# Data Interpretation Technology of GPR Survey Based on Variational Mode Decomposition
## 4 Time Frequency Analysis of GPR Simulation Signal  
### Time Frequency Analysis of VMD  
A simulation model was created in order to evaluate the contribution of the time frequency analysis based on Matlab 2016 platform (The MathWorks, Natick, MA, USA). During the simulation signal acquisition of GPR, the size of the assumed structural model is shown in Figure 5a. There was one steel cylinder, where the center coordinates were (2.5, 1.5) and the cylinder radius was 0.2 m. For the simulation parameters, the diectric permittivity and electrical conductivity of the concrete were 10 and 0.001 S/m, while the diectric permittivity and electrical conductivity of the steel were 1 and 106 S/m. The computation area was 5.0 m \(\times\) 3.0 m. The grid size was 0.002 m and the length of the time window was 40 ns. The Ricker wave was considered as input excitation and the central frequency was 0.5 GHz. The transceiver distance was 0.04 m and the number of the simulation sampling trace was 230. Along the direction of the x axis, the 230 time-series GPR signal was synthesized and Figure 5b shows the scanner result of the simulation with the finite difference time domain (FDTD). In Figure 5b, the reflected signal of the direct wave is significantly shown and the reinforcement reflex arc is also displayed in the center of the concrete. However, the reflected arc was relatively weak and it was not clearly distinguished in the internal structure. Based on the data of the GPR simulation \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\xi\) & \\ \hline
**EMD** & **EEMD** & **VMD** \\ \hline
0.065 & 0.0125 & 0.0119 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation index of energy leakage. Figure 5: Simulation model of GPR: (**a**) forward geometry model; and, (**b**) simulation signal of GPR. scan, the three-dimensional body can be constituted after the time frequency analysis. Figure 6 shows the results. Figure 6 shows the 3D data of GPR \(H(x,t,\omega)\). The data structure consists of two parts, in accordance with the direct wave and reflection wave signal of reinforcement, and the concrete data effectively displays internal structure information. However, the internal details of the structure are not well displayed in the 3D GPR data and the body of the 3D GPR data needs slicing for analysis. From what is mentioned above, it can be concluded that the transverse profile is the division frequency section, the longitudinal profile is the time frequency section, and the horizontal profile is the space frequency section. The sliced 3D data body of GPR was processed to study the internal structure detection effects with the time frequency analysis of GPR. First, the data volume \(H(x,t,\omega)\) was transversely cut to obtain a frequency division section. Figure 7 shows the frequency division section \(H(x,t)\), with a central frequency of 0.5 GHz. In Figure 7, the main frequency contour displays the reflex arcs of the hyperbola below the direct wave and the reflected signal of the reinforcement as compared with Figure 5b, which has been significantly enhanced. The effect of the abnormality detection significantly improved. Figure 6: Three-dimensional (3D) Frequency property data of GPR. Figure 7: Frequency division section of GPR. Secondly, the GPR data \(H(x,t,\omega)\) processed longitudinal cutting and the time frequency section \(H(t,\omega)\) could be obtained. Figure 8 displays the time frequency section at the center of the GPR line. In Figure 8, the two extreme points are 4 ns and 20 ns. The two time positions correspond to the travel times of the direct wave and reinforcement reflection wave, with both frequencies in the 0.5 GHz GPR transmitter main frequency. Finally, the GPR data body \(H(x,t,\omega)\) processed the horizontal slice. The space frequency section \(H(x,\omega)\) could be obtained. In Figure 9, the space frequency section shows the layer at time 20 ns. In Figure 9, the extreme range in the x-axis is about 2.1 m-2.5 m, in relation to the bar diameter.