Auto Sweptback Wing Based on Low Scattering Demand for an Unmanned Aerial Vehicle in Phase Flight

Abstract

In order to study the optimal sweepback angle when a variant unmanned aerial vehicle (UAV) exhibits a low radar cross-section (RCS) indicator during phase flight, an auto sweep scheme based on electromagnetic scattering evaluation and an improved particle swarm optimization algorithm was presented in this article. An aircraft model with variable swept wings was built, and high-precision grids were used to discretize the target surface. The results showed that the optimal sweep angle did not change with the increase in the initial azimuth angle when the observation field was horizontal and the ending azimuth was 90°. While the increase in the elevation angle affected the optimal sweepback angle of the aircraft under the given conditions, when the observation initial azimuth angle was 90°, the auto sweep scheme could reduce the mean and some minima of the RCS indicator curve of the aircraft and could provide the aircraft with an optimal sweep angle under different observation conditions. The presented method was effective in learning the optimal sweep angle of the aircraft when low scattering characteristics were required during the phase flight.

1. Introduction

The variety of wing sweep design can change the lift and drag characteristics of an aircraft, and then different flight missions can be implemented. Under a certain sweepback angle, the electromagnetic scattering characteristics of an aircraft are relatively fixed, which makes it difficult to improve its viability. In a specific flight phase, in order to show low electromagnetic scattering characteristics as much as possible, the question of how to determine a suitable sweep angle has attracted a lot of attention [1,2,3].

By designing different sweep angle parameters, three deployment states of wings have been explored and discussed [4,5]. Based on a forward-swept wing model, a forward-swept and backward-swept wing was built, and the related parameters were studied [6]. The vector loop equation of the compound linkage mechanism was established for the swept wing, and the mobility of the mechanism was analyzed [7,8]. On the basis of the establishment of the unmanned aerial vehicle (UAV) model with different sweepback angles, the flight environment was simulated, where the genetic algorithm was used to obtain the best variable sweepback law [9]. A new type of seamless shear variable-sweep wing with a good performance shear skin was presented, where the deformation principle was based on the fact that the whole structure had a degree of freedom [10], that is, the sweep angle of the outer wing was driven by the forward and backward movement of a telescopic cylinder fixed on the inner wing. It was necessary to use variable swept wings to fly at middle and low altitudes for the study of aerodynamic characteristics, and it was also worth exploring more about the electromagnetic scattering characteristics.

A radar cross section (RCS) is usually used to characterize the electromagnetic scattering characteristics of an aircraft [11]. The RCS of a Z-shaped variant flying wing has been studied, where the physical optics (PO) were used to calculate the scattering contribution of the facet, and the physical theory of diffraction (PTD) was used to calculate the edge contribution [12]. The backscattering characteristics of the target aircraft were measured at different wing sweepback angles [13]. Because of its high prediction ability, the Bayesian network was used to analyze the probability of potential conflicts detected by air traffic control to avoid collisions between various aircrafts, which meant that the safety distance between each aircraft was ensured through the minimum separation of the side, vertical and longitudinal [14]. The quasi-static principle (QSP) was used to simulate the rotation of rotor blades, where the equivalent current method was used to evaluate the diffraction contribution of edges [15]. The full array method (FAM) was used to calculate the external storage form of different weapons and fuel tanks [16]. The electromagnetic scattering characteristics of tailless aircraft intake and exhaust systems were studied and discussed [17,18]. The golden sine algorithm was introduced into the traditional bat algorithm to search for the optimal individual in all dimensions and in one dimension [19]. The electromagnetic scattering characteristics of the rotor at different blade pitch angles were evaluated [20]. A prediction method based on particle swarm optimization (PSO) and the radial basis function was established to simulate the battle command of enemy aircraft [21,22,23]. In a certain phase of flight, the question of how to determine the optimal sweep angle to make a UAV meet the requirements of low electromagnetic scattering characteristics becomes a challenge.

As mentioned, the research on variable swept wings has mainly focused on the design of driving mechanism, the analysis of aerodynamic characteristics and the law of the sweep angle, while the electromagnetic scattering characteristics of UAVs with swept-back wings have received less attention. More importantly, the question of how to control the wing sweep angle to minimize the RCS of the target in a specific phase of flight is a difficult problem. Therefore, we tried to establish an automatic sweepback method based on an improved search algorithm and RCS calculation to set the wing sweepback angle so that it could meet the requirements of low scattering characteristics in the flight phase. This research is of great engineering value for the covert flight of swept-wing aircraft.

The structure of this manuscript is arranged as follows. The research method is presented in Section 2. The UAV model with a swept wing is presented in Section 3. The relevant results are discussed in Section 4. Finally, a summary of the full text is made.

2. Auto Swept Scheme

In a given flight phase, the schematic diagram of radar detection received by the aircraft with a variable swept wing is shown in Figure 1, where F_rh means the radar wave frequency and horizontal polarization, noting that the subscript v indicates the vertical polarization mode. α is the azimuth between the radar station and the aircraft, and β is the elevation angle. The purpose of the auto-swept scheme (ASS) was to determine the appropriate sweep angle for this variable wing.

2.1. Auto Sweep Target

In order to show the lowest RCS on the flight path, the wing-sweep angle automatically set here should meet the following objective:

$$A_{\mathrm{A}}=A_{\mathrm{ss}}\left|\min {\sigma }_{\mathrm{m}}\left\{\begin{array}{cc}\left[{\alpha }_{\mathrm{n}},{\alpha }_{\mathrm{m}}\right],& \left[{\beta }_{\mathrm{n}},{\beta }_{\mathrm{m}}\right]\end{array}\right\}\right.$$

(1)

where A_A stands for the automatically set sweep angle, A_s is the sweepback angle of the wing, as shown in Figure 2, where the additional subscript s represents the optimal solution of the sweepback angle required to meet the requirement of low scattering during flight. σ_m is the mean RCS of an aircraft in a phase flight. [α_n, α_m] indicates the value range of the azimuth, which also implies that the azimuth changes linearly from the initial value to the terminal value during a phase flight, and [β_n, β_m] indicates the value range of the elevation angle. The radar station can be set at the high ground so that it is at the same level as the aircraft. When the aircraft is flying horizontally:

$$A_{\mathrm{A}}=A_{\mathrm{ss}}\left|\min {\sigma }_{\mathrm{m}}\left\{\begin{array}{cc}\left[{\alpha }_{\mathrm{n}},{\alpha }_{\mathrm{m}}\right],& \left[A_{\mathrm{sn}},A_{\mathrm{sm}}\right],\beta =0\end{array}\right\}\right.$$

(2)

where [A_sn, A_sm] indicates the value range of A_s.

2.2. Sweep Angle Determination

The full-array method (FAM) is used to preliminarily determine the optimal solution within a sweep angle range:

$$A_{\mathrm{A}}=A_{\mathrm{ss}}\left|\min {\sigma }_{\mathrm{m}}\left\{A_{\mathrm{ss}}\in {\mathit{M}}_{\mathrm{AS}}\right\}\right.$$

(3)

where M_AS is the full-array matrix of the sweepback angle.

The improved particle swarm optimization (PSO) algorithm was used in this paper to determine the optimal solution of the sweepback angle. The fitness function is defined as:

$$F_{\mathrm{fitness}}={\sigma }_{\mathrm{m}}\left\{\begin{array}{cc}\left[{\alpha }_{\mathrm{n}},{\alpha }_{\mathrm{m}}\right],& \left[A_{\mathrm{sn}},A_{\mathrm{sm}}\right]\end{array}\right\}$$

(4)

where F_fitness is the fitness function. The search speed of particles is updated as follows:

$$V_i^{k+1}={\omega }^k{V}_i^k+R_1{C}_1\left(P_i^k-x_i^k\right)+R_2{C}_2\left(P_{\mathrm{s}}^k-x_i^k\right)$$

(5)

where V is the search speed of particles, P represents the population of particles, x is the position of the particle [19,22], the superscript k represents the current generation of the population, and the subscript i indicates the individual number. ω is the inertia weight. C₁ and C₂ represent the learning factors of particles, and R₁ and R₂ are two random numbers:

$$R_i=O_{\mathrm{tr}}\left[0,1\right],\begin{array}{cc}& i=1,2,3\end{array}$$

(6)

where R_i is a random number; the subscript is used to distinguish the number of random parameters. O_tr is the true random operator. For the learning factors,

$$C_2=C_1+\mathsf{\Delta }{C}_{12}$$

(7)

$$\mathsf{\Delta }{C}_{12}=0.125\left(A_{\mathrm{sm}}-A_{\mathrm{sn}}\right)$$

(8)

where ∆C₁₂ represents the learning factor increment. When this increment is greater than 0, the global search capability is improved.

The generation method of the inertia weight is as follows:

$${\omega }^k={\omega }_{\mathrm{s}}-R_3\frac{k}{N_{\mathrm{g}}}\left({\omega }_{\mathrm{s}}-{\omega }_e\right)$$

(9)

where N_g is the number of total generations, R₃ is a random number, and ω_s and ω_e are two limits of ω. Noting that the value of R3 also depends on the true random operator.

The position of particles is updated as follows:

$$x_i^{k+1}=x_i^k+V_i^k$$

(10)

When the fitness reaches the minimum value, the optimal solution of the sweep angle is obtained:

$$A_{\mathrm{ss}}=x_{\mathrm{s}}\left|\min F_{\mathrm{fitness}}\right.$$

(11)

where x_s indicates the position of the particle when obtaining the optimal solution. Refer to Appendix A for a comparison of search algorithms.

2.3. Electromagnetic Scattering Evaluation

The schematic of electromagnetic scattering of the UAV with a variable swept-back wing is shown in Figure 3. The model of an aircraft can be seen as a combination of the fuselage and two wings, and thus the following equation is obtained:

$$m_{\mathrm{a}}\left(A_{\mathrm{s}}\right)=\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}}\right),m_{\mathrm{w}2}\left(A_{\mathrm{s}}\right),m_{\mathrm{f}}\right)$$

(12)

where m_a is the model of the aircraft, m_w is the model of the wing, the additional numerical subscripts are used to distinguish the wing numbers, and m_f is the model of the fuselage.

The surface of the model divided by triangular facets can be obtained in the following form:

$${\mathit{M}}_{\mathrm{a}}\left(m_{\mathrm{a}}\left(A_{\mathrm{s}}\right)\right)=\left[{\mathit{M}}_{\mathrm{w}1}\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}}\right)\right),{\mathit{M}}_{\mathrm{w}2}\left(m_{\mathrm{w}2}\left(A_{\mathrm{s}}\right)\right),{\mathit{M}}_{\mathrm{f}}\left(m_{\mathrm{f}}\right)\right]$$

(13)

where M_a is the grid coordinate matrix of the aircraft model, M_w is the grid coordinate matrix of the wing model, and M_f is the grid coordinate matrix of the fuselage model.

Considering the sweepback of wing 1,

$${\mathit{M}}_{\mathrm{w}1}^y\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}1}\right)\right)={\mathit{M}}_{\mathrm{w}1}^{}\left(y\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}1}\right)\right)-Y_{\mathrm{w}1}\right)$$

(14)

$${\mathit{M}}_{\mathrm{w}1}^z\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}1}\right)\right)=\left[\begin{array}{ccc}\cos A_{\mathrm{s}1}& -\sin A_{\mathrm{s}1}& 0\\ \sin A_{\mathrm{s}1}& \cos A_{\mathrm{s}1}& 0\\ 0& 0& 1\end{array}\right]\times {\mathit{M}}_{\mathrm{w}1}^y\left(m_{\mathrm{w}1}\left(A_{\mathrm{s}1}\right)\right)$$

(15)

where Y_w1 is the distance from the center of the rotation axis of wing 1 to the xz plane, noting that this rotation axis is parallel to the z axis. For wing 2,

$${\mathit{M}}_{\mathrm{w}2}^y\left(m_{\mathrm{w}2}\left(A_{\mathrm{s}2}\right)\right)={\mathit{M}}_{\mathrm{w}2}^{}\left(y\left(m_{\mathrm{w}2}\left(A_{\mathrm{s}2}\right)\right)+Y_{\mathrm{w}2}\right)$$

(16)

$${\mathit{M}}_{\mathrm{w}2}^z\left(m_{\mathrm{w}2}\left(A_{\mathrm{s}2}\right)\right)=\left[\begin{array}{ccc}\cos A_{\mathrm{s}2}& -\sin A_{\mathrm{s}2}& 0\\ \sin A_{\mathrm{s}2}& \cos A_{\mathrm{s}2}& 0\\ 0& 0& 1\end{array}\right]\times {\mathit{M}}_{\mathrm{w}2}^y\left(m_{\mathrm{w}2}\left(A_{\mathrm{s}2}\right)\right)$$

(17)

where Y_w2 is the distance from the center of the rotation axis of wing 2 to the xz plane. The two wing models are then returned to their original positions and the aircraft model is updated. For a given incident wave, the illumination area can be extracted as:

$$\left[S_{\mathrm{I}},S_{\mathrm{D}}\right]\Leftarrow {\mathit{M}}_{\mathrm{a}}\left(m_{\mathrm{a}}\left(A_{\mathrm{s}}\right)\right)$$

(18)

where S_I is the illumination area, and S_D is the dark area. In the current coordinate system, the attitude of the aircraft remains unchanged during flight. PO is used to calculate the electromagnetic scattering contribution of the panel, and PTD is used to evaluate the edge diffraction. For adjacent areas with edge features,

$${\mathit{J}}_{\mathrm{S}}={\mathit{J}}_{\mathrm{PO}}+{\mathit{J}}_{\mathrm{PTD}}$$

(19)

where J_S means the surface current. J_PO represents the current corresponding to PO. J_PTD refers to the current corresponding to PTD.

The RCS of the target can be obtained as:

$$\sigma ={\left|{\displaystyle \sum _{i=1}^{N_{\mathrm{F}}}\left(\sqrt{{\sigma }_{\mathrm{F}}}\right)}\begin{array}{c}\\ i\end{array}+{\displaystyle \sum _{j=1}^{N_{\mathrm{E}}}\left(\sqrt{{\sigma }_{\mathrm{E}}}\right)\begin{array}{c}\\ j\end{array}}\right|}^2$$

(20)

where σ means the RCS, subscript F represents the facet contribution, and E refers to the edge contribution. N_E is the number of edges and N_F means the number of facets.

The verification of the RCS of the aircraft is show in Figure 4, where the solid red line is the result of the presented method, and the blue dotted line is the result of PO+ MOM (method of moment)/MLFMM (multilayer fast multipole method). The MOM is a numerical calculation method based on Maxwell’s integral equation, whose essence is to solve linear equations with an impedance matrix. The MLFMM is a fast method used to reduce the computing time and storage, which is used to assist the operation of the MOM. It can be seen that the two curves were similar in shape, mean level, peak value, and fluctuation range. At α = 160°, the two curves reached the same maximum value of 13.38 dBm² because, at this time, the surface near the trailing edge of wing 2 and the tail of the fuselage provided the main scattering contributions. These results showed that the presented calculation method was feasible and accurate for evaluating the RCS of the target.

3. Model

When no additional sweepback angle was set, the trailing edge of the aircraft’s wing was parallel to the yz plane, as shown in Figure 5, where L_f is the length of the fuselage, as shown in

Table 1. Main dimensions of the fuselage.

Parameter	Lf (m)	Yw2 (m)	Wf1 (m)	Hv (m)	Wf2 (m)
Value	10.641	1.2	1.02	1.108	3.1

. H_v is the distance from the vertex of the vertical tail to the xy plane. W_f1 and W_f2 are the width of two parts of the fuselage. The connection between the fuselage and the wing was processed by a triangular wing root plus arc cutting, which enabled the wing to form a leading-edge transition with the delta wing when the outer wing reached the maximum sweep angle [24,25,26,27].

The trailing edge of the wing was partially cut off so that the wing could complete the sweep deformation, as shown in Figure 6, where L_w is the length of wing 1, as shown in

Table 2. Main dimensions of wing 1.

Parameter	Lw (m)	Cw1 (m)	Yw1 (m)	Rw1 (m)	Lte (m)
Value	5.3	0.49	1.2	0.35	5.006

. C_w1 is the chord length of the wing. L_te is the length of the trailing edge of the wing. R_w1 is the arc radius of the wing root. The two wings adopted the same shape design and were symmetrically distributed on both sides of the xz plane.

A high-precision unstructured grid was used to process the model surface, as shown in Figure 7, where the global minimum grid size was used to improve the overall grid quality as in

Table 3. Grid size of the aircraft.

Region	Limit (mm)	Region	Limit (mm)
Global minimum	1	Wing trailing edge	2
V-tail trailing edge	2	Wing tip edge	3
V-tail leading edge	3	Wing leading edge	3
Fuselage edge	5	Wing surface	35
V-tail surface	35	Fuselage surface	35

. For areas such as the leading edge of a wing, fuselage edge, outer end of wing, and V-shaped vertical tail, local grid technology was used to improve the grid quality.

4. Results and Discussion

Figure 8 shows the RCS of wing 1 under different radar wave frequencies, where the radar wave is horizontally polarized. It can be seen that the shapes of these three RCS curves were basically similar. The RCS mean of the curve at 6 GHz was −8.0077 dBm², as shown in

Table 4. RCS record of wing 1, where A_s = β = 0°.

Frh (GHz)	3	4	5	6	7
Mean (dBm2)	−9.3433	−8.9249	−8.4286	−8.0077	−7.5518

. With the increase in the radar wave frequency from 3 GHz to 7 GHz, the average index of RCS showed a slow increasing trend because the scattering contribution of the wing surface panels was strengthened, while diffraction from the tip and leading/trailing edges provided a small contribution [28,29,30]. These mean values reflected that the wing had a good low scattering level under the current observation conditions. To facilitate the comparison of the results, the following discussion was conducted when the radar wave frequency was set to 5 GHz.

4.1. Preliminary Analysis

Figure 9 shows that the three curves were similar in peak value and fluctuation range when the elevation angle was set to different values, where F_rv represents the radar wave frequency, and the additional subscript v represents the vertical polarization. The maximum RCS of the β = 0° curve was 7.653 dBm², which occurred at A_s1 = 17.8°, and that of the β = 5° curve was 7.888 dBm², which was also at A_s1 = 17.8°. As the elevation angle increased from 0° to 9°, as shown in

Table 5. RCS mean of wing 1, where α = 20°.

β (°)	0	3	5	7	9
Mean (dBm2)	−12.2337	−12.0511	−11.9652	−11.9023	−11.8431

, the RCS mean value decreased because the scattering intensity of the surface near the leading edge of the wing was weakened, and the contribution of the tip end face and the narrow surface of the trailing edge was also suppressed. It can be seen that with the increase in the sweep angle, the RCS of the wing as a whole showed a trend of first increasing and then decreasing, and at the same time it also showed many local fluctuations, which also implied that a change in the wing sweep angle would have a certain impact on the RCS of the aircraft.

Figure 10 presents that there were some differences in the surface scattering characteristics between the straight wing and the swept wing under the same incident wave irradiation. Due to the oval and arc design, the fuselage nose showed a large red area (about −22 dBm²). There were many red and orange areas on the surface near the leading edge of the delta wing at the junction of wing 1 and the fuselage, while the red color of the leading edge of the delta wing on the other side was lighter because the panel in these areas could more easily deflect incident electromagnetic waves to other directions. Since no additional sweep angle was set, the leading edge of wing 1 showed a lot of dark red (about −18 dBm²) and orange. The lighting area of the fuselage was mostly orange (about −58 dBm²) and yellow (about −65 dBm²). Because of the sweep angle of wing 2, the orange red of the leading edge of wing 2 was lighter than that of wing 1. These results showed that there was a difference between the scattering contribution of the wing with a sweep angle and that of the straight wing, and this difference became more complicated when the range of the statistical azimuth angle was expanded.

4.2. Results Obtained by FAM

Figure 11 indicates that there was an appropriate sweepback angle required to minimize the average RCS of the aircraft during a given phase flight. For the curve at α_n = 30°, the RCS mean of the aircraft first decreased and then increased with the increase in the wing sweep angle. When A_s = 3.2°, the mean RCS of the aircraft within the given azimuth range reached the minimum value of −1.393 dBm². Then, the RCS curve increased slowly with a small amount of fluctuation with the increase in the sweepback angle, where the mean RCS of the curve was −0.5167 dBm². With the increase in the initial azimuth during the phase flight, the shape of the RCS curve was generally similar, the mean value of the curve was significantly increased, and local fluctuations were also different, while the position of the wing sweep angle with the lowest RCS index remained unchanged. The minimum RCS of the α_n = 60° curve was 0.1316 dBm², and that of the α_n = 50° curve was −0.4412 dBm². These results showed that under the current observation conditions, different initial azimuths did not change the optimal sweepback position, while the mean level of the RCS curve was affected.

Figure 12 reveals that different elevation angles obviously affected the optimal sweep angle setting of the wing. For the case of β = 5°, the RCS curve showed large slow fluctuation in the first half, while there were many small fluctuations in the second half. When the wing sweepback angle was set at 29.6°, the average RCS of the aircraft during the phase flight reached the minimum, namely −4.436 dBm², while the minimum RCS of the β = 0° curve was −2.105 dBm², which appeared at A_s = 40°. As the angle of rise increased from 0° to 5°, the mean value of the RCS curve decreased from −1.1091 dBm² to −3.7521 dBm² because the strong scattering characteristics of the leading edge of both the wing and delta wing were greatly weakened. When β = −5°, the minimum value of the RCS curve was −4.077 dBm², where the best sweep angle was 7.4°. These results showed that when the observation azimuth range remained unchanged, the change in the elevation angle affected the optimal sweep angle of the wing.

4.3. Auto Sweep Angle

Figure 13 manifests that the optimal solution of the wing automatic sweepback scheme could be obtained by the improved search algorithm, where pop0 represents the initial population of the sweepback angle, and pop means the population that is constantly updated throughout the search process. The optimum sweep angle was determined to be 0.5932°. At this time, the aircraft showed the lowest electromagnetic scattering characteristics in the given phase flight, that is, the RCS average index was −2.8439 dBm². The distribution of these data points shows the aggregation area of multiple local peaks and local minima. The initial population was randomly generated, while the aggregation area of the updated population covered several local minima and showed a tendency to approach A_ss. The RCS of several individuals in the population exceeded −2.08 dBm², which was also a reflection of the gathering region near the maximum peak. These results showed that the established auto sweep scheme was feasible to determine the sweepback angle of the wing in the phase flight.

Figure 14 provides that the RCS curve of the optimal individual was below the initial individual curve at most azimuths, where the red solid line represents the RCS result of an individual in the initial population. Within the azimuth angle of 85.25°~91.5°, the RCS of the curve with A_s = 29.98° was slightly smaller than that of the curve with A_ss, which showed that the curve with A_ss did not show an absolute advantage at all the given azimuths. In the range of azimuth of 116°~123.8°, the RCS value of the A_s curve was obviously larger than that of the A_ss curve, where at α = 119.8°, the RCS of the red line reached 5.218 dBm², while that of the other line was −1.262 dBm², which was because the sweepback angle of A_s = 29.98° made the end face of a wing tip almost perpendicular to the incident wave, resulting in a greatly enhanced specular scattering contribution of the facets on this end face. In the range of azimuth of 126.5°~146.3°, the blue line was basically above the red line. When the observation azimuth reached the maximum value, the RCS of the A_s curve also reached the maximum of 8.0137 dBm², while the maximum of the A_ss curve was 5.883 dBm², appearing at α = 90.25° because, at this time, the outer end of wing 1 and the side of fuselage of the aircraft under the A_ss setting provided a greater scattering contribution. These results indicated that the variant UAV under the auto sweep scheme could exhibit a lower RCS mean level.

Figure 15 presents that the auto sweep scheme changed when the given phase flight changed. Under the current observation conditions, the radar station was located in front of the aircraft at the beginning, and the initial population was distributed discretely in the swept-back range. As the aircraft arrived at the end observation angle, more and more population individuals constantly searched for the minimum value in the interval and covered some maximum values. When A_s = 37.1986°, the average RCS index of the aircraft reached the minimum value of −2.68 dBm², where this sweep angle was recorded as A_ss. It can be seen that some other minima also appeared in the interval near the optimal solution, while this did not affect the global detection ability of the search algorithm. These results showed that the established automatic sweepback scheme was feasible for determining the optimal sweepback angle of the aircraft in different observation ranges.

4.4. Comparison of Optimal Solutions

Figure 16 indicates that the optimal solution of the wing sweep angle obtained by the two methods was consistent under the current observation conditions. The blue solid line of FAM was drawn by connecting evenly distributed data points in sequence, which could well reflect the trend change in the ordinate value with the abscissa, where the optimal solution of the sweep angle was 30.6°, and the corresponding RCS indicator was −1.2586 dBm². For the results of the auto sweep scheme, the RCS indicator was −1.2593 dBm² when the optimal solution was obtained, where A_ss = 30.4401°. For the initial population, the sweepback angle of some individuals was 5.235°, 6.967°, and 16.03°. As the number of generations increased, new individuals gradually moved closer to areas with more minima, where many new individuals appeared near the sweepback angles of 21.56°, 24.34°, 31.33°, and 35.86°. Therefore, the RCS level of the population was rapidly reduced to below −1.019 dBm². In order to improve the accuracy of the optimization solution, FAM relies on smaller data intervals, which also means that more operation space is required. For more information on the comparison of the wing sweep search results, please refer to the analysis and discussion in Appendix A. The improved search algorithm could randomly generate high-precision initial individuals within a given range and had more effective global and local search capabilities. On the basis of these two methods, the optimal solution of the automatic sweepback scheme was generated.

Figure 17 manifests that the A_ss curve had more and smaller local minima compared with the other two curves. When the azimuth angle increased from 80° to 86.25°, the local maxima of the three curves were similar. At α_n = 86°, the RCS of the A_ss curve dropped to the minimum value of −24.8263 dBm², and that of the A_s = 17.79° curve was −13.25 dBm². In the range of azimuth of 100.3°~103.8°, the RCS of the A_s = 11.37° curve was significantly higher than that of the other two curves because the side of the fuselage, the leading edge of the delta wing, and the outer end face of wing 1 provided more scattering contributions. When α_n = 106°, the RCS of the A_ss curve was −22.4 dBm², where the scattering intensity of the surface near the leading edge of wing 1 was effectively weakened. These results showed that the RCS curve of the aircraft under the automatic sweepback scheme performed satisfactorily in terms of the mean and minimum values.

Figure 18 presents that the low scattering intensity area of the aircraft under the automatic sweepback scheme had a lower scattering level compared with the example. For the case at α = 103° where A_s = 11.37°, the side lighting area of the fuselage nose showed more red (about −28 dBm²) and orange (about −35 dBm²). There were many orange and yellow (about −58 dBm²) areas on the vertical tail and side of the fuselage. The surface near the leading edge of the delta wing had more yellow, while the upper surface of the trailing edge of the delta wing had less green (about −82 dBm²). The leading edge and trailing edge of the wing showed low scattering characteristics, but the tip end face of wing 1 was red because this end face could not effectively deflect the incoming electromagnetic waves to the non-threat direction.

For the case where α = 86°, the aircraft adopted the automatic sweepback scheme. The low scattering area of the whole aircraft surface was dark blue (about −152 dBm²). Although the azimuth changed, there were still many strong scattering sources on the fuselage and vertical tail surfaces. As the azimuth decreased, the upper orange surface of the leading edge of the delta wing increased slightly, while the upper surface of trailing edge turned blue and dark blue. Under the combined action of the wing sweep angle and azimuth angle, the upper surface near the leading edge of wing 1 appeared to have some yellow and a little orange (about −62 dBm²). A small amount of orange-red appeared at the joint of wing 1 and the delta wing. It is worth noting that the end face of the tip of wing 1 turned orange. These results showed that the scattering contribution of the wing was lower than that of the fuselage, while the influence of the mean value caused by the change in the sweepback angle cannot be ignored.

5. Conclusions

The auto sweep scheme was established to calculate the RCS of an aircraft under different sweepback angles and determine the optimal sweepback angle in a phase flight. The electromagnetic scattering characteristics of this UAV were analyzed, and the RCS mean in the phase flight was obtained. Based on these investigations and discussions, the following conclusions could be drawn:

(1)

This aircraft had a low electromagnetic scattering level, and its average RCS slowly increased with the increase in the radar wave frequency in the given range. The average RCS of the wing in the phase flight slowly increased with the increase in the elevation angle within the given range.

(2)

When the observation plane was horizontal and the terminal azimuth was 90°, increasing the initial azimuth did not change the optimal sweepback angle of the aircraft under the given conditions, while when the observation initial azimuth angle was 90°, the increase in the elevation angle affected the optimal sweepback angle of the aircraft under the given conditions.

(3)

The auto sweep scheme could effectively capture the minimum sweepback angle of the aircraft in the phase flight while reducing the mean and some minima of the aircraft RCS indicator curve, thus making the aircraft show a lower electromagnetic scattering level under different observation conditions.