A signal processing methodology for assessing the performance of ASTM standard test methods for GPR systems

TL;DR: This work proposes a GPR signal processing methodology, calibrated and validated on the basis of a consistent amount of data collected by means of laboratory-scale tests, to assess the performance of the above standard test methods for GPR systems.

About: This article is published in Signal Processing.The article was published on 2017-03-01 and is currently open access. It has received 27 citations till now. The article focuses on the topics: Ground-penetrating radar.

Summary

1. INTRODUCTION

• Ground penetrating radar (GPR) is an increasingly popular non-destructive testing (NDT) technique that emits a short pulse of electromagnetic energy into the subsurface [1, 2].
• In Germany, instructions on the use of radar systems for non-destructive testing in civil engineering [10] and for gaining inventory data of road structures [11] are available.
• Furthermore, a novel pre-processing method for GPR signals, based on the minimum gradient method, is discussed in [28].
• In line with the above and according to the guidance provided by the mentioned ASTM standards, this paper is (to the best of the authors’ knowledge) the first study that focuses on the ASTM SNR test, thereby aiming at providing a detailed analysis of the bias and variance of the testing variable under consideration (i.e. the SNR).

2. BASIC FRAMEWORK ON GPR PRINCIPLES AND REFERENCE ASTM

• STANDARDS 2.1 GPR working principles and main applications.
• The hardware of a GPR system utilized for the measurement of the subsurface conditions usually consists of a transmitter and a receiver antenna, a radar control unit, and suitable data storage and display devices.
• Measurements can be traditionally performed in two main survey configurations, namely, with ground-coupled or air-coupled antennas, as a function of the main purposes and type of survey.
• To cite a few, the authors can mention the evaluation of layer thicknesses [44] and subsurface moisture [45, 46], the assessment of damage conditions in hot-mix asphalt (HMA) layers [47], load-bearing layers and subgrade soils [48-51], the inspection of concrete structures [52, 53].

2.2 ASTM standard test methods

• The ASTM society is an international organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, and services.
• For air-launched antennas, four main tests are mentioned and worthy to be verified, namely, i) the signal-to-noise ratio (SNR), ii) the signal stability, iii) the linearity in the time axis and time window accuracy, and iv) the long-term stability test.
• To the best of the authors’ knowledge, no in-depth study is provided in the literature about the analysis of the compliance with the SNR test of a GPR signal, which conversely appears to be one of the main requirements by the manufacturers.
• The Standard recommends to perform the SNR test on each of the above 100 waveforms and to take the average signal-to-noise value of the 100 waveforms as reference “signal-to-noise of the system”.

3. SIGNAL PROCESSING METHODOLOGY FOR ASTM STANDARD

• The SNR test method, as defined by the D 6087 – 08 ASTM Standard [24], is here taken as the reference parameter for assessing the performance of the GPR signals, in terms of bias and variance.
• Only three papers investigating on the precision of the GPR measurements have been found in the literature.
• Nevertheless, none of these papers provides any discussion about the precision of the SNR test method, especially in terms of bias.
• Hence, bias stands for the average difference to be expected between the estimator and the underlying parameter.
• Afterwards, the authors provide such a discussion in Section 3.2, evaluating the bias and variance of the testing variable under consideration.

3.1 Optimal threshold tuning

• Nevertheless, no further information is provided on how the threshold has been set, nor to which accuracy (or signal stability) of the GPR equipment this threshold corresponds.
• The authors provide the signal processing methodology to evaluate the proper threshold for the specific GPR equipment, according to a fixed desired (i.e. target) level of accuracy.
• First of all, the authors evaluate the SNR of the system as the average SNR over a number of L trials as follows: 𝑆𝑁𝑅 = 1 𝐿 ∙ ∑ 𝑆𝑁𝑅𝑗 𝐿 𝑗=1 , (4) In particular, SNRj is the SNR of the j-th experiment, and defined as the ratio between the mean signal and the noise peaks, respectively.
• Since all the terms of the sum in (4) represent SNRs of different experiments, they also represent physically independent and hence statistically independent random variables.
• Then, let us now define with PACC the desired (or target) level of accuracy (in percentage) requested to the GPR system.

3.2 Performance evaluation

• It is evaluated the performance of the SNR test method, by theoretically assessing the bias and the variance of the estimation error of the testing variable in (4).
• In the following analysis, the authors first evaluate the bias and the variance of SNR̂𝑗, and then they compute the bias and variance in (11).
• The algebraic expressions (12) and (13) are trivially derived from a computation of the partial derivatives of the expressions in (4).
• It has to be noted that both the estimations in (22) and (23) vary with 1/K, meaning that the SNR estimator is consistent (i.e. as the number of considered radar waveforms K becomes larger and larger, the estimate tends to the true value).

4.1 Laboratory set-up

• Several laboratory-scale tests were performed according to the set-up shown in Fig.
• This may be mostly due to the deflections induced to the surveying apparatus by the combination of remarkable traffic speeds and damaged conditions of the pavement surface when performing GPR measurements in real roads.
• Considerations on the signal response in near-field and far-field conditions can also be drawn.
• The floor under the antennas was covered by a 200 cm × 200 cm copper sheet acting as perfect electric conductor (PEC), and capable to completely reflect the propagation waves and generating a pulse with maximum amplitude.
• Measurements at each of the aforementioned heights were performed using three air-coupled GPR systems with different central frequencies of 1 and 2 GHz.

4.2 Experimental outcomes

• The assumptions made in the previous Section have been firstly empirically verified.
• As in the previous case, the authors can notice a maximum variation of the signal and noise peak within the 6% for the 2 GHZ EU equipment, whereas this value is between the 6-7% in the case of the 2GHz NA system.
• Variances of the noise peak for 100 consecutive radar traces.
• Hence, the authors can now evaluate the performance of the SNR test method, by computing the bias and variance of the estimation errors, according to (21) and (22).
• The threshold value modifies accordingly to h. Figs. 10 and 11 show how the accuracy of the GPR signal varies versus the threshold in the cases of the 2GHZ EU and the 2GHZ NA GPR systems, respectively.

5. CONCLUSION

• This paper has devised a signal processing methodology for assessing the performance of the international standard test methods released by the American Society for Testing and Materials (ASTM) about the application of GPR techniques.
• The theoretical expressions for the bias and variance of the estimation error have been evaluated by a reduced Taylor’s expansion up to the second order.
• Therefore, a closed form expression for theoretically tuning the optimal threshold according to a fixed target value of the GPR signal stability has been proposed.
• The overall study has been extended to three air-coupled GPR systems with different antennas to analyze the specific relationship between the frequency of investigation, the optimal thresholds, and the signal stability.
• The results achieved from several trials at the laboratory scale confirm the consistency of such a methodology for assessing the performance of these international standard test methods for GPR systems.

Figures

Fig. 8. (a) Bias and (b) Variance of the estimation error for a GPR with a central frequency of 2GHz NA, and three different heights (30, 40, and 50 cm) from the metal plate.

Fig. 7. (a) Bias and (b) Variance of the estimation error for a GPR with a central frequency of 2GHz EU, and three different heights (30, 40, and 50 cm) from the metal plate.

Fig. 1. Typical reflection pattern of a GPR measurement in multi-layered structures with an aircoupled radar system: (a) trend of reflections in a cross-section of a multi-layered structure; (b) sketch of the relevant GPR signal trace.

Fig. 3. Normalized (to 1) amplitude variations for 100 consecutive radar traces of: (a) the signal peak (As), and (b) the noise peak (An) after PEC reflection, with the 1GHz GPR system.

Fig. 10. Accuracy vs. optimal threshold for a GPR with a central frequency of 2GHz EU at three different heights (30, 40, and 50 cm) from the metal plate

Fig. 9. Accuracy vs. optimal threshold for a GPR with a central frequency of 1GHz at three different heights (30, 40, and 50 cm) from the metal plate

Fig. 4. Normalized (to 1) amplitude variations for 100 consecutive radar traces of: (a) the signal peak (As), and (b) the noise peak (An) after PEC reflection, with the 2GHz EU GPR system.

Fig. 5. Normalized (to 1) amplitude variations for 100 consecutive radar traces of: (a) the signal peak (As), and (b) the noise peak (An) after PEC reflection, with the 2GHz NA GPR system.

Fig. 2. Laboratory-scale set-up for the investigation at 30 cm of height between the bottom of the radar box and the PEC surface.

Fig. 11. Accuracy vs. optimal threshold for a GPR with a central frequency of 2GHz NA at three different heights (30, 40, and 50 cm) from the metal plate

Fig. 12. Threshold values (for a signal accuracy of 90%) for GPR systems with different antennas (1GHz, 2GHz NA, and 2GHz EU) at three heights (30, 40, and 50 cm) from the metal plate.

Fig. 6. (a) Bias and (b) Variance of the estimation error for a GPR with a central frequency of 1GHz, and three different heights (30, 40, and 50 cm) from the metal plate.

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This work proposes a GPR signal processing methodology, calibrated and validated on the basis of a consistent amount of data collected by means of laboratory-scale tests, to assess the performance of the above standard test methods for GPR systems. Finally, the study is extended to GPR systems with different antenna frequencies to analyze the specific relationship between the frequency of investigation, the optimal thresholds, and the signal stability.