Introduction
The rapid development of wind power generation has led to a large increase in the number of wind turbines. The rotating blades of wind turbines excite dynamic radar echoes with Doppler characteristics under the irradiation of radar. These echoes interfere with the radar signals and seriously affect the accuracy of radar target recognition. The most commonly used method to suppress this interference is to obtain the dynamic radar echoes and Doppler characteristics of the wind turbines, which provide a basis for the clutter filtering of radar echoes [1–4].
To obtain the radar echo of dynamic wind turbines, the most traditional method is experimental measurement [5–7]. However, this method requires a great deal of human labor and materials to construct the experimental platform, and the process of receiving radar echoes is also cumbersome. Moreover, the experiment is easily influenced by the environment, and it is hard to replicate results; consequently, experimental research is mostly used to verify the validation of simulation results [7–9]. Thus, simulation is the best option to gain dynamic radar echoes [10–13].
Given the high accuracy of traditional high-frequency electromagnetic (EM) algorithms, several strategies based on these algorithms are used to simulate dynamic radar echoes [14, 15]. Nevertheless, as wind turbines belong to the maximum electrical size target, and the radar frequency tends to be high, calculating the radar echoes of wind turbines consumes a large amount of computing resources. It is also necessary to change the blade attitude of wind turbines repeatedly to obtain the dynamic radar echoes, further increasing the calculation scale. The current EM algorithm therefore only focuses on the simulation of the dynamic radar echo from a single wind turbine [16]. Even when the simplified algorithm is used [17, 18], only the dynamic radar echo simulation of four wind turbines is possible. Therefore, finding an efficient and accurate numerical simulating algorithm to simulate the radar echoes of multiple wind turbines has become a research hotspot.
The scattering point algorithm is first used for simulating the dynamic radar echoes [11], equivalent wind turbine blades to a series of continuously linearly distributed scattering points. The dynamic radar echo equation for arbitrary scattering points is derived accordingly, eliminating the repeated attitude modeling process in the EM algorithm and greatly reducing the calculation scale. However, the model is too perfect and can only be used for qualitative analysis. The scattering points may not always be continuously distributed; therefore, Tang et al. [10, 12] proposed the scattering point spacing tactic, which discretized the distribution of scattering points and provided the best value of spacing. However, this tactic still arranged the scattering points linearly, making it difficult to simulate the impact of irregular edges on radar echoes. Consequently, an algorithm was put forward to establish the three-dimensional (3D) scattering point model [19], using triangle surface elements to divide the surface model of a wind turbine [20, 21] into a collection of triangular elements and taking the center of the triangular element as the scattering point source. In this way, the accuracy of the simulated radar echo is improved, and the curved surface of the blades is also fully considered.
Nevertheless, to guarantee the accuracy of the algorithm, this approach requires a massive number of scattering points to be extracted resulting in a significant increase in the consumption of computing resources and unacceptable calculation resource consumption when simulating radar echoes from multiple wind turbines. Hence, it is of great significance to find a way to decrease the calculation resource consumption without sacrificing much accuracy. Considering that the scattering points directly facing the radar always make a greater contribution to radar echo, we can achieve this by eliminating those parts that make less contribution to the radar echo. In the field of image classification, we found a Z-buffer algorithm [22] that can efficiently determine the parts that directly face the radar and be applied to simulate the dynamic radar echo from wind turbines.
Thus, this paper introduces the 3D scattering point model and proposes an algorithm to accelerate the simulation speed of the traditional 3D scattering point model when solving radar echoes from multiple wind turbines. The scattering points that make less contribution to radar echo are eliminated to depress the computational resource consumption of the traditional model. One to eight GW77/1500 wind turbine radar echoes and corresponding Doppler signatures are simulated to certify the accuracy and velocity of the two models. A scaling model experiment is carried out to corroborate the validity of the accelerated algorithm. The presented strategy can lead to the simplification of the 3D scattering point model and be applied to the process of estimating the radar echo of wind farms.
Methodology
1. Traditional 3D Scattering Point Model
The 3D scattering point model is just a combination of the surface model and the scattering point model. When using the surface model to solve the radar echo of a wind turbine, it is first necessary to divide the integral 3D model of the wind turbine into a series of triangular facets. Fig. 1 shows the basic principle of triangulated facet division in the surface model.
In the figure,
T k + a k , 3 + ; a k , 3 - t k + t k -
On this basis, combined with Rao–Wilton–Glisson (RWG) basis functions and the Galerkin method [26], the surface electric field integral equation is transformed into a matrix equation to obtain the corresponding scattered electric field and radar echoes. The concept of quasi-static is adopted to obtain the radar echo results of the dynamic wind turbine. Constantly changing the posture of the surface model and solving the scattered electric field results at each moment also enables the dynamic radar echo of the wind turbine to be acquired.
According to the idea of the surface model, the main source of computational resource consumption lies in the process of solving the surface-induced current and repeatedly adjusting the posture of the wind turbine. Considering the superiority of the scattering point rotation formula in dealing with the problem of wind turbine rotation, the surface model is extracted into multiple scattering points. Each triangular facet is considered the source of the scattering field, and its geometric center is extracted as the scattering point of the 3D scattering point model. Fig. 2 shows the process of constructing a 3D scattering point model using GW77/1500 as an example.
Solving the scattering field of the surface element can be simplified to calculating a scattering point instead of performing a complex surface element scattering field integral solution. Furthermore, the process of repeatedly adjusting the posture of the wind turbine can be replaced by the rotation formula of scattering points, which can greatly reduce the calculation consumption. This also enables this methodology to be used in calculating the dynamic radar echoes of a large number of wind turbines.
Fig. 3 shows the traditional 3D scattering point model constructed with the example of GW77/1500, in which (xPi,0, yPi,0, zPi,0) is the coordinates of each scattering point Pi in the initial attitude of the 3D scattering point model, and θ is the initial rotation angle of the model.
After the coordinates of all the scattering points are obtained, the relative distance RPi(t) from each scattering point to the radar at each moment can be obtained as follows:
where RPi(t) is the relative length from the i-th scattering point to the radar at moment t. xB, yB, and zB are the x, y, and z axis coordinates of the radar. xPi(t), yPi(t), and zPi(t) are the x, y, and z axis coordinates of the i-th scattering point at moment t.
The coordinates of scattering points at each moment can be obtained by multiplying the initial coordinates with the rotation matrix of the 3D space. Since the wind turbine rotates around the axis of rotation, the x-axis, the coordinates of the scattering points at any given moment can be expressed as:
where θ(t) is the angle between the wind turbine blades and the y-axis at moment t, which is the rotation angle, and θ(t)=θ0+wt. w is the rotational speed of the wind turbine, r/min. xPi,0, yPi,0, and zPi,0 are the initial x, y, and z axis coordinates of the i-th scattering points. θ0 is the initial angle between the wind turbine blades and the y-axis, which can be obtained from the initial coordinates of the scattering points.
Combined with the radar echo calculation formula of the rotation scattering point model, the radar echo Sblade(t) of the wind turbine blade can be obtained as follows [19]:
where Sblade(t) is the radar echo at moment t. N is the volume of scattering points for each wind turbine. fc is the central frequency of radar incident waves. λ is the wavelength of the incident wave.
The combination of all the scattering points at a certain moment can depict the attitude of the wind turbine model. With the formula above, the radar echoes of each scattering point can be solved, and by cumulative summation the radar echo of the wind turbine at each moment can be obtained. Finally, the dynamic radar echo of the wind turbine can be obtained by sequentially arranging the radar echo of the wind turbine at each moment in the observation time window.
This method can improve the computing speed to an acceptable range, making it possible to calculate the dynamic radar echo of each wind turbine within an hour. However, it still takes around 20 minutes to simulate the radar echo of one rotational wind turbine composed of scattering points, the number of which can ensure the required calculation accuracy.
With the increasing number of wind turbines in wind farms, even if EM coupling [18] between wind turbines is not considered, the calculation scale of dynamic radar echo will be greatly raised. Thus, it is still of great significance to accelerate the simulation speed of the traditional 3D scattering point model when solving radar echoes from multiple wind turbines.
2. Problems in the Traditional Model
As can be seen from the analysis above, after the position of scattering points is obtained, the simulation algorithm based on the 3D scattering point model assumed that the radiation field of each scattering point was the same, which is, in fact, quite different from the actual situation. The wind turbine has two sides, facing in and facing away from the radar incident wave; hence, the radiation from them is obviously not the same.
The side facing the radar incident wave can reflect more of that wave back to the radar, making the radiation intensity on that side much higher than on the side facing away from the radar incident wave. Even if the side facing away from the radar still radiates EM waves to the space around it due to the influence of induced currents, only a small amount of these waves can be received by the radar.
However, in this methodology, in the blade edge region that can reflect the irregular shape of the wind turbine blade, fewer scattered points are obtained by division, and the scattered points along the axial direction of the blade are more distributed. If this simulation algorithm is adopted, all the scattering points facing away from the radar will be included in the calculation, artificially enhancing the influence of the scattering points distributed along the axial direction on the radar echo.
This will result in the irregular surface effect of the wind turbine being weakened if there are not enough scattering points. Even if the number of scattering points increases, the echo characteristics radiated by the axial scattering points will be reinforced. Fig. 4 exhibits Doppler features from the literature [19] and reproductions obtained with their methods. The number of scattering points is 54,571 and 96,838.
As the number of scattering points increases, a curve clearly appears in the Doppler feature, which is thought to be the effect of the erratic blade [21, 27]. Furthermore, when there were enough scattering points, an extra straight flicker emerged in the root of the Doppler stroboscopic location. This is caused by the accumulation of scattering points facing away from the radar, which, in fact, is overcalculated.
3. Z-Buffer Accelerated Algorithm
The scattering points facing away from the radar contribute less to the radar echo. Taking that into consideration will lead to extra computation consumption. Finding a way to filter out the scattering points in the traditional 3D scattering point model that are facing away from the direction of the incident radar wave can improve the solution speed of the echo simulation algorithm without sacrificing much accuracy of the calculation.
In the field of image classification, we found a Z-buffer algorithm [22] that can distinguish occlusion according to the depth information of the 3D image and quickly obtain the projection view, simulating the image recognition process of the human eye. This algorithm has also been applied to shadowing determination for mesh-based physical optics analysis in [28, 29] and has been proven to have high computational efficiency.
Thus, we consider adopting the Z-buffer methodology to eliminate the scattering points that are not exposed to radar in the 3D model of the wind turbine to accelerate the traditional numerical simulation algorithm. Fig. 5 shows the main idea and process of the algorithm.
First, the 3D model is divided into a triangulated panel by 3D software, the viewing angle and pixel resolution are determined, and the projection surface is constructed. After that, each panel is sliced according to the pixel resolution to determine which pixels are covered, and the depth and color value of each slice are stored in the Z-buffer. With the data obtained, the depth of all face elements stored in each pixel can be continuously compared, and the color value of the face element with the largest depth is taken as the color value of the pixel.
During the process of comparison, the image pyramid approach is commonly used to accelerate the slicing process [30]. From the bottom to the top of the projection surface, the obtained occlusion results are continuously utilized to carry over the occlusion discrimination process of the previous layer. By increasing the depth by one layer, the pixel resolution of the depth calculation can be reduced, thereby reducing the computational scale of the depth solution. Through multiple iterative comparisons, the face element information with the largest depth at each pixel can be obtained, and the final projected image after occlusion elimination can be obtained.
4. Accelerated Scattering Point Model
However, as there is no color value information in the scattering point model of a wind turbine, it is hard to apply the Zbuffer methodology to accelerate the scattering model immediately. Considering that the main purpose of the modification is to obtain the position of all the scattering points directly facing the radar, the two-dimensional (2D) coordinates on the projection plane of the scattering points are the main information to be obtained.
The traditional Z-buffer must therefore be modified to speed up the traditional 3D scattering model of wind turbines. Fig. 6 shows the overall flowchart of the occlusion process for the 3D scattering point model of a wind turbine.
Although the process of occlusion discrimination consumes a certain number of computational resources, it can eliminate nearly half of the scattered points. When the accelerated model is used to numerically simulate the dynamic radar echo of multiple wind turbines, it can save a great number of computing resources.
As the number of wind turbines increases, the advantages of this acceleration algorithm will gradually become significant. The process of constructing the accelerated scattering point model can be divided into the following steps:
Step 1: The 3D software is used to divide the triangular surface element of the wind turbine surface model to obtain the 3D scattering point model. The Z-buffer bottom projection surface with the maximum resolution is then constructed.
Step 2: All the scattering points are labeled, and the depth from each scattering point to the projection surface is determined.
Step 3: The underlying projection surface is partitioned, and the area where the scattering point is located in the pixel units of the projection surface is determined. The pixel depth value of each partition is initialized.
Step 4: All the scattering points within the partition are traversed. If a scattering point appears at a pixel position for the first time, the information in the pixel position will update to the depth of the scattering point, and the corresponding label of the scattering point is recorded. When another scattering point is also within the range of the pixel, the depth values of the two scattering points are compared, and the label of the point with the larger depth value is selected and recorded in the Z-buffer.
Step 5: After all partitions are compared separately, the depth values corresponding to the selected labels of all partitions are compared until the deepest scattering point in each pixel unit is found.
Step 6: With the label found, the scattering points closest to the radar in each pixel unit can be found, and the corresponding projected coordinates can be calculated based on the information of the selected labels.
This algorithm mainly focuses on accelerating the calculation process of simulating the radar echoes from each wind turbine and ignores the EM coupling between different wind turbines. However, the error caused by neglecting EM coupling is within acceptable limits, and the model constructed according to this algorithm can be used as a base model for subsequent studies. Thus, it can provide some inspiration for accelerating the procedure of simulating the dynamic radar echo of a wind turbine array.
Simulation
1. Reproduction Results
We need to compare the solving speed of the traditional and accelerated models when simulating dynamic radar echoes of multiple wind turbines; however, the literature [19] has only simulated the echo of one wind turbine. Hence, the model proposed in the literature must first be reproduced to facilitate the simulation of radar echoes from multiple wind turbines.
Therefore, in this section, the traditional algorithm is recurrence. The 3D scattering model of the GW77/1500 wind turbine is constructed, and the dynamic radar echo and Doppler signature are simulated.
Because the tower is stationary, the dynamic characteristics are only related to the rotation of the blades. We only modeled the wind turbine blades when simulating radar echo to reduce the computational scale. Furthermore, considering that the parameter settings in the literature [19] are designed to correspond to experimental parameters, it is not necessary to be completely consistent. Some simulation parameters have been modified for the convenience of simulation, and the simulation parameters are set as follows.
The length of the blade is 36.5 m, the rotation speed of the blade is 20 r/min, the center frequency of the far-field radar incident wave is 1 GHz, the pulse repetition frequency is 1,000 Hz, and the observation time window is 3 seconds, this being how long it takes for a wind turbine to rotate for one cycle.
The simulation central processing unit (CPU) is the Intel Core i5-12400, the clock frequency is 2.5 GHz, and the computing memory is 16 GB. The graphics card used for accelerated computing is the Intel UHD Graphics 730.
First, the commercial simulation software Feko is used to triangulate the 3D surface model of a wind turbine with the default algorithm. The divided triangular panel parameters are obtained and imported into MATLAB for further simulation. Fig. 7 shows the repetition results of the 3D scattering point model with 96,838 scattering points, and Fig. 8 shows the corresponding time domain radar echo and Doppler signature under the new parameter setting.
Compared to the results in the literature [19], it can be seen that when the number of scattering points was increased in the time domain waveform of the radar echo, the sub-peak values of the reconstructed radar echoes are more concentrated. This is because as the number of scattering points increases, the blade shape becomes relatively more continuous, thus making the continuity of radar echo stronger.
From the Doppler waveform, it can be seen that the surface characteristics of the wind turbine are more pronounced due to the increase in the number of scattering points. In addition, the maximum Doppler frequency shift in our reproduction results is relatively smaller; this is caused by the different center frequencies of the radar in the simulation.
2. Solution Speed Comparison
To compare the solution speed of the 3D scattering points and accelerated algorithms, the 3D scattering points model recurrence in the previous section with 96,838 scattering points is used. After the occlusion discrimination, the number of scattering points decreased to 55,999, and over one third of the points were eliminated.
Consequently, the radar echoes of one to eight wind turbines are simulated with the traditional 3D scattering points and accelerated algorithms. Since our paper is only concerned with the calculated speeds, the arrangement of the wind turbines is not taken into account, and all the wind turbines are arranged in a straight line. Coordinate transformation [18] is used to realize the entire modeling of the wind turbine array, and then the corresponding radar echo is solved.
Due to the long calculation time and large number of echoes obtained, only the relationship between the number of wind turbines and calculation times is shown in Fig. 9.
The blue and red lines represent the calculation time when simulating the dynamic radar echo from one to eight wind turbines with the traditional 3D scattering point model and the model constructed with the accelerated strategy proposed in this paper, respectively.
As show in Fig. 9, the calculation time of the proposed method is initially longer than that of the traditional method. That is because when simulating the radar echoes of dynamic wind turbines, the accelerated strategy first needs to project the 3D model with the principle of occlusion discrimination, which requires a certain amount of computation.
However, our proposed model is quicker than the traditional strategy. After the number of wind turbines grows by more than three, the calculation time of our proposed solution is significantly shorter than that of the traditional algorithm: before simulating, our solution can remove a large number of scattering points that make a lower contribution to the radar echo, thereby reducing the computational scale to solve the radar echo for wind turbines.
According to the calculation, the average radar echo solution time of the traditional algorithm is around 1,125 seconds for each wind turbine, and that of our algorithm is 437.5 seconds. Our algorithm can accelerate the speed of the traditional algorithm by around 1.57 times.
3. Accuracy Verification
The previous section demonstrated that the acceleration algorithm can effectively improve the solution speed of the traditional 3D scattering point algorithm. In this section, we continue to demonstrate that our simulation algorithm can meet the accuracy requirements to simulate the dynamic radar echo of wind turbines.
Fig. 10 shows the 3D model of the wind turbines and the model obtained by the accelerated algorithm in which the coordinates of the rotation center of the wind turbines are (0, −200, 0) and (0, 200, 0). As shown in the figure, the accelerated algorithm can effectively obtain the image projection of the 3D scattering point model on the observation surface and simulate the visible scattering point results under the observation perspective. The appearance of the wind turbine is consistent with the front view of the 3D wind turbine model.
Fig. 11 shows the comparison of time-domain radar echoes under the traditional algorithm and the accelerated algorithm with normalized data. As shown in the figure, the number of peaks that occur within a cycle does not change, and the main peak also occurs at the same time. However, the normalized amplitude of the sub-peak value under the accelerated algorithm is relatively larger because the normalized amplitude is calculated with the following formula:
Since the occlusion algorithm eliminates a large number of scattering points, the radiation amplitude of the main peak in the radar echo has decreased. Hence, the maximum Sblade(t) of the radar echo decreased, making the overall normalized amplitude increase.
The error in the radar echo compared with the traditional algorithm at each moment can then be calculated with the formula:
where error(t)(%) is the percentage of error at moment t. Sblade,acc(t) and Sblade,3D(t), respectively, are the radar echo of the accelerated algorithm and the 3D scattering points algorithm at moment t.
Fig. 12 presents the comparison of the time-domain results of radar echoes and corresponding error results at each moment. The percentage error results are almost all under 10%, and the main errors occur at the moment the main peaks appear. As the occlusion methodology has eliminated a large number of unnecessary scattering points, the amplitude of the main peaks has clearly decreased. Moreover, at the tip of the blade, there are fewer scattering points initially, which makes the error at these moments larger.
Fig. 13 shows the corresponding Doppler signatures of these two methods. After the occlusion and concealment of the scattering points, the obtained Doppler features are consistent with the signature of the traditional 3D scattering point model. There are six Doppler strobes in each cycle. Their roots appear to be bending, showing that the accelerated algorithm can greatly reflect the curved surface of the wind turbine blades.
To further verify the accuracy of the proposed algorithm, we compared it with the algorithm we mentioned in the introduction, and all these algorithms were used to simulate the radar echo from a single wind turbine with the same simulation setting. The simulation results are shown in Table 1.
We select the physical optics (PO)-method of moments (MoM) algorithm [14] as an example of the expectation–maximization (EM) algorithm. The spacing of the scattering point spacing algorithm is set to 0.0004 m, making the number of scattering points consistent with the 3D scattering point model. The reference radar echo for calculating the average accuracy is obtained by the EM algorithm.
It can be seen that although the EM algorithm is thought to be the relevant accuracy method, the process of solving the EM scattering integrals of the surface elements leads to a great consumption of computational resources. The scattering point spacing model can greatly reduce the computational resources, but the average error percentage is more than 20%, which is unacceptable. Introducing the proposed model introduced reduces the average error percentage by 10%.
When the accelerated algorithm is applied, both the calculation time and average error percentage decrease, which seems to be an unusual result. However, it happened because we were using the PO-MoM algorithm to obtain the reference radar echo. During the process of solving the radar echo with this method, the occlusion process is contained in the PO algorithm. In other words, the proposed accelerated algorithm can be viewed as an application of this kind of EM algorithm to the 3D scattering point model.
Experiment
1. Scaled Model Experiment
To further verify the effectiveness of the accelerated algorithm proposed, we conducted an outdoor far-field scaled model experiment at the China Ship Research and Design Center in Wuhan, Hubei Province.
Fig. 14 shows the equipment used for the experiment, including the scaled model and the horn antenna system. Fig. 14(a) is the 1:60.7 scaled model of the widely used GW 77/1500 wind turbine. Two scaled models composed of the blades, tower, nacelle, base, and control system were used in this experiment. The blade of the model is 0.61-m long, and the surface is constructed with a nonuniform rational B-spline. The height of the tower is 1.4 m, and the control system is set in the base beneath to adjust the rotation speed.
The horn antenna system includes the horn antenna and the vector network analyzer. The horn antenna plays the role of farfield radar, which can transmit and receive EM waves at the same time. The center frequency of the incident wave from the horn antenna is 10 GHz. The equipment below the antenna is the vector network analyzer, which was used to analyze and store the receiving data from the antenna.
Fig. 15 is the platform for the experiment. The distance between the two wind turbines is around 5.6 m, and the position of the antenna lies in the perpendicular bisector of the two wind turbines. The distance between the antenna and the connection of the two wind turbines is 24.3 m. The rotation speed of these two wind turbines is 20 r/min.
2. Analysis of Measurement Result
Considering the great difficulty of filtering the clutter based on Doppler features in real wind farms, we only measure the time-domain radar echo to verify the effectiveness of the accelerated algorithm.
Fig. 16 shows the origin data received from the horn antenna system, but since the measuring time is over one cycle of rotation, the origin data need to be cut for comparison. The time-domain radar echoes obtained by the algorithm mentioned in this paper and the experiment data clipped into a rotation cycle are compared in Fig. 17. We also compared experiment results and accelerated algorithm results in the same graph in Fig. 18.
As can be seen from the figure, these three radar echoes all have six main peaks in one rotation cycle. However, the main peaks in the experimental echo do not always occur at the same time as the simulated echoes. There is a certain offset that appears at 0.5 seconds and 1 second of the echo. That may be because, in the process of the experiment, the rotation speed of the wind turbines would be affected by the ambient wind. This can cause a subtle change in the rotation speed of the wind turbines, which will affect the time at which the main peaks appear.
Moreover, the sub-peak amplitude of the experimental echo is relatively larger. This is because the actual measurement environment is not ideal, and the EM wave will gradually be weakened in the process of propagation in the medium. Hence, the normalized amplitude of the sub-peaks increases, and the fluctuation of the sub-peaks is thus enhanced. However, the waveform tendency of the sub-peaks of the experiment results is consistent with that of the accelerated algorithm.
Overall, the proposed accelerated algorithm can greatly accelerate the simulation speed while ensuring accuracy when simulating the dynamic radar echo of multiple wind turbines.
Conclusion
In this paper, the traditional Z-buffer methodology is modified to be applied to the scattering point model, and an accelerated algorithm for numerically simulating the dynamic radar echo of a wind turbine is proposed accordingly. Eliminating the scattering points that cannot be directly illuminated by the radar, which make a relatively smaller contribution to the radar echo, can reduce the calculation scale of the traditional 3D scattering points algorithm. Although the process of elimination itself takes a certain amount of calculation resources, the projected model saves a great deal of computing resources, which can be used for simulating the dynamic radar echo of multiple wind turbines.
The radar echoes of one to eight dynamic GW77/1500 wind turbines are then simulated with the proposed algorithm. The comparison of calculation times verified that the proposed method can accelerate the calculation speed by 1.57 times. The radar echoes and corresponding Doppler signatures obtained by the traditional 3D scattering point and accelerated algorithms are contrasted, taking two wind turbines as an example. The results show that except for the main peaks in the radar echo, which have an inevitable significant deviation in amplitude, the error of the other parts can be greatly controlled (below 10%). It was verified that the proposed algorithm can accelerate the simulation speed without sacrificing much computational accuracy.
An experiment with two GW77/1500 scaled models of wind turbines was also carried out to verify the effectiveness of the accelerated algorithm proposed. It was found that the radar echo obtained by the proposed algorithm can effectively meet the requirements for simulating the dynamic radar echo of multiple wind turbines, which can provide some support for the rapid simulation of the radar echo of wind farms.
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