FREQUENCY-WAVENUMBER DOMAIN PROCESSING FOR HIGH-RESOLUTION DAMAGE LOCALIZATION - Научное сообщество
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FREQUENCY-WAVENUMBER DOMAIN PROCESSING FOR HIGH-RESOLUTION DAMAGE LOCALIZATION

05.03.2026 11:04

[3. Nauki techniczne]

Автор: Alexander Pysarenko, associate professor, PhD, Odessa State Academy of Civil Engineering and Architecture



Plate structures, which encompass a wide variety of engineering components including advanced laminar composites, are extensively utilized across numerous industrial sectors such as marine engineering, automotive manufacturing, and heavy infrastructure development. These materials are valued for their exceptional strength to weight ratios and their ability to be tailored for specific mechanical requirements. However, the complex nature of these components makes it inherently difficult to detect certain types of structural degradation. Damage such as localized corrosion in metallic elements or internal delamination within composite layers can significantly compromise the integrity of the entire system [1]. Such defects often remain hidden beneath the surface, necessitating the implementation of sophisticated condition monitoring and non-destructive evaluation strategies. Traditional methods like radiographic testing, eddy current inspection, and magnetic particle testing have long served as the primary tools for ensuring the operational safety of structures containing composite inserts. While these techniques are well-established, their practical engineering application often involves considerable challenges. They frequently require stringent safety precautions, specialized equipment, and time-consuming calibration processes that can hinder the efficiency of maintenance routines.

The evolution of structural diagnostics has led to the widespread adoption of methods based on the analysis of acoustic and guided wave propagation. In plate-like structures, mechanical energy typically travels in the form of Lamb wave packets. These waves are characterized by their ability to propagate over long distances, making them ideal for inspecting large areas. Analysts often rely on wave parameters such as attenuation, reflection, scattering coefficients, and time of flight to identify and characterize structural faults. However, the interpretation of guided wave signals is notoriously difficult due to their dispersive and multimodal nature [2]. In these materials, wave velocity changes with frequency, and multiple modes can exist simultaneously, leading to overlapping signals that obscure the signatures of damage. Improving the sensitivity and accuracy of damage detection therefore requires effective methods for the isolation of specific wave modes.

Wavenumber analysis provides a powerful framework for addressing these complexities. Wavenumber spectroscopy algorithms have been successfully employed to localize and visualize changes in thickness or material properties caused by the initiation of damage. By transforming spatial data into the wavenumber domain, researchers can separate the various components of the wave field based on their spatial frequencies. Local wavenumber estimation techniques allow for the quantitative assessment of the dimensions and depth of internal defects like delaminations. Furthermore, achieving a high-fidelity evaluation of damages within the bulk of a composite requires the application of both instantaneous and local wavenumber filtering to the recorded wave packet data. 

The practical implementation of wavenumber filtering involves a structured scanning process. Typically, a piezoelectric transducer is fixed to the surface of the plate to generate a continuous excitation at a specific frequency. The scanning is performed over a uniformly discretized two-dimensional grid of M х N points, where M and N represent the spatial coordinates in the horizontal and vertical directions. Once the scan is complete, the recorded responses are organized into a three-dimensional matrix where two dimensions represent space and the third represents time. 

The study introduces a modified two-dimensional wavelet-based approach for identifying structural degradation through wavenumber analysis. Central to this methodology is the principle that the wavenumber, acting as the inverse of the wavelength, maintains a constant value for any specific combination of frequency, material properties, and component thickness. Consequently, any observed deviation in the wavenumber serves as a clear indicator of structural damage within the composite material. The wavenumber spectra derived from the measured steady state response are characterized as a superposition of various propagating modes existing at the chosen excitation frequency.

Within the defined frequency range, the structural response incorporates both zero order symmetric and antisymmetric modes. The isolation of these specific modes is a priority for wavenumber-based diagnostics, as the presence of multiple modes complicates the automated interpretation of spectra. By employing laser scanning of a stationary state wave field, the research demonstrates the ability to focus specifically on a single mode. The effectiveness of this volume damage detection technique is determined by the selection of the mother wavelet function.

Numerical results compared with experimental data confirm that structural defects are identified with higher precision through two-dimensional wavelet wavenumber filtering. A key finding is that the wavelet-based damage indicator identifies wavenumber shifts with a spatial resolution that far exceeds the standard two-dimensional Fourier transform. This increased resolution allows for a detailed mapping of localized flaws, providing a more sensitive tool for the quantitative assessment of composite integrity. The integration of wavelet analysis with stationary wave fields offers a refined pathway for detecting subtle internal changes that might be overlooked by traditional signal processing techniques. 

References:

1. Beaumont, P. W. (2020). The structural integrity of composite materials and long-life implementation of composite structures. Applied Composite Materials, 27(5), 449-478. https://doi.org/ 10.1007/s10443-020-09822-6

2. Mitra, M., & Gopalakrishnan, S. (2016). Guided wave based structural health monitoring: A review. Smart Materials and Structures, 25(5), 053001. https://doi.org/ 10.1088/0964-1726/25/5/053001



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