compared and discussed. 

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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. 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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