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Automatic detection of multiple pavement layers from GPR data


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NDT&E International 41 (2008) 69–81 www.elsevier.com/locate/ndteint

Automatic detection of multiple pavement layers from GPR data
Samer Lahouara,b,, Imad L. Al-Qadic
a

rieur des Sciences Applique et de Technologie de Sousse, Cite Taffala, Ibn Khaldoun, Sousse 4003, Tunisia es Department of Electronics, Institut Supe b Microelectronic and Instrumentation Laboratory, Faculty of Sciences of Monastir, Tunisia c Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N Mathews MC 250, Urbana, IL 61801, USA Received 13 March 2007; received in revised form 7 September 2007; accepted 10 September 2007 Available online 19 September 2007

Abstract One of the problems encountered in the nondestructive testing of pavements with ground penetrating radar (GPR) is the detection of multiple-layer reections within the GPR return. Detecting reections is especially problematic when the pavement layers are thin with respect to the probing pulse width, in which case overlapping between the reected pulses occurs, causing the weak reections to be masked by the stronger reections in their vicinity. In this study, the problem is solved by iteratively detecting the strong reections present within the GPR signal using either a threshold or a matched lter detector. The detected pulses are then used in a reection model to synthesize a signal ‘‘similar’’ to the measured GPR signal in the least-squares sense. The synthesized signal is then subtracted from the measured signal to reveal the masked weak reections, which are later detected iteratively using the same method. This technique was successfully applied to eld GPR data collected from an experimental pavement site: the Virginia Smart Road. r 2007 Elsevier Ltd. All rights reserved.
Keywords: Ground penetrating radar; Multiple layers; Detection; Pavement; Matched lter detector; Threshold detector; Least-squares tting

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. GPR system description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Interface reection detection and time-delay estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Proposed solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Threshold detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. MF detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Performance comparison between the detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Experimental results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Virginia Smart Road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Field results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Accuracy estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A. Least-squares tting of GPR data to a theoretical reection model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. 70 70 70 71 72 73 74 75 75 75 76 78 79 79 79 80

Corresponding author. Department of Electronics, Institut Superieur des Sciences Appliquees et de Technologie de Sousse, Cite Taffala, Ibn Khaldoun, Sousse 4003, Tunisia. E-mail address: Samer.Lahouar@issatso.rnu.tn (S. Lahouar).

0963-8695/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2007.09.001

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1. Introduction Ground penetrating radar (GPR) [1] is designed specically to penetrate the ground surface and to look into the subsurface to locate inhomogeneities within the investigated dielectric medium. It is currently used in many areas as a nondestructive investigation tool:



Geophysics, in which GPR is used to estimate the structure of the earth sediments and to nd the depth of bedrock, water tables, and such. Archeology, in which GPR is used to locate buried archeological structures before digging to prevent their accidental damage. Law enforcement, in which GPR is used as an investigative tool to locate buried bodies and as a safety tool to locate landmines. Civil engineering testing, in which GPR is used to assess the performance of civil structures, such as buildings, bridges, pavements, and tunnels.

For pavement evaluation, GPR is mainly used to measure the thicknesses of the various layers composing a exible pavement system. For new pavements, measuring the layer thicknesses ensures that the constructed pavement conforms to the design. For existing pavements, accurate measurement of layer thicknesses is important for pavement engineers to optimize pavement maintenance or rehabilitation plans. It should be noted that measurements of layer thicknesses for old pavements are usually unavailable due to poor documentation or to initial differences between design and construction. Although GPR technology has developed, its routine use for evaluating pavements and bridges remains minimal. In fact, only a few (approximately 11) Departments of Transportation (DOT) currently own a GPR system, and these DOTs do not systematically use GPR in their Pavement Management System (PMS) decision-making. The limited use of GPR for pavement evaluation is due mainly to the lack of reliable automated procedures for data analysis, as well as the difculty of manually interpreting the large amounts of GPR data collected during pavement surveys. There are three major problems to overcome in order to automate GPR data analysis for pavement surveys: rst, detection of the wanted reections in the collected GPR signal; second, accurate estimation of the reection timedelays; and third, estimation of the medium’s dielectric properties, which are used to estimate the propagation speed of the electromagnetic (EM) waves within the pavement system. In order to facilitate GPR data analysis, a exible pavement system is usually assumed to be composed of two distinct layers: a homogeneous hot-mix asphalt (HMA) layer and a granular base layer [2]. This assumption reduces the GPR reection detection problem into a simpler peak search problem. This technique yields an

average HMA thickness error of 7.5% for layer thicknesses between 50 and 500 mm, as reported by Maser [2]. Loizosa and Plati [3] reported an average error between 5% and 10%, depending on the utilized dielectric constant estimation technique. In another study, Al-Qadi et al. [4] found an average thickness error of 2.9% for HMA layers ranging from 100 to 250 mm. It should be mentioned that in the latter study, the thickness of the individual HMA layers, which were composed of a HMA base layer overlaid by two different HMA intermediate layers, were estimated during the pavement construction by analyzing the GPR data collected on each layer after it was constructed, therefore the HMA layer was not considered homogenous. Finally, it should be noted that for pavement thickness estimation from GPR data a thickness error comparable to 2.7% is acceptable since this error is obtained by direct thickness measurements on a core from different sides as indicated in [4]. Consequently, in order to increase the accuracy of pavement layer thicknesses estimated from GPR data, the reections from all the layers composing the pavement system should be detected and then taken into account in the thickness computation. This paper presents a fast and accurate technique for solving this problem of multiple layer interface detection from GPR data. Layer dielectric constant estimation techniques from GPR data are out of the scope of this study and are discussed in [3,5]. 2. Background 2.1. GPR system description The GPR system used in this study is an ultra-wideband impulse (or pulsed) radar, which sends a short EM pulse through an air-coupled antenna to the surface and then records the reected pulses for a xed period of time (typically less than 20 ns for pavement surveys). The reections occur whenever there is a contrast in the dielectric properties of the surveyed structure. For pavements, a dielectric contrast usually exists either between two different layers or when a large enough inhomogeneity (by comparison to the incident signal’s wavelength) is present within a layer. For pavement evaluation, air-coupled antennas are usually utilized to transmit and receive the GPR signals. The antennas are mounted at approximately 0.50 m above ground on the back of the survey van, as shown in Fig. 1, to allow for highway-speed surveys. The antennas are usually horn shaped and have a frequency bandwidth of 1 GHz, which corresponds to a pulse width of approximately 1 ns [6]. To increase the spectral efciency of the antennas, a bipolar bell-shaped pulse (Mexican hat) is used as the incident GPR signal. This pulse shape achieves a spectral efciency near 98% for wide bandwidths [7]. Unlike other ultra-wideband radars, where the incident pulses get distorted when propagating from the transmitter to the receiver [7], the shapes of the GPR-reected pulses

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Tx/Rx Air, d0 t0

Amplitude

HMA, d1

t1

Base, d2

t2

Time

Subgrade

Fig. 1. GPR survey van and air-coupled horn antennas.

Fig. 2. Ideal GPR reected signal collected from a typical exible pavement system composed of three layers.

from pavements do not signicantly differ from the original incident pulse shape. This is due to three main reasons:



The propagation paths are relatively short for GPR surveys over pavements. In fact, the two-way propagation paths hardly exceed 2 m in length. The reecting targets (layer interfaces) are large compared to the probing signal wavelength. The dielectric properties of the pavement materials do not vary signicantly within the GPR bandwidth [8,9].

Consequently, the time domain GPR signal, yr(t), could be assumed to be composed of a series of scaled and time-delayed replicas of the incident pulse x(t) as indicated by [10] ! N 1 i X X yr t Ai x t tj nt, (1)
i0 j0

affects the accuracy of the results of the overall GPR system. In fact, erroneous detection of the reected pulses within the GPR signal (either false alarms or missed detections) results in reporting an incorrect number of layers and, therefore, incorrect layer thicknesses. It should be noted that the performance of the layer interface detector is greatly enhanced by applying suitable bandpass lters to the recorded GPR signals, either during data collection or during data analysis, in order to reduce the additive noise n(t). In this study, two bandpass lters were applied: a lter with a large pass band was applied during data collection (to ensure that no interesting features are removed by the lter) and another lter with a narrower pass band was applied during data processing. 2.2. Interface reection detection and time-delay estimation Previous studies showed that detecting multiple pulses within a signal in the presence of noise can be implemented optimally using a matched lter (MF) detector [11], which is designed based on the known incident pulse x(t) [12]. In the case of an air-coupled GPR system, the incident signal x(t) is measured by placing a large copper plate (perfect EM reector with a reection coefcient of 1) underneath the antenna and then collecting the reected signal, which represents the negative of the incident signal. The output signal of the MF would then peak at times corresponding to the time-delays ti. Thus, the problem of time-delay estimation is transformed into a simpler problem of local maxima search on the output signal of the MF. It should be noted that for this search to be successful (i.e., detection of all the reected pulses present within the reected signal), the time-delay between any two successive pulses should be greater than the duration of the autocorrelation function (ACF) of the incident signal x(t) [11]. If this condition is not satised, some peaks in the MF output would be obscured by the stronger reections in their

where x(t) is the incident GPR pulse, N is the total number of layers composing the pavement system, Ai is the relative amplitude of the reected pulse at the ith interface, n(t) is additive noise, and tj is the two-way travel time through the jth layer (with t0 the two-way travel time through air). It should be noted that this formulation assumes that no multiple reections from the same interface are present within the reected signal. This assumption is usually valid since the layer interfaces are not strong EM reectors. Fig. 2 shows an ideal GPR reected signal collected from a typical exible pavement system composed of three layers: HMA layer, aggregate base layer, and subgrade (original soil). In order to analyze GPR data, the individual reected pulses within the GPR signal should be detected and their exact time-delays estimated. Detection of layer interface reections represents one of the most important stages of GPR data analysis because its outcome considerably

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Layer 1

r1=4

d1=40mm

0

2 Layer 2
r2=5

d2=150mm 4

Surface reflection

Layer 3

r3=4

d3=75mm Time (ns) 6

Overlap

Layer 4

r4=9

d4=150mm

8

Layer 3/4 reflection

Layer 5

r5=11

d5= ∞

10 Layer 4/5 reflection
0

12
2 4

14

Incident

Fig. 3. (a) Typical exible pavement structure of ve layers. (b) Corresponding GPR reected signal (incident GPR pulse is shown in the bottom-right corner).

vicinity, thus leading to missed detections. The condition that the time-delay between any successive reected pulses is greater than the duration of the ACF of the incident signal is seldom veried for GPR signals collected over pavements. The reason is that the presence of thin layers within pavements (e.g., the top wearing surface layer) usually yields overlapped reected pulses, as depicted in Fig. 3. This gure shows a ltered GPR reected signal (Fig. 3b) collected from a ve-layer pavement system containing two thin layers (Fig. 3a). Hence, the MF cannot be applied, in this case, reliably to detect all the GPR reected signals. Kurtz et al. [13] addressed the problem of detecting overlapped pulses in the GPR signal by iteratively subtracting time-delayed and scaled replicas of the incident pulse x(t) from the reected signal yr(t) for each successfully detected pulse, thus removing the strong reections. The problem with this technique, however, is that the amplitude of the subtracted pulse is estimated based on the amplitude of the detected pulse, which can be different from the real amplitude because of the overlap with other pulses in the vicinity [14]. This usually creates spurious reections in the obtained-difference signal that would be detected as real reections in the next iterations. In the case of GPR, detecting layer interface reections and estimating their corresponding time-delays could be viewed as a pure estimation problem. With this approach, a given number of pulses are assumed present within the GPR reected signal, and an optimal estimator is used to estimate their respective time-delays and amplitudes. It is known in estimation theory that one of the most optimal (i.e., unbiased with minimum variance) and realizable estimators is the maximum likelihood estimator (MLE) [15]. Several studies concerning the time-delay estimation of multiple pulses within a signal have shown that, in the

case of white Gaussian noise, the MLE is equivalent to a nonlinear least-squares tting (NLS) problem [10,16]. In the time domain, least-squares tting is achieved by minimizing the error I of Eq. (10) in Appendix A, where the unknown parameters are the relative amplitudes Ai and the time-delays ti. Because the time-delays are unknown, the solution presented in Appendix A is invalid for this case, and the problem is highly nonlinear with no trivial solution. The different solutions proposed for this NLS problem were mainly focused on reducing the size of the search space of the unknowns. For example, Li and Wu [10] reduced the N-dimensional search space of the NLS problem into a set of N one-dimensional search spaces over all the possible values of the time-delays. However, it should be noted that because of the large number of possible time-delay values, the search space remains, in this case, relatively large and, thus, the technique is computationally intensive and not suitable for real-time processing. 3. Proposed solution Appendix A shows that if the reection time-delays, ti, are known, then the reection amplitudes are optimally found using least-squares tting, which by denition guarantees a minimum error between the measured signal, yr(t), and the modeled signal, yrs(t). Thus, if all possible reected pulses and their corresponding time-delays are found, then least-squares tting can be used to select the optimum set of reection time-delays (among all detected pulses) that ensures a minimum error between measured, and modeled signals in the least-squares sense. The modeled signal found can then be subtracted from the measured signal to yield a difference signal, d(t), composed mainly of weak reections originally masked by the

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stronger reections in their surroundings. The detection process can then be repeated on the difference signal to nd the time-delays of the weak reections. These time-delays are then combined with the rst set of time-delays to obtain the time-delays of all the reected pulses. This stage can be followed by another least-squares tting operation to nd the optimum set of reection time-delays that yields a minimum square error between the measured signal and the modeled signal. The whole process could be repeated until no new reections are detected within the difference signal. The proposed combined detection/estimation technique can be summarized by the following algorithm: (1) Initialization: assign the measured reected signal yr(t) to d(t) and set the array of detected time-delays ti to null. (2) Use a detector to detect and estimate the time-delay tj of the strongest pulse present within the signal d(t). Add the time-delay tj to the set of already detected time-delays ti. (3) Use the time-delays ti to nd the optimum synthesized reected signal yrs(t) that approximates the signal yr(t) in the least-squares sense as shown by Eqs. (10) and (16)–(18) in Appendix A. (4) Compute the difference signal d(t) yr(t)-yrs(t). (5) Repeat at step (2) until no more pulses are detected in the signal d(t). (6) Determine the optimum subset of time-delays among the set ti that yields a minimum least-squares error between the measured signal yr(t) and the synthesized signal yrs(t). This step is introduced to remove all false alarms reported by the detector. (7) Determine the reection amplitudes Ai from the optimum least-squares t found in step (6). According to the aforementioned algorithm, leastsquares tting is used to correct any detection errors made by the detector; therefore, the detection stage can be realized by different detectors, even if they do not have high performance. It should be noted, however, that the only errors that would be corrected at the least-squares stage are the false alarms. Thus, the detector should have a high probability of detection without severe constraints on the probability of false alarm. Another requirement that should be met by the detector is that it should be independent of the reected pulses amplitudes since the exact amplitudes would be, in turn, determined based on the detected time-delays as explained in Appendix A. Thus an error in the time-delays estimation would produce a bad curve tting and, therefore, errors in estimated amplitudes, especially if pulses with similar amplitudes are overlapped. However, since in GPR data (Fig. 3b) strong pulses would usually mask weaker pulses (due to the wave attenuation through the pavement materials and the low contrast in the dielectric constants within the same material where thin layers are found), the effect of the amplitude on the detector performance would be minimized.

Different types of detectors can be used in the detection stage (step 2 in the algorithm) of the proposed technique. In this study a threshold detector and a MF detector were considered. 3.1. Threshold detector The simplest detector that can be used to detect a signal embedded in noise is a threshold detector. A threshold detector compares the level of the analyzed signal to a xed threshold; then it declares the signal present or absent depending on whether or not the analyzed signal’s level exceeds a specied threshold. This detection technique assumes that the minimum detectable reections are above noise level, which can usually be used as a suitable value for the threshold. For the case of GPR data, since the reected pulses might have different polarities than the incident pulse (depending on the dielectric properties of the pavement materials), two thresholds should be used: a positive threshold to detect ‘‘positive’’ reections and a negative threshold to detect ‘‘negative’’ reections. Due to the shape of the GPR pulses (see Fig. 3), this approach would lead to the detection of at least three separate peaks (one positive peak surrounded by two negative peaks or vice versa) corresponding to each reected pulse. Although the obtained peaks can be grouped together to form the actual detected pulses, this procedure is cumbersome because a different number of peaks are detected for each pulse, especially for low amplitude reections. The multiple-peaks problem could be eliminated in this case if an envelope detector were used before the threshold detector. Envelop detectors are commonly used in amplitude modulation (AM) communication systems to extract the modulation envelope and to reject the high frequency carrier signal [17]. Even though GPR signals are composed of ultra-wide band pulses that do not have a carrier frequency, an envelope detector applied to this type of signals would still extract the envelope describing the variations of their amplitude. Mathematically, the real envelope xe(t) of any real signal x(t) is dened as the magnitude of the corresponding analytic signal, as given by [17] ^ xe t jxa tj jxt j xtj, (2) ^ where xa(t) and xt are the analytical signal and Hilbert transform [17] of the signal x(t), respectively. With an envelope detector, a pulse is declared detected if the amplitude of the analyzed signal’s envelope exceeds a xed threshold selected above noise level. Since the envelope of a signal is always positive by denition, only a positive threshold value is used. Fig. 4 shows the output of an envelope detector for a typical GPR signal along with the reported detected pulses. An algorithm that can be used to nd the local maxima (corresponding to the reected pulses) of the envelope of the analyzed GPR signal is as follows:

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12000 10000 8000 6000 Amplitude 4000 2000 0 -2000 -4000 -6000 -8000 0 2 4 6 8 Time (ns) 10 12 14 Threshold Detections Envelope Original Signal

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Fig. 4. Typical detections obtained after applying an envelope detector followed by a threshold detector.

(1) compute the real envelope of the difference signal d(t) using Eq. (2); (2) nd the maximum value of the envelope; (3) compare the maximum value found to the selected threshold vt. If the maximum value is less than the threshold, then terminate the detection procedure; otherwise, take the time-delay of the maximum value as the time-delay tj of the detected pulse. For radar data analysis, the threshold value used by the threshold detector is generally selected based on the Neyman–Pearson criterion [12]. With this criterion, the probability of false alarm is chosen as large as tolerable by the application. The detector is then designed to maximize the probability of detection. If the noise embedded in the GPR signal is assumed to be white Gaussian with a variance s2, then at the output the envelope detector will have a Rayleigh probability density function [2], given as follows: u u2 pu 2 exp 2 ; with uX0. (3) s 2s When the noise level exceeds the selected threshold value, a false alarm error is produced. Therefore, the probability of false alarm Pf is the probability that the noise exceeds the threshold, which is given from Eq. (3) as Z 1 r r2 exp 2 dr Pf pvt oro1 2 2s vt s 2 v exp t 2 , 4 2s where vt is the selected threshold. From Eq. (4), the detector threshold can be found as a function of the probability of false alarm according to the following: p vt 2s2 log Pf . (5) Eq. (5) shows the dependence of the threshold used in the detection procedure on noise power. Practically, the noise variance s2 could be estimated from the processed

GPR signal by assuming that a segment at the end of the signal is composed of noise only (as in Fig. 4 for the signal portion after 12 ns). This assumption is usually valid for GPR data collected over pavements since a ‘‘buffer zone’’ is added to the range of the deepest detectable layer to ensure that all interfaces would be detected if the layer thicknesses increase unexpectedly. 3.2. MF detector An optimal detector that can be used to decide between the presence or absence of a known signal x(t) embedded in white Gaussian noise of variance s2 is the MF. The impulse response h(t) of the MF is given by [12] ht xT t, (6)

where T is the duration of the signal x(t) introduced to make the lter h(t) causal. It can be shown that at time T the MF output exhibits a maximum signal-to-noise ratio (SNR) [12]. Using the MF detector, a signal x(t) is declared present if the corresponding MF output exceeds a xed threshold St at time T. In this case, the MF output would have a maximum (or a minimum, depending on whether the polarity of the detected signal is reversed compared to the original signal or not) at time T. Using this property of the MF, the following algorithm for detecting multiple reected pulses within the difference signal d(t) could be derived: (1) compute the MF impulse response h(t) using Eq. (6); (2) lter the signal d(t) using h(t) to obtain the ltered signal yMF(t); (3) nd the maximum absolute value ymaxMF of yMF(t) and its corresponding time sample tmax; (4) compare the value ymaxMF to the threshold St. If ymaxMF is less than St, then terminate the detection procedure; otherwise, the value (tmaxT) corresponds to the travel time tj of the strongest reection present within yr(t).

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d(t) yMF(t) Travel time tj ymaxMF

75



Iteration 1

Iteration 2 Iteration 3 Iteration 4 Iteration 5

leads to an inability to experimentally estimate the probability of detection. There is no control over the SNR of the reected GPR signals. The only way to change the SNR of the processed signal is to add randomly generated noise to it. This operation would not give an accurate estimate of the detector performance since the processed data would be simulated data rather than real eld data.

Amplitude

0

100

200

300

400

500

A more appropriate method for comparing the performance of the detectors when applied to eld GPR data is to use the square error ratio (SER), dened as follows: " #, M1 M1 X X 2 SER yr t yrs t yr t2 , (8)
t0 t0

Time (samples)

Fig. 5. Iterative detection procedure for a ve-layer structure.

Fig. 5 shows ve iterations of the difference signal d(t) and the MF output yMF(t) used to detect the individual reected pulses from a GPR signal collected from the velayered pavement structure shown in Fig. 3a. As for the envelope detector, the threshold St used with the MF is determined from the maximum tolerable probability of false alarm Pf based on the Neyman– Pearson criterion. It can be shown that St is given by [14] p S t erfc1 Pf s2 E , (7) where E is the total energy of the known signal x(t) and erfc1(u) is the inverse complementary error function dened as erfc(u) 0.5erf(u), with erf(u) is the error function dened in [18]. In this case, the noise power s2 could be estimated from the reected signal yr(t) by assuming that the trailing part of the signal is composed of noise only. 3.3. Performance comparison between the detectors Typically, the performance of a detector is evaluated using the receiver operating characteristic (ROC) [12], which gives the detector’s probability of detection versus its probability of false alarm for various values of the SNR. A good detector should have a probability of detection near one and a probability of false alarm near zero, even for low values of SNR. If the ROC curves cannot be found theoretically, they are usually estimated using simulation techniques such as the Monte Carlo simulation. Practically, it is difcult to estimate the ROC of a given detector from eld GPR data. The difculties arise from the following points:

where yr(t) is the measured GPR signal, M the number of samples in yr(t), and yrs(t) is a synthesized signal obtained by tting the detected pulses to the reection model in the least-squares sense as shown in Appendix A. According to this denition, it is seen that the smaller the SER, the higher the similarity between the measured GPR signal and the synthesized signal. The high similarity between the signals translates, in turn, to a more accurate estimation of the reection time-delays. Another parameter that could be considered to be a good indicator of the detector’s performance is the number of detected layers N. In fact, if the number of layers composing the pavement is known a priori, then the number of detected layers would indicate the occurrence of false alarms if the reported number is greater than the known number and missed detections in the converse case. A large number of detected layers could also indicate the presence of distress within the pavement system, especially for in-service pavements. 4. Experimental results In order to assess the performance of the threshold and the MF detectors to detect and estimate the time-delays of the reected pulses in GPR signals, they were used to process eld GPR data collected from a known experimental pavement site: the Virginia Smart Road. 4.1. Virginia Smart Road The Virginia Smart Road, located in southwest Virginia, is a unique, state-of-the-art, full-scale research facility for pavement research and evaluation of Intelligent Transportation Systems (ITS). The completed facility will consist of a 9.6-km connector highway between State Route 460 in Blacksburg, Virginia and Interstate 81. The rst 3.2 km currently serve as a controlled test facility. The pavement research facility includes 12 different sections that are each approximately 100 m long. The pavement performance of all the 12 sections is closely monitored through a complex array of sensors (strain gages, pressure cells, thermocouples, etc.)



The accuracy of the time-delays reported by the detector cannot be checked experimentally since the ‘‘true’’ timedelays are difcult to nd, especially when overlap occurs between the reected pulses, as in Fig. 2. This

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76 S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81 Table 1 Pavement designs used at the Virginia Smart Road Section Wearing surface (mm) 38 38 38 38 38 38 38 38 38 38 38 38
a b

Base HMA BM25.0 (mm) 150 150 150 150 225 150 100 100 100 225 244 150

Base HMA SM9.5A (mm)

OGDLa (mm)

21-Ab Aggregate (mm) 150 150 150 150 150 150 150 150 150

21-B Aggregate (mm) 175 175 175 175 75 150 150 75 75 150 150 75

A B C D E F G H I J K L

75 75 75 75

50 50 50

75 75 75 75 75

150

Open graded drainage layer. Cement stabilized base.

embedded in the pavement and networked to an onsite control room where the data is collected [19]. The pavement designs of the 12 Smart Road exible sections are summarized in Table 1 (all designations are in accordance with Virginia Department of Transportation specications). 4.2. Field results and discussion To compare the performance of the threshold detector to that of the MF detector, a large set of GPR data (approximately 1250 scans per pavement section, i.e. 15,000 scans in total) collected over different periods of time from the exible sections at the Virginia Smart Road were used. The data were collected using a 1 GHz aircoupled antenna at a spatial frequency of 10 scans/m. Before applying the detectors, the data was preprocessed using a 2 GHz lowpass lter to remove any additive noise without affecting the reections of interest. Then, for each collected scan, both detectors were applied with various probabilities of false alarm ranging from 1016 to 0.4, and the SER and the number of detected layers N were recorded. The results were then averaged over sections with similar numbers of layers and layer thicknesses. The sections that were considered analogous for this analysis are summarized in Table 2. The number of layers presented in this table represents the number of layers with sufcient contrast in their dielectric constants to produce a detectable reection in the GPR signal. Since layer thicknesses inuence the degree of overlap between the successive reected pulses and, thus, might affect the performance of the detector, sections with different layer thicknesses were considered dissimilar even if they had an equal number of layers. A layer is considered thin or thick depending on whether its thickness is less or greater than the GPR resolution in that layer, which is dened by [14] cT Dd p , 2 r (9)

Table 2 Sections used for detector performance evaluation Sections E A, B, C, D, J, L F G H Number of detectable layers 3 (WS, BM-25.0, Base) 4 (WS, BM-25.0, OGDL, Base) 3 (WS, BM-25.0, Base) 4 (WS, BM-25.0, SM, Base) 5 (WS, BM-25.0, SM, OGDL, Base) Comments Thick layers except for WS Thick layers except for WS Thin layers Thin layers Thin layers

where Dd is the GPR resolution, c is the speed of light in free space, T is the incident pulse width, and er is the dielectric constant of the considered layer. The variations of the average SER and the average number of detected layers N versus the probability of false alarm found with the threshold and the MF detectors are presented in Fig. 6a through Fig. 6e for the ve layer categories of Table 2, respectively. The x-axis in these gures represents the probability of false alarm in logarithmic scale. Based on Fig. 6, it is found that for all the cases studied and with both detectors, the SER increases as the probability of false alarm decreases, whereas the number of detected layers N decreases and converges to the real number of layers. Hence, a minimum SER between the measured and synthesized GPR signals is equivalent, in all cases, to the detection of a number of layers greater than the real number (i.e., high false alarm rate). This result is similar to what is found in the ROC, where a high probability of detection produces a high probability of false alarm. Therefore, for a correct evaluation of the detectors’ performance, both the SER and the average number of detected layers N should be used jointly. For the cases of three and four thick layers and the case of three thin layers, the performance results depicted in

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S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81 77

2.0 1.8 SER (%) 1.6 1.4 1.2 1.0 0.8 1E-16 1E-14

SER (MF) SER (Threshold) N (MF) N (Threshold)

4.2 4.0 SER (%) 3.8 N 3.6 3.4 3.2

2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1E-16 1E-14 1E-12 1E-10 1E-08 Pf 1E-06 1E-04
SER (MF) SER (Threshold) N (MF) N (Threshold)

4.5 4.4 4.3 N N 4.2 4.1 4.0 3.9 3.8 1E-02 1E+00

1E-12

1E-10

1E-08 Pf

1E-06

1E-04

1E-02

3.0 1E+00

2.4 2.2 2.0 SER (%) 1.8 1.6 1.4 1.2 1.0 1E-16 1E-14
SER (MF) SER (Threshold) N (MF) N (Threshold)

4.4 4.2 4.0 3.8 3.6 3.4 3.2 1E-08 Pf 1E-06 1E-04 1E-02 3.0 1E+00 N SER (%)

1E-12

1E-10

2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1E-16

SER (MF) SER (Threshold) N (MF) N (Threshold)

1E-14

1E-12

1E-10

1E-08 Pf

1E-06

1E-04

1E-02

4.4 4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5 3.4 1E+00

2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1E-16

SER (MF) SER (Threshold) N (MF) N (Threshold)

1E-14

1E-12

1E-10

1E-08 Pf

1E-06

1E-04

1E-02

4.4 4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5 3.4 1E+00

SER (%)

Fig. 6. Comparison between the performance of the threshold and the matched lter detectors: (a) 3, (b) 4 thick layers, (c) 3, (d) 4 and (e) 5 thin layers.

Fig. 6a–c respectively, show that the MF detector outperforms the threshold detector. In fact, in all three cases, the SER that results from the MF detector is lower than the one resulting from the threshold detector for all probabilities of false alarm. At the same time, the number of detected layers is higher than the real number of layers (i.e., three or four) for both detectors for high probabilities of false alarm, but it converges to the real number of layers for lower probabilities of false alarm. Thus, when the probability of false alarm Pf is suitably selected, the reections detected by the MF would be better approximations of the real reections than those detected by the threshold detector. The relatively large difference in the SER of the two detectors is a good indicator that some of the interface reections detected by the threshold detector do not correspond to real reections, even though the number of detected layers is almost equal for the low probabilities of false alarm.

In contrast, the performance results illustrated in Fig. 6d and e show that the threshold detector outperforms the MF detector for the cases of four and ve thin layers. In fact, these gures show that the SER found by the MF is higher than the SER found by the threshold detector for all Pf values. Moreover, for the MF, it is noticed that the number of detected layers decreases below the real number of layers for the low false alarm probability values. This result is an indication of missed detections if the probability of false alarm is not chosen adequately. At the same time, the average number of layers detected by the threshold detector is higher than the real number of layers for high probabilities of false alarm, but it converges toward the true number of layers when the probability of false alarm decreases. The same variations of the average number of detected layers are observed for the ve thin layers (Fig. 6c), except that, in this case, the number of layers reported by

N

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78 S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81
GPR Signal Generated Signal Detected Peaks Section A, SER = 0.9%

Section E, SER = 1.1%

Amplitude

Section F, SER = 1.7%

Section G, SER = 1.0%

Section H, SER = 1.1%

0

2

4

6

8

10 Time (ns)

12

14

16

18

20

Fig. 7. Reected GPR signals, detected pulses, and generated signals for the ve different pavement sections.

both detectors (maximum average of 4.25 layers for the MF and 4.30 layers for the threshold detector) is less than the real number of layers (i.e., ve), even for high probabilities of false alarm. Hence, both detectors failed in this situation to detect all the layers composing the pavement, yet the threshold detector still shows a better performance than the MF for any Pf value. The degradation in the MF detector performance compared to that of the threshold detector, when the number of layers composing the pavement system increases and the layers are relatively thin, could be explained by the breakdown of the assumptions made in the derivation of the MF detector. In fact, to get a high MF detection performance, the pulses that compose the reected GPR signals should not deviate very much from the incident pulse x(t). This condition is usually more difcult to satisfy for thin layers because of the overlap between consecutive reections, which distorts the pulse shape. These distortions generally grow more severe as the layers become thinner and their number increases. Nevertheless, when only one thin layer is present, the performance of the MF is not degraded much and, indeed, it outperforms the threshold detector (as in the cases of Fig. 6a and b). Finally, it should be noted that with both detectors, the probability of false alarm, Pf, should be adequately chosen in order to be able to detect the correct interface reections and, thus, the correct number of layers. If the real number of layers is a priori known, the probability of false alarm should be chosen so that the number of layers reported by the detector equals the real number of layers. However, if the real number of layers is unknown, the probability of false alarm should be chosen as the lowest

possible value that would yield a number of layers converging to a constant value (versus the probability of false alarm). The results of applying the adequate detector (threshold or MF) to one GPR scan taken from each of the ve sections are presented in Fig. 7. The detectors were applied using a probability of false alarm, Pf, equal 103. Fig. 7 shows also all the detected peaks for each scan, along with the signal generated based on least-squares tting. For the ve sections, the maximum SER found for all sections was about 1.7%. 4.3. Accuracy estimation To estimate the accuracy of the multiple reections detection procedure, the outlined algorithms were applied to GPR signals collected from marked locations at different sections of the Virginia Smart Road, where cores were later taken for direct thickness measurements. The GPR data was also processed using the classic detection method where only the strong reections are detected (i.e., considering the HMA layers as a single homogeneous layer). The results obtained by the two methods are presented in Table 3. In Table 3, the ‘‘single’’ thickness represents the thickness estimated from GPR data by considering all HMA layers as a single homogeneous layer. In contrast, the ‘‘multiple’’ thickness represents the total thickness found after detecting all detectable reections within the HMA layers, estimating the dielectric constant and thickness of all the layers, and then adding them together. For both results the dielectric constants of the layers were estimated based on the detected reection amplitudes as

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S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81 Table 3 Accuracy estimation of the multiple reections detection compared to the single detection Core # HMA thick (mm) Core A1 A2 A3 A4 B2 D1 D2 E1 E2 F1 F2 F3 G1 G2 H2 J1 J2 282 273 266 268 283 276 265 292 285 211 210 206 195 204 286 286 355 Single 313 276 259 252 322 315 301 317 302 247 247 239 209 214 302 330 405 Multiple 272 276 259 252 266 271 255 298 283 211 211 204 193 202 270 292 367 Error (%) Single 10.9 1.1 2.8 5.9 13.9 14.3 13.4 8.6 5.8 16.9 17.4 16.2 7.2 4.9 5.7 15.3 14.2 10.2 Multiple 3.7 1.1 2.8 5.9 5.9 1.7 3.9 2.1 0.8 0.2 0.3 0.8 1.0 1.0 5.5 2.0 3.5 2.5 79

5. Conclusion A technique to automatically detect all detectable reections, including masked weak reections, within GPR signals was presented. In particular, it was shown that, depending on the thicknesses and the number of layers composing a pavement system, different types of detectors should be used to locate the interface reections in the GPR signal. Specically, if most of the pavement layers are thick, a MF detector would be the optimal detector to use. However, if multiple thin layers are part of the pavement system, a threshold detector should be used. For detection purposes, the pavement layers are considered thin or thick by comparison to the GPR pulse width. To detect the reections from all the layers in the pavement system, the detector should be applied iteratively. After each iteration, the time-delays of the detected pulses are used to generate a signal comparable to the GPR signal in the least-squares sense. The synthesized signal is then subtracted from the measured GPR signal to expose the weak reections initially masked by the stronger reections in their vicinity. Experimental results on eld data using both detectors showed promising results. In fact, by comparing the GPR results to thicknesses measured directly on cores an average absolute thickness error of 2.5% was found when all reections were detected. This error increased to 10.2% when only the strong reections were considered in the analysis.

Average absolute error (%)

described in [5]. As indicated in Table 3, the multiple detection technique is more accurate (2.5% average absolute thickness error) than the classic technique (10.2% error). The enhancement in the thickness error is essentially due to:

Acknowledgments This research is based upon work supported by the National Science Foundation under Grant No. 9457978. Any opinions, ndings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reect the views of the National Science Foundation. The assistance of Amara Loulizi, Thomas Freeman, and William Hobbs in this work is greatly appreciated.





Better estimation of the dielectric constants since the reection amplitudes, on which the dielectric constant computation is based, are computed after least-squares tting. The dielectric constant of each layer is considered in the computation of the thickness instead of considering a single dielectric constant for all the layers.

Appendix A. Least-squares tting of GPR data to a theoretical reection model As shown by Eq. (1), the reected GPR signal can be modeled, without the additive noise term, as follows: ! N 1 n X X yrs t An x t ti .
n0 i0

(10)

If the number of layers N are assumed known and the two-way travel times ti are estimated from the measured GPR signal yr(t), then the only model parameters that need to be estimated are the reection amplitudes An. The sum of squares of the error between the measured GPR signal yr(t) and the signal computed from the model given by (10) is calculated as follows: " ! #2 N 1 n X X X yr t An x t ti : (11) I
t n0 i0

To achieve a minimum mean-square error (MSE) between the measured and modeled GPR signals, the sum of squared errors given by (11) should be minimized with respect to all the model parameters An. Thus, the partial derivatives of I with

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80 S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81

respect to the parameters An should be set to zero: " !# ! N 1 n k X X X X qI 2 yr t An x t ti ti 0; x t qAk t n0 i0 i0 Rearranging and simplifying (12) leads to the following: ! ! ! N 1 n k k X X X X X X An x t ti x t ti yr tx t ti ;
n0 t i0 i0 t i0

for k 0; . . . ; N 1.

(12)

for k 0; . . . ; N 1.

(13)

Eq. (13) could be expanded in the form of a set of equations according to: 8 > > > > > > > > < P xt t0 tN1 xt t0 yr txt t0 t t t P P P A0 xt t0 xt t0 t1 AN1 xt t0 tN1 xt t0 t1 yr txt t0 t1 A0 P x2 t t0 AN1 P
t t t

> > > > > P P P > >A > 0 xt t0 xt t0 tN1 AN1 x2 t t0 tN1 yr txt t0 tN1 :
t t t

. . .

(14)

which is equivalent in a matrix format to: MA Y, where A A0 " Y X
t

(15) T

A1



AN1

, X
t

(16) #T yr txt t0 t1 tN1 ,
P P
t t

yr txt t0
P
t

X
t

yr txt t0 t1

(17)
3

2

x2 t t0

P
t

6 P 6 xt t0 xt t0 t1 6 6 t M6 6 . . 6 . 6 4P xt t0 xt t0 tN1
t

xt t0 t1 xt t0 P 2 x t t0 t1
t

. ..

xt t0 tN1 xt t0

. . . P xt t0 t1 xt t0 tN1
t

7 xt t0 tN1 xt t0 t1 7 7 7 7. 7 . . 7 . 7 P 2 5 x t t0 tN1
t

(18) Thus the model parameters An that ensure a minimum MSE between the measured GPR signal yr(t) and the theoretical signal yrs(t) could be determined according to: A M1 Y. (19)

References
[1] Daniels DJ. Surface-penetrating radar. London, UK: The Institution of Electrical Engineers; 1996. [2] Maser KR. Measurement of as-built conditions using ground penetrating radar. In: Structural materials technology: an NDT conference, 1996. p. 61–7. [3] Loizosa A, Plati C. Accuracy of pavement thicknesses estimation using different ground penetrating radar analysis approaches, NDT&E International 40. Amsterdam: Elsevier; 2007. p. 147–57. [4] Al-Qadi IL, Lahouar S, Loulizi A. Successful application of groundpenetrating radar for quality assurance-quality control of new pavements. In: Transportation research record no. 1861, construction, 2003. p. 86–97.

[5] Al-Qadi IL, Lahouar S, Jiang K, MeGhee KK, Mokarem D. Validation of ground penetration radar accuracy for estimating pavement layer thicknesses. In: Proceedings of the transportation research board 84th annual meeting. Washington, DC, 2005. [6] Skolnik ML. Introduction to radar systems. 2nd ed. New York: McGraw-Hill; 1980 [chapter 10]. [7] Taylor JD. Ultra-wideband radar technology. New York: CRC Press; 2001. [8] Loulizi A, Al-Qadi IL, Lahouar S. Ground penetrating radar signal modeling to assess concrete structures. Am Concr Inst Mater J 2002;99(3):282–91. [9] Al-Qadi IL, Lahouar S, Loulizi A. In-situ measurements of hot-mix Asphalt dielectric properties. J Non-Destr Test Eval 2001;34(6): 427–34.

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S. Lahouar, I.L. Al-Qadi / NDT&E International 41 (2008) 69–81 [10] Li J, Wu R. An efcient algorithm for time delay estimation. IEEE Trans Signal Process 1998;46(8):2231–5. [11] Ehrenberg JE, Ewart TE, Morris RD. Signal-processing techniques for resolving individual pulses in a multipath signal. J Acoust Soc Am 1978;63(6):1861–5. [12] McDonough RN, Whalen AD. Detection of signals in noise. 2nd ed. New York: Academic Press; 1995. [13] Kurtz JL, Fisher JW, Skau G, Armaghani J, Moxley JG. Advances in ground penetrating radar for road surface measurements. Radar Sensor Technol II, SPIE 1997;3066:11–21. [14] Lahouar S. Development of data analysis algorithms for interpretation of ground penetrating radar data. PhD dissertation, Blacksburg, VA: Department of Electrical Engineering, Virginia Tech, 2003. 81 [15] Kay SM. Fundamentals of statistical signal processing, estimation theory, vol. 1. New Jersey: Prentice-Hall Signal Processing Series; 1993. [16] Li J, Stoica P. Efcient mixed-spectrum estimation with applications to target feature extraction. IEEE Trans Signal Process 1996;44(2):281–95. [17] Ziemer RE, Tranter WH. Principles of communications: systems, modulation, and noise. 5th ed. New York: Wiley; 2002. [18] Papoulis A. Probability, random variables, and stochastic processes. 3rd ed. New York: WCB/McGraw-Hill; 1991. [19] Al-Qadi IL, Nassar WM, Loulizi A, Flintsch GW, Freeman T. Flexible pavement instrumentation at the Virginia Smart Road. The 79th transportation research board annual meeting. Washington, DC, paper no. 001275, 2000.


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