A Novel Algorithm for Accurate Void Size Extraction for Improving Pavement Safety

By Dr Silpaja Chandrasekar, PhDReviewed by Susha Cheriyedath, M.Sc.Nov 14 2023

In a paper published in the journal Scientific Reports, researchers presented a novel approach to address a critical challenge in pavement safety—measuring geometric parameters within void areas. Their void size extraction algorithm utilized the continuous wavelet transform (CWT) method and ground-penetrating radar (GPR) signals. The algorithm effectively visualized invalid areas by processing GPR signals with CWT and reconstructing a 3D image.

Leveraging differences in time and frequency domains, the void detection algorithm accurately identified voids in width and depth. Extensive testing in numerical and laboratory models demonstrated the method's high precision, offering a reliable means for Department of Transportation departments to estimate void dimensions in pavement and ensure structural safety through informed pre-maintenance activities.

Background

The challenge of voids in cement pavement, resulting from factors like uneven construction, subgrade settlement, and environmental stresses, threatened structural integrity. Void size significantly impacted slab-bearing capacity, and its increase led to settlement, misalignment, and eventual slab breakage. Implementing non-destructive testing (NDT) methods was imperative to address this concern, ensuring accurate maintenance guidance before the potential risk of slab failure.

Various void detection methods exist, with GPR being the most effective in pavement applications. Existing studies leveraged deep learning and statistical parameters from GPR signals, but boundary determination and feature sensitivity challenges persisted.

GPR Signal Processing Techniques

F-K Migration Algorithm: The F-K migration algorithm enhances GPR imaging accuracy by mitigating the hyperbolic effect observed on both sides of a target. Unlike envelope lines, the algorithm effectively focuses scattered energy, utilizing the principle that GPR-generated electromagnetic waves undergo multiple refractions and reflections underground. The algorithm calculates wave fields during reflections, enabling the inversion of echo data for migration results. F-K migration involves the Fourier transform, derived from the wave function's general summation expression. The migration function is a linear summation of coefficients obtained from Stationary Wavelet Transform (SWT), where each component holds time-frequency information. Selecting migration components with effective SWT signals reconstructs the final target profile.

CWT: GPR signals, characterized as transient non-stationary signals, find practical analysis through the CWT. Unlike traditional Fourier transform, CWT's fixed window size and adaptable shape provide time-frequency localization, capturing local and global signal characteristics. CWT extracts a coefficient matrix from the time domain, allowing time-frequency energy spectrum analysis. Given the distinct GPR features of void and typical areas, especially in amplitude, converting the signal to the time-frequency domain reveals high energy in invalid areas. The expression for CWT involves the GPR signal and the mother wavelet, with the nonorthogonal complex Morlet wavelet balancing time and frequency localization. This waveform effectively matches the GPR Ricker reflection wavelet, comprehensively analyzing signal energy distribution in the time-frequency domain.

Void Geometry: Processing & Parameters

Void Geometric Parameters Extraction Algorithm: The GPR, utilizing spherical waves for signal transmission and reception, often includes various clutters. Employing specific GPR signal processing methods, including static correction, energy gain, background removal, band-pass filtering, and the F-K migration algorithm, enhances the signal-to-noise ratio (SNR) and highlights void characteristics.

The F-K migration algorithm effectively focuses scattered energy, eliminating hyperbolic effects caused by electromagnetic waves undergoing multiple refractions and reflections underground. Ricker wavelet, characterized by local energy attenuation, is employed to analyze the reflected wavelet's energy and frequency, closely linked to target size and medium differences. Proposing a CWT energy reconstruction method addresses large amplitude or high-energy phenomena in target areas, thereby revealing the horizontal and vertical distribution of void areas with improved resolution.

Void Parameters and Reconstructed Energy Spectrum: The reconstructed energy spectrum, derived from the CWT energy reconstruction method, effectively highlights target areas and unveils the spatial energy distribution. A 3D visualization of the energy spectrum aids in identifying void areas, represented by local convex peaks indicating energy concentration. Dimensionality reduction of the energy spectrum facilitates the extraction of invalid width parameters, utilizing a 1D energy function.

A discrete wavelet transform (DWT) with the Symlets 4 wavelet is applied to refine the curve and mitigate noise interference. The algorithm determines threshold values, locates void boundaries, and extracts invalid width parameters. Further, the S-transform is employed to enhance depth accuracy, with the upper depth of void areas determined by analyzing the reflection Ricker wavelet in the A-scan signal. The proposed extraction algorithm offers a comprehensive method for accurately determining invalid geometric parameters, which is crucial for pavement assessment and maintenance planning.

Conclusion

To summarize, the algorithm validation encompassed the creation of a numerical model, simulating a cement pavement with seven rectangular air void areas. Subsequent processing involved F-K migration to alleviate hyperbolic effects, utilizing Ground Penetrating Radar Modeling and Simulation Software (gprMax) 3.15 for simulation.

Comparison between standard and void signals unveiled distinctive time-frequency spectra. The CWT method enhanced these differences, producing a 3D energy spectrum highlighting invalid areas. The proposed algorithm successfully identified null geometrical parameters in numerical and lab models, showcasing accurate width and depth detection. The method exhibited a mean error of approximately 1.5% in the numerical model and 4.2% in the lab model, establishing its effectiveness for pavement analysis and void identification.