A method for estimating steel bar diameter based on resonance feature extraction of dual-polarization ground penetrating radar

Abstract

The present invention discloses a method for estimating the diameter of steel bars based on the resonance feature extraction of dual-polarization ground penetrating radar. The method obtains the full polarization scattering characteristics of the target by measuring the scattering fields of the steel bars in two mutually perpendicular polarization directions. The scattering fields in the two directions are added together to form a dual-polarization combined scattering field, thereby eliminating the sensitivity of the target scattering characteristics to angle. The resonant frequency and resonant wavelength of the steel bars are extracted by finding the maximum point, and characteristic information that can characterize the target size is obtained. Finally, the theoretical model and the observed value of the resonant wavelength are fitted by the least squares method to obtain an accurate estimation of the steel bar diameter.

Description

Technical Field

[0001] The present invention relates to a method for estimating the diameter of steel bars based on the extraction of resonance features of a dual-polarization ground-penetrating radar. The method is applicable to estimating the diameter of steel bars buried in media such as concrete, soil, and sand using a dual-polarization shallow-layer ground-penetrating radar, and belongs to the technical field of radar signal processing. Background Art

[0002] Ground penetrating radar (GPR) is a novel nondestructive detection technology. It utilizes wide-bandwidth electromagnetic waves to penetrate soil, walls, and other environments, enabling the location and structural information of non-visible targets within them to be obtained without damaging the environment. Due to its advantages, such as fast measurement speed, high resolution, and ability to detect non-visible targets, GPR has been widely used in geological surveys, road construction, archaeological excavations, counter-terrorism rescue, and other fields. Traditional GPR uses a pair of linearly polarized antennas to transmit and receive electromagnetic waves (referred to as single-polarization GPR). It measures the scattering characteristics of underground targets in a specific polarization direction. For some simple targets that scatter electromagnetic waves only in a single polarization direction (such as planes and thin lines), single-polarization GPR can effectively detect them. However, real-world underground targets often have complex electromagnetic scattering characteristics, making single-polarization GPR inadequate for adequate detection. Consequently, dual-polarization GPR was invented, which measures the scattering characteristics of a target in two mutually perpendicular polarization directions to obtain complete target information.

[0003] The location, protective layer thickness, and diameter of rebar are key parameters affecting the quality and safety of urban buildings. These parameters must be accurately measured during the construction and acceptance phase. Currently, this task is primarily accomplished using rebar detectors based on the electromagnetic induction (EMI) principle. While rebar detectors can accurately locate and measure rebar diameters, they suffer from high false alarm rates, multiple solutions for diameter measurement, and difficulty measuring deeper targets due to limitations in their measurement principles. Ground-penetrating radar (GPR) overcomes these limitations, offering promising applications in rebar detection. While GPR can accurately measure rebar location and protective layer thickness, its diameter measurement remains inaccurate. Therefore, research on GPR-based rebar diameter estimation methods is of great practical significance.

[0004] Researchers at home and abroad have conducted extensive research on rebar diameter estimation using ground-penetrating radar (GPR). Traditional diameter estimation methods primarily include curve fitting (CF) and full waveform inversion (FWI). In recent years, diameter estimation methods based on machine learning (ML) have also attracted considerable attention. Furthermore, attention has been paid to the dual-polarization characteristics of electromagnetic scattering from rebar, and rebar diameter estimation has been achieved using the dual-polarized scattering width ratio (DPSWR). The basic idea of the curve fitting method is to mathematically model the propagation delay of electromagnetic waves and obtain a diameter estimate by performing a least-squares fit of the model parameters from the observed echoes. However, this method has been shown to be highly sensitive to delay measurement errors caused by various factors, resulting in low estimation accuracy and making it unsuitable for use with measured data. Methods based on full waveform inversion theory attempt to iteratively perform forward / inverse fitting of the radar device's transmitted and received waveforms. While this method offers high theoretical accuracy, it is computationally complex and sensitive to initial value settings, with no guarantee of convergence. Therefore, it is also unsuitable for practical detection. Machine learning-based methods, which directly map echo information to rebar diameters through artificial neural networks, have become a popular rebar diameter estimation method in recent years. Their offline computational complexity is low, and their estimation accuracy is high. However, their accuracy is significantly limited by the training dataset, and due to the difficulty in obtaining measured datasets, this method remains difficult to implement in practice. The rebar diameter method based on the dual-polarization scattering width ratio measures the rebar diameter by using the ratio of the broadband scattering widths of the rebar in the TM and TE polarization modes. This method achieves high accuracy when the rebar axis is parallel to the antenna polarization direction. However, when the rebar axis deviates from the antenna polarization direction, the accuracy of all other estimation methods, including this one, decreases significantly. Overall, existing rebar diameter estimation methods using ground-penetrating radar still have limitations, such as sensitivity to the angle between the antenna and the rebar, sensitivity to measurement errors in time delay, low estimation accuracy, high computational complexity, and poor robustness. These limitations hinder their application in practical engineering surveys. Summary of the Invention

[0005] In view of this, the present invention provides a steel bar diameter estimation method based on dual-polarization ground penetrating radar resonance feature extraction, which can overcome the problems of traditional estimation methods such as high sensitivity to angle and delay errors, low estimation accuracy, high computational complexity and poor algorithm robustness.

[0006] The technical solutions for implementing the present invention are as follows:

[0007] A steel bar diameter estimation method based on dual-polarization ground penetrating radar resonance feature extraction is proposed. First, the steel bar echo obtained from the dual-polarization ground penetrating radar is preprocessed with clutter suppression. The median subtraction (MS) method is used to remove interference such as the direct wave from the transmitting and receiving antennas and the surface reflection wave in the radar echo in the HH and VV polarization channels respectively, highlighting the reflection hyperbola of the steel bar. The symmetry-based algorithm (SBA) is used to locate the radar channel where the hyperbola vertex is located, and the target wavelet (TW) in the HH and VV polarization channels is extracted respectively. Then, the known radar device source wavelet (SWR) is respectively converted into the target wavelet. The target wavelet (SW) and the measured target wavelet are Fourier transformed into the frequency domain. Based on the principle of frequency domain deconvolution, the frequency domain scattering characteristics of the target in the HH and VV polarization channels are obtained by dividing the spectrum of the target wavelet by the spectrum of its corresponding source wavelet. The scattering characteristics calculated in the HH and VV polarization channels are added frequency-wise to obtain a scattering characteristic curve that does not change with the polarization direction and the angle between the rebar axis. The frequency of the maximum point in the curve is extracted, which is the resonant frequency of the rebar. Then, based on the pre-determined dielectric constant of the background medium (generally, 9 for concrete and 3 for sand), the resonant frequency is converted into a resonant wavelength through the dielectric constant. The resonant wavelength is an essential characteristic of the rebar size. Finally, the measured resonant wavelength is parameter-fitted to the theoretical resonant wavelength model using the least squares method to obtain an estimated value for the rebar diameter.

[0008] Furthermore, the method specifically comprises the following steps:

[0009] Step 1: Establish an observation signal model;

[0010] Step 2: Use dual-polarization ground-penetrating radar to detect steel bars. Use the median cancellation method to suppress clutter on the target echoes in the HH and VV polarization channels, highlight the target reflection hyperbola, locate the radar channel at the hyperbola vertex based on the principle of symmetry, and extract the target wavelets in the HH and VV polarization channels respectively.

[0011] Step 3: Based on the principle of frequency deconvolution, the frequency spectrum of the target wavelet is divided by the frequency spectrum of the source wavelet in the HH and VV polarization channels respectively to obtain the frequency domain dual-polarization scattering characteristics of the steel bar. The scattering characteristics of the two polarization channels are added together to eliminate the angle sensitivity, and the resonant frequency and resonant wavelength of the target are extracted from the combined scattering spectrum. The resonant frequency is converted to the resonant wavelength using the known background dielectric constant.

[0012] Step 4: Perform least squares parameter fitting on the measured resonant wavelength and the theoretical model to obtain an estimated value of the steel bar diameter;

[0013] Furthermore, in step 2, the average number of channels for symmetry calculation is P=10.

[0014] Furthermore, in step 3, the selected frequency range hyperparameter C=6.

[0015] Beneficial effects:

[0016] 1. The present invention is applied to the field of ground-penetrating radar signal processing. Through experiments, various typical algorithms for estimating steel bar diameter using ground-penetrating radar (curve fitting method, full waveform inversion method, machine learning method, and dual-polarization scattering width ratio method) are compared. The present invention can quickly and accurately provide millimeter-level high-precision estimation of the diameter of steel bars inside concrete.

[0017] 2. The present invention uses dual-polarization ground-penetrating radar to measure the scattering characteristics of the target in two mutually perpendicular polarization directions, and uses the dual-polarization combined scattering field to eliminate the sensitivity of the scattering field to the angle between the antenna and the steel bar. It can be applied to diameter estimation when the direction of the steel bar axis is unknown.

[0018] 3. The present invention fully considers the dual-polarization resonant scattering characteristics of the steel bar target, extracts the resonant frequency and resonant wavelength of the steel bar by finding the maximum point of the scattering characteristic curve, and uses the least squares parameter fitting method to obtain an accurate estimation of the steel bar diameter. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] FIG1 is a flow chart of signal processing according to an embodiment of the present invention.

[0020] Figure 2 Schematic diagram of analyzing the electromagnetic wave scattering characteristics of steel bars in the method of the present invention, wherein (a) is the HH polarization mode and (b) is the VV polarization mode.

[0021] Figure 3 It is a schematic diagram of analyzing the bipolar compound scattering characteristics of steel bars as x and y change in the method of the present invention.

[0022] Figure 4 1 is a schematic diagram of a B-scan for detecting buried steel bars using a dual-polarization ground penetrating radar in step 2 of the present invention; wherein (a) is a B-scan for HH polarization detection, and (b) is a B-scan for VV polarization detection.

[0023] Figure 5 2 is a schematic diagram of the effect of using the MS method to suppress clutter on the original B-scan in step 2 of the present invention; wherein (a) is the clutter suppression result of HH polarization, and (b) is the clutter suppression result of VV polarization.

[0024] Figure 6 Schematic diagram of the hyperbola vertex determination algorithm based on the symmetry principle used in step 2 of the present invention; wherein (a) is a schematic diagram under HH polarization, and (b) is a schematic diagram under VV polarization.

[0025] Figure 7 It is the target wavelet under HH polarization and VV polarization extracted in step 2 of the present invention;.

[0026] Figure 8 It is the scattering characteristic curve of the steel bar under HH polarization and VV polarization calculated in step 3 of the present invention.

[0027] Figure 9 It is the bipolar combined scattering characteristic curve of the steel bar calculated in step 3 of the present invention.

[0028] Figure 10 Schematic diagram of a simulation scenario in an embodiment of the present invention; (a) is a schematic diagram under HH polarization, and (b) is a schematic diagram under VV polarization.

[0029] Figure 11 1 and 2 are the VV polarization and bipolarization combined scattering characteristic curves under different angles θ of the simulation data in an embodiment of the present invention; wherein (a) is the scattering characteristic curve under VV polarization, and (b) is the bipolarization combined scattering characteristic curve.

[0030] Figure 12 1 and 2 are the VV polarization and bipolarization combined scattering characteristic curves at different angles θ of the measured data in an embodiment of the present invention; wherein (a) is the scattering characteristic curve under VV polarization, and (b) is the bipolarization combined scattering characteristic curve.

[0031] Specific implementation process

[0032] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0033] The present invention provides a method for estimating the diameter of steel bars based on the resonance feature extraction of dual-polarization ground penetrating radar. Figure 1 : is a signal processing flow chart of an embodiment of the present invention. Figure 1 As shown, the present invention is achieved by the following steps:

[0034] Step 1: Establish an observation signal model;

[0035] The steel bar echo signal received by the ground penetrating radar can be expressed as:

[0036] r k,H / V (t) = s H / V (t)*h k (t)*g k,H / V (t)+n k,H / V (t)

[0037] where r k,H / V (t) represents the radar received signal, k represents the radar channel number, H / V represents the HH or VV polarization channel, s H / V (t) represents the source wavelet of the radar equipment in the HH or VV polarization channel, h k (t) represents the attenuation caused by electromagnetic waves penetrating and propagating in concrete, g k,H / V (t) represents the scattering characteristics of the steel bar in the kth radar channel under the HH or VV polarization channel, * represents the convolution operation, n k,H / V (t) represents the interference and noise received by the radar equipment in a certain polarization channel.

[0038] Among them, the source wavelet s of the radar equipment H / V (t) is usually obtained by measuring a large metal plate; since concrete is generally considered to be a uniform and lossless half-space medium, h k (t) does not change with the polarization channel in the above formula. When the transmitting and receiving antennas are located directly above the steel bars, that is, when the electromagnetic waves are incident vertically on the concrete surface, h k (t) can be regarded as a constant h less than 1. Ignoring the existence of noise, when the transceiver antenna is located directly above the steel bar (i.e., the radar channel where the target hyperbola vertex is located), the steel bar echo signal r received by the ground penetrating radar is H / V (t) can be simplified as:

[0039] r H / V (t) = h·s H / V (t)*g H / V (t)

[0040] Where · represents the multiplication operation, and its frequency domain form is:

[0041] R H / V (f) = h·S H / V (f)G H / V (f)

[0042] where R H / V (f) and S H / V (f) are r H / V (t) and s H / V The Fourier transform of (t), g H / V (t) and G H / V (f) are the time domain / frequency domain scattering characteristics of steel bars under different polarization channels. H / V (f) characteristics, the steel bar can be abstracted as a slender ideal conductor cylinder, such as Figure 2 As shown, assuming that its radius is a, its length is infinite, its axis direction coincides with the y-axis, and the wave number size in the uniform and lossless region is In the free space, a plane electromagnetic wave is incident on the steel bar surface from the +z direction to the -z direction. The angle between the electric field direction and the steel bar axis (i.e., the y axis) is θ, and the electric field strength is E0, which is called the HH polarization channel. Let there be a plane electromagnetic wave with the same incident direction as this electromagnetic wave, but the electric field direction is perpendicular to the electric field direction under the HH channel, and its electric field strength is E1, which is called the VV polarization channel. According to the plane wave decomposition principle and the cylinder in TM y and TE y From the scattering characteristics of the mode, it can be seen that the backscattered electric field intensity of the steel bar under the two polarization channels is:

[0043]

[0044]

[0045] Among them J n (·) and J′ n (·) are the nth order Bessel function and its first order derivative, and is the second nth order Hankel function and its first-order derivative, and ρ is the distance from the radar to the target. The above formula represents the scattering characteristics of the steel bar target in the frequency domain. By further eliminating the influence of the incident electric field strength E0 and E1, the frequency domain scattering characteristics of the steel bar G are obtained. k,H / V (f) is:

[0046]

[0047]

[0048] The above formula shows that the scattering characteristics of steel bars in a single polarization channel are highly correlated with the angle θ. Traditional methods for estimating steel bar diameters all use the VV polarization channel for detection and assume that θ = 90°. When the angle changes, these methods will produce large estimation errors. In the present invention, the influence of θ is eliminated by constructing a dual-polarization combined scattering field, that is,

[0049]

[0050] The above formula shows that the combined scattered field G(f) has nothing to do with the angle θ, thus eliminating the influence of θ. Assuming x = k0a, G(f) changes with x and y as follows Figure 3 shown. Figure 3 It shows that the maximum point of G(f) is always at x=d n , appears when n=1,2,3..., where d n is a set of constants, d n=[0.93, 2.07, 3.23, ...], and has almost nothing to do with the value of y. Since these maximum points all appear in the resonance region of the combined scattering spectrum, they are called the resonance points of the steel bar. is the resonant frequency of the steel bar, is the resonant wavelength of the steel bar. The resonant wavelength of the steel bar is only related to the constant d n It is related to the radius a, so the resonant wavelength is the decisive feature to characterize the size of the steel bar.

[0051] Step 2: Use dual-polarization ground-penetrating radar to detect rebars. Use the median cancellation method to suppress clutter on the target echoes in the HH and VV polarization channels, highlighting the target reflection hyperbola. Based on the principle of symmetry, locate the radar channel at the hyperbola vertex and extract the target wavelets in the HH and VV polarization channels.

[0052] The B-scan obtained by using a dual-polarization ground penetrating radar with a center frequency of 2.6 GHz and a Ricker wavelet signal waveform to detect a steel bar with a diameter of 20 mm, a concrete dielectric constant of 6, a protective layer thickness of 10 cm, and an angle of θ = 90° is as follows: Figure 4 As shown. In the B-scan under the HH and VV polarization channels, in addition to the reflected hyperbola caused by the steel bars, there are also many clutter and noise including the direct wave from the transmitting and receiving antennas and the reflected wave from the concrete surface. These clutter and noise will affect the extraction of the target hyperbola and need to be removed by using clutter suppression methods. The present invention uses the MS method to pre-process the original echo. The processed radar echo is r′ k，H / V (t):

[0053] r′ k，H / V (t) = MS {r k,H / V (t)}

[0054] Where MS{·} represents MS method processing. Figure 4 The effect of clutter suppression is as follows: Figure 5 As shown. k，H / V In (t), the direct coupling waves between the transmitting and receiving antennas and the reflected waves on the concrete surface are eliminated, and the reflection hyperbola of the steel bars is highlighted.

[0055] Then, the radar channel where the hyperbola vertex is located is determined using SBA. In SBA, the symmetry can be expressed as follows:

[0056]

[0057] Where k represents the radar channel being calculated, t represents the sampling point in the time domain, each radar channel has N sampling points, the position of the mobile transceiver antenna is moved to measure the steel bar M times, and M radar channels are obtained. P is a hyperparameter, indicating that P radar channels are used for symmetry calculation at a time. The processing results of SBA are as follows Figure 6 As shown in the figure, the minimum point in the curve is the position with the strongest symmetry, which reflects the radar channel where the hyperbola vertex is located. The above operation is performed on both HH and VV polarization channels, and the radar channel where the vertex is located is selected as r′ H (t) and r′ V (t).

[0058] Finally, from r′ H (t) and r′ V (t) Artificially cut out the target wavelet part such as Figure 7 shown.

[0059] Step 3: Based on the principle of frequency deconvolution, the frequency spectrum of the target wavelet is divided by the frequency spectrum of the source wavelet in the HH and VV polarization channels respectively to obtain the frequency domain dual-polarization scattering characteristics of the steel bar. The scattering characteristics of the two polarization channels are added together to eliminate the angle sensitivity, and the resonant frequency and resonant wavelength of the target are extracted from the combined scattering spectrum. The resonant frequency is converted to the resonant wavelength using the known background dielectric constant.

[0060] Assume that the radar source wavelet s has been obtained in the two polarization channels of HH and VV by measuring the metal plate. H (t) and s V (t), the target wavelet r′ under the two polarization channels is obtained in step 2 H (t) and r′ V (t), and perform Fourier transform on them to the frequency domain to obtain the source wavelet S in the frequency domain H (f), S V (f) and target wavelet R′ H (f), R′ V (f) According to the signal model in step 1 and the frequency domain deconvolution principle, the scattering characteristics of the steel bar in the two polarization channels of HH and VV can be calculated. The calculated scattering characteristics are as follows: Figure 8 As shown:

[0061]

[0062]

[0063] The value range of f is f min ≤f≤f max , which corresponds to S H / V(f) The range with stronger energy is used to ensure that the calculated values have a high signal-to-noise ratio and accuracy, that is:

[0064] f min ≤f≤f max

[0065]

[0066] In the above formula, C is a hyperparameter used to control the size of the frequency band, and max{·} represents the maximum value. The scattering characteristics of the two polarization channels are then added together to obtain the combined scattering field to eliminate the sensitivity of the individual scattering fields to the angle θ between the steel bar and the antenna, namely:

[0067] G′(f)=G′ H (f)+G′ V (f) = hG H (f)+hG V (f) = hG(f)

[0068] The resulting scattered field is Figure 9 In the above formula, h is a constant less than 1, which represents the attenuation caused by the electromagnetic wave penetrating the medium. In actual detection, h is an unknown quantity, but it does not affect the extraction of the resonant frequency of the steel bar.

[0069] Figure 9 There are two maxima in the graph, and these frequencies are the resonant frequencies of the steel bars. The resonant frequencies in the graph are 1.8 GHz and 4.0 GHz, respectively. Given that the dielectric constant of concrete is 6, the resonant wavelengths of the steel bars are 0.068 m and 0.031 m.

[0070] Step 4: Perform least squares parameter fitting on the measured resonant wavelength and the theoretical model to obtain an estimated value of the steel bar diameter;

[0071] The signal model in step 1 shows that the resonant wavelength λ of the steel bar n Only with constant d n It is related to the radius a and its expression is Assume that the resonant wavelengths of Q steel bars are calculated from step 3 They correspond to n=q, q+1,...,q+Q-1, and there are Where q is a positive integer. Depending on the size of Q, the radius estimation can be divided into the following three cases:

[0072] 1. Q ≥ 2

[0073] In this case, the resonant wavelength and radius satisfy the following relationship:

[0074]

[0075] in d q =[d q ,...,d q+Q-1 ] T When the value of q is known, the radius of the steel bar can be estimated by the least square method:

[0076]

[0077] However, in the measured data, the value of q is often unknown. Therefore, we can take q = 1, 2, 3, ... in turn by trial and error, and select the radius estimation result that minimizes the fitting error, that is:

[0078]

[0079] Experience shows that the value of q in the above formula generally does not exceed 3. This is the final radius estimation result. The estimated value of the target diameter is

[0080] 2. Q = 1

[0081] In this case, it is not possible to determine the value of q by trial and error and minimizing the fitting error. However, since this situation often corresponds to a small diameter of the steel bar, only the first resonant wavelength of the target is within the selected frequency band, so this situation often corresponds to q = 1. The estimated value of the diameter in this case is:

[0082]

[0083] 3. Q = 0

[0084] This situation indicates that none of the target's resonant frequencies appear within the selected frequency range, so it is impossible to accurately estimate the target's diameter. The target size can only be roughly calculated by taking the highest frequency of the selected frequency band as a resonant point:

[0085]

[0086] In this case the selected frequency range should be increased. Example

[0087] To verify the effectiveness of the proposed rebar diameter estimation method (Dual-polarized Resonance Method, DPRM) based on dual-polarized ground-penetrating radar resonance feature extraction, dual-polarized ground-penetrating radar simulation data was used to verify the effectiveness of the proposed method. This method was also compared with other GPR rebar diameter estimation methods, including curve fitting (CF), full waveform inversion (FWI), machine learning (ML), and dual-polarized scattering width ratio (DPSWR). The performance of the algorithm was evaluated using two metrics: the error between the estimated and true diameter values; a lower error indicates a more accurate estimation result; and the computational time of the algorithm; a lower computational time indicates a faster implementation speed.

[0088] The simulation data was generated using gprMax ground penetrating radar simulation software, which calculates the propagation of electromagnetic waves in space based on the finite-difference time-domain (FDTD) principle and has high calculation accuracy. The simulation settings set the electric field direction of the transceiver antenna in the HH polarization to the y direction, and the electric field direction of the transceiver antenna in the VV polarization channel to the x direction. The radar source wavelets under the two polarizations are both Ricker wavelets with a center frequency of 2.6GHz. The antenna type is Hertzian Dipole, the waveform amplitude is 1000, the transceiver antenna is located 1cm above the concrete surface, the transceiver antenna spacing is 6cm, and the transceiver antenna step is 1cm; the simulation time window length is 10ns, and the spatial resolution is 1mm; the concrete is set to a uniform medium with a dielectric constant of 6 and a conductivity of 0.01S / m; the steel bar is an infinitely long cylinder of ideal conductor material with a diameter of 20mm, located 10cm below the concrete surface. The simulation scene diagram is as follows Figure 10 As shown in Figure 2. A total of four scenarios were simulated, with the angles θ between the axis of the steel bar and the positive direction of the y-axis being 0°, 30°, 60°, and 90°, respectively. The simulated B-scan echoes of these four scenarios were processed using the CF, FWI, ML, DPSWR, and DPRM methods, respectively. The VV polarization and dual-polarization combined scattering characteristic curves calculated using the proposed DPRM method are shown in Figure 2. Figure 11As shown in the figure, the VV polarization scattering characteristics vary significantly at different angles, while the bipolarization combined scattering characteristics remain virtually unchanged, thus eliminating the effect of angle on diameter estimation. A comparison of the estimation error and computation time of the five methods is shown in Table 1. Based on the simulation data processing results, all five rebar diameter estimation methods can accurately estimate the rebar diameter at an angle of θ = 90°. However, when the angle θ ≠ 90°, the accuracy of the other methods decreases significantly, while the proposed method maintains a high estimation accuracy. Furthermore, at an angle of θ = 90°, the proposed DPRM method is comparable to the FWI method in accuracy, with a diameter estimation error of approximately 0.3 mm. However, FWI has the slowest computational speed and cannot meet the requirements of real-time detection. The ML method balances computational accuracy and speed, but is difficult to apply in certain scenarios requiring high accuracy. The DPSWR method has the second lowest estimation accuracy because it is more suitable for thin rebars. The CF method has the lowest accuracy, with an estimation error of approximately 13 mm, but its computational speed is very fast. When the angle θ decreases from 90° to 0°, the proposed DPRM method can always maintain a high estimation accuracy, while other methods will have large errors, which shows the superiority of this method.

[0089] Table 1: Comparison of estimation error and computation time of different algorithms for simulation data

[0090]

[0091]

[0092] The measured data uses the SIR-4000 ground penetrating radar of Geophysical Survey Systems Inc. (GSSI) in the United States, equipped with a 2600MHz antenna to detect the steel bars inside the sand medium. The device transmits a signal frequency range of approximately 1000-4500MHz, with a sampling window of 5ns, 2048 sampling points, and an antenna step of 1cm. Similar to the simulation experiment, the measured experiment measured a total of four scenes, where the angles θ between the axis direction of the steel bar and the positive direction of the y-axis were 0°, 30°, 60°, and 90°, respectively. Five steel bar diameter estimation algorithms were used to process it, among which the VV polarization and dual-polarization combined scattering characteristic curves calculated using the proposed DPRM method are shown in the following figure. Figure 12As shown in the figure, the VV polarization scattering characteristics vary significantly at different angles, while the bipolarization combined scattering characteristics remain almost unchanged, thus eliminating the influence of angle on diameter estimation. A comparison of the rebar diameter estimation results is shown in Table 2. The curve fitting method requires high accuracy in target positioning delay and is sensitive to measurement noise, resulting in large estimation errors. The full waveform inversion method uses an iterative inversion method to obtain accurate reconstruction information of the underground scene, but it is sensitive to noise and the setting of scene initial values, has poor robustness, and high computational complexity, making it difficult to use for real-time processing. Although the machine learning method has good performance on simulated data, it performs poorly on measured data due to the difficulty in obtaining measured data sets. The proposed method uses the sum of the scattered fields of the rebar in two perpendicular polarization directions to construct a bipolarization combined scattering characteristic curve that is insensitive to angle. It also extracts the resonant scattering characteristics of the rebar and performs a least squares fit with the theoretical model. It has the highest diameter estimation accuracy and is adaptable to rebar diameter estimation at any angle, verifying the effectiveness and robustness of the algorithm.

[0093] Table 2: Comparison of estimation error and calculation time of different algorithms for measured data

[0094]

[0095] The above experimental results demonstrate that the proposed rebar diameter estimation method based on dual-polarization ground-penetrating radar resonance feature extraction can achieve high estimation accuracy when there is an arbitrary angle between the rebar and the antenna, while also having a fast calculation speed, thus verifying the effectiveness of the algorithm. Compared with existing ground-penetrating radar rebar diameter estimation methods, the present invention obtains the target's full polarization scattering characteristics by measuring the scattering field of the rebar in two mutually perpendicular polarization directions, and adds the scattering fields in the two directions to form a dual-polarization combined scattering field, thereby eliminating the sensitivity of the target scattering characteristics to angles. By finding the maximum point, the resonant frequency and resonant wavelength of the rebar are extracted, and characteristic information that can characterize the target size is obtained. Finally, the theoretical model and the observed value of the resonant wavelength are fitted by the least squares method, which can accurately estimate the rebar diameter.

[0096] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating steel bar diameter based on resonance feature extraction of dual-polarization ground penetrating radar, characterized in that: The method comprises the following steps: Step 1: Establish an observation signal model; Step 2: Use dual-polarization ground-penetrating radar to detect steel bars. Use the median cancellation method to suppress clutter on the target echoes in the HH and VV polarization channels, highlight the target reflection hyperbola, locate the radar channel at the hyperbola vertex based on the principle of symmetry, and extract the target wavelets in the HH and VV polarization channels respectively. Step 3: Based on the principle of frequency deconvolution, the frequency spectrum of the target wavelet is divided by the frequency spectrum of the source wavelet in the HH and VV polarization channels respectively to obtain the frequency domain dual-polarization scattering characteristics of the steel bar. The scattering characteristics of the two polarization channels are added together to eliminate the angle sensitivity, and the resonant frequency and resonant wavelength of the target are extracted from the combined scattering spectrum. The resonant frequency is converted to the resonant wavelength using the known background dielectric constant. Step 4: Perform least squares parameter fitting on the measured resonant wavelength and the theoretical model to obtain an estimated value of the steel bar diameter.

2. The method for estimating steel bar diameter based on dual-polarization ground penetrating radar resonance feature extraction according to claim 1, characterized in that: In step 1, the time domain signal model of the received echo of the radar channel where the hyperbola vertex is located is: r H / V (t)=h·s H / V (t)*g H / V (t) Its frequency domain form is: R H / V (f)=h·S H / V (f)G H / V (f) Among them, r H / V (t) and R H / V (f) represents the time domain and frequency domain forms of the radar received signal, respectively. H / V represents the HH polarization or VV polarization channel. h represents the attenuation caused by the electromagnetic wave penetrating and propagating in the concrete. Since concrete is generally considered to be a uniform and lossless half-space medium, h does not change with the polarization channel. When the transmitting and receiving antennas are located directly above the steel bars, that is, when the electromagnetic wave is incident vertically on the concrete surface, h can be considered to be a constant less than 1. g H / V (t) and G H / V (f) are the time domain / frequency domain scattering characteristics of steel bars under different polarization channels, s H / V (t) represents the source wavelet of the radar equipment in the HH or VV polarization channel.

3. The method for estimating steel bar diameter based on dual-polarization ground penetrating radar resonance feature extraction according to claim 1, characterized in that: In step 1, the theoretical bipolar combined scattering characteristic expression of the steel bar is: Among them, G H (f) and G V (f) represents the frequency domain scattering field of the steel bar under HH polarization and VV polarization channels, G(f) represents the combined scattering field, a is the radius of the cylinder, ρ is the distance from the radar to the target, k0 is the wave number, which can be obtained from Said, J n (·) and J′ n (·) is the nth-order Bessel function and its derivative, and is the second kind n-th order Hankel function and its derivative.

4. The method for estimating steel bar diameter based on dual-polarization ground penetrating radar resonance characteristic extraction according to claim 1, characterized in that: In step 2, the expression used for symmetry calculation is: Where, the average number of channels P = 10, k represents the radar channel being calculated, t represents the sampling point in the time domain, each radar channel has N sampling points, the position of the mobile transceiver antenna is moved to measure the steel bar M times, and M radar channels are obtained. P is a hyperparameter, indicating that P radar channels are used for symmetry calculation at a time, z H / V [k] represents the value calculated by applying the SBA algorithm to the k-th radar wave, and H / V represents the HH polarization or VV polarization channel.

5. The method for estimating steel bar diameter based on dual-polarization ground penetrating radar resonance feature extraction according to claim 1, characterized in that: In step 3, the frequency range is determined by the following expression: f min ≤f≤f max Among them, the frequency range hyperparameter C=6, S H / V (f) is the radar wavelet, H / V indicates the HH polarization or VV polarization channel, f is the frequency, and the value range of f is f min ≤f≤f max , which corresponds to S H / V (f) is a strong energy range. This formula shows that f can be obtained under certain restrictions. min With f max , to ensure that the values obtained by subsequent calculations have a high signal-to-noise ratio and accuracy. C is a hyperparameter used to control the size of the frequency band. max{·} represents the maximum value operation.

6. The method for estimating steel bar diameter based on dual-polarization ground penetrating radar resonance feature extraction according to claim 1, characterized in that: In the step 4, the diameter of the steel bar is estimated for three different situations; When the number of resonant wavelengths is ≥ 2, the radius is estimated using the following expression: When the number of resonant wavelengths = 1, the diameter is estimated using the following expression: When the resonant wavelength = 0, the following expression is used to roughly estimate the diameter: Among them, a is the radius of the cylinder, ρ is the distance from the radar to the target, k0 is the wave number, d n is a set of constants, d n =[0.93,2.07,3.23,…], is the resonant frequency of the steel bar, is the resonant wavelength of the steel bar, This is the final radius estimation result. The estimated value of the target diameter is

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