A SAFT Method for the Detection of Void Defect inside a Ballastless Track Structure Using Ultrasonic Array Sensors

High-precision ultrasound imaging of void defects is critical for the performance and safety assessment of ballastless track structures. The sound propagation velocity of each layer in the ballastless track structure is quite different. However, the traditional concrete Synthetic Aperture Focusing Technique (SAFT) ultrasound imaging method is based on the assumption that the concrete has a single constant shear wave velocity. Thus, it is not a suitable method for the ultrasonic imaging of multilayer structures. In this paper, a Multilayer SAFT high-precision ultrasound imaging method is proposed. It is based on the ray-tracing technique and uses the Fermat principle to find the refraction point that minimizes the delay of the acoustic wave propagation path at the interface of the discrete layers. Then, the acoustic wave propagation path is segmented by the position of the refraction point, and the propagation delay of the ultrasonic wave is obtained segment by segment. Thus, the propagation delay of the ultrasonic wave is obtained one by one, so that the propagation delay of the ultrasonic wave in the multilayer structure can be accurately obtained. Finally, the focused image is obtained according to the SAFT imaging algorithm. The finite element simulation and experimental results show that the Multilayer SAFT imaging method can accurately track the propagation path of the ultrasonic wave in ballastless track structures, as well as accurately calculate the propagation delay of the ultrasonic wave and the lengths of void defects. The high accuracy of the Multilayer SAFT imaging represents a significant improvement compared to traditional SAFT imaging.


Introduction
By the end of 2018, the total length of the Chinese high-speed railway reached 29,000 km [1]. The ballastless track structure is the main track structure of China's high-speed rail lines, accounting for more than 50% of the operating lines [2]. The high-speed rail ballastless track structure is a typical multilayer structure in which the track slab (concrete material) and bedplate (concrete material) are bonded together by cement, asphalt, and mortar [3]. The high-speed rail ballastless track structure is an important bearing component. Under the influence of dynamic load, temperature, and other environmental factors, the phenomenon of void defects will frequently occur [4]. Taking the Shanghai-Hangzhou high-speed railway in the Shanghai Railway Administration as an example, a total of 3912 defects were found in 2018. Void defects have become a major source of danger affecting are analyzed. Finally, the Russian MIRA-A1040 concrete ultrasonic tomography scanner is used to acquired ultrasonic echo signals in a ballastless track structure, and the effectiveness of multilayer SAFT imaging is verified by experiments.

SAFT Imaging Method
The principle of the SAFT imaging method is shown in Figure 1. In a group of ultrasonic transducer arrays, ultrasonic waves are sequentially emitted by one probe. The other probes receive ultrasonic waves. The received ultrasonic echo signals are processed by DAS. Lastly, a reconstructed B-scan image is produced. When information such as the position and size of the defects in the object to be measured are unknown, SAFT imaging can be used to calculate the value of all the pixels by traversing the imaging region.
As shown in Figure 1, it is assumed that the sensor position is un (n = 1, 2, 3...n), while the exciting sensor position coordinates are (xi, zi). The receiving sensor position coordinates are (xj, zj). The position coordinate of any pixel D is (x, z). The time delay tij (x, z) experienced by the ultrasonic wave is transmitted from the position of the exciting sensor ui and then reaches the position of the receiving sensor uj via point D, as shown in Equation (1): where the ri is given by: and v is the speed at which sound waves travel in the object being measured, i, j = 1,2,3…n. When the exciting and receiving transducer positions are ui and uj, respectively, the value of any pixel D (x, z) can be expressed as Equation (2): where Iij (x, z) represents the value of pixel D (x, z) when the exciting and receiving transducer positions are ui and uj. Sij represents the amplitude envelope of the received signal when the exciting and receiving transducer positions are ui and uj. According to Equation (3), the value of any pixel can be obtained in the imaging area grid: When information such as the position and size of the defects in the object to be measured are unknown, SAFT imaging can be used to calculate the value of all the pixels by traversing the imaging region.
As shown in Figure 1, it is assumed that the sensor position is u n (n = 1, 2, 3...n), while the exciting sensor position coordinates are (x i , z i ). The receiving sensor position coordinates are (x j , z j ). The position coordinate of any pixel D is (x, z). The time delay t ij (x, z) experienced by the ultrasonic wave is transmitted from the position of the exciting sensor u i and then reaches the position of the receiving sensor u j via point D, as shown in Equation (1): where the r i is given by: and v is the speed at which sound waves travel in the object being measured, i, j = 1,2,3 . . . n.
When the exciting and receiving transducer positions are u i and u j , respectively, the value of any pixel D (x, z) can be expressed as Equation (2): where I ij (x, z) represents the value of pixel D (x, z) when the exciting and receiving transducer positions are u i and u j . S ij represents the amplitude envelope of the received signal when the exciting and receiving transducer positions are u i and u j . According to Equation (3), the value of any pixel can be obtained in the imaging area grid:

Multilayer SAFT Imaging Method Based on Ray Tracing Technique
The SAFT imaging method makes it easier to achieve the ultrasound imaging of a single medium object, while for multilayer structures like ballastless track structures, ultrasound imaging calculations are much more complicated. The ultrasonic phenomenon occurs when the ultrasonic wave penetrates the interface between two adjacent layers of multilayer structures, and the sound propagation path at this time is composed of the refracting line segments in each layer. According to the conventional SAFT calculation model, the ultrasonic propagation delay is calculated using Equation (1). For multilayer structures (especially when the wave velocity of each layer medium is large), the calculation of the propagation delay using Equation (1) will produce a large error.
The difficulty of SAFT imaging in multilayer structures lies in accurately obtaining the propagation delay of acoustic waves, that is, accurately obtaining the propagation path. The ray-tracing technique is one of the effective methods to solve this problem. As shown in Figure 2, α is the incident angle of the acoustic wave and θ is the angle of refraction of the acoustic wave. The time at which the acoustic wave is refracted from point A through point P and propagates to point B can be expressed by Equation (4).
where t is the total delay of the acoustic wave propagating from A to B, v 1 is the speed of sound in the first layer of the medium, and v 2 is the speed of sound in the second layer of the medium.

Multilayer SAFT Imaging Method Based on Ray Tracing Technique
The SAFT imaging method makes it easier to achieve the ultrasound imaging of a single medium object, while for multilayer structures like ballastless track structures, ultrasound imaging calculations are much more complicated. The ultrasonic phenomenon occurs when the ultrasonic wave penetrates the interface between two adjacent layers of multilayer structures, and the sound propagation path at this time is composed of the refracting line segments in each layer. According to the conventional SAFT calculation model, the ultrasonic propagation delay is calculated using Equation (1). For multilayer structures (especially when the wave velocity of each layer medium is large), the calculation of the propagation delay using Equation (1) will produce a large error.
The difficulty of SAFT imaging in multilayer structures lies in accurately obtaining the propagation delay of acoustic waves, that is, accurately obtaining the propagation path. The ray-tracing technique is one of the effective methods to solve this problem. As shown in Figure 2, α is the incident angle of the acoustic wave and θ is the angle of refraction of the acoustic wave. The time at which the acoustic wave is refracted from point A through point P and propagates to point B can be expressed by Equation (4).
where t is the total delay of the acoustic wave propagating from A to B, v1 is the speed of sound in the first layer of the medium, and v2 is the speed of sound in the second layer of the medium. The ray-tracing technique is a method to calculate the acoustic wave propagation time according to Snell's law or Fermat's shortest time principle. The actual path of soundwave from point a to point B conforms to Snell's Law (Equation (5)). At the same time, according to Fermat's principle, the actual acoustic wave propagation time from point A to point B is the shortest.
As shown in Figure 3, in order to calculate the time when the acoustic wave reaches a certain point D of the second layer, firstly, the traversal method is used to find the refraction point that makes the acoustic wave propagation path delay the shortest at the interface of the discrete layer. Then the acoustic wave propagation path is segmented by the position of the refraction point, and the ultrasonic propagation is obtained one by one. When the propagation delay of the ultrasonic wave in the multilayer structure is accurately obtained, a focused image can finally be obtained according to the DAS algorithm. The specific algorithm is as follows: Step 1: Calculate the acoustic wave from the probe ui through point Pk to the pixel point of the refractive time tik of D using Equation (6). The ray-tracing technique is a method to calculate the acoustic wave propagation time according to Snell's law or Fermat's shortest time principle. The actual path of soundwave from point a to point B conforms to Snell's Law (Equation (5)). At the same time, according to Fermat's principle, the actual acoustic wave propagation time from point A to point B is the shortest.
As shown in Figure 3, in order to calculate the time when the acoustic wave reaches a certain point D of the second layer, firstly, the traversal method is used to find the refraction point that makes the acoustic wave propagation path delay the shortest at the interface of the discrete layer. Then the acoustic wave propagation path is segmented by the position of the refraction point, and the ultrasonic propagation is obtained one by one. When the propagation delay of the ultrasonic wave in the multilayer structure is accurately obtained, a focused image can finally be obtained according to the DAS algorithm. The specific algorithm is as follows: Step 1: Calculate the acoustic wave from the probe u i through point P k to the pixel point of the refractive time t ik of D using Equation (6).
Step 2: Obtain the time delay t i of the refractive propagation path from Equation (7).
Step 3: Calculate the total time delay t ij (x, z) for the acoustic wave that propagates from sensor u i through pixel point D in the second layer medium to sensor u j according to Equation (8).
Combining the ray-tracing technique with the SAFT imaging method can solve the problem of the traditional SAFT imaging method, which is not applicable to multilayer structures due to the change of the refractive propagation path when the acoustic wave propagates through the layer interfaces. With the proposed method, however, high-resolution imaging of a multilayer structure can be realized. The value in the second layer medium can be calculated by using Equation (9): where z > h 1 , I" (x, z) represents the value of pixel point (x, z) in the second layer medium and S ij represents the amplitude envelope curve of the received signal when the exciting and receiving sensor positions are u i and u j , respectively. Step 3: Calculate the total time delay tij(x, z) for the acoustic wave that propagates from sensor ui through pixel point D in the second layer medium to sensor uj according to Equation (8).
where z > h1, I'' (x, z) represents the value of pixel point (x, z) in the second layer medium and Sij represents the amplitude envelope curve of the received signal when the exciting and receiving sensor positions are ui and uj, respectively.

Finite Element Model
The commercial sound field finite element software PZFlex was used to establish a two-dimensional finite element simulation model of ballastless track structures. As shown in Figure 4, the finite element model is divided into a first layer for the track plate from the top to the bottom, a second layer for the mortar layer, and a third layer for the bedplate. The material parameters of each layer are shown in Table 1. Twelve transducer positions are arranged on the surface of the track plate, and the distance between the transducers is 30 mm. A void area of 300 mm in length and 30 mm in width was placed in the mortar layer.
In order to avoid the boundary reflection wave affecting the imaging result, the four boundaries of the model were set as the absorption boundaries. The specific finite element parameter settings are

Finite Element Model
The commercial sound field finite element software PZFlex was used to establish a two-dimensional finite element simulation model of ballastless track structures. As shown in Figure 4, the finite element model is divided into a first layer for the track plate from the top to the bottom, a second layer for the mortar layer, and a third layer for the bedplate. The material parameters of each layer are shown in Table 1. Twelve transducer positions are arranged on the surface of the track plate, and the distance    As shown in Figure 5, the data are collected by one transmission and multiple collections, that is, one of the 12 array transducers is used as an exciting source to excite the transverse wave signal in the track slab, and the remaining 11 transducers receive the signals and collect a total of 132 sets of data.  In order to avoid the boundary reflection wave affecting the imaging result, the four boundaries of the model were set as the absorption boundaries. The specific finite element parameter settings are shown in Table 2. The excitation signal used in this paper was a three-cycle sine wave modulated by the Hanning window with 50 kHz central frequency. As shown in Figure 5, the data are collected by one transmission and multiple collections, that is, one of the 12 array transducers is used as an exciting source to excite the transverse wave signal in the track slab, and the remaining 11 transducers receive the signals and collect a total of 132 sets of data.  Figure 5. Full wavefield data.    Figure 6 shows that the transient sound field distribution at each moment in the finite element simulation process. Figure 6 is a transient sound field distribution diagram, showing the measurements at 49.8, 69.7, 89.6, and 129.4 µs at the time when the sixth sensor is employed as the excitation source.  Figure 5. Full wavefield data.    Figure 7 shows that the received signal contains a larger energy surface wave. The presence of this surface wave signal will seriously affect the image quality. In the case of finite element simulation, the signal obtained by the finite element model under healthy conditions is used as the reference signal, and the defect scattering signal is obtained by subtracting the reference signal from the finite element model simulation signal containing the defect, thereby eliminating the influence of the surface wave. Figure 8 is a time-domain of a set of signals. Figure 8a is the original signal (including surface waves). Figure 8b is the signal after removing the surface wave.  Figure 7 shows that the received signal contains a larger energy surface wave. The presence of this surface wave signal will seriously affect the image quality. In the case of finite element simulation, the signal obtained by the finite element model under healthy conditions is used as the reference signal, and the defect scattering signal is obtained by subtracting the reference signal from the finite element model simulation signal containing the defect, thereby eliminating the influence of the surface wave. Figure 8 is a time-domain of a set of signals. Figure 8a is the original signal (including surface waves). Figure 8b is the signal after removing the surface wave.   The collected 132 sets of defect scattering signals were ultrasonically imaged using the traditional SAFT imaging algorithm and the multilayer SAFT imaging algorithm, separately. Figure 9a shows the imaging results obtained by the conventional SAFT algorithm. It can be seen that when imaging is performed using only a single wave velocity, the imaging position of the defect differs greatly from the actual position. This is because the wave velocity of the track slab and the bonding layer are greatly different, and the propagation delay of the ultrasonic wave is calculated by using a single wave velocity. Figure 9b shows the imaging results obtained by the Multilayer SAFT algorithm. It can be seen that the position of the defect is in good agreement with the actual position due to the consideration of the propagation wave velocity of different ultrasonic waves in different media. At the same time, there are still some areas where the value is higher on the lower side of the defect area. This phenomenon is caused by the underlying reflected wave generated when the sound wave propagates to the bottom layer. Figure 10 shows a cross-sectional view of the imaging results   Figure 7 shows that the received signal contains a larger energy surface wave. The presence of this surface wave signal will seriously affect the image quality. In the case of finite element simulation, the signal obtained by the finite element model under healthy conditions is used as the reference signal, and the defect scattering signal is obtained by subtracting the reference signal from the finite element model simulation signal containing the defect, thereby eliminating the influence of the surface wave. Figure 8 is a time-domain of a set of signals. Figure 8a is the original signal (including surface waves). Figure 8b is the signal after removing the surface wave.  The collected 132 sets of defect scattering signals were ultrasonically imaged using the traditional SAFT imaging algorithm and the multilayer SAFT imaging algorithm, separately. Figure 9a shows the imaging results obtained by the conventional SAFT algorithm. It can be seen that when imaging is performed using only a single wave velocity, the imaging position of the defect differs greatly from the actual position. This is because the wave velocity of the track slab and the bonding layer are greatly different, and the propagation delay of the ultrasonic wave is calculated by using a single wave velocity. Figure 9b shows the imaging results obtained by the Multilayer SAFT algorithm. It can be seen that the position of the defect is in good agreement with the actual position due to the consideration of the propagation wave velocity of different ultrasonic waves in different media. At the same time, there are still some areas where the value is higher on the lower side of the defect area. This phenomenon is caused by the underlying reflected wave generated when the sound wave propagates to the bottom layer. Figure 10 shows a cross-sectional view of the imaging results The collected 132 sets of defect scattering signals were ultrasonically imaged using the traditional SAFT imaging algorithm and the multilayer SAFT imaging algorithm, separately. Figure 9a shows the imaging results obtained by the conventional SAFT algorithm. It can be seen that when imaging is performed using only a single wave velocity, the imaging position of the defect differs greatly from the actual position. This is because the wave velocity of the track slab and the bonding layer are greatly different, and the propagation delay of the ultrasonic wave is calculated by using a single wave velocity. Figure 9b shows the imaging results obtained by the Multilayer SAFT algorithm. It can be seen that the position of the defect is in good agreement with the actual position due to the consideration of the propagation wave velocity of different ultrasonic waves in different media. At the same time, there are still some areas where the value is higher on the lower side of the defect area. This phenomenon is caused by the underlying reflected wave generated when the sound wave propagates to the bottom layer. Figure 10 shows a cross-sectional view of the imaging results of the two methods in the x and z-directions. As can be seen from Figure 10a, the defect length range of the imaging result by the SAFT algorithm is (57.3 mm, 443 mm), the error is 85.7 mm, the length center position is x = 250 mm, and the error is 0 mm. The defect length range of the imaging results using the Multilayer SAFT algorithm is (70.7 mm, 428.2 mm) with an error of 57.5 mm, the center position of the length is x = 250 mm, and the error is 0 mm. From Figure 10b, the height range of the imaging result by the SAFT algorithm is (270.8 mm, 340.3 mm), the error is 39.5 mm, the z-direction center position is z = 307.7 mm, and the error is 62.7 mm. The height range of the imaging results using the Multilayer SAFT algorithm is (232.6 mm, 265.3 mm) with an error of 2.7 mm, the center position in the z-direction is z = 251.6 mm, and the error is 6.6 mm. It can be seen from the above results that the Multilayer SAFT algorithm considering the propagating wave velocity in different media has better imaging accuracy than the SAFT imaging algorithm using single wave velocity. The length characterization accuracy is improved by 32.9% and the height characterization accuracy is improved by 93.2%. The center characterization accuracy of the defect in the z-direction is improved by 93.2%. of the two methods in the x and z-directions. As can be seen from Figure 10a, the defect length range of the imaging result by the SAFT algorithm is (57.3 mm, 443 mm), the error is 85.7 mm, the length center position is x = 250 mm, and the error is 0 mm. The defect length range of the imaging results using the Multilayer SAFT algorithm is (70.7 mm, 428.2 mm) with an error of 57.5 mm, the center position of the length is x = 250 mm, and the error is 0 mm. From Figure 10b, the height range of the imaging result by the SAFT algorithm is (270.8 mm, 340.3 mm), the error is 39.5 mm, the z-direction center position is z = 307.7 mm, and the error is 62.7 mm. The height range of the imaging results using the Multilayer SAFT algorithm is (232.6 mm, 265.3 mm) with an error of 2.7 mm, the center position in the z-direction is z = 251.6 mm, and the error is 6.6 mm. It can be seen from the above results that the Multilayer SAFT algorithm considering the propagating wave velocity in different media has better imaging accuracy than the SAFT imaging algorithm using single wave velocity. The length characterization accuracy is improved by 32.9% and the height characterization accuracy is improved by 93.2%. The center characterization accuracy of the defect in the z-direction is improved by 93.2%.

Experimental System
A 1:1 model of the ballastless track structure, as shown in Figure 11, was established in the laboratory to verify the accuracy of the algorithm studied in this paper. The material ratio and materials of each layer in the 1:1 model of the ballastless track structure were strictly in accordance with the "Code for Design of Durability of Railway Concrete Structures" (TB 10005-2010), and the construction process was conducted in accordance with "CRTSII type slab ballastless track concrete track slab" ( TB/T 3399-2015) production. In the production process of the 1:1 model, a void defect of the two methods in the x and z-directions. As can be seen from Figure 10a, the defect length range of the imaging result by the SAFT algorithm is (57.3 mm, 443 mm), the error is 85.7 mm, the length center position is x = 250 mm, and the error is 0 mm. The defect length range of the imaging results using the Multilayer SAFT algorithm is (70.7 mm, 428.2 mm) with an error of 57.5 mm, the center position of the length is x = 250 mm, and the error is 0 mm. From Figure 10b, the height range of the imaging result by the SAFT algorithm is (270.8 mm, 340.3 mm), the error is 39.5 mm, the z-direction center position is z = 307.7 mm, and the error is 62.7 mm. The height range of the imaging results using the Multilayer SAFT algorithm is (232.6 mm, 265.3 mm) with an error of 2.7 mm, the center position in the z-direction is z = 251.6 mm, and the error is 6.6 mm. It can be seen from the above results that the Multilayer SAFT algorithm considering the propagating wave velocity in different media has better imaging accuracy than the SAFT imaging algorithm using single wave velocity. The length characterization accuracy is improved by 32.9% and the height characterization accuracy is improved by 93.2%. The center characterization accuracy of the defect in the z-direction is improved by 93.2%.

Experimental System
A 1:1 model of the ballastless track structure, as shown in Figure 11, was established in the laboratory to verify the accuracy of the algorithm studied in this paper. The material ratio and materials of each layer in the 1:1 model of the ballastless track structure were strictly in accordance with the "Code for Design of Durability of Railway Concrete Structures" (TB 10005-2010), and the construction process was conducted in accordance with "CRTSII type slab ballastless track concrete track slab" ( TB/T 3399-2015) production. In the production process of the 1:1 model, a void defect

Experimental System
A 1:1 model of the ballastless track structure, as shown in Figure 11, was established in the laboratory to verify the accuracy of the algorithm studied in this paper. The material ratio and materials of each layer in the 1:1 model of the ballastless track structure were strictly in accordance with the "Code for Design of Durability of Railway Concrete Structures" (TB 10005-2010), and the construction process was conducted in accordance with "CRTSII type slab ballastless track concrete track slab (TB/T 3399-2015) production. In the production process of the 1:1 model, a void defect with a length of 300 mm, a width of 300 mm, and a height of 15 mm, was pre-buried at the interface between the second layer and the third layer. In the experiment, the ultrasonic echo signal was collected by Russian MIRA-A1040 concrete ultrasonic tomography, as shown in Figure 12a, and the acquired signal was exported and subjected to signal processing and ultrasonic imaging in MATLAB software. The MIRA-A1040 consists of 48 drypoint contact (DPC) transmitting and receiving transducers mounted in a matrix antenna. As shown in Figure 12b, the MIRA-A1040 array has 12 channels spaced 30 mm apart. Each channel has four transducers with a lateral spacing of 25 mm. In the data acquisition, when 12 channels are sequentially used as the transmitter of the transverse wave in the i-th channel, the 12-i channels after the channel are used as receivers to collect data, so that 66 sets of data can be collected. The sampling frequency used in the experiment was 1 MHz and the probe center frequency was 50 kHz.  Using Equation (10), the surface wave velocity Vr of the track slab can be calculated:

Method of Suppressing Surface Wave
where u is the Poisson's ratio of the material, ρ is the material density, and E is the material's elastic modulus. In the experiment, the ultrasonic echo signal was collected by Russian MIRA-A1040 concrete ultrasonic tomography, as shown in Figure 12a, and the acquired signal was exported and subjected to signal processing and ultrasonic imaging in MATLAB software. The MIRA-A1040 consists of 48 drypoint contact (DPC) transmitting and receiving transducers mounted in a matrix antenna. As shown in Figure 12b, the MIRA-A1040 array has 12 channels spaced 30 mm apart. Each channel has four transducers with a lateral spacing of 25 mm. In the data acquisition, when 12 channels are sequentially used as the transmitter of the transverse wave in the i-th channel, the 12-i channels after the channel are used as receivers to collect data, so that 66 sets of data can be collected. The sampling frequency used in the experiment was 1 MHz and the probe center frequency was 50 kHz. In the experiment, the ultrasonic echo signal was collected by Russian MIRA-A1040 concrete ultrasonic tomography, as shown in Figure 12a, and the acquired signal was exported and subjected to signal processing and ultrasonic imaging in MATLAB software. The MIRA-A1040 consists of 48 drypoint contact (DPC) transmitting and receiving transducers mounted in a matrix antenna. As shown in Figure 12b, the MIRA-A1040 array has 12 channels spaced 30 mm apart. Each channel has four transducers with a lateral spacing of 25 mm. In the data acquisition, when 12 channels are sequentially used as the transmitter of the transverse wave in the i-th channel, the 12-i channels after the channel are used as receivers to collect data, so that 66 sets of data can be collected. The sampling frequency used in the experiment was 1 MHz and the probe center frequency was 50 kHz.  Using Equation (10), the surface wave velocity Vr of the track slab can be calculated:

Method of Suppressing Surface Wave
where u is the Poisson's ratio of the material, ρ is the material density, and E is the material's elastic modulus.   Figure 13b shows the time domain of the signal after the surface wave signal is removed by channel 1 and the signal from channel 4 is received. It can be seen that this method better suppresses the influence of surface wave signals. Figure 14 depicts the time domain of the signal received by channel 1 as the excitation source, the signal received by channels 2-12, and the signal after the surface wave signal is removed. It can be seen that the surface wave signals in the 11 groups of signals are well suppressed.  Using Equation (10), the surface wave velocity V r of the track slab can be calculated:

Method of Suppressing Surface Wave
where u is the Poisson's ratio of the material, ρ is the material density, and E is the material's elastic modulus. The surface wave propagation delay t 1 from the exciting sensor position (x i , z i ) to the receiving sensor position (x j , z j ) can be expressed as The surface signal of the experimental signal can be removed by windowing the experimental signal using Equation (12).
In the equation, S ij is the signal after removing the surface wave, S ij is the original signal, and ε is the suppression coefficient. t 1 is the surface wave delay and t 2 is the time domain width of the excitation signal. Figure 13b shows the time domain of the signal after the surface wave signal is removed by channel 1 and the signal from channel 4 is received. It can be seen that this method better suppresses the influence of surface wave signals. Figure 14 depicts the time domain of the signal received by channel 1 as the excitation source, the signal received by channels 2-12, and the signal after the surface wave signal is removed. It can be seen that the surface wave signals in the 11 groups of signals are well suppressed.

Analysis of Experimental Results
The traditional SAFT imaging algorithm and the Multilayer SAFT imaging algorithm were used to perform ultrasonic imaging results on 66 sets of signal data collected by the MIRA-A1040 concrete ultrasonic tomography scanner in the pre-embedded void defect area. Figure 15 shows the imaging result obtained using the conventional SAFT imaging algorithm. Figure 15a shows the imaging result using the acquired original signal, and Figure 15b shows the imaging result using the signal after the removal of the surface wave. Figure 16 depicts the imaging result obtained by the Multilayer SAFT imaging algorithm. Specifically, Figure 16a shows the imaging result using the acquired original signal, and Figure 16b shows the imaging result using the signal after the removal of the surface wave. It can be seen from the imaging results of Figure 15b and Figure 16b that the Multilayer SAFT imaging algorithm fully considers the propagation speed of the ultrasonic wave in the track slab, mortar layer, and bedplate, making it more accurate than the traditional SAFT algorithm in terms of locating the void defect in the ballastless track structure. In addition, the presence of surface waves produces large artifacts in the imaging results, causing the imaging values of the depletion defects to be relatively low. After the surface waves are suppressed, the imaging quality of the depletion defects is obviously improved. A cross-sectional view of the imaging results of the two methods in the x and z-directions is shown in Figure 17. As can be seen in Figure 17a, the defect length range in the imaging results using the conventional SAFT imaging algorithm is (71.6 mm, 424.9 mm) with an error of 53.3 mm, the center position of the length is x = 244.5 mm, and the error is 5.5 mm. Using the Multilayer SAFT imaging algorithm, the defect length range is (78.3mm, 417.2mm), the error is 38.9 mm, the length center position is x = 244.5 mm, and the error is 5.5 mm. It can be seen from Figure 17b that the height range of the imaging result using the conventional SAFT algorithm is (218.9 mm, 309.1 mm), the error is 46.2 mm, the center position in the z-direction is z = 278.8 mm, and the error is 33.8 mm. The height range of the imaging structure using the Multilayer SAFT imaging algorithm is (218 mm, 265.3 mm) with an error of 17.3 mm, the center position in the z-direction is z = 248.1 mm with an error of 3.1 mm. From the above results, it is clear that the Multilayer SAFT imaging algorithm, which considers the propagation wave velocity in different media, is significantly better than the SAFT imaging algorithm using single wave velocity. The length characterization accuracy is improved by 27% and the height characterization accuracy is improved by 62.6%. Furthermore, the positioning accuracy of the center position in the z-direction is increased by 90.8%.

Analysis of Experimental Results
The traditional SAFT imaging algorithm and the Multilayer SAFT imaging algorithm were used to perform ultrasonic imaging results on 66 sets of signal data collected by the MIRA-A1040 concrete ultrasonic tomography scanner in the pre-embedded void defect area. Figure 15 shows the imaging result obtained using the conventional SAFT imaging algorithm. Figure 15a shows the imaging result using the acquired original signal, and Figure 15b shows the imaging result using the signal after the removal of the surface wave. Figure 16 depicts the imaging result obtained by the Multilayer SAFT imaging algorithm. Specifically, Figure 16a shows the imaging result using the acquired original signal, and Figure 16b shows the imaging result using the signal after the removal of the surface wave. It can be seen from the imaging results of Figures 15b and 16b that the Multilayer SAFT imaging algorithm fully considers the propagation speed of the ultrasonic wave in the track slab, mortar layer, and bedplate, making it more accurate than the traditional SAFT algorithm in terms of locating the void defect in the ballastless track structure. In addition, the presence of surface waves produces large artifacts in the imaging results, causing the imaging values of the depletion defects to be relatively low. After the surface waves are suppressed, the imaging quality of the depletion defects is obviously improved. A cross-sectional view of the imaging results of the two methods in the x and z-directions is shown in Figure 17. As can be seen in Figure 17a, the defect length range in the imaging results using the conventional SAFT imaging algorithm is (71.6 mm, 424.9 mm) with an error of 53.3 mm, the center position of the length is x = 244.5 mm, and the error is 5.5 mm. Using the Multilayer SAFT imaging algorithm, the defect length range is (78.3mm, 417.2mm), the error is 38.9 mm, the length center position is x = 244.5 mm, and the error is 5.5 mm. It can be seen from Figure 17b that the height range of the imaging result using the conventional SAFT algorithm is (218.9 mm, 309.1 mm), the error is 46.2 mm, the center position in the z-direction is z = 278.8 mm, and the error is 33.8 mm. The height range of the imaging structure using the Multilayer SAFT imaging algorithm is (218 mm, 265.3 mm) with an error of 17.3 mm, the center position in the z-direction is z = 248.1 mm with an error of 3.1 mm. From the above results, it is clear that the Multilayer SAFT imaging algorithm, which considers the propagation wave velocity in different media, is significantly better than the SAFT imaging algorithm using single wave velocity. The length characterization accuracy is improved by 27% and the height characterization accuracy is improved by 62.6%. Furthermore, the positioning accuracy of the center position in the z-direction is increased by 90.8%.

Conclusions
With the aim of solving the high-precision ultrasonic imaging problem of detecting void defects in ballastless track structures, this paper combines ray tracing technology and the SAFT imaging algorithm to propose a Multilayer SAFT imaging algorithm. The finite element simulation and experimental results show that the Multilayer SAFT imaging algorithm can improve imaging precision of void defects. The specific results are as follows: (1) Based on the shortest path principle of Fermat, the function of the position of the refraction point and the propagation path of the forward tracking ultrasonic wave were obtained. Thereby, the tracking of the propagation path of the acoustic wave in the ballastless track structure was realized,

Conclusions
With the aim of solving the high-precision ultrasonic imaging problem of detecting void defects in ballastless track structures, this paper combines ray tracing technology and the SAFT imaging algorithm to propose a Multilayer SAFT imaging algorithm. The finite element simulation and experimental results show that the Multilayer SAFT imaging algorithm can improve imaging precision of void defects. The specific results are as follows: (1) Based on the shortest path principle of Fermat, the function of the position of the refraction point and the propagation path of the forward tracking ultrasonic wave were obtained. Thereby, the tracking of the propagation path of the acoustic wave in the ballastless track structure was realized,

Conclusions
With the aim of solving the high-precision ultrasonic imaging problem of detecting void defects in ballastless track structures, this paper combines ray tracing technology and the SAFT imaging algorithm to propose a Multilayer SAFT imaging algorithm. The finite element simulation and experimental results show that the Multilayer SAFT imaging algorithm can improve imaging precision of void defects. The specific results are as follows: (1) Based on the shortest path principle of Fermat, the function of the position of the refraction point and the propagation path of the forward tracking ultrasonic wave were obtained. Thereby, the tracking of the propagation path of the acoustic wave in the ballastless track structure was realized,

Conclusions
With the aim of solving the high-precision ultrasonic imaging problem of detecting void defects in ballastless track structures, this paper combines ray tracing technology and the SAFT imaging algorithm to propose a Multilayer SAFT imaging algorithm. The finite element simulation and experimental results show that the Multilayer SAFT imaging algorithm can improve imaging precision of void defects. The specific results are as follows: (1) Based on the shortest path principle of Fermat, the function of the position of the refraction point and the propagation path of the forward tracking ultrasonic wave were obtained. Thereby, the tracking of the propagation path of the acoustic wave in the ballastless track structure was realized, and the propagation delay of the ultrasonic wave in the ballastless track structure could be accurately calculated. (2) A two-dimensional finite element model of ultrasonic wave propagation in a ballastless track structure was established. The ultrasonic signal matrix was captured in the finite element model. The acquired signal was ultrasonically imaged by conventional SAFT imaging and the multilayer SAFT imaging method, separately. Compared with traditional SAFT imaging, this method improved the length characterization accuracy by 32.9%, the height characterization accuracy by 93.2%, and the positioning accuracy in the z-direction center position by 93.2%. (3) A model of a ballastless track structure with a 1:1 ratio was constructed in the laboratory.
Ultrasonic echo signals were acquired by a MIRA-A1040 concrete ultrasonic tomography scanner. The data were exported and processed in MATLAB software. The experimental results showed that, according to the characteristics of the time domain of the experimental signal, selecting a reasonable window function can effectively remove the influence of surface waves. The Multilayer SAFT imaging method provided better accuracy determination in the two directions (the length and height) of the void defect. These results were significantly improved compared with those achieved by the traditional SAFT algorithm. The length characterization accuracy was improved by 27%, the height characterization accuracy was improved by 62.6%, and the positioning accuracy in the z-direction center position was improved by 90.8%.
In summary, the Multilayer SAFT algorithm fully considers the different propagation speeds of the ultrasonic wave in different layers of a ballastless track structure and thus improves imaging precision of void defects. In this way, it can overcome the problem of the traditional of SAFT imaging algorithm, which is not applicable for the imaging of void defects in multilayer ballastless track structures.

Conflicts of Interest:
The authors declare no conflict of interest.