We present in this paper a framework for the automatic detection and localization of defects inside bridge decks. Using Ground-Penetrating Radar (GPR) raw scans, this framework is composed of a feature extraction algorithm using fractals to detect defective regions and a deconvolution algorithm using banded-independent component analysis (ICA) to reduce overlapping between reflections and to estimate the radar waves travel time and depth of defects. Results indicate that the defects' estimated horizontal location and depth falling within 2 cm (76.92% accuracy) and 1 cm (84.62% accuracy) from their actual values.
Ground-penetrating radar (GPR) is a nondestructive technique that creates a continuous two-dimensional cross-sectional image of the scanned medium and its internal objects. The GPR antenna transmits polarized pulses of electromagnetic waves through the scanned medium where portion of these radiations gets attenuated due to natural absorption. At the boundary between two electrically different materials (i.e., different dielectric constants or electrical conductivities), some radiations reflect back while the rest refract and continue their penetration. The A-scan and B-scan are the two commonly used formats for raw GPR data presentation. The A-scan, also known as a trace, is obtained by placing the GPR antenna above the target surface and recording reflected signals. The B-scan, also known as a line scan, is obtained by moving the GPR antenna over the target surface and recording the reflected signals at regular intervals. Each column of the B-scan is a single A-scan taken at a specific location.
According to a 2006 study by the American Society of Civil Engineers, 29% of bridges in the United States are considered structurally deficient or functionally obsolete due to overdue maintenance [
(a) is a simulated concrete bridge deck (slab) with embedded defects during construction. The green arrow indicates a parallel survey line to the first rebar from left (bottom rebar mesh) while the red arrow indicates a perpendicular survey line to the rebar (top rebar mesh). (b) is the finished slab.
Figure
GPR scan data of a 6-inch concrete slab with two embedded delamination defects.
The main challenge in using GPR for bridge deck condition assessment is the need for an experienced operator who can manually interpret raw scans and determine the defect types and locations. Since defects have irregular shapes with different refractive indices from their surrounding medium, they emerge as new objects or layers in GPR scans. Consequently, automating the detection process will require a feature extraction method that can efficiently model different types of irregular shapes with reduced computational needs.
The reported work of using GPR in bridge deck condition assessment can be categorized into three groups: manual analysis, signal and image processing, and inverse scattering approaches. Manual analysis methods are time consuming, and the accuracy of the detection process depends on the technician’s trained eye [
This paper presents an automated algorithm for determining the coordinates of defects in bridge decks using only the underlying B-scan with no need for training the algorithm using other scans. Therefore, the proposed algorithm saves the time and effort involved in inspection and provides a more accurate condition assessment method.
The word
Fractal sets can be divided into self-similar sets and self-affine sets. Self-similar sets describe data that repeat themselves (or their statistics) when different axes are magnified by the same factor while self-affine sets describe data that preserve their shape (or their statistics) only when different axes are scaled differently. Mathematically if a signal
Number of independent variables required to describe a point in a set is the topological dimension of that set. The Hausdorff-Besicovitch dimension (HBD) of a fractal set is a fractional number greater than its topological dimension that can be used to measure irregularity of that set. In practice, it is difficult to measure the HBD of a fractal set in its rigorous definition [
For a signal, the estimated fractal dimension will be in the range between 1 and 2. If the estimated FD is close to 1, a high neighbor-to-neighbor correlation will be present (smooth signal). If the estimated FD is close to 2, a high negative correlation will be present (nonsmooth signal). Figure
(a) and (b) are two scans extracted from B-scan of Figure
Both roughness and topology of interfaces inside the scanned medium are imprinted in the recorded GPR traces where these traces are considered as self-affine functions of time [
A raw GPR trace
Such a problem can be solved using the deconvolution process to reduce overlapping between reflections from closely spaced targets and recover impulse response of the scanned slab. Many deconvolution algorithms have been proposed in the literature such as singular value decomposition (SVD) [
Six different deconvolution methods including Wiener-based methods were examined in [
The convolution process of (
Independent component analysis is a statistical technique that can be used to decompose source signals
Utilizing the prior information about nature of the convolution matrix (i.e., banded matrix), the blind deconvolution problem can be converted into a blind source separation problem. However, this represents a single-input single-output ICA model which is inadequate for the underlying problem since statistics of the independent components cannot be characterized. In order to form a multidimensional ICA model (
Unfortunately, these two equations are inadequate for the ICA model as is since the first few rows/columns of
A number of banded-ICA deconvolution algorithms were proposed to deconvolve GPR traces [
There are different methods to estimate depth of a target from GPR scans such as ground truth (velocity analysis), dielectric tables, and hyperbolic shape analysis [
In the hyperbolic shape analysis method, the velocity of radar waves is estimated based on shape of the hyperbolic reflections using the Migration function in RADAN, a software package developed exclusively for GPR data by GSSI Inc. [
The proposed framework consists of three stages to identify and localize defects in concrete as shown in Figure
Block diagram of the proposed defect detection algorithm.
In this work, a fractal-based feature extraction (FBFE) algorithm is proposed and applied to each A-scan extracted from the B-scan. FBFE can be summarized in the following steps after normalizing all traces to zero mean. Feature vectors can be constructed according to the scanning method (see Figure When the scan is conducted perpendicular to the rebar, the first feature vector, When the scan is parallel to the rebar, the first feature vector, The fractal Brownian motion method is used to estimate the fractal dimension of the GPR trace Each feature vector is a column in the feature matrices The mean and standard deviation vectors, ( The index of segments of lengths greater than a threshold The center trace within each defective segment is labeled as by the defect’s column number. Dividing it over the total number of columns in the B-scan and multiplying it by the length of the B-scan, the horizontal location of defect is determined as
A number of evaluation measures are used in this paper to assess the classification performance of the proposed FBFE algorithm. We define false negative FN as the case of failure to detect a defect and false positive FP as the case of declaring a nonexisting defect. Precision is defined according to (
Our banded-ICA algorithm is a modified version of a previously developed algorithm in [ Let The mixture matrix Since the source signal to be estimated (impulse response) is sparse and consists a number of sharp spikes with relatively flat area between them (representing the layered structure of the scanned concrete deck), the separating matrix Mahalanobis transformation is used to whiten the mixture matrix EFICA is used to decompose the whitened mixture matrix in order to recover It should have a minimum number of spikes It should lead to the minimum mean square error (MMSE) according to
The velocity-analysis-based depth estimation method can be presented as follows. The initial total range of a GPR trace is 10 ns. After applying zero-correction step, the new total range of the GPR trace is found using
Velocity of radar waves through layers of the scanned medium can be approximated using ( Using (
Two 15 cm deep concrete slabs were constructed to simulate bridge decks: one with several embedded defects of known dimensions and locations as shown in Figure
A 1.5 GHz (GSSI model 5100) bistatic antenna is used to scan the concrete slabs with the dielectric constant set to 6.25 [
Figures
(a), (b), (c), (d), and (e) are five normal B-scans while (f) is a defective B-scan.
Figure
Table
Actual and estimated horizontal location of defects in the 15 cm slab*.
Scan | Actual location | Estimated location | Diff |
---|---|---|---|
Scan 2 | 85.73 | 87.07 | 1.34 |
Scan 5 | 22.23 | 22.12 | 0.11 |
73.03 | 74.14 | 1.11 | |
Scan 6 | 8.89 | 9.73 | 0.84 |
Scan 7 | 8.89 | 10.11 | 1.22 |
16.51 | 17.15 | 0.64 | |
Scan 9 | 27.31 | 24.46 | 2.85 |
Scan 10 | 8.26 | 6.96 | 1.30 |
28.58 | 26.59 | 1.99 | |
Scan 11 | 9.53 | 8.76 | 0.77 |
48.26 | 44.73 | 3.53 | |
Scan 13 | 36.83 | ND | ND |
Scan 14 | 49.53 | 54.89 | 5.36 |
81.28 | 83.21 | 1.93 | |
Average | 1.77 |
*All measurements are in cm; ND means the defective segment is not detected.
Table
False positive, false negative, accuracy, precision, and recall for the FBFE algorithm.
FP Rate | FN Rate | Accuracy | Precision | Recall |
---|---|---|---|---|
0% | 4.76% | 95.24% | 100% | 92.86% |
The fBm method takes the difference between a shifted version of the signal and the original signal which covers most of the neighbor-to-neighbor variations and consequently has high accuracy as Table
The marked defective traces from the FBFE method were used for the deconvolution process to reduce overlapping between reflections from adjacent targets and estimate the round-trip travel time to and from the embedded defects and rebar. The velocity analysis method is used to estimate depth (in cm) of detected defects as shown in Table
Actual and estimated depth of defects in the 15 cm slab*.
Scan | Actual depth | Estimated depth | Diff |
---|---|---|---|
Scan 2 | 3.61 | 4.78 | 1.17 |
Scan 5 | 2.54 | 2.98 | 0.44 |
5.08 | 6.35 | 1.27 | |
Scan 6 | 1 | 0.47 | 0.53 |
Scan 7 | 2.54 | 3.14 | 0.6 |
3.81 | 4.41 | 0.6 | |
Scan 9 | 1 | 1.53 | 0.53 |
Scan 10 | 2.54 | 1.95 | 0.59 |
1 | 0.89 | 0.11 | |
Scan 11 | 3.81 | 4.34 | 0.53 |
2.54 | 2.41 | 0.13 | |
Scan 13 | 5.08 | ND | ND |
Scan 14 | 5.08 | 4.13 | 0.95 |
3.61 | 3.73 | 0.12 | |
Average | 0.58 |
*All measurements are in cm; ND means the defective segment is not detected.
Given a raw B-scan as an input, applying the feature extraction algorithm followed by banded-ICA deconvolution algorithm marks the defective regions. Figure
(a) and (b) are raw and processed B-scans with embedded air-void defect.
(a) and (b) are raw and processed B-scans with two embedded delamination defects.
(a) and (b) are raw and processed B-scans with embedded air-void defect.
Figure
(a) and (b) are raw and processed B-scans with two embedded delaminations-defects.
Figure
(a) and (b) are raw and processed B-scans with embedded air-void defect.
(a) and (b) are raw and processed B-scans with embedded delamination and air-void defects.
Figure
(a) and (b) are raw and processed B-scans with two embedded delamination defects.
(a) and (b) are raw and processed B-scans with embedded delamination and air-void defects.
None of the methods discussed in the literature were able to provide defect coordinates [
The dielectric constant reflects velocity of radar waves through the scanned medium. Higher value of the dielectric constant indicates a slower travel time and thus shallower penetration. The depth estimation accuracy depends on the proper choice of the dielectric constant during the data collection process as (
One possible way of finding the proper value of
The estimated velocity of radar waves for the constructed slab is found as 12 cm/ns. Therefore, the dielectric constant is
Since the concrete slab has homogenous materials, the dielectric constant should not change significantly with depth (as opposed to the soil). Therefore, assuming a constant value of the dielectric constant for the concrete slabs should not affect the depth estimation accuracy [
The densest recommended number of scans per cm for concrete structures using the 1.5 GHz antenna is 4 scans per cm [
The variable
The value of
Distribution of the statistical features (fractal dimension, RMS, energy, and number of local maximum points) used for scan 10.
An automated defect detection and localization framework for concrete bridge decks is presented in this paper. The framework consists of three algorithms: (1) fractal-based feature extraction algorithm to detect defective regions; (2) banded-ICA deconvolution algorithm to reduce overlapping reflections from closely spaced targets and to recover travel time to and from detected defects and rebar; (3) velocity analysis method to estimate depth of detected defects. This framework was implemented and tested using fourteen raw GPR scans of two simulated 15 cm concrete bridge decks with known defect types and locations; five of the fourteen are from the normal slab, and the rest are from the defective one. The nine defective scans contained fourteen defective regions.
At the boundary (e.g., change of material, moisture) between two electrically different materials (i.e., different dielectric constants or electrical conductivities), some of the transmitted GPR radiations reflect back while the rest refract and continue their penetration. The reflected radiations at the boundaries appear as spikes in the impulse response of the scanned medium, making the detection of these layers (and potentially defects) possible.
Results indicate that the FBFE algorithm detected thirteen out of fourteen defective regions with average difference between actual and estimated horizontal locations of 1.77 cm resulting in high accuracy, recall, and precision. Results also demonstrate that the FBFE algorithm has low false negative and false positive rates. The proposed FBFE algorithm is able to detect and mark defective regions using only the underlying B-scan with no need for a number of B-scans for the purpose of algorithm training as required by other methods. Additionally, the results of the banded-ICA deconvolution algorithm and the velocity analysis method indicate that the average difference between actual and estimated depth is 0.58 cm.
Finally, the current state of the art in GPR-based condition assessment is focused on identification (full or partial) of defective regions without localization. Our integrated FBFE and banded-ICA framework was also able to correctly identify and label the defective regions (thirteen out of fourteen—nine full and four partial). In addition, we were able to fully identify defect coordinates for nine cases and to partially mark four additional cases. Since our ultimate goal is to maximize full defect detection, future work will focus on further refinements to the algorithm to improve the full detection results.
While the banded-ICA deconvolution algorithm is robust, it is computationally demanding. Therefore, future work should improve its execution time and reduce its computational complexity. Future work should also focus on integrating a classifier into our framework for defect-type characterization. Finally, future work will focus on evaluating and validating the proposed framework using real bridges’ GPR data.
Partial support of this work was provided by Western Michigan University FRACAA-2009 Award. The authors would like to acknowledge Western Michigan University for its support and contributions to the Information Technology and Image Analysis (ITIA) Center.