Spacecraft swarm threat assessment method based on neural network

Abstract

This invention discloses a spacecraft swarm threat assessment method based on a neural network. The implementation steps include: constructing and training a neural network containing formation and behavioral region intentions; inputting sampled data received by sensors into the trained neural network; calculating the impulse required for the primary tracking spacecraft to complete an orbital transfer and rendezvous with the target spacecraft within the orbital transfer time, based on the Lambert orbital transfer function; and using the analytic hierarchy process (AHP) to linearly weight the formation, intentions, orbital transfer time, impulse, and the relative distance between the target spacecraft and the primary tracking spacecraft to obtain a comprehensive threat index. This invention considers more comprehensive threat factors for actively approaching spacecraft swarms, assigns weights to each threat factor using the AHP, and proactively mitigates risks based on the comprehensive assessment index.

Description

Technical Field

[0001] This invention belongs to the field of radar communication technology, and further relates to a neural network-based threat assessment method for spacecraft swarms within the field of electronic countermeasures technology. This invention can be used to assess the threat level posed by spacecraft swarms to target spacecraft. Background Technology

[0002] With the increasing frequency of human space activities, the functions of spacecraft in space have become increasingly diversified. Clusters of multiple spacecraft are becoming more flexible and rapid, thus increasing the threat posed by these clusters to target spacecraft. This necessitates more sophisticated methods for assessing the threat posed by spacecraft clusters in order to effectively counter such threats.

[0003] In their paper "Safety Analysis Method of On-orbit Spacecraft Facing Approach Threat" (Journal of Astronautics, 2020, 41(8):1084-1093), Yu Datang et al. proposed a threat assessment method for a single tracker to a target spacecraft. The implementation scheme of this method is as follows: First, construct a pulse impulse calculation model. When the single tracker and the target spacecraft are on opposite sides, the double-pulse Lambert function is used to perform a simple evaluation of the pulse required for orbital approach. Second, construct a rendezvous sampling interval calculation model. When using the Lambert function for calculation, the duration of the traversed transfer orbit is used as the rendezvous sampling interval, and it corresponds one-to-one with the pulse impulse solution set obtained. Third, construct a minimum relative distance calculation model. No matter what complex maneuver the single tracker performs, the ultimate goal is to approach the target spacecraft. Therefore, the relative distance between the two will inevitably decrease. The smaller the relative distance, the greater the threat. Fourth, build a multi-index weighted comprehensive evaluation and decision-making model. The comprehensive evaluation value of the whole scheme can be obtained by multiplying the evaluation values ​​of each index with the corresponding index weights and summing them. The drawback of this method is that, in actual space operations, tracking spacecraft composed of clusters are more flexible, with varied formations and behaviors, and carry more information. Using a single tracking spacecraft makes it difficult to conduct a more comprehensive threat assessment of the current complex and ever-changing space situation.

[0004] In their paper "Threat Analysis Method for Active Approach Spacecraft" (Modern Defense Technology, 2022, 50(6):11-18), Wu Lijun et al. proposed a threat index calculation model to estimate the threat level of a tracking spacecraft to a target spacecraft. The implementation scheme of this method is as follows: First, a security analysis architecture analysis is performed. Under the premise of precise orbit determination of the target spacecraft and the non-cooperative approaching spacecraft with maneuverability (hereinafter referred to as the tracker), the mission mode of the tracking spacecraft is analyzed, and the pulse impulse and time required for rendezvous are obtained using the double-pulse Lambert function as threat elements. Second, after the threat elements are extracted, the pulse impulse and rendezvous time are standardized to give a threat index calculation model. Third, the most threatening approach route is selected to weight the threat elements. The weight coefficients of pulse impulse and rendezvous time are set to 0.6 and 0.4, respectively, and the comprehensive threat index is calculated. The drawback of this method is that it uses fixed values ​​to directly assign threat index weights to pulse impulse and rendezvous time. When the space environment in which the spacecraft cluster is located changes, it cannot reflect the impact of the space environment on the threat pulse impulse and rendezvous time weights of the target spacecraft in a timely manner. As a result, the comprehensive threat index cannot predict the threat of the spacecraft cluster in advance and thus misses the risks. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by proposing a spacecraft swarm threat assessment method based on neural networks. This method solves the problem that swarm tracking spacecraft cannot perform threat assessments on target spacecraft, and addresses the risk omission caused by ignoring the weighting of the space environment's threat impulse and rendezvous time on target spacecraft.

[0006] The approach to achieving the objective of this invention is to simulate the flight trajectory of each spacecraft in a spacecraft swarm formation, determine the primary tracking spacecraft and the target spacecraft in the swarm, generate feature tensors corresponding to each behavioral region, label the feature tensors corresponding to each behavioral region with the corresponding formation and intent, form a training set with all feature tensors and their labels, input the data received by the sensors into a neural network and the Lambert orbital transfer function respectively, and obtain four threat elements: formation, intent, impulse, and orbital transfer time. The relative distance between the target spacecraft and the primary tracking spacecraft is taken as a fifth threat element. The weights of the five threat elements are calculated using the analytic hierarchy process (AHP), and the weights of all threat elements are weighted with the normalized index value to obtain a comprehensive threat index.

[0007] The specific steps for implementing this invention include the following:

[0008] Step 1: Generate a training set that includes formation and behavioral region intentions;

[0009] Step 2: Build and train the neural network, update the network parameters using the training set, and obtain the trained neural network;

[0010] Step 3: Input the sampled data received by the sensor into the trained neural network to obtain two threat elements: formation and intent.

[0011] Step 4: Based on the Lambert orbital transfer function, calculate the pulse impulse required for the primary tracking spacecraft to complete the orbital transfer and rendezvous with the target spacecraft at each sampling point within each behavior region in each formation, thus obtaining the two threat factors: orbital transfer time and pulse impulse.

[0012] Step 5: Using the analytic hierarchy process (AHP), calculate the weights of formation, intent, orbital transfer time, impulse, and the relative distance between the target spacecraft and the primary tracking spacecraft at each sampling point for each threat element.

[0013] Step 6: Weight all threat elements by normalized index values ​​to obtain the comprehensive threat index.

[0014] Compared with existing technologies, the present invention has the following advantages:

[0015] First, this invention introduces the concept of a cluster based on a single tracking spacecraft. By forming a cluster of tracking spacecraft, it overcomes the shortcomings of existing technologies in assessing the threat of non-cooperative cluster trackers to target spacecraft in complex and ever-changing spaces. By separately assessing the threat of different formations and behaviors of the spacecraft cluster, it overcomes the shortcomings of existing technologies in ensuring the on-orbit safety of target spacecraft under different space situations. This invention enables the assessment of the threat level of target spacecraft by clusters of multiple tracking spacecraft in different formations and with different intentions.

[0016] Secondly, this invention introduces a neural network. By training the cluster of target spacecraft and tracking spacecraft with a model of formation and intent, it overcomes the data imbalance caused by directly setting the six orbital parameters of the spacecraft in the prior art. This makes the neural network constructed by this invention have good generalization ability. In scenarios with different six orbital parameters, this invention can make accurate predictions about the cluster of target spacecraft and tracking spacecraft to be detected.

[0017] Third, this invention uses the analytic hierarchy process (AHP) to calculate the weights of each threat element, overcoming the shortcomings of existing technologies that directly assign weights using fixed values ​​and cannot directly reflect the impact of the space environment on the weights of different threat elements. This invention has the advantage of being able to quantitatively analyze different threat elements under different space environments, thereby comprehensively considering the impact of the weights of threat elements on the comprehensive threat index. Attached Figure Description

[0018] Figure 1 This is a flowchart of an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the formation of various spacecraft clusters in the embodiments of the present invention;

[0020] Figure 3 This is a comprehensive threat index diagram of the formations of various spacecraft clusters in each behavioral area in embodiments of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0022] Reference Figure 1 The specific implementation steps of the embodiments of the present invention will be described in further detail below.

[0023] Step 1: Generate a test set and a training set that include formation and behavioral region intentions.

[0024] Step 1.1: Simulate the flight trajectory of each spacecraft in the spacecraft swarm formation to determine the primary tracking spacecraft and the target spacecraft in the swarm. Extract the position and velocity data of each spacecraft in the x, y, and z directions for each behavioral region in each simulated trajectory diagram.

[0025] The primary tracking spacecraft and target spacecraft in each formation determined in this embodiment of the invention, as well as the extracted data for each behavioral region, are shown in Table 1:

[0026] Table 1. Summary of data extracted from each behavioral region by the primary tracking spacecraft and the target spacecraft.

[0027]

[0028] Step 1.2: Using the position and velocity coordinates of each spacecraft in the x, y, and z directions extracted from each behavior region, calculate the relative distance between the target spacecraft and the main tracking spacecraft at each sampling point in each behavior region for each formation.

[0029] The relative distance between the target spacecraft and the main tracking spacecraft is calculated using the following formula:

[0030]

[0031] in, These represent the positions of the primary tracking spacecraft and the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation, respectively. Let represent the coordinates of the main tracking spacecraft located at the l-th sampling point within the j-th behavior region of the i-th formation. Let represent the coordinates of the location at the l-th sampling point within the j-th behavior region of the i-th formation of the target spacecraft. Let t represent the relative distance between the target spacecraft and the primary tracking spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation, i = 1, 2, 3, 4, 5, j = 1, 2, 3, l = 1, 2, ..., N, where N represents the total number of sampling points within the j-th behavior region of the i-th formation, and t represents the primary tracking spacecraft. * Indicates the target spacecraft.

[0032] In this embodiment of the invention, five formations were selected: column formation, lower triangle formation, upper triangle formation, horizontal formation, and circling formation. Based on the principle that the sampling segment traversed by the target spacecraft and the tracking spacecraft from their orbital launch points to the intersection of the two orbits is defined as the approaching behavior region, the approaching behavior regions for the column formation, lower triangle formation, upper triangle formation, and horizontal formation are determined. Based on the principle that the sampling segment traversed by the target spacecraft and the tracking spacecraft from the intersection of the two orbits to the orbital apogee is defined as the departing behavior region, the departing behavior regions for the column formation, lower triangle formation, upper triangle formation, and horizontal formation are determined. Based on the principle that the sampling segment where the target spacecraft and the tracking spacecraft do not intersect along the entire flight path is defined as the circling behavior region, the circling behavior region for the circling formation is determined. Table 2 shows the total number of x, y, and z position components extracted from each sampling point within each behavior region of each formation for both the tracking spacecraft and the target spacecraft.

[0033] Table 2. Overview of positional components extracted from each behavioral region for each formation.

[0034]

[0035]

[0036] Reference Figure 2 The present invention provides a detailed description of the main tracking spacecraft, target spacecraft, approach behavior region, distance behavior region, and orbiting behavior region determined in the embodiments of the present invention.

[0037] Figure 2 (a) is a flight trajectory diagram of four spacecraft in a column formation. The x-axis, y-axis, and z-axis constitute a spatial coordinate system for the flight trajectories of the four spacecraft in space, with units of 10. 4 km. Figure 2In (a), the green curve represents the flight trajectory of the target spacecraft, the red curve represents the flight trajectory of the first tracking spacecraft, the blue curve represents the flight trajectory of the second tracking spacecraft, and the black curve represents the flight trajectory of the third tracking spacecraft.

[0038] In this embodiment of the invention, when determining the primary tracking spacecraft, except for the triangular formation, the red curve is determined as the flight trajectory of the primary tracking spacecraft based on the principle of selecting the tracking spacecraft closest to the target spacecraft as the primary tracking spacecraft, except for the triangular formation. When determining the target spacecraft, except for the triangular formation, the green curve is determined as the flight trajectory of the target spacecraft based on the principle of selecting the spacecraft operating on the orbit with the largest orbital inclination. When determining the approach behavior region in this embodiment of the invention, because the relative distance between the primary tracking spacecraft and the target spacecraft tends to decrease, the sampling segment traversed by the target spacecraft and the primary tracking spacecraft from their launch point to the intersection of the two orbits is determined as the approach behavior region. Therefore, the sampling segment for each of the four spacecraft selected for the approach behavior region is determined to be 500-900. In this embodiment of the invention, when determining the area far from the behavior zone, since the relative distance between the main tracking spacecraft and the target spacecraft tends to increase, the sampling segment that the target spacecraft and the main tracking spacecraft pass through from the intersection of the two orbits to the apogee of the orbit is determined as the area far from the behavior zone. Therefore, the sampling segment of each of the four spacecraft selected for the area far from the behavior zone is determined to be 1050-1300.

[0039] Figure 2 (b) shows the flight trajectories of four spacecraft in a lower triangular column formation. The spatial coordinate system, the meanings of the different colored curves, and the determination of the approach and departure areas are the same as in the column formation. In this embodiment, when determining the primary tracking spacecraft, based on the principle that when the spacecraft cluster formation is a triangle, a tracking spacecraft operating alone on a single orbit is selected as the primary tracking spacecraft, the red curve is determined as the trajectory of the primary tracking spacecraft. In this embodiment, when determining the primary tracking spacecraft, based on the principle that when the spacecraft cluster formation is a triangle, a spacecraft operating alone on a single orbital inclination and departing simultaneously with the primary tracking spacecraft is selected as the target spacecraft, the green curve is determined as the flight trajectory of the target spacecraft. In this lower triangle formation, the sampling ranges for the four spacecraft selected in the approaching behavior region are: 600-900 for the target spacecraft, the main tracking spacecraft, and the third tracking spacecraft, and 700-1000 for the second tracking spacecraft; the sampling ranges for the four spacecraft selected in the far-away behavior region are: 1050-1300 for the target spacecraft, the main tracking spacecraft, and the third tracking spacecraft, and 1150-1400 for the second tracking spacecraft.

[0040] Figure 2(c) shows the flight trajectories of four spacecraft in an upper triangular column formation. The spatial coordinate system, the meanings of the different colored curves, and the determination of the approach and departure zones are the same as in the column formation. The rules for determining the target spacecraft and the primary tracking spacecraft are the same as in the lower triangular formation. In this upper triangular formation, the sampling segments for the four spacecraft selected in the approach zone are: 600-900 for the target spacecraft, the primary tracking spacecraft, and the third tracking spacecraft; and 700-1000 for the second tracking spacecraft. The sampling segments for the four spacecraft selected in the departure zone are: 1100-1400 for the target spacecraft, the primary tracking spacecraft, and the third tracking spacecraft; and 1200-1500 for the second tracking spacecraft.

[0041] Figure 2 (d) shows the flight trajectories of four spacecraft in a horizontal-one-column formation. The spatial coordinate system, the meanings of curves of different colors, the approaching behavior region, the departing behavior region, the primary tracking spacecraft, and the target spacecraft are determined using the same principles as in the column formation. In this horizontal-one-column formation, the sampling segments for the four spacecraft selected in the approaching behavior region are: 600-850 for the target spacecraft and the primary tracking spacecraft, 700-950 for the second tracking spacecraft, and 800-1050 for the third tracking spacecraft. The sampling segments for the four spacecraft selected in the departing behavior region are: 1050-1300 for the target spacecraft and the primary tracking spacecraft, 1150-1400 for the second tracking spacecraft, and 1250-1500 for the third tracking spacecraft.

[0042] Figure 2 (e) is a flight trajectory diagram of four spacecraft in a column formation, showing the composition of the spatial coordinate system, the meaning of curves of different colors, and that the target spacecraft and the main tracking spacecraft are the same as in the column formation.

[0043] In this embodiment of the invention, when determining the orbiting behavior area, the orbiting behavior area is determined according to the principle that the target spacecraft and the main tracking spacecraft do not intersect on the entire flight trajectory. In this orbiting formation, the sampling segments of the four spacecraft in the orbiting behavior area are determined as follows: 600-1000 for the target spacecraft, 300-700 for the main tracking spacecraft, 900-1300 for the second tracking spacecraft, and 1800-2200 for the third tracking spacecraft.

[0044] Step 1.3: Generate a feature tensor corresponding to each behavior region. The rows of this tensor represent the type of formation, and the columns represent the number of behavior regions. Each tensor value is equal to the position or velocity within the j-th behavior region of the i-th formation.

[0045] According to the following tensor Γ ijk The feature tensor corresponding to each generated behavioral region:

[0046]

[0047] Among them, Γ ijk This represents the position or velocity within the j-th action area of ​​the i-th formation. When k=1, it represents the position within the j-th action area of ​​the i-th formation, i.e., Γ. ij1 =s ij When k=2, it represents the velocity Γ within the j-th action area of ​​the i-th formation. ij2 =v ij .

[0048] Expanded matrix form:

[0049]

[0050] Among them, Γ ij The tensor s represents the j-th behavior region of the i-th formation. ij1 v ij2 These represent the position and velocity within the j-th behavior area of ​​the i-th formation, respectively.

[0051] In each embodiment of the invention, each formation includes four spacecraft within each behavioral region, and the feature tensor corresponding to each behavioral region includes the position and location of each spacecraft.

[0052] Step 1.4: Annotate the feature tensor corresponding to each behavior region to generate the corresponding formation and intent labels.

[0053] In this embodiment of the invention, the feature tensor corresponding to each labeled behavior region is generated in the corresponding formation and intent labels, as shown in Table 3:

[0054] Table 3 lists the feature tensors generated for each behavior region and the corresponding formation and intent labels.

[0055]

[0056]

[0057] Step 1.5: Combine all feature tensors and their labels into a dataset. Randomly select 80% of the data in the dataset to form the training set and 20% of the data to form the test set.

[0058] The spacecraft cluster consists of at least three tracking spacecraft and one target spacecraft.

[0059] The formations in the embodiments of this invention include five types: column formation, lower triangle formation, upper triangle formation, horizontal formation, and circular formation. The methods for constructing these formations are as follows:

[0060] The four spacecraft in the column formation operate on four orbits with the same radius but different inclinations. The four spacecraft start simultaneously from the four orbital starting points to form the column formation.

[0061] In the lower triangle formation, the first and second spacecraft operate independently in the first and second orbits, respectively, while the third and fourth spacecraft operate in the third orbit. The three orbits have the same radius but different inclinations. The fourth spacecraft is required to depart before the third spacecraft, and the third orbit must be above the second orbit.

[0062] The upper triangle formation is constructed in the same way as the lower triangle formation, but the third track must be below the second track.

[0063] In a horizontal formation, the second, third, and fourth spacecraft operate in the same orbit, while the first spacecraft operates alone in another orbit. The three orbits have the same radius but different inclinations. The fourth spacecraft is required to launch first, followed by the third spacecraft, and the first and second spacecraft launch last, simultaneously.

[0064] The second, third, and fourth spacecraft in the orbital formation operate in the same orbit, while the first spacecraft operates in a separate orbit. The orbits of the second, third, and fourth spacecraft surround the orbit of the first spacecraft. The target spacecraft and the main tracking spacecraft depart simultaneously from the orbital starting point. The fourth spacecraft departs first, followed by the third spacecraft, and the first and second spacecraft depart last.

[0065] The primary tracking spacecraft in the spacecraft cluster must meet one of the following conditions:

[0066] Condition 1: When the formation of the spacecraft cluster is a triangle, the tracking spacecraft that is running alone in a single orbit is selected as the primary tracking spacecraft.

[0067] Condition 2: Except for the triangular formation, the tracking spacecraft closest to the target spacecraft shall be the primary tracking spacecraft.

[0068] The target spacecraft in the spacecraft cluster must meet one of the following conditions:

[0069] Condition 1: When the formation of the spacecraft cluster is a triangle, the spacecraft that is operating alone on a maximum orbital inclination and launches simultaneously with the main tracking spacecraft is selected as the target spacecraft.

[0070] Condition 2: Except for the triangular formation, select the spacecraft operating in the orbit with the largest orbital inclination as the target spacecraft.

[0071] Determining the behavioral region between the target spacecraft and the main tracking spacecraft refers to identifying the following three types of behavioral regions within the flight trajectory of each spacecraft in each formation:

[0072] The first category defines the approximation behavior region as the sampling segment traversed by the target spacecraft and the main tracking spacecraft from the launch point of their orbits to the intersection of their orbits.

[0073] The second category defines the sampling segment traversed by the target spacecraft and the main tracking spacecraft from the point where the two orbits intersect to the apogee as the area far from the behavior zone.

[0074] The third category defines the orbital behavior region as the sampling segment where the target spacecraft and the main tracking spacecraft do not intersect along the entire flight path.

[0075] Step 2: Build and train the neural network, update the network parameters using the training set, and obtain the trained neural network.

[0076] Step 2.1: Construct a neural network consisting of a first fully connected layer, a second fully connected layer, and an activation layer connected in series. Set the dimensions of the input features for the first and second fully connected layers to 13 and 64, respectively. Set the dimension of the output features to 64. The activation layer uses the ReLU function.

[0077] Step 2.2: Set the training parameters. Set the probability of random dropping in the Dropout layer to 0.8 and the learning rate to 0.001.

[0078] Step 2.3: Input the training set into the neural network, and use the Adam optimizer and gradient descent method to iteratively update the parameters of the neural network until the cross-entropy loss function of the network converges, thus obtaining the trained neural network.

[0079] The cross-entropy loss function is as follows:

[0080]

[0081] Where H represents the loss value between the predicted label and the true label in the training set, g represents the index of the sampling point contained in each behavior region in the training set, G represents the total number of sampling points in all behavior regions in the training set, n represents the index of the formation and intent in the training set, N represents the total number of formation and intent categories in the training set, and p g q represents the true label of the g-th sampling point contained in each behavior region in the training set. g Let represent the predicted label of the g-th sampling point contained in each behavior region in the training set, and log(·) represents the logarithmic operation with the natural constant 2 as the base.

[0082] The test set is input into the trained neural network model, which outputs the labels for formation and intent prediction. The ratio of the number of correctly predicted labels to the total number of labels is calculated, and the resulting accuracy is shown in Table 4.

[0083] Table 4 Accuracy Summary

[0084] Test categories Accuracy formation 97.7％ intention 94.7％

[0085] Step 3: Input the sampled data received by the sensor into the trained neural network to obtain two threat elements: formation and intent.

[0086] In this embodiment, the data received by the sensor on the sampling segment is input into the trained neural network, and the formation and behavior region of each sampling point in each sampling segment can be obtained as shown in Table 5.

[0087] Table 5. Overview of the formation and behavior areas of each sampling point received by the sensor.

[0088]

[0089]

[0090] Step 4: Based on the Lambert orbital transfer function, calculate the pulse impulse required for the primary tracking spacecraft to complete the orbital transfer and rendezvous with the target spacecraft at each sampling point within each behavior region in each formation, thus obtaining the two threat factors: orbital transfer time and pulse impulse.

[0091] The Lambert orbital transfer function is as follows:

[0092]

[0093] in, This represents the pulse impulse required for the primary tracking spacecraft to travel from its orbit to the target spacecraft's orbit via a transfer orbit at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the velocity vector of the main tracking spacecraft after its orbital change at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the initial velocity vector of the main tracking spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the pulse impulse required for the primary tracking spacecraft to rendezvous with the target spacecraft along its orbit at the l-th sampling point within the j-th behavior region of the i-th formation. Let represent the velocity vector of the target spacecraft after the set orbital transfer time at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the velocity vector of the primary tracking spacecraft as it travels along the transfer orbit to the orbit of the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. Let t represent the total pulse impulse required for the primary tracking spacecraft to perform an orbital transfer and rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation, where i = 1, 2, 3, 4, 5, j = 1, 2, 3, l = 1, 2, ..., N, N represents the total number of sampling points within the j-th behavior region of the i-th formation, and t represents the primary tracking spacecraft. * Indicates the target spacecraft.

[0094] In this embodiment, at each sampling point within each behavioral area of ​​each formation, the orbital transfer time of the primary tracking spacecraft is set to 9 hours. A sampling point is taken every 0.008 seconds, resulting in a total of 40,500,000 sampling points. The upper limit of the total pulse required for the primary tracking spacecraft to complete the orbital transfer and rendezvous with the target spacecraft is 10 km / s. At each sampling point, the primary tracking spacecraft performs an orbital transfer every 300 seconds (37,500 sampling points), for a total of 54 orbital transfers. The total pulse impulse required for each orbital transfer is obtained, thus yielding the orbital transfer time and its corresponding total pulse impulse set. Under the premise that the total pulse impulse is less than or equal to the set upper limit of the total pulse impulse, the minimum orbital transfer time is selected, and the total pulse impulse corresponding to this orbital transfer time is used as the pulse impulse threat element.

[0095] Step 5: Using the analytic hierarchy process (AHP), calculate the weights of formation, intent, orbital transfer time, impulse, and the relative distance between the target spacecraft and the primary tracking spacecraft at each sampling point for each threat element.

[0096] The steps for calculating the weights of each threat element using the analytic hierarchy process are as follows:

[0097] The first step is to determine the assessment scale. The basic scale of the analytic hierarchy process includes five items: equally important, slightly important, quite important, extremely important, and absolutely important, and is assigned a measurement value of 1, 3, 5, 7, and 9. There are also four items between the five basic scales, and are assigned a measurement value of 2, 4, 6, and 8.

[0098] The second step involves comparing each of the five threat elements pairwise according to the assessment scale. The orbital transfer time is selected, and its importance is compared with relative distance, impulse, formation, and intent. When comparing orbital transfer time to itself, the value is 1. When comparing orbital transfer time to relative distance, decreases and increases in relative distance are more important, with orbital transfer time being slightly less important than relative distance. The nominal scales assigned to orbital transfer time and relative distance are 5 and 8, respectively. When comparing orbital transfer time to impulse, the primary tracking spacecraft must rendezvous with the target within a limited sampling period, and the impulse cannot exceed a certain value. The importance of orbital transfer time and impulse is similar, with nominal scales assigned to orbital transfer time and impulse being 6 and 5, respectively. When comparing orbital transfer time to formation and intent, orbital transfer time is slightly more important, with nominal scales assigned to orbital transfer time and formation being 3 and 2, respectively, and to orbital transfer time and intent being 4 and 3, respectively.

[0099] When comparing the importance of relative distance with impulse, formation, and intent, relative distance is far more important than impulse, formation, and intent because the closer the distance during approach maneuvers, the greater the threat to the target spacecraft. The nominal scales assigned to relative distance and impulse are 9 and 4, respectively; those assigned to relative distance and formation are 7 and 2, respectively; and those assigned to relative distance and intent are 9 and 3, respectively.

[0100] When comparing the importance of impulse, formation, and intention, impulse is slightly more important than formation and intention. Therefore, when comparing the importance of impulse and formation, the nominal scales assigned are 5 and 3, respectively. When comparing the importance of impulse and behavior, the nominal scales assigned are 5 and 4, respectively.

[0101] When comparing the importance of formation and intention, formation is considered slightly more important than intention because intention is determined by formation. Therefore, the nominal scales assigned to the intentions of formation are 3 and 2 respectively. The numbers in the diagonal squares should be reciprocals of each other. The resulting order of importance for the five threat elements is shown in Table 6.

[0102] Table 6. A Comparison of Pairwise Elements of the Five Threats

[0103]

[0104] The third step is to obtain the following comparison matrix based on the table comparing the five threat elements pairwise.

[0105]

[0106] Where A represents the comparison matrix of the five threat elements;

[0107] The fourth step is to calculate the eigenvectors of the comparison matrix A, obtaining the weight values ​​for each threat element as follows:

[0108] b=[0.1949, 0.3715, 0.1844, 0.1277, 0.1214] T

[0109] Where b represents the eigenvector calculated from the comparison matrix A, and the superscript T indicates the transpose operation.

[0110] Fifth, perform a consistency check on the constructed comparison matrix according to the following formula:

[0111]

[0112] Where CI represents a quantitative indicator measuring the degree of inconsistency, n represents the number of threat elements, and λ represents the number of threat elements. max CR represents the largest eigenvalue calculated from the comparison matrix, RI represents the consistency ratio, and RI represents the average random consistency index. When CR ≤ 0.1, the judgment matrix is ​​said to have satisfactory RI consistency; otherwise, it does not have satisfactory consistency.

[0113] For n = 1 to 11, the values ​​of the average random consistency index RI are shown in Table 7:

[0114] Table 7. Summary of Average Random Consistency Indices

[0115] n 1 2 3 4 5 6 7 8 9 10 11 RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 1.51

[0116] In this embodiment of the invention, the five threat elements include: orbital transfer time, relative distance between the target spacecraft and the primary tracking spacecraft, impulse, formation, and intent, with corresponding weights of 0.1949, 0.3715, 0.1844, 0.1277, and 0.1214, respectively. Because there are five threat elements, n is set to 5. In Table 7, when n = 5, RI is set to 1.12. λ is obtained from the comparison matrix A. max The value of is 5.1404. The calculated value of CI is 0.0351 and the value of CR is 0.0313. Since CR < 0.10, the consistency of the judgment matrix A is acceptable.

[0117] Step 6: Weight all threat elements by normalized index values ​​to obtain the comprehensive threat index.

[0118] The method for normalizing all threat elements is as follows:

[0119]

[0120] in, This represents the normalized value of the pulse impulse required for the primary tracking spacecraft to perform an orbital transfer and rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the upper limit of the pulse impulse required for the primary tracking spacecraft to rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the normalized value of the orbital transfer time required for the primary tracking spacecraft to perform an orbital transfer and complete rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the maximum orbital transfer time required for the primary tracking spacecraft to perform an orbital transfer and complete rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. This represents the orbital transfer time required for the primary tracking spacecraft to perform an orbital transfer and complete rendezvous with the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. r represents the normalized value of the relative distance between the primary tracking spacecraft and the target spacecraft at the l-th sampling point within the j-th behavior region of the i-th formation. ijmax This represents the maximum relative distance between the primary tracking spacecraft and the target spacecraft within the j-th behavior region of the i-th formation.

[0121] The formula for calculating the comprehensive threat index is as follows: by weighting all threat elements with the normalized index value, the overall threat index is obtained:

[0122]

[0123] in, This represents the comprehensive threat index at the l-th sampling point within the j-th action region of the i-th formation, where the primary tracking spacecraft undergoes an orbital transfer and the target spacecraft completes a rendezvous. r represents the number of threat elements, and b... r This represents the weight of each threat element in matrix b. Let r represent the normalized values ​​of each threat element at the l-th sampling point within the j-th behavior region of the i-th formation, where r = 1, 2, 3, 4, 5.

[0124] In this embodiment of the invention, the total data after normalizing the orbital transfer time, the relative distance between the target spacecraft and the main tracking spacecraft, and the pulse impulse at each sampling point in each behavioral region of each formation is shown in Table 8.

[0125] Table 8. Summary of sampling time interval, relative distance, and pulse impulse after normalization.

[0126]

[0127]

[0128] In this embodiment of the invention, the formation and intent of the spacecraft cluster are processed using BPA distribution, and the steps are as follows:

[0129] The first step is to perform a weighted average for high threat (H), medium threat (M), low threat (L), high-medium threat (HM), medium-low threat (ML) and other cases (HML), respectively. The specific weighting method is as follows: m(H)_ave=b(4)*f_m(H)+b(5)*be_m(H);

[0130] m(M)_ave=b(4)*f_m(M)+b(5)*be_m(M);

[0131] m(L)_ave=b(4)*f_m(L)+b(5)*be_m(L);

[0132] m(HM)_ave=b(4)*f_m(HM)+b(5)*be_m(HM);

[0133] m(ML)_ave=b(4)*f_m(ML)+b(5)*be_m(ML);

[0134] m(HML)_ave=1-m(H)_ave-m(M)_ave-m(L)_ave-m(HM)_ave-m(ML)_ave

[0135] Where m(H)_ave, m(M)_ave, m(L)_ave, m(HM)_ave, m(ML)_ave, and m(HML)_ave represent the weighted average values ​​of high threat (H), medium threat (M), low threat (L), high-medium threat (HM), medium-low threat (ML), and other cases (HML), respectively; b(4) and b(5) represent the fourth and fifth values ​​in the feature vector matrix b, respectively; f_m(H), f_m(M), f_m(L), f_m(HM), and f_m(ML) represent the threat levels of the five formations, respectively; and be_m(H), be_m(M), be_m(L), be_m(HM), and be_m(ML) represent the threat levels of the three intentions in the five formations, respectively.

[0136] The second step is to use the equal distribution method (Smets), assuming that each element has an equal probability of appearing. Therefore, the BPA value of the multi-element proposition is evenly distributed among the elements as follows:

[0137]

[0138] Among them, A cLet A represent the set of three scenarios: high threat (H), medium threat (M), and low threat (L). M Let |A| represent the set of three cases: high threat (H), medium threat (M), low threat (L), high-medium threat (HM), low-medium threat (ML), and other cases (HML). M | indicates that it is A M The number of elements in the array, m_ave(A M ) represents the basic probability assignment of various threat types under the BPA distribution, where c = 1, 2, 3.

[0139] The third step is to perform BPA distribution on the formation and intent according to the following formula, and then fuse the results: BetP(H)=m_ave(H)+m_ave(H,M) / 2+m_ave(H,M,L) / 3

[0140] BetP(M)=m_ave(M)+m_ave(H,M) / 2+m_ave(M,L) / 2+m_ave(H,M,L) / 3BetP(L)=m_ave(L)+m_ave(M,L) / 2+m_ave(H,M,L) / 3

[0141] BetP(H), BetP(M), and BetP(L) represent the probabilities of the formations and intentions of high threat (H), medium threat (M), and low threat (L) after fusion of the results.

[0142] Fourth, following the formula below, the probability of the fused formation and intent of the cluster of spacecraft is weighted and summed to obtain the threat expression based on formation and behavior as follows:

[0143] Threat=0.8×BetP(H)+0.2×BetP(M)+0×BetP(L)

[0144] Threat represents the threat value obtained based on formation and behavior.

[0145] Fifth step, calculate the comprehensive threat index according to the following formula:

[0146]

[0147] b1+b2+b3+b4+b5=1,b i ∈[0,1], i=1,2,3,4,5

[0148] in, This represents the threat index of the primary tracking spacecraft to the target spacecraft at the l-th sampling point within the j-th behavioral region of the i-th region. Let b represent the normalized values ​​of the total pulse impulse required for rendezvous at the l-th sampling point within the j-th behavioral region of the i-th region, the orbital transfer time, and the relative distance between the target spacecraft and the main tracking spacecraft, respectively. i This represents the weight corresponding to each threat indicator in matrix b.

[0149] In this embodiment of the invention, the intention of each behavioral region in each formation is distributed using BPA, and the normalized values ​​of the intention of each behavioral region in each formation are shown in Table 9:

[0150] Table 9: Overview of BPA distribution for formations and intentions

[0151]

[0152]

[0153] Reference Figure 3 The comprehensive threat index diagrams of various spacecraft cluster formations in different behavioral areas in the embodiments of the present invention are further described below:

[0154] Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) These are threat assessment index diagrams of the target spacecraft at each sampling point within the approach behavior area during orbital transfers by the main tracking spacecraft in column formation, lower triangle formation, upper triangle formation, and horizontal formation, respectively. The horizontal axis represents the sampling segment of the main tracking spacecraft within the approach behavior area for each of the column formation, lower triangle formation, upper triangle formation, and horizontal formation, respectively. The vertical axis represents the threat assessment index of the target spacecraft at each sampling point within the approach behavior area during orbital transfers by the main tracking spacecraft in each of the column formation, lower triangle formation, upper triangle formation, and horizontal formation, respectively.

[0155] Figure 3 (e) Figure 3 (f) Figure 3 (g) Figure 3 (h) represents the threat assessment index of the target spacecraft at each sampling point far from the behavior area when the main tracking spacecraft performs an orbital transfer in the column formation, lower triangle formation, upper triangle formation, and horizontal formation. The horizontal axis represents the sampling segment of the main tracking spacecraft far from the behavior area in the column formation, lower triangle formation, upper triangle formation, and horizontal formation, respectively. The vertical axis represents the threat assessment index of the target spacecraft at each sampling point far from the behavior area when the main tracking spacecraft performs an orbital transfer in the column formation, lower triangle formation, upper triangle formation, and horizontal formation, respectively.

[0156] Figure 3(i) Threat assessment index map of the target spacecraft at each sampling point in the orbital behavior area when the main tracking spacecraft in the orbital formation performs an orbital transfer. Figure 3 In (i), the horizontal axis represents the sampling segment of the primary tracking spacecraft within the orbital behavior area, and the vertical axis represents the threat assessment index of the target spacecraft at each sampling point within the orbital behavior area when the primary tracking spacecraft performs an orbital transfer.

[0157] Under the above conditions, the comprehensive threat index diagrams of various spacecraft cluster formations of the present invention in each behavioral region are analyzed:

[0158] Depend on Figure 3 (a) Figure 3 (b) Figure 3 (d) It can be seen that within the approach behavior area of ​​the column formation, lower triangle formation, and horizontal formation, the threat assessment index fluctuated to varying degrees between sampling points 729 and 730. Figure 3 In (c), the upper triangular formation experienced a sudden change in the threat assessment index between sampling points 682 and 683 within the approach behavior region. Table 10 shows the changes in pulse impulse and orbital transfer time at the sudden change point.

[0159] Table 10: Summary of Pulse and Orbit Transfer Time Changes at Each Formation Change Point

[0160]

[0161] Table 10 shows that the pulse speed at the abrupt change point is 9.9995 km / s, approaching 10 km / s. Within the acceptable range, the following is required: Therefore, starting from the next sampling point, the orbital transfer time needs to increase from 3001s to 9901s. As the orbital transfer time increases, the required pulse impulse decreases. That is, with increased time, sufficient time is given for the orbital transfer, resulting in a smaller change in pulse impulse. In column formations, lower triangle formations, upper triangle formations, and horizontal formations, the overall threat index of the primary tracking spacecraft to the target spacecraft increases within the approaching action area; while in the far-away action area, the overall threat index of the primary tracking spacecraft to the target spacecraft decreases.

Claims

1. A spacecraft swarm threat assessment method based on neural networks, characterized in that, Threat assessments are conducted on different formations and behaviors of spacecraft swarms. The analytic hierarchy process (AHP) is used to quantify each threat element, and a comprehensive threat index is calculated. The steps of this assessment method include the following: Step 1: Generate a training set that includes formation and behavioral region intentions; Step 2: Build and train the neural network, update the network parameters using the training set, and obtain the trained neural network; Step 3: Input the sampled data received by the sensor into the trained neural network to obtain two threat elements: formation and intent. Step 4: Based on the Lambert orbital transfer function, calculate the pulse impulse required for the primary tracking spacecraft to complete the orbital transfer and rendezvous with the target spacecraft at each sampling point within each behavior region in each formation, thus obtaining the two threat factors: orbital transfer time and pulse impulse. Step 5: Using the analytic hierarchy process (AHP), calculate the weights of formation, intent, orbital transfer time, impulse, and the relative distance between the target spacecraft and the primary tracking spacecraft at each sampling point for each threat element. Step 6: Weight all threat elements by normalized index values ​​to obtain the comprehensive threat index.

2. The spacecraft swarm threat assessment method based on neural networks according to claim 1, characterized in that, The steps for generating the training set described in step 1 are as follows: The first step is to simulate the flight trajectory of each spacecraft in the formation of the active approach spacecraft swarm to determine the main tracking spacecraft and the target spacecraft in the swarm; and to extract the position and velocity data of each spacecraft in the x, y, and z directions in each behavioral region of each simulated trajectory map. The second step is to calculate the relative distance between the target spacecraft and the main tracking spacecraft at each sampling point in each behavior region for each formation by extracting the position and velocity components of each spacecraft in the x, y, and z directions for each spacecraft in each behavior region; The third step is to generate a feature tensor corresponding to each behavior region. The rows of this tensor represent the number of behavior regions, the columns represent the types of formations, and each tensor value is equal to the position or velocity within the j-th behavior region of the i-th formation. The fourth step is to annotate the feature tensors corresponding to each behavior region to generate corresponding formation and intent labels; The fifth step is to assemble all the feature matrices and their labels into a training set.

3. The spacecraft swarm threat assessment method based on neural networks according to claim 2, characterized in that, The active approach spacecraft cluster consists of at least three tracking spacecraft and one target spacecraft.

4. The spacecraft swarm threat assessment method based on neural networks according to claim 2, characterized in that, The formations include five types: column formation, lower triangle formation, upper triangle formation, horizontal formation, and circular formation; their formation methods are as follows: The four spacecraft in the column formation operate on four orbits with the same radius but different inclinations. The four spacecraft start simultaneously from the four orbital starting points to form the column formation. In the lower triangle formation, the first and second spacecraft operate independently in the first and second orbits, respectively, while the third and fourth spacecraft operate in the third orbit. The three orbits have the same radius but different inclinations. The fourth spacecraft is required to depart before the third spacecraft, and the third orbit must be above the second orbit. The upper triangle formation is constructed in the same way as the lower triangle formation, but the third track must be below the second track. In a horizontal formation, the second, third, and fourth spacecraft operate in the same orbit, while the first spacecraft operates alone in another orbit. The three orbits have the same radius but different inclinations. The fourth spacecraft is required to launch first, followed by the third spacecraft, and the first and second spacecraft launch last, simultaneously. The second, third, and fourth spacecraft in the orbital formation operate in the same orbit, while the first spacecraft operates in a separate orbit. The orbits of the second, third, and fourth spacecraft surround the orbit of the first spacecraft. The target spacecraft and the main tracking spacecraft depart simultaneously from the orbital starting point. The fourth spacecraft departs first, followed by the third spacecraft, and the first and second spacecraft depart last.

5. The spacecraft swarm threat assessment method based on neural networks according to claim 2, characterized in that, The primary tracking spacecraft in the active approach spacecraft cluster must meet one of the following conditions: Condition 1, when the formation of the active approach spacecraft cluster is a triangle formation, then the tracking spacecraft operating alone in an orbit is selected as the primary tracking spacecraft; Condition 2, except for the triangle formation, the tracking spacecraft closest to the target spacecraft is selected as the primary tracking spacecraft.

6. The spacecraft swarm threat assessment method based on neural networks according to claim 2, characterized in that, The target spacecraft in the active approach spacecraft cluster must meet one of the following conditions: Condition 1: When the formation of the active approach spacecraft swarm is a triangle, the spacecraft that is operating alone on a maximum orbital inclination and launches simultaneously with the main tracking spacecraft is selected as the target spacecraft. Condition 2: Except for the triangular formation, select the spacecraft operating in the orbit with the largest orbital inclination as the target spacecraft.

7. The spacecraft swarm threat assessment method based on neural networks according to claim 2, characterized in that, The step described in the first step, extracting the position and velocity data of each spacecraft in the x, y, and z directions within each behavioral region of each simulated trajectory map, refers to determining the following three types of behavioral regions in the flight trajectory of each spacecraft in each formation: The first category defines the sampling segment that the target spacecraft and the main tracking spacecraft pass through from the launch point of their orbits to the intersection of their orbits as the approximation behavior region. The second category defines the sampling segment that the target spacecraft and the main tracking spacecraft pass through from the point where the two orbits intersect to the apogee as the area far from the behavior zone; The third category defines the orbital behavior region as the sampling segment where the target spacecraft and the main tracking spacecraft do not intersect along the entire flight path.

8. The spacecraft swarm threat assessment method based on neural networks according to claim 1, characterized in that, The steps for constructing and training the neural network described in step 2 are as follows: The first step is to build a neural network consisting of a first fully connected layer, a second fully connected layer, and an activation layer connected in series. The input features of the first fully connected layer have a dimension of 13, and the output features have a dimension of 64. The input features of the second fully connected layer have a dimension of 64, and the output features have a dimension of 10. The activation layer is implemented using the ReLU function. The second step is to set the probability of random dropping in the Dropout layer to 0.8 and the learning rate to 0.

001. The third step is to input the training set into the neural network and use the Adam optimizer and gradient descent method to iteratively update the parameters of the neural network until the cross-entropy loss function of the network converges, thus obtaining the trained neural network. The cross-entropy loss function is as follows: ； Where H represents the loss value between the predicted output label and the true label in the training set, and g represents the index of the sampling points contained in each behavior region in the training set. This represents the total number of sampling points across all behavior regions in the training set, where n represents the sequence number of the formation or intent in the training set, and N represents the total number of formation or intent categories in the training set. This represents the true label of the g-th sampling point contained in each behavior region of the training set. This represents the predicted label of the g-th sampling point contained in each behavior region of the training set. This represents the logarithmic operation with base 2.

9. The spacecraft swarm threat assessment method based on neural networks according to claim 1, characterized in that, The Lambert orbital transfer function mentioned in step 4 is as follows: ； in, Indicates the main tracking spacecraft in the 19th century. The first formation Within the first behavioral area At each sampling point, the pulse impulse required for the primary tracking spacecraft to travel from its orbit through a transfer orbit to the target spacecraft's orbit. Indicates the first The first formation Within the first behavioral area At each sampling point, the velocity vector of the main tracking spacecraft after its orbital change. Indicates the first The first formation Within the first behavioral area At each sampling point, the initial velocity vector of the main tracking spacecraft, Indicates the first The first formation Within the first behavioral area At each sampling point, the pulse impulse required for the primary tracking spacecraft to rendezvous with the target spacecraft along its orbit. Indicates the first The first formation Within the first behavioral area At each sampling point, the velocity vector of the target spacecraft after the set orbital transfer time. Indicates the first The first formation Within the first behavioral area At each sampling point, the velocity vector of the primary tracking spacecraft as it travels along the transfer orbit to the orbit of the target spacecraft. Indicates the first The first formation Within the first behavioral area At each sampling point, the total pulse impulse required for the primary tracking spacecraft to perform an orbital transfer and rendezvous with the target spacecraft. , , N represents the first The first formation The total number of sampling points within each behavioral area Indicates the main tracking spacecraft, Indicates the target spacecraft.

10. The spacecraft swarm threat assessment method based on neural networks according to claim 1, characterized in that, The steps in step 5, which involve calculating the weights of each threat element using the analytic hierarchy process, are as follows: The first step is to compare the five threat elements in pairs according to the assessment criteria to obtain a comparison matrix. The rows and columns in the matrix represent the five threat elements, and each value represents the importance of the threat element in the row to the threat element in the column. ； Where A represents the comparison matrix of the five threat elements; The second step is to calculate the comparison matrix. The eigenvectors are used to obtain the weights of each threat element in matrix b, as follows: ； Where b represents the eigenvector calculated from the comparison matrix A, and the superscript T indicates the transpose operation.

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