A configuration carrier frequency joint optimization method for improving main lobe jamming resistance performance of distributed radar

Abstract

The application discloses a kind of based on anti main lobe interference performance's heterogeneous distributed radar configuration carrier frequency joint optimization method, technical scheme contains the following steps: step one, distributed radar anti-interference scene modeling and optimization problem construction;Step two, optimal configuration design algorithm based on PSO algorithm;Step three, based on the sub-pulse frequency point design algorithm of minimizing PGLL.The optimal distributed radar deployment strategy and sub-pulse frequency point design under the condition of the inconsistent gain of main and auxiliary radars and the fewer number of nodes can be obtained, so that the distributed radar can obtain the optimal output signal-to-noise ratio in a certain sub-pulse when interference occurs at any angle within the main lobe.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar configuration optimization, and relates to a configuration carrier frequency joint optimization method for improving the main lobe interference resistance performance of a distributed radar. BACKGROUND

[0002] In modern battlefield, the intensity of electronic countermeasures is increasing day by day, and the interference threat faced by the radar is becoming more and more serious. From the spatial distribution, the radar interference can be divided into side lobe interference and main lobe interference. For the side lobe interference, the traditional array radar can realize effective suppression of the interference through adaptive beam forming technology or side lobe canceller. However, when the jammer and the target are located in the main lobe of the radar at the same time to form the main lobe interference, the energy of the interference signal is higher after being modulated by the main lobe gain, and the radar cannot suppress the interference while retaining the target signal due to the limitation of angle resolution, which will seriously limit the target detection ability of the radar.

[0003] The distributed array radar deploys multiple node radars on a long baseline to obtain extremely high angle resolution. When resisting the main lobe interference, it can form an extremely narrow null to suppress the interference signal while retaining the energy of the target signal. In the practical application of the distributed array radar, considering the cost and convenience, the current distributed radar anti-interference mainly adopts the main auxiliary joint distributed radar system, which deploys a main radar that can transmit and receive signals and a small number of auxiliary radars that can only receive signals on a long baseline. The existing researches on the anti-interference problem of the distributed array radar mainly focus on the design of anti-interference algorithm.

[0004] Due to the sparse deployment of the distributed array radar on a long baseline, the grating lobe problem cannot be avoided. The existing researches mainly consider optimizing the node positions to reduce the influence of the grating lobe, and usually consider dozens or even hundreds of nodes. However, the few nodes and long baseline of the one-main-multiple-auxiliary distributed array radar make it insufficient to reduce the grating lobe level only by changing the node positions. SUMMARY

[0005] Therefore, the application provides a heterogeneous distributed radar configuration carrier frequency joint optimization method based on the main lobe interference resistance performance. Not only the node positions are optimized, but also multiple sub-pulses of different frequencies are designed, so that the distributed radar can obtain the optimal output signal-to-noise ratio in a certain sub-pulse when the interference occurs at any angle in the main lobe. Compared with the scheme of only optimizing the radar node positions, the application has obvious advantages in improving the main lobe interference resistance performance.

[0006] The configuration carrier frequency joint optimization method for improving the main lobe interference resistance performance of the distributed radar specifically includes the following steps:

[0007] Step 1, modeling of the anti-interference scene of the distributed radar and construction of the optimization problem;

[0008] Step two, optimal configuration design algorithm based on PSO algorithm;

[0009] Step three, sub-pulse frequency point design algorithm based on minimizing PGLL;

[0010] Step one includes the following sub-steps:

[0011] (1) Distributed radar anti-jamming scene modeling;

[0012] (2) Configuration carrier frequency joint optimization problem construction;

[0013] Step two includes the following sub-steps:

[0014] (1) Particle swarm initialization based on distance constraint and main and auxiliary heterogeneous;

[0015] (2) Fitness calculation based on multi-carrier frequency projection;

[0016] (3) Particle swarm projection based on distance constraint;

[0017] (4) Particle motion and velocity update;

[0018] (5) Improved particle swarm algorithm based on multiple initialization.

[0019] Further, the optimization function in step one for projecting the frequency point change range to a single frequency point is:

[0020]

[0021] In the formula, Φ is the angle range to be optimized, according to the principle of distributed radar anti-main lobe interference, the range is within the main lobe of the main radar, and outside the main lobe of the full array; Since the positions of each subarray of the main radar are determined by the center position of the main radar, the actual number of nodes to be optimized is M'+1; In practice, due to the constraints of radar volume and electromagnetic compatibility requirements, the minimum distance between nodes needs to be greater than d c , and the array baseline length is l.

[0022] Further, in step two, the particle swarm optimization (PSO) algorithm is used to solve the optimization problem, and the sub-pulse frequency point is selected by gradually optimizing the PGLL. The position of the main radar is considered as a separate parameter for optimization.

[0023] Further, in step two, the angle range to be optimized is the angle range within the main lobe of the main radar and outside the main lobe of the full array; In the optimization process, only the center position of the main radar is considered, and the main radar is expanded to multiple subarrays only when calculating the fitness.

[0024] Furthermore, the method for projecting the particles before and after the motion in step two is as follows:

[0025] Project d onto x before the motion.

[0026] d = [d1, d2, ..., d M′+1 ]

[0027] =[0,x2+d c ,…,x i +(i-1)d c ,…,l]

[0028] =x+D c

[0029] in:

[0030] x = [0, x2, ..., x] i ,…,l] 0≤x2…≤x i …≤x M′ ≤l-(M′+1)d c

[0031] D c =[0,d c ,…,(i-1)d c ,…,0]

[0032] After the particles move, the sorted x and D are then compared. c After summing, the particles are projected onto d to ensure that they always satisfy the spacing constraint.

[0033] Furthermore, the velocity update formula for the particle swarm optimization algorithm in step two is as follows:

[0034]

[0035] In the formula x Iopt For the current best solution in the particle's history, x Gopt This is the current globally optimal solution; x i k For the current particle, ω represents the current velocity of the particle. v c1 is the inertia coefficient, which can vary within a certain range as the iteration progresses; c2 is the individual learning factor, used to adjust the influence of the particle's historical optimal solution on the particle's motion direction; c3 is the global learning factor, used to adjust the influence of the current global optimal solution on the particle's motion direction; r1 and r2 are individual learning and global learning random numbers, which increase the randomness of the search process to a certain extent. This represents the updated particle velocity.

[0036] Further, in step two, in order to reduce the poor fitness of the initialized particles and make the algorithm fall into a local optimal solution, the optimal particle is reserved and the particle swarm is reinitialized after every 100 iterations, so as to obtain a better optimization effect.

[0037] Further, in step three, the strategy of gradually optimizing the frequency points of the sub-pulse is as follows: if there is a frequency point in the frequency range that can reduce the PGLL, the frequency point is added to the current frequency point set.

[0038] Further, the response of the cost function at each angle in step three is the minimum value of the response of each frequency point, which is expressed as:

[0039] L(θ j )=minL n (θ j )

[0040]

[0041] In the formula, f n is the nth frequency point, L n is the cost function value under the nth frequency point, L is the overall cost function value after integrating the minimum cost function values of each frequency point, d Gopt is the optimal configuration obtained by the particle swarm algorithm.

[0042] Beneficial effects:

[0043] 1. The present application introduces the frequency as a new "increment" into the distributed array radar to improve the anti-interference performance by using multiple sub-pulses with different frequencies on the basis of the design of the node position of the distributed array radar.

[0044] 2. The present application proposes a new optimization function and optimization architecture for the inconsistent main and auxiliary gains, radar spacing and other constraint conditions, and realizes the optimization of the radar position considering the frequency change of the sub-pulse through the PSO algorithm with constraints.

[0045] 3. The present application proposes a gradual optimization strategy of the frequency points of the sub-pulse in the case of the existing optimized array configuration, which effectively reduces the optimization dimension. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a schematic diagram of a distributed array radar;

[0047] Figure 2 is a schematic diagram of multi-carrier frequency interference suppression processing;

[0048] Figure 3 is a schematic diagram of carrier frequency item scaling;

[0049] Figure 4 is a schematic diagram of particle generation with constraints;

[0050] Figure 5 Upper and lower bounds of angle spread caused by frequency variation;

[0051] Figure 6 Optimized configuration;

[0052] Figure 7 Cost function values at different frequencies;

[0053] Figure 8 Multi-frequency joint optimization result;

[0054] Figure 9 PGLL comparison;

[0055] Figure 10 Comparison of main lobe interference suppression performance. DETAILED DESCRIPTION

[0056] In order to facilitate the understanding of the present application, the specific embodiments of the present application are further described in detail below in combination with the drawings and embodiments. The following embodiments are used to illustrate the present application, but are not used to limit the scope of the present application. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive.

[0057] A configuration carrier frequency joint optimization method for improving the main lobe interference suppression performance of a distributed radar specifically comprises the following steps:

[0058] Step one, distributed radar anti-jamming scene modeling and optimization problem construction

[0059] (1) Distributed radar anti-jamming scene modeling

[0060] In view of the problem that the antenna gain of a low-cost receiving auxiliary radar is inconsistent with that of a main radar, the main radar is split into multiple sub-arrays with the same gain as the auxiliary radar and uniformly distributed in the present application, which is convenient for subsequent modeling. In the present application, the distributed array radar is only used for main lobe interference suppression, so even if the distance between the split sub-arrays is greater than half a wavelength, it does not affect the modeling of signals only in the main lobe angle range. The distributed array radar is shown in Figure 1 .

[0061] Since the ground-based distributed array radar can usually only improve the angle resolution in the azimuth direction to resist main lobe interference, it is usually a one-dimensional array. Considering the full array echo of a single interference scene:

[0062] s(t)=a(θ0)s0(t)+a(θ j )s j (t)+N(t) (1)

[0063] In the formula, a(θ0), a(θ j) are the K-dimensional steering vectors of target and jammer respectively, K is the total number of array channels (the number of main radar subarray + the number of auxiliary radar). Wherein the number of main radar subarray is M, the number of auxiliary radar is M', the gain of each channel is consistent. s0(t), s j (t) are the complex envelopes of target and jammer respectively, N(t) is the noise matrix.

[0064] Assuming that the jammer + noise covariance matrix R can be obtained, the optimal weight vector form for anti-jamming is:

[0065]

[0066] The output signal-to-noise ratio obtained by the weight vector is:

[0067]

[0068] In the formula:

[0069]

[0070] According to the Sherman-Morrison formula: It can be obtained

[0071]

[0072] In the formula ε j is the single-channel jammer-to-noise power ratio

[0073] Put into the equation of the output signal-to-noise ratio:

[0074]

[0075] In the formula ε s is the target signal-to-noise power ratio.

[0076] When the jammer-to-noise ratio is large enough, the above formula can be simplified as:

[0077]

[0078] From the above formula, it can be seen that the parameter that determines the output signal-to-noise ratio is the inner product of the target signal and the jammer steering vector, which represents the correlation of the target and the jammer in space.

[0079] And the distributed array radar is distributed in a longer baseline with fewer nodes, which inevitably produces the problem of grating lobes. When the jammer is located at the grating lobe position of the target angle, the steering vectors of the target direction and the jammer direction are highly correlated. According to formula (7), a grating null will be formed at the target at this time, causing the output signal-to-noise ratio loss.

[0080] It can be seen that when the target angle is fixed, the output signal-to-noise ratio after interference suppression is positively correlated with the gain of the direction pattern at the interference angle. Therefore, to obtain a higher output signal-to-noise ratio, it is necessary to lower the peak grating lobe level (PGLL) of the full array direction pattern as much as possible.

[0081] (2) Configuration and carrier frequency joint optimization problem construction

[0082] |a(θ j )a H (θ0)| 2 which can be expanded as:

[0083]

[0084] In the formula, the value of the inner product of the steering vector is related to the target angle, the interference angle, the array configuration, and the carrier frequency. A reasonable carrier frequency can avoid interference at the grating lobe position of the target. The array configuration (related to d i ) and the signal carrier frequency (related to f) can be optimized to make the output signal-to-noise ratio of the target at the angle θ j reach the theoretical optimum, that is, the following optimization problem is considered:

[0085]

[0086] However, in practice, the angle relationship between the interference and the target cannot be directly obtained, so the main radar transmits a series of sub-pulses with different carrier frequencies, so that the desired output signal-to-noise ratio can be obtained in a certain sub-pulse.

[0087] Therefore, the optimization target is considered to be located at any angle within the main lobe of the interference, and multiple carrier frequencies are used to make the cost function value at any interference angle be smaller under a certain carrier frequency. As Figure 2 shown.

[0088] According to formula (8), if the radar uses multiple carrier frequencies for interference suppression, it is equivalent to changing the carrier frequency term f to scale the angle term sinθ j -sinθ0, so the effect of carrier frequency change on the beam direction pattern can be equivalent to scaling in the angle dimension, as Figure 3 shown.

[0089] In the figure, the response of a certain distributed radar at other angles when the beam is directed at 0° under two different carrier frequencies. It can be observed that switching different carrier frequencies is equivalent to translating in the angle dimension. Since the change of sinθ j -sinθ0 is not a linear relationship with the change of θ j -θ0, the translation amount also changes with θj The range of the angle corresponding to the carrier frequency can be calculated by formula (8) assuming the beam points to 0°. Let the center frequency be f0 and the frequency variation range be Δf.

[0090]

[0091] According to formula (10), when the carrier frequency is switched, the response at sinθ j when the frequency f0+Δf is equivalent to the response at when the frequency f0. Therefore, in the case of multiple carrier frequencies, the anti-jamming effect at a certain angle depends on the minimum value of the inner product of the steering vector in the range of the surrounding angle scaled by the multiple carrier frequencies.

[0092]

[0093] In formula, Φ is the angle range to be optimized, which is within the main lobe of the main radar and outside the main lobe of the full array according to the principle of anti-main lobe jamming of the distributed radar. Since the positions of the sub-arrays of the main radar are determined by the center position of the main radar, the actual number of nodes to be optimized is M'+1. In practice, due to the constraints of the radar volume and electromagnetic compatibility, the minimum distance between the nodes needs to be greater than d c , and the array baseline length is l.

[0094] In addition, according to formula (8), assuming that the azimuth angle of the target relative to the baseline increases, the beam points to the target. In the case where the angle between the target and the jammer is constant, the value of sinθ j -sinθ0 gradually decreases as θ0 increases, which is also reflected in the response of the cost function, which is still an inflation. After optimization, the PGLL for the target located at 0° is still the PGLL for the target located at other azimuth angles, so only the case where the target is located at 0° needs to be optimized.

[0095] The present application considers a main multi-auxiliary distributed array radar system, which transmits signals by the main radar and receives signals by all node radars of the full array. The system parameters are as follows

[0096]

[0097] The algorithm parameters are as follows

[0098]

[0099] Step two, optimal configuration design algorithm based on PSO algorithm

[0100] Obviously, the optimization problem of formula (11) is non-convex. In view of the algorithm convergence speed and the like, the present application adopts a particle swarm optimization (PSO) to solve the optimization problem of formula (11). Then, a strategy of step-by-step optimization of PGLL is adopted to select a sub-pulse frequency point.

[0101] (1) Particle swarm initialization based on distance constraint and primary-secondary heterogeneous

[0102] In order to consider the node heterogeneity problem, the position of the primary radar needs to be optimized as a separate parameter. Therefore, when initializing the particles, the present application considers generating with the primary radar as the origin, as shown in FIG. 1, wherein the black dot is the primary radar and the white dot is the auxiliary radar. Figure 4

[0103] The baseline length l and the minimum distance d c between nodes are constraints. The primary radar is located at the origin 0, the left node is generated randomly, and the left node can be generated in the range of l-2d c . When the left node is generated, the right node can be determined according to the baseline length constraint l. In order to strictly ensure that the distance between nodes is greater than d c , the remaining nodes need to be generated in the range of l-(M'+1)d c , and adjusted according to the specific position. After the particle swarm is generated, all particles are translated so that the left end point of all configurations is located at 0 and the right end point is located at l.

[0104] (2) Fitness calculation based on multi-carrier frequency projection

[0105] Due to the symmetry of the antenna pattern, only half of the angle range needs to be calculated. And the present application mainly aims at the main lobe interference, and only needs to consider the angle range within the main lobe range of the primary radar. Therefore, the angle range to be optimized is the angle range within the main lobe range of the primary radar, outside the main lobe of the full array.

[0106] According to the multi-carrier frequency projection method in the last section, the angle range corresponding to the carrier frequency range is calculated. In some parameter cases, the angle expansion range is as shown in FIG. 2. Figure 5

[0107] In the optimization process, only the center position of the primary radar is considered, and the primary radar is expanded into multiple sub-arrays only when calculating the fitness.

[0108] (3) Particle swarm projection based on distance constraint

[0109] ​​The initial created particles are strictly constrained, so that the distance constraint condition in the optimization problem can be met. However, in order to ensure that the constraint is still met during the movement of the particles, the original particles need to be pre-processed. We project the particles before and after movement in the following way: before movement, project d to x, as shown in equation 13.

[0110]

[0111] wherein:

[0112] x = [0, x2, …, x i …, l] 0≤x2…≤x i …≤x M′ ≤l-(M′+1)d c (13)

[0113] D c = [0, d c …, (i-1)d c …, 0] (14)

[0114] After the movement of the particles, the sorted x and D c are summed and projected to d, so that the particles always meet the distance constraint.

[0115] (4) Particle movement and velocity update

[0116] The velocity update formula of the particle swarm algorithm is as follows:

[0117]

[0118] wherein x Iopt is the historical optimal solution of the current particle, x Gopt is the current global optimal solution; x i k is the current particle, is the velocity of the current particle; ω v is the inertia coefficient, which can vary within a certain range during the iteration process; c1 is the individual learning factor, which is used to adjust the influence of the historical optimal solution of the particle on the movement direction of the particle; c2 is the global learning factor, which is used to adjust the influence of the current global optimal solution on the movement direction of the particle; r1 and r2 are individual learning and global learning random numbers, which increase the randomness of the search process to a certain extent; is the updated particle velocity.

[0119] It should be noted that, due to the inconsistency of the power and aperture of the main radar and other radars, the main radar needs to be moved as a separate item.

[0120] (5) Improved particle swarm algorithm based on multiple initialization

[0121] To reduce the poor fitness of initialization particles and make the algorithm fall into local optimal solution, only the optimal particle is reserved and the particle swarm is reinitialized after every 100 iterations to obtain better optimization effect.

[0122] According to the PSO optimal configuration solving method based on frequency range projection provided in the application, the optimal configuration is obtained according to formula (11) and the system parameters and algorithm parameters in step one, as shown in the following table and Figure 6 .

[0123]

[0124] Step three, sub-pulse frequency point design algorithm based on minimum PGLL

[0125] After the configuration is optimized by the above algorithm, the deployment positions of each node radar are obtained. Although the sub-pulse frequency variation range is coupled into the optimization function, in practice, considering the real-time requirement, the number of sub-pulses should be limited. The specific frequency points of the sub-pulses need to be further obtained according to the configuration optimization result.

[0126] According to the multi-sub-pulse anti-interference scheme provided in the application, the response of the cost function at each angle is the minimum value of the response of each frequency point, as shown in formula (16).

[0127]

[0128] In the formula, f n is the nth frequency point, L n is the cost function value under the nth frequency point, L is the overall cost function value after integrating the minimum cost function values of each frequency point, d Gopt is the optimal configuration obtained by the particle swarm algorithm.

[0129] Therefore, for any frequency point set U, the PGLL after adding a new frequency point is less than or equal to the original PGLL. The application considers a step-by-step sub-pulse frequency point design scheme, that is, the cost function response under the current frequency point set is calculated, the angle at which the PGLL is obtained, a new frequency point is searched in the frequency range to make the cost function response at this angle minimum, and the new frequency point is added to the original frequency point set. Repeat this process until the PGLL value approaches the upper bound of the PSO optimization result or reaches the upper limit of the number of sub-pulses. When initializing the frequency point set U, the maximum frequency point or the minimum frequency point is preferentially added to improve the algorithm efficiency.

[0130] The radar position optimization result is brought into the sub-pulse frequency point design algorithm, and the cost function values of each frequency point in the angle range are obtained as shown in formula (17), and the optimized sub-pulse frequency points are shown in the following table. Figure 7 .

[0131]

[0132] After the algorithm processing, in the current configuration, only 6 frequency points have made the PGLL reach the upper limit of the optimization result. Adding additional sub-pulses will not further reduce the fitness. At this time, the main lobe in the cost function value after integrating the configuration optimization result and the sub-pulse frequency point optimization result is as shown in Figure 8 Figure 9

[0133] A target signal of about 19dB and a noise suppression type interference of 40dB are constructed, the target is always located at 0°, and the angle of the interference signal changes between 0-1.5°. The weights are calculated by using two beam forming algorithms (MVDR and MMSE) to obtain the main lobe interference suppression, and the output signal-to-noise ratio is as shown in Figure 10

[0134] Figure 10 The results show that the configuration carrier frequency joint optimization method has obvious performance benefits in the anti-main lobe interference, and the output signal-to-noise ratio is improved as a whole compared with the scheme of optimizing only the node position. When using the MVDR algorithm, the worst output signal-to-noise ratio is improved by more than 2.8dB; and when using the MMSE algorithm, the worst output signal-to-noise ratio is improved by 5.4dB.

[0135] In summary, the above is only an embodiment of the present application, and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.​​​

Claims

1. A method for joint optimization of carrier frequency based on anti-mainlobe interference performance of heterogeneous distributed radar configuration, characterized in that, The method comprises the following steps: Step one, distributed radar anti-jamming scene modeling and optimization problem construction; Step two, optimal configuration design algorithm based on PSO algorithm; Step three, sub-pulse frequency point design algorithm based on minimum PGLL; Step one comprises the following sub-steps: (1) distributed radar anti-jamming scene modeling; (2) configuration carrier frequency joint optimization problem construction, the optimization function of the frequency point change range projection to a single frequency point is: ； ； In the formula is the angle range to be optimized, according to the principle of distributed radar anti-main lobe interference, the range is within the main lobe of the main radar, and outside the main lobe of the full array, since the positions of each subarray of the main radar are determined by the center position of the main radar, the actual number of nodes to be optimized is , is the number of auxiliary radars, is the frequency variation range, in practice, due to the constraints of radar volume and electromagnetic compatibility requirements, the minimum distance between nodes is set to , and the array baseline length is ; Step two comprises the following sub-steps: (1) Initialization of particle swarm based on distance constraint and primary-secondary heterogeneous, the position of primary radar is optimized as a single variable, the baseline length , the minimum distance between nodes is the constraint; the primary radar is located at the origin 0, the left node is generated randomly first, the left node is generated in the range of ; when the left node is generated, the right node can be determined according to the constraint of baseline length ; in order to strictly ensure that the distance between nodes is greater than , the remaining nodes need to be generated in the range of , and adjusted according to the specific position; after the generation of the particle swarm is completed, all particles are translated, so that the left end point of all configurations is located at 0, and the right end point is located at ; (2) fitness calculation based on multi-carrier frequency projection, the angle range to be optimized is the angle range within the main lobe of the main radar and outside the main lobe of the full array, in the optimization process, only the central position of the main radar is considered, and the main radar is expanded into multiple sub-arrays only when the fitness is calculated; (3) particle swarm projection based on distance constraint; (4) particle motion and velocity update; (5) improved particle swarm algorithm based on multiple initialization, in order to reduce the poor fitness of the initialized particles and make the algorithm fall into a local optimal solution, only the optimal particle is reserved and the particle swarm is reinitialized after each 100 iterations, so that better optimization effect is obtained; (6) the optimization problem is solved by using the particle swarm algorithm, and the sub-pulse frequency point is selected by using the strategy of gradually optimizing PGLL; The strategy of gradually optimizing the sub-pulse frequency point in step three is as follows: if there is a frequency point in the frequency range which can reduce PGLL, the frequency point is added to the current frequency point set; The response of the cost function at each angle is the minimum value of the response of each frequency point, which is expressed as: ； In the formula is the cost function value of the first frequency point, is the cost function value of the first frequency point, is the cost function value of the first frequency point, is the cost function value of the first frequency point, is the overall cost function value after integrating the minimum cost function of each frequency point, is the optimal configuration obtained by the particle swarm algorithm.

2. The method of claim 1, wherein the method is characterized by, The projection method of the particles before and after the motion in step two is as follows: Before exercise projected to : ； Wherein: ； ； After the particles are moved, the sorted with the distance constraint vector summed and projected to guarantee that the particles always satisfy the distance constraint.

3. The method of claim 1, wherein the method is characterized by, The velocity update formula of the particle swarm algorithm in step two is as follows: ； wherein is the current particle history best solution, is the current global best solution; is the current particle, is the current particle velocity; is the inertia coefficient, which can vary within a certain range along the iteration process; is the individual learning factor, which is used to adjust the influence of the particle history best solution on the direction of particle movement; is the global learning factor, which is used to adjust the influence of the current global best solution on the direction of particle movement; and are the individual learning and global learning random numbers, which increase the randomness of the search process to a certain extent; is the updated particle velocity.

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