5.1. Simulated Models
We use two examples to illustrate the advantages of the proposed CM-SMWA. One is the simulated simple cylinder, and the other is the simulated power lines. The cylinder is close to the shape characteristics of the power line, which can quickly verify the performance of the proposed method under simple conditions.
- (1)
Simulated simple cylinder
Figure 5 shows a cylindrical model used in the experiment, with the diameter
= 0.4 m and length
= 20 m. In
Figure 5, 60°, 90°, and 120°, respectively, represent the incident angles of the electromagnetic wave. The detailed parameters of the simulated cylinder are provided in
Table 1.
In order to prevent force or gravity breakage, most power lines with a diameter greater than 10 mm use steel-cored aluminum stranded wire for long-distance transmission.
Figure 6 shows a typical power line, LGJ50-8, which has a steel core and six outer aluminum stranded wires. The physical structure of the power lines is generally aluminum stranded or steel-cored aluminum stranded wire.
In
Figure 6,
represents the distance between two strands, P represents the winding cycle of a single strand, D represents the diameter of the stranded wire, and d represents the diameter of the outermost single aluminum stranded wire. The detailed parameters of the power line are listed in
Table 2.
The Bragg scattering principle of power lines is shown in
Figure 7. The echo strength point equation of the Bragg scattering angle can be obtained as follows:
In Equation (36), represents the n-th scattering peak angle (n-th Bragg) and represents the wavelength. The phenomenon of scattering of peaks at a specific incident angle is called Bragg scattering, and represents the main lobe perpendicular to the power lines, while other peak angles are called side lobes. Since the electromagnetic wave has phase information, when the received electromagnetic waves have the same phase, the superposition of wave peaks makes the reflection the strongest. Considering the stranded periodic structure of power lines, when the incident wave reaches the surface of the adjacent stranded wire and the wave path difference is an integer multiple of 1/2 a wavelength, the backscattered echoes will be superimposed in phase, that is, the incident angle satisfies the characteristics of Bragg scattering.
5.3. Numerical Calculation Comparison
All examples were run on a computer with a processor frequency of 2.6 GHz and 32 GB memory. The error threshold of the ACA was set at 1 × 10−3. The angle = 90° was perpendicular to the long axis of the power lines for all simulations.
- (1)
Simulated simple cylinder
Figure 8 shows that the CM-SMWA with an extension can obtain the RCS results with a similar accuracy to the MoM method. However, a large extension will lead to an increase in the amount of CM calculation. Thus, we set the extension to 0.1
in this paper.
The CM-SMWA is compared with the MoM and the CM method. The extensions of groups in the CM method and the CM-SMWA are set at 0.1.
Figure 9 shows the comparison of the simulation results of the different algorithms for the cylinder. It can be seen from
Figure 9 that the detection results of the CM and CM-SMWA are similar to that of the MoM method. It shows that although the CM is only extended by 0.1, both the CM method and the CM-SMWA method have good accuracy for the cylinder. The difference from the MoM method is concentrated in the position of the minimum value, as shown in the subfigure in
Figure 9, which shows that the difference between the CM-SMWA and the conventional MoM is small.
Table 3 presents the comparison results of the computing time and memory requirement of the different algorithms. The number of CMs for each group is set at 70, and so the required CM occupies the same memory for both the CM method and CM-SMWA, which was 4.5 MB. As shown in
Table 3, compared with the MoM and CM method, the CM-SMWA reduces the memory greatly and has advantages in computing time. Because the target is relatively small, the CM-SMWA saves little time.
In the millimeter waveband, the frequency bands of 35 GHz, 76 GHz, and 94 GHz have the smallest electromagnetic wave propagation loss, and so the power line RCS is mainly concentrated around this band for research.
The LGJ50-8 power line was selected for the numerical simulation. The specific parameters are shown in
Table 2. The length of the power line model is selected as two times P, that is, 2 × P = 0.276 m, which is equivalent to two stranded cycles of the power lines in
Table 2. The power line model is discretized by the RWG basis function with an average side length of 0.1
, and a total of 34,848 RWG basis functions are used. The six level binary tree is used, the power lines are divided into 64 segments, and the number of CMs in each group is fixed at 300. The extension for generating CMs in the CM method and the CM-SMWA is 0.1
. The simulation results of the power line RCS with the different algorithms at 35 GHz horizontal–horizontal (H-H) polarization are shown in
Figure 10.
From the comparison in
Figure 10, it can be seen that the simulation results of the latter two methods are close to the MoM, indicating that the three methods can effectively simulate the power lines. As shown in the subfigure in
Figure 10, the positions with relatively large relative errors displayed in the form of dB are also concentrated in the low RCS part and mainly concentrated in the positions below −40 dB, and the absolute error of the RCS is not large.
According to related research [
37], the Bragg scattering strengths of different polarization power lines are different. In order to further confirm the characteristics of power lines with different polarizations, V-V polarization simulations are simultaneously carried out in this paper. The extension of each segment for generating CMs is set at 0.1
. The V-V polarization simulation is as seen in
Figure 10.
As can be seen from
Figure 11, which shows the simulation results of the power line V-V polarization RCS with the different algorithms at 35 GHz, the method proposed in this paper can accurately simulate V-V polarization. The comparison results are shown in
Table 4. As can be seen in
Table 4, the calculation time of the CM-SMWA is much less than the other two methods. In terms of memory consumption, the CM-SMWA has great advantages over the other two methods. In terms of accuracy, the CM method is slightly different from the CM-SMWA method, but it is very close. It can be seen that the accuracy of the simulation of the V-V polarization and H-H polarization RCS using our method can be close to that of the MoM method.
Figure 12 compares the simulation results of the V-V polarization and the H-H polarization at 35 GHz. It can be seen from the comparison that the V-V polarization is about 10 dB stronger than the RCS of the Bragg sidelobes (
n = ±1) of the H-H polarization. The vertical angle (incident angle
= 90° echo) intensity of the power lines is almost the same. Therefore, for this power line, the detection effect of the V-V polarized microwave radar is obviously better at 35 GHz.
For the detection radar of millimeter wave power lines, the selectable band is Ka~W, and 76 GHz can be used as a low-cost or on-chip radar [
38], and so it also includes the mainstream research 76 GHz. Due to the shorter wavelength of this band, more basis functions need to be established for the simulation. This makes the calculation and storage of the MoM matrix extremely large, and it is difficult for conventional equipment to simulate. Therefore, the length of the power lines in Example 3 is halved, and the simulation is carried out under the condition of 76 GHz. The length of the power lines is selected as P (with P = 0.138 m), the target is discretized by the RWG basis function with an average side length of 0.1
, and a total of 81,822 basis functions are used. The number of levels for the binary tree is
L = 7, which means the power line is divided into 128 segments. The number of CMs for each segment is fixed at 300, and the extension of each segment for generating CMs is set at 0.1
.
The simulation results of the H-H polarization are shown in
Figure 13 and the results of the V-V polarization are shown in
Figure 14. It can be seen that the angle with a large error is mainly concentrated at the minimum, and because in actual radar detection the echo of power lines is affected by ground clutter, this “minimum point” error is weaker than the ground clutter, and so these errors are acceptable for the power line simulation.
The comparison of the power line results calculated by the different algorithms at a 76 GHz simulation are shown in
Table 5. Our method has obvious advantages in terms of CPU time and storage. Due to excessive memory usage, the total time of the MoM method in
Table 5 is the estimated time.
Figure 15 compares the RCS of the H-H polarization and V-V polarization power lines under the condition of 76 GHz. According to the RCS comparison results, the vertical angle (incident angle
= 90°) echo of the H-H polarization is more than 10 dB stronger than the V-V polarization. For the Bragg sidelobes with
d = 3.2 mm, the V-V polarization is stronger than the H-H polarization, and so it is basically consistent with the conclusion obtained in [
37], and it also proves that the power line fast simulation method proposed in this paper can effectively evaluate the power line RCS.
Figure 16 shows the comparison of the simulation results of the H-H polarization and V-V polarization. It can be seen that the V-V polarization of the power line RCS in this paper is still stronger than the H-H polarization at 94 GHz. While the Bragg first sidelobes (
n = ±1) have the same levels, the Bragg second and third sidelobe (
n = ± 2, ± 3) V-V polarizations are stronger. Therefore, due to higher RCS levels, it is easier to detect V-V polarization power lines at 94 GHz.
According to the power line results calculated by the CM-SMWA at 94 GHz (shown in
Table 6), the calculation time and memory of the CM-SMWA are still acceptable (116,820 basis functions), indicating that the method in this paper meets the calculation requirements of different frequencies.