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GPRInvNet: Deep Learning-Based Ground Penetrating Radar Data Inversion for Tunnel Lining

Bin Liu, Yuxiao Ren, Hanchi Liu, Hui Xu, Zhengfang Wang, Anthony G. Cohn, Peng Jiang

arXiv:1912.05759v3cs.CVcs.LGeess.IVphysics.geo-ph

TL;DR

The paper addresses the challenge of mapping complex GPR B-Scan data to spatially aligned permittivity maps of tunnel linings. It proposes GPRInvNet, whose trace-to-trace encoder and decoder process adjacent-trace information while retaining alignment, and reports clear-boundary reconstructions for complex defects with satisfactory real-data performance.

  • Problem

    Mapping time-series GPR B-Scan data to spatially aligned permittivity maps is difficult because defect signals involve adjacent traces and complex lining echoes can obscure irregular defects.

  • Method

    GPRInvNet combines a trace-to-trace encoder that enhances each trace using adjacent traces with a decoder for reconstructing permittivity maps.

  • Results

    GPRInvNet reconstructed complex tunnel-lining defects with clear boundaries, outperformed existing baselines, and achieved satisfactory results on real GPR data.

  • Takeaways & Limitations

    Adding real background GPR patches to synthetic training data enabled GPRInvNet to generalize to real data, particularly for rebars and water-bearing defects.

Abstract

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A DNN architecture referred to as GPRInvNet was proposed to tackle the challenges of mapping the ground-penetrating radar (GPR) B-Scan data to complex permittivity maps of subsurface structures. The GPRInvNet consisted of a trace-to-trace encoder and a decoder. It was specially designed to take into account the characteristics of GPR inversion when faced with complex GPR B-Scan data, as well as addressing the spatial alignment issues between time-series B-Scan data and spatial permittivity maps. It displayed the ability to fuse features from several adjacent traces on the B-Scan data to enhance each trace, and then further condense the features of each trace separately. As a result, the sensitive zones on the permittivity maps spatially aligned to the enhanced trace could be reconstructed accurately. The GPRInvNet has been utilized to reconstruct the permittivity map of tunnel linings. A diverse range of dielectric models of tunnel linings containing complex defects has been reconstructed using GPRInvNet. The results have demonstrated that the GPRInvNet is capable of effectively reconstructing complex tunnel lining defects with clear boundaries. Comparative results with existing baseline methods also demonstrated the superiority of the GPRInvNet. For the purpose of generalizing the GPRInvNet to real GPR data, some background noise patches recorded from practical model testing were integrated into the synthetic GPR data to retrain the GPRInvNet. The model testing has been conducted for validation, and experimental results revealed that the GPRInvNet had also achieved satisfactory results with regard to the real data.

I. INTRODUCTION

GPR inversion maps complex B-Scan measurements to subsurface dielectric information, but tunnel lining clutter and irregular defects make this challenging. GPRInvNet addresses these issues with trace-to-trace encoding and achieves strong reconstruction results on synthetic and real data.

  • Tunnel lining inspection uses GPR echoes to infer subsurface structural conditions and defect-related dielectric information.
  • Existing GPR inversion methods include velocity analysis, ray-based methods, reverse-time migration, tomography, and full-waveform inversion.
  • DNN-based GPR studies have mainly addressed classification or object detection rather than reconstructing subsurface dielectric images.
  • Tunnel lining rebars and irregular defects create complex B-Scan patterns that can mask defect echoes and make different defect shapes appear similar.
  • GPRInvNet uses trace-to-trace encoding to enhance each GPR trace with adjacent-trace information while preserving spatial alignment with permittivity-map features.
  • The framework reconstructed diverse complex tunnel-lining defects and produced good results on real GPR data after validation.

B. DNNs for the GPR Image to Subsurface Image Transformations

Mapping GPR B-Scans to subsurface permittivity maps requires handling spatial alignment, complex echoes, and ambiguous defect signatures. The paper frames this task formally and motivates trace-wise feature processing for reconstruction.

  • Prior GPR image-to-subsurface studies reconstructed subsurface images with encoder-decoder, U-Net, and GAN architectures, but did not reconstruct permittivity maps.
  • Encoder-decoder networks with DSSIM loss slightly outperformed U-Net and GAN for the reported GPR image-to-image transformation.
  • The inversion task maps each GPR B-Scan D_i to a tunnel-lining permittivity map P_i with depth H and width W.
  • Each B-Scan contains time-series traces whose signals relate to dielectric properties at different depths and detection distances across the lining width.
  • Rebar clutter can mask defect echoes, while irregular defects with different shapes may generate similar B-Scan profiles through multiple waves and scattering.
  • Defect signals can appear in several adjacent traces, so a lining location may depend on more than its corresponding GPR trace.

B. Architecture of GPRInvNet

GPRInvNet combines a trace-to-trace encoder with a decoder to reconstruct permittivity maps from GPR B-Scan data while preserving spatial alignment. The encoder enriches each trace using neighboring traces, separately condenses trace features, and aligns them with sensitive zones in the output map.

  • Architecture: GPRInvNet uses a specially designed trace-to-trace encoder and a corresponding decoder for GPR inversion.The decoder is topologically identical to the decoder component in SeisInvNet.
  • Architecture: The trace-to-trace design retains input-output spatial alignment while using neighboring traces to enhance effective GPR information.These are identified as two benefits compared with existing networks.
  • Architecture: Convolutional layers enrich each GPR trace with information from adjacent traces without initially compressing its spatial dimension.Neighboring-trace features are fused rather than extracting global context from the entire B-Scan.
  • Architecture: Fully connected layers separately condense the enhanced features of each trace and align them to corresponding columns of the permittivity map.The aligned output region is termed the trace’s sensitive zone.
  • Architecture: Each enhanced trace produces a spatially aligned sensitive zone, and splicing these zones reconstructs the complete permittivity map.The network can reconstruct permittivity maps column by column from raw GPR data.

C. Trace-to-trace Encoder

The trace-to-trace encoder uses convolutional layers to enrich each trace with local neighborhood information, then separately compresses trace features for spatially aligned inversion. Five convolutional and five fully connected layers form the encoder, with five 5 × 5 layers providing the selected receptive field.

  • Encoder design: The encoder consists of five convolutional layers followed by five fully connected layers that separately condense each trace’s features.This structure gives the encoder its trace-to-trace designation.
  • Feature enrichment: Convolutional feature maps preserve the input B-Scan dimensions while incorporating information from several adjacent traces.The design reflects that one abnormality’s echoes often appear across adjacent traces.
  • Feature visualization: With three convolutional layers, visualized feature maps retain more hyperbolic morphology, while five and seven layers mitigate it around abnormality zones.The comparison covers anhydrous defects, water-bearing defects, and defects beneath rebar.
  • Feature enrichment: Five 5 × 5 convolutional layers provide a receptive field of 21, whereas five 3 × 3 layers provide a receptive field of 11.The 5 × 5 kernels outperformed the experimented 3 × 3 kernels.
  • Spatial alignment: Separately condensing each trace preserves spatial alignment between B-Scan features and corresponding permittivity-map columns.The resulting trace features are spliced to form feature maps with the same dimensional ratio as the permittivity map.

D. Decoder and Loss Function

The decoder expands encoded trace features into permittivity-map regions and splices those regions into a complete reconstruction. Training combines an L2 loss with multi-scale structural similarity to reduce pixel error while optimizing structural similarity.

  • Decoder: The decoder uses a 4 × 4 up-convolution, six 3 × 3 convolutions, and one up-sampling operation to generate map-sized outputs.A dropout method is used to randomly abandon feature maps to avoid over-fitting and improve robustness.
  • Decoder: Each encoded trace feature is used to reconstruct a small sensitive zone, and all sensitive zones are spliced into the full permittivity map.The trace-aligned feature has size C × E, while its reconstructed region has size H × 1.
  • Loss function: The loss function combines the L2 norm with multi-scale structural similarity (MSSIM).The formulation compares inversion results with ground-truth permittivity maps across multiple scales.
  • Loss function: Simultaneously minimizing norm metrics and maximizing MSSIM optimizes both structural similarity and per-pixel error rates.The scale weights are denoted by λ_r, and R denotes the total number of scales.

A. Building the Data Set

The study generated synthetic GPR data for common tunnel-lining defects using numerical simulations and varied defect geometries, material properties, and background structures.

  • Data-set scope: Synthetic data covered lining voids, cracks, lining-rock delamination, leakages, and concrete non-compactness with irregular shapes.The data set was designed to represent common tunnel-lining defect types.
  • Numerical simulation: The FDTD simulations used a 2.0 m-wide, 0.7 m-deep permittivity model with a 0.01 m spatial grid and CPML boundary treatment.Each permittivity map consisted of 90 × 220 meshes.
  • Source specification: The source wavelet was a 600 MHz Ricker wavelet, with fc denoting its center frequency.The wavelet equation is given in the data-generation description.
  • Model construction: The simulated model included concrete, surrounding rock, and rebars as the tunnel-lining background.Interfaces and irregular defect geometries were generated with spline-based constructions.
  • Defect variation: Defect dimensions were varied, including voids from 16 × 5 cm to 60 × 40 cm and cracks 20–60 cm long.Other simulated defects included delamination and noncompactness with additional size ranges.

B. Experimental Process

The experiments trained and evaluated GPRInvNet against Enc-Dec and FWI on synthetic tunnel-lining data, showing stronger reconstruction of complex defects and quantitative performance than Enc-Dec.

  • Experimental setup: The data set contained 432000 pairs, divided into 360000 training, 36000 validation, and 36000 testing pairs.A supplementary set was also introduced to examine conductivity effects on relative-permittivity inversion.
  • Baselines: GPRInvNet was compared with the DNN-based Enc-Dec model and the physics-driven FWI method on the same testing data.The comparison focused on reconstructing complex tunnel-lining permittivity maps.
  • Qualitative reconstruction: Enc-Dec reconstructed some simple defects but often produced blurred boundaries and incorrectly reconstructed a water-bearing defect with varied material properties.GPRInvNet reconstructed defects with relatively clear boundaries and shapes consistent with the ground truths, including defects beneath rebars.
  • Quantitative results: On the test set, GPRInvNet achieved MAE 0.00286, MSE 0.000374, SSIM 0.973784, and MSSIM 0.980623.These metrics were reported as better than Enc-Dec’s corresponding values.
  • Architectural interpretation: GPRInvNet’s trace-oriented encoding retained spatial alignment and detailed features that Enc-Dec could lose during fixed-kernel compression and vector decoding.The authors connect this design difference to improved small-rebar and defect-boundary reconstruction.

E. Comparison With FWI

The study compared GPRInvNet with multiscale FWI, which reconstructs permittivity through serial frequency inversion, and found GPRInvNet stronger on complex defects and substantially faster per image.

  • FWI procedure: Multiscale FWI used serial inversion at 200 MHz for envelopes and permittivity, followed by 600 MHz for permittivity details.The procedure updated the model across frequency scales to reduce local-minimum and cycle-skipping problems.
  • Simple defects: FWI roughly reconstructed cracks, voids, and delamination in non-reinforced concrete, but its boundaries were relatively blurred.Anhydrous defects were reconstructed somewhat better than water-bearing defects.
  • Complex defects: For defects beneath rebars, FWI often reconstructed only the rebar region and submerged the defects in the reconstructed pseudomorph.The authors attribute this behavior to rebar masking and strong dielectric-property contrasts.
  • Comparison: GPRInvNet provided more satisfying reconstructions with clear boundaries for anhydrous and water-bearing defects beneath rebars than FWI.The overall performance of GPRInvNet was reported as better than traditional FWI.
  • Computational cost: A single B-Scan inversion took approximately 60 min with multiscale FWI and approximately 0.027 s with a trained GPRInvNet.The authors describe the trained network as suitable for near-real-time GPR inversion, while training is performed once.

F. Comparison of Permittivity Values

Permittivity profiles from GPRInvNet generally matched the ground truth more closely than Enc-Dec and FWI, including difficult water-bearing and rebar-obscured defects.

  • Profile comparison: Figures 8 and 9 compare inverted relative-permittivity values along cutting lines I–V for simple and complex tunnel-lining defects.The curves provide depth-wise comparisons against the ground truth and competing methods.
  • Overall profile fidelity: GPRInvNet’s permittivity curves were essentially the ground truth except for slightly different amplitudes, with reduced oscillation relative to Enc-Dec and FWI.At line V, it detected a permittivity variation at 40 cm that the other methods missed.
  • Anhydrous defect: For an anhydrous defect, GPRInvNet estimated relative permittivity near 2 versus the true value 1, while Enc-Dec and FWI estimated 4 and 3.The comparison was made at line I, depth 20 cm in Fig. 9.
  • Rebar and water-bearing defects: For rebar, GPRInvNet estimated 296 against the true value 300, while FWI estimated 50 and Enc-Dec failed to recognize it.This was the maximum-deviation rebar example reported for GPRInvNet.
  • Rebar and water-bearing defects: For a water-bearing defect with true relative permittivity 80, GPRInvNet estimated approximately 78, compared with Enc-Dec’s 68.GPRInvNet also uniquely predicted the variation of a water-bearing defect beneath rebar in the cited example.

G. Comparative Study of Resolution

The study evaluated GPRInvNet’s vertical and horizontal resolution using synthetic targets at varied frequencies, bandwidths, depths, and separations. Resolution was generally near a quarter wavelength, with depth-dependent horizontal performance.

  • Resolution definition: The study defined imaging resolution as the ability to discriminate individual subsurface targets, while noting that DNN-based GPR inversion lacked established resolution analyses.Vertical resolution concerns targets at different depths; horizontal resolution concerns targets at the same depth.
  • Vertical resolution: GPRInvNet distinguished anhydrous targets, water-bearing targets, and rebars with vertical intervals of 7, 5, and 3 cm, respectively.These tests used different central frequencies and corresponding bandwidths.
  • Horizontal resolution: GPRInvNet detected horizontally separated targets at depths from 15 to 45 cm, including 3 and 5 cm intervals at 45 cm.Reconstructed target shapes were slightly more blurred at 45 cm than at 25 cm.
  • Horizontal resolution: Horizontal resolution decreased with depth, with shallow targets achieving higher resolution than deeper targets.This depth dependence agreed with the cited theoretical analysis.
  • Resolution boundary: GPRInvNet provided desirable resolution slightly larger than a quarter wavelength but could not clearly distinguish targets separated by less than a quarter wavelength.The network used high-frequency information from the full GPR waveforms.

V. EXPERIMENTS ON REAL DATA

The real-data experiment addressed the mismatch between complex field-like GPR data and the synthetic training data available for DNN inversion. Real background-noise patches were combined with synthetic scans to retrain and test GPRInvNet on concrete-model measurements.

  • Experimental model: The experiment used a concrete model containing rebars, anhydrous cracks, and water-bearing defects to evaluate GPRInvNet on real measurements.The model was approximately 4 × 2 × 0.7 m, with defects and rebars deployed at specified locations.
  • Motivation: Real GPR data were more complex than synthetic data because practical structures were inhomogeneous and environmental noise affected the measurements.Large paired collections of real B-Scans and corresponding permittivity maps were also difficult to acquire.
  • Synthetic-to-real adaptation: Real background-noise recordings were preprocessed, sampled as patches, normalized, and added pixelwise to synthetic B-Scan images to create paired training data.The resulting data retained synthetic ground-truth permittivity maps while incorporating real environmental background noise.
  • Training and testing: GPRInvNet was retrained for 100 epochs using synthetic data augmented with real background patches, without including real defect data in training.The real defect scans were reserved for testing.

C. Experimental Results and Analysis

GPRInvNet outperformed Enc-Dec and FWI in comparative tests on real GPR data and reconstructed synthetic and experimental tunnel-lining defects with clear or near-ground-truth shapes. The authors nevertheless identified limited profile fidelity on complex real data and the absence of field validation.

  • Real-data comparison: On real data, GPRInvNet outperformed Enc-Dec and FWI overall, especially for rebars and water-bearing defects.It recovered four rebar locations and profiles, while Enc-Dec missed the rebar layer and FWI recovered only an approximate distribution.
  • Real-data reconstruction: GPRInvNet reconstructed anhydrous cracks, water-bearing voids, and rebars with shapes close to the ground truths in the model-testing experiments.For anhydrous cracks, all three methods recovered profiles, but GPRInvNet’s shapes were closer to the true model.
  • Architecture contribution: The proposed architecture was designed to reconstruct high-quality relative permittivity maps while retaining spatial alignment between B-Scan images and permittivity maps.Its encoder was designed to use the GPR recordings and preserve this alignment.
  • Synthetic-data results: On synthetic data, GPRInvNet reconstructed complex tunnel-lining defects with clear boundaries and outperformed existing baseline methods.The synthetic evaluation included dielectric properties and irregular defect shapes.
  • Generalization: Adding real background GPR acquisitions to the training pool enabled a model trained on synthetic data to generalize to real GPR defect measurements.The reported real-data benefit was particularly strong for rebars and water-bearing defects.
  • Limitations: Because real GPR data were complex, only rough defect profiles could be reconstructed, and the study did not validate the method with field experimental data.The authors identified both issues as topics for further research.
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