From Fourier Amplitudes to Persistence Images for Impact-Echo Defect Detection
Abstract
Impact-echo testing is a nondestructive testing method used to detect internal defects in concrete structures. However, boundary reflections, structured interference, and measurement noise can produce complex Fourier amplitude spectra, making defect classification difficult. We constructed a two-dimensional frequency--amplitude persistence image (FA-PI) from the Fourier amplitude spectrum. Using a fixed parameterization of exact multi-parameter persistent homology, each retained Fourier component is represented with frequency-bin location as one coordinate and amplitude as the other, and Gaussian kernels are then applied in this two-dimensional space. This construction has a direct analytical connection to the corresponding one-dimensional Gaussian-smoothed Fourier amplitude spectrum. FA-PI was evaluated on an experimental backfill-void dataset and a public bridge-deck impact-echo dataset, and compared with raw and Gaussian-smoothed Fourier amplitude spectra using a linear classifier with a Softmax output and identical signal-level data splits. The evaluation included original signals and signals corrupted by Gaussian noise, sinusoidal interference, or mixed noise, with matching noise types and signal-to-noise ratios during training, validation, and testing. Performance was assessed using accuracy and macro-averaged precision, recall, and F1-score. Across the two datasets, FA-PI consistently outperformed the raw and Gaussian-smoothed Fourier baselines in the noisy-condition summaries. These findings indicate that representing Fourier spectral components in a two-dimensional frequency--amplitude space can improve impact-echo defect classification beyond frequency-axis smoothing alone.
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BibTeX
@misc{kim2026from,
title = {{From Fourier Amplitudes to Persistence Images for Impact-Echo Defect Detection}},
author = {Keunsu Kim and Suyoung Choi and Meiyan Kang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18732},
eprint = {2610.18732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18732},
}
RIS
TY - UNPB
TI - From Fourier Amplitudes to Persistence Images for Impact-Echo Defect Detection
AU - Keunsu Kim
AU - Suyoung Choi
AU - Meiyan Kang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18732
UR - https://arxiv.org/abs/2610.18732
AB - Impact-echo testing is a nondestructive testing method used to detect internal defects in concrete structures. However, boundary reflections, structured interference, and measurement noise can produce complex Fourier amplitude spectra, making defect classification difficult. We constructed a two-dimensional frequency--amplitude persistence image (FA-PI) from the Fourier amplitude spectrum. Using a fixed parameterization of exact multi-parameter persistent homology, each retained Fourier component is represented with frequency-bin location as one coordinate and amplitude as the other, and Gaussian kernels are then applied in this two-dimensional space. This construction has a direct analytical connection to the corresponding one-dimensional Gaussian-smoothed Fourier amplitude spectrum. FA-PI was evaluated on an experimental backfill-void dataset and a public bridge-deck impact-echo dataset, and compared with raw and Gaussian-smoothed Fourier amplitude spectra using a linear classifier with a Softmax output and identical signal-level data splits. The evaluation included original signals and signals corrupted by Gaussian noise, sinusoidal interference, or mixed noise, with matching noise types and signal-to-noise ratios during training, validation, and testing. Performance was assessed using accuracy and macro-averaged precision, recall, and F1-score. Across the two datasets, FA-PI consistently outperformed the raw and Gaussian-smoothed Fourier baselines in the noisy-condition summaries. These findings indicate that representing Fourier spectral components in a two-dimensional frequency--amplitude space can improve impact-echo defect classification beyond frequency-axis smoothing alone.
ER -