A spacecraft orbit threat avoidance decision method based on FGCM

Abstract

The application discloses a spacecraft orbit threat avoidance decision method based on FGCM and belongs to the field of space science and technology, and solves the problem that a spacecraft is difficult to make autonomous decisions in the face of orbit threat scenarios such as non-cooperative targets. The application establishes a spacecraft avoidance behavior strategy model based on FGCM by defining input and output nodes of the model and state value rules thereof, predicts the task scenario in which the spacecraft is located based on FGCM, reduces the influence of uncertainty in the autonomous decision process, optimizes the gray cause-and-effect correlation weight value of the model by using a genetic algorithm, obtains a reliable spacecraft threat avoidance behavior strategy, and realizes that the spacecraft can autonomously generate a corresponding behavior strategy to avoid threats in the face of non-cooperative target threats.

Description

Technical Field

[0001] This invention belongs to the field of aerospace science and technology, and relates to a spacecraft orbital threat avoidance decision-making method based on FGCM. Background Technology

[0002] With the deepening development and continuous maturation of space science and technology, space orbits are becoming increasingly crowded, and the risk of collisions is surging. In order to cope with threats from non-cooperative targets such as collisions with malfunctioning satellites and attacks from hostile satellites, spacecraft need to develop reasonable avoidance strategies based on the perception results of the mission scenario among possible options.

[0003] In the prior art, for the autonomous decision-making problem in complex and uncertain environments, the paper "Differential game-based air combat maneuver generation using scoring function matrix" (Park H, Lee B, Tahk M, et al. International Journal of Aeronautical and SpaceSciences, 2016, 17(2): 204-213.) proposes a maneuver adjustment method based on differential game theory, which can obtain a better maneuver strategy. However, this method is computationally complex and has the problem of repeated solution. In addition, the literature “A survey of deep learning techniques for autonomous driving” (Grigorescu S, Trasnea B, Cocias T, et al. Journal of Robotic Systems, 2020, 37(3): 362-386.) and “Maneuver decision-making in autonomous air combat technology: progress and prospects” (Dong Yiqun, Ai Jianliang. Acta Aeronautica Sinica, 2020, 41(S2):724-264) proposed autonomous decision-making methods represented by expert systems and machine learning. However, expert systems rely on human experience to make decisions, and machine learning needs to obtain decision results through massive sample training, which makes it difficult to make decisions in complex and uncertain space environments.

[0004] Fuzzy Grey Cognutative Map (FGCM), as an evolutionary model of fuzzy cognitive maps, integrates the advantages of fuzzy theory and grey system theory. Compared to fuzzy cognitive maps, FGCM can clearly represent the process of decision-making models and map precise node values ​​to a grey region. It is easier to represent the uncertain relationships and incomplete information between the nodes of the model, making it suitable for autonomous decision-making in highly uncertain space environments. The process of FGCM is similar to the evolution of a nonlinear dynamical system, where the state at the next moment can be obtained from the state at the previous moment. Its process depends on the internal grey causal association weights of the model. Summary of the Invention

[0005] The purpose of this invention is to provide a spacecraft orbital threat avoidance decision-making method based on FGCM, in order to solve the problem that spacecraft have difficulty making autonomous decisions when facing orbital threats such as non-cooperative targets during on-orbit operation.

[0006] The present invention solves the above-mentioned technical problems through the following technical solutions:

[0007] A spacecraft orbital threat avoidance decision-making method based on FGCM includes the following steps:

[0008] S1. Based on the orbital threats faced by the spacecraft, define the input and output nodes and state value rules of the decision-making method;

[0009] S2. Establish a decision-making model for spacecraft to avoid orbital threats based on FGCM;

[0010] S3. Optimize the FGCM grey causal association weights of the avoidance decision model based on scene data and genetic algorithm;

[0011] S4. Apply the optimized avoidance decision model to orbital threat avoidance decision-making.

[0012] Furthermore, the specific rules for the input nodes and state values ​​mentioned in step S1 are as follows:

[0013] Taking the orbital threats faced by spacecraft as the research object, the threat distance, threat velocity, threat anomaly, threat payload behavior status, and threat level are selected as input nodes for the decision-making method; node C1 represents the threat distance, node C2 represents the threat velocity, node C3 represents the threat anomaly, node C4 represents the threat payload behavior status, and node C5 represents the threat level.

[0014] The rules for selecting the value of node C1 are as follows:

[0015]

[0016] Where e=2.72, l represents the actual relative distance between the threat and the spacecraft, l1 represents the maximum observable distance of the threat from the spacecraft, and l2 represents the minimum safe distance for the spacecraft to avoid a collision.

[0017] The rules for selecting the value of node C2 are as follows:

[0018]

[0019] Where, v0=(v max +v min ) / 2, σ=α(v max +v min v represents the actual relative velocity of the threat approaching the spacecraft. max v min These are the maximum and minimum speeds at which the threat approaches the spacecraft, respectively, and α represents the ambiguity factor, which is a constant between 0 and 1;

[0020] The value of node C3 is described by a switch. If a threat suddenly attacks or harasses the node, C3=1; otherwise, C3=0.

[0021] The value of node C4 is between 0 and 1. The specific rules need to be represented by a set of fuzzy values ​​according to the type of load. If the load is a camera, the set of fuzzy values ​​is {silent: 0.1, aiming: 0.4, extending: 0.7}.

[0022] The value of node C5 is between 0 and 1 and can be obtained directly. The larger the value, the higher the threat level.

[0023] Furthermore, the specific rules for the output node and its state value in step S1 are as follows:

[0024] The behavior strategy selected by the spacecraft is selected as the output node. Node C6 is defined to represent the behavior strategy selected by the spacecraft, including 5 behavior strategies: normal operation, attitude maneuver, orbital maneuver, emergency avoidance, and release of interference.

[0025] The value of node C6 is between 0 and 1, and is represented by a fuzzy membership set: {normal operation: 0.1, attitude maneuver: 0.3, orbital maneuver: 0.5, emergency avoidance: 0.7, release interference: 0.9}.

[0026] Furthermore, the method for establishing a spacecraft's decision-making model for mitigating orbital threats based on FGCM in step S2 is as follows:

[0027] Using the Fuzzy Gray Cognitive Map (FGCM) as a framework, the mathematical expression for the gray state value of each node is as follows:

[0028]

[0029] in, This represents the gray state value of the j-th node at time t+1, where j represents the result node, and j=1,2,…,6. Let represent the gray state value of the i-th node at time t, where i represents the cause node, i=1,2,…,6, and S represents the set of all nodes in the FGCM. Let f represent the gray causal association weights from node i to node j, and let f represent the node update function. ∈[ , ]and ≤ , This represents the lower bound of the state value of the j-th node at time t+1. This represents the upper bound of the state value of the j-th node at time t+1. ∈[ , ]and ≤ , This represents the lower bound of the state value of the i-th node at time t. This represents the upper bound of the state value of the i-th node at time t. ∈[ , ]and ≤ , This represents the lower bound of the causal association weights from node i to node j. This represents the upper bound of the causal association weights from the i-th node to the j-th node;

[0030] The mathematical form of the node update function is:

[0031]

[0032] Where λ is a constant greater than 0; The operation rules are as follows:

[0033]

[0034] Here, min() means taking the minimum value of the element within the parentheses, and max() means taking the maximum value of the element within the parentheses;

[0035] The computational expression for transforming the j-th node of a fuzzy gray cognitive graph from a gray state value to a state value is:

[0036]

[0037] Here, η is the adjustment factor, and its value is between 0 and 1.

[0038] Furthermore, the method for optimizing the gray causal association weights of FGCM based on scene data and genetic algorithm described in step S3 is as follows:

[0039] S31. Update the causal weight matrix of the decision model. ;

[0040] S32. Use a genetic algorithm to optimize the model parameters.

[0041] Furthermore, the causal correlation weight matrix of the avoidance decision model described in step S31 The form is:

[0042]

[0043] In this matrix, the elements equal to 0 indicate that there is no causal relationship between the two nodes of FGCM, and the remaining elements need to be obtained through optimization using a genetic algorithm.

[0044] Furthermore, the specific method for optimizing model parameters using a genetic algorithm as described in step S32 is as follows:

[0045] ① Initialize the decision model

[0046] Assume the population size H = 500, the maximum number of generations G = 200, and the crossover probability P. c =0.7, mutation probability P m =0.1, evolutionary algebra calculator g=1;

[0047] Each chromosome is encoded using real numbers:

[0048]

[0049] Each element in L is randomly initialized, ensuring that each element is between -1 and 1.

[0050]

[0051] ② Calculate the fitness function

[0052]

[0053] Where ε represents the data training error, and the specific calculation formula is as follows:

[0054]

[0055] Where N represents the number of training samples, This represents the actual value of the j-th node of the n-th sample in the FGCM model. This represents the predicted value of the j-th node for the n-th sample in the FGCM model;

[0056] ③ Select Operation

[0057] Calculate the probability of each chromosome being selected:

[0058]

[0059] Among them, P h Let h represent the probability of the h-th chromosome being selected, where h = 1, 2, …, H, and fitness. h This indicates the fitness of the h-th chromosome;

[0060] According to the rules of roulette, a new population is formed based on the fitness of each chromosome, and the new population then proceeds to steps ④ and ⑤ in sequence.

[0061] ④ Cross operations

[0062] Randomly generate a constant p between 0 and 1 c If p c <P c Then, randomly select H / 4 pairs of chromosomes to swap the corresponding coding elements, ensuring that the crossover operation is performed on a per-weight basis corresponding to the FGCM node; if p c ≥P c If so, proceed directly to step ⑤;

[0063] ⑤ Mutation operation

[0064] Randomly generate a constant p between 0 and 1 m If p m <P m Then, a chromosome is randomly selected and mutated at a random position, ensuring that the mutation operation is performed on a unit of weight corresponding to the FGCM node; if p m ≥P m If so, proceed directly to step ⑥;

[0065] ⑥ Termination condition judgment

[0066] Update g = g + 1. If g ≤ G, then jump to step ②; if g > G, then terminate the loop and select the chromosome with the highest fitness as the optimal grey causal association weight for the FGCM model.

[0067] The advantages of this invention are:

[0068] This invention establishes a spacecraft avoidance behavior strategy model based on Fuzzy Gray Cognitive Graph (FGCM) by defining the input and output nodes of the model and their state value rules. Based on FGCM, the model predicts the mission scenario of the spacecraft, reducing the impact of uncertainty in the autonomous decision-making process. By using a genetic algorithm to optimize the gray causal association weights of the model, a reliable spacecraft threat avoidance behavior strategy is obtained, enabling the spacecraft to autonomously generate corresponding behavior strategies to avoid non-cooperative target threats. Attached Figure Description

[0069] Figure 1 This is a flowchart of the decision-making method of the present invention;

[0070] Figure 2 This is a model structure diagram of the decision-making method of this invention;

[0071] Figure 3 This is a schematic diagram of the decision output of the decision-making method of the present invention;

[0072] Figure 4 This is a schematic diagram of the crossover operation in the genetic algorithm of the decision-making method of this invention;

[0073] Figure 5 This is a schematic diagram of the genetic algorithm mutation operation of the decision-making method of this invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0076] Example 1

[0077] like Figure 1 As shown in the figure, a spacecraft orbital threat avoidance decision-making method based on FGCM according to an embodiment of the present invention includes the following steps:

[0078] S1. Based on the orbital threats faced by the spacecraft, define the input and output nodes and state value rules for the decision-making method.

[0079] S11. Input Nodes and State Value Rules

[0080] like Figure 2As shown, taking the orbital threat faced by a spacecraft as the research object, the threat distance, threat speed, threat anomaly, threat payload behavior status, and threat level are selected as input nodes for the decision-making method; node C1 represents the threat distance, node C2 represents the threat speed, node C3 represents the threat anomaly, node C4 represents the threat payload behavior status, and node C5 represents the threat level.

[0081] The rules for selecting the value of node C1 are as follows:

[0082] (1)

[0083] Where e=2.72, l represents the actual relative distance between the threat and the spacecraft, l1 represents the maximum observable distance of the threat from the spacecraft, and l2 represents the minimum safe distance for the spacecraft to avoid a collision.

[0084] The rules for selecting the value of node C2 are as follows:

[0085] (2)

[0086] Where, v0=(v max +v min ) / 2, σ=α(v max +v min v represents the actual relative velocity of the threat approaching the spacecraft. max v min These are the maximum and minimum speeds at which the threat approaches the spacecraft, respectively. α represents the ambiguity factor and is a constant between 0 and 1, preferably α = 0.4.

[0087] The value of node C3 is described by a switch. If a threat suddenly attacks or harasses the node, C3=1; otherwise, C3=0.

[0088] The value of node C4 is between 0 and 1. The specific rules need to be represented by a set of fuzzy values ​​according to the type of load. If the load is a camera, the set of fuzzy values ​​is {silent: 0.1, aiming: 0.4, extending: 0.7}.

[0089] The value of node C5 is between 0 and 1 and can be obtained directly. The larger the value, the higher the threat level.

[0090] S12, Output Nodes and Value Rules

[0091] The behavior strategy for spacecraft selection is selected as the output node, and node C6 is defined to represent the behavior strategy for spacecraft selection, such as... Figure 3 As shown, it includes five behavioral strategies: normal operation, attitude maneuvering, orbital maneuvering, emergency avoidance, and release of interference;

[0092] The value of node C6 is between 0 and 1, and is represented by a fuzzy membership set: {normal operation: 0.1, attitude maneuver: 0.3, orbital maneuver: 0.5, emergency avoidance: 0.7, release interference: 0.9}.

[0093] S2. Establishing a spacecraft avoidance decision model for orbital threats based on FGCM.

[0094] The spacecraft orbital threat avoidance decision model uses a fuzzy grey cognitive graph (FGCM) as its basis, and the mathematical expression for the grey state value of each node is as follows:

[0095] (3)

[0096] in, This represents the gray state value of the j-th node at time t+1, where j represents the result node, and j=1,2,…,6. Let represent the gray state value of the i-th node at time t, where i represents the cause node, i=1,2,…,6, and S represents the set of all nodes in the FGCM. Let f represent the gray causal association weights from node i to node j, and let f represent the node update function. ∈[ , ]and ≤ , This represents the lower bound of the state value of the j-th node at time t+1. This represents the upper bound of the state value of the j-th node at time t+1. ∈[ , ]and ≤ , This represents the lower bound of the state value of the i-th node at time t. This represents the upper bound of the state value of the i-th node at time t. ∈[ , ]and ≤ , This represents the lower bound of the causal association weights from node i to node j. This represents the upper bound of the causal association weights from the i-th node to the j-th node;

[0097] The mathematical form of the node update function is:

[0098] (4)

[0099] Wherein, λ is a constant greater than 0, preferably λ=3; The operation rules are as follows:

[0100] (5)

[0101] Here, min() means taking the minimum value of the element within the parentheses, and max() means taking the maximum value of the element within the parentheses;

[0102] The computational expression for transforming the j-th node of a fuzzy gray cognitive graph from a gray state value to a state value is:

[0103] (6)

[0104] Wherein, η is an adjustment factor, the magnitude of which is between 0 and 1, preferably η=0.7.

[0105] S3. Optimize the FGCM grey causal association weights of the avoidance decision model based on scene data and genetic algorithm;

[0106] S31. Update the causal weight matrix of the avoidance decision model. ;

[0107] By analyzing spacecraft orbital threat avoidance scenarios, the causal correlation weight matrix of the decision-making model can be identified. The general form is:

[0108] (7)

[0109] In this matrix, the elements that are equal to 0 indicate that there is no causal relationship between the two nodes of FGCM, and the remaining elements need to be obtained through genetic algorithm optimization.

[0110] S32. Optimize model parameters using a genetic algorithm.

[0111] ① Initialize the decision model

[0112] Assume the population size H = 500, the maximum number of generations G = 200, and the crossover probability P. c =0.7, mutation probability P m =0.1, evolutionary algebra calculator g=1;

[0113] Each chromosome is encoded using real numbers:

[0114] (8)

[0115] Each element in L is randomly initialized, ensuring that each element is between -1 and 1.

[0116]

[0117] ② Calculate the fitness function

[0118] (9)

[0119] Where ε represents the data training error, and the specific calculation formula is as follows:

[0120] (10)

[0121] Where N represents the number of training samples, This represents the actual value of the j-th node of the n-th sample in the FGCM model. This represents the predicted value of the j-th node for the n-th sample in the FGCM model;

[0122] ③ Select Operation

[0123] Calculate the probability of each chromosome being selected:

[0124] (11)

[0125] Among them, P h Let h represent the probability of the h-th chromosome being selected, where h = 1, 2, …, H, and fitness. h This indicates the fitness of the h-th chromosome;

[0126] According to the rules of roulette, a new population is formed based on the fitness of each chromosome, and the new population then proceeds to steps ④ and ⑤ in sequence.

[0127] ④ Cross operations

[0128] like Figure 4 As shown, a constant p between 0 and 1 is randomly generated. c If p c <P c Then, randomly select H / 4 pairs of chromosomes to swap the corresponding coding elements, ensuring that the crossover operation is performed on a per-weight basis corresponding to the FGCM node; if p c ≥P c If so, proceed directly to step ⑤;

[0129] ⑤ Mutation operation

[0130] like Figure 5 As shown, a constant p between 0 and 1 is randomly generated. m If p m <P m Then, a chromosome is randomly selected and mutated at a random position, ensuring that the mutation operation is performed on a unit of weight corresponding to the FGCM node; if p m ≥P m If so, proceed directly to step ⑥;

[0131] ⑥ Termination condition judgment

[0132] Update g = g + 1. If g ≤ G, then jump to step ②; if g > G, then terminate the loop and select the chromosome with the highest fitness as the optimal grey causal association weight for the FGCM model.

[0133] S4. The optimized FGCM model is used for orbital threat avoidance strategies.

[0134] Suppose satellite A is orbiting at an altitude of 500km. Satellite B, with the same orbital parameters but a phase lag of 30°, carrying a camera payload, approaches to a distance of 10km behind satellite A and stays there for 1 hour. Following step S1, the state of this scenario at a certain moment is quantified: C1=0.7, C2=0.43, C3=0.82, C4=0, C5=0.85. Based on the optimized FGCM model, we know that C6=0.198. Therefore, satellite A should perform attitude maneuvers at this time to avoid the threat posed by satellite B.

[0135] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A spacecraft orbital threat avoidance decision-making method based on FGCM, characterized in that, Includes the following steps: S1. Based on the orbital threats faced by the spacecraft, define the input and output nodes and state value rules of the decision-making method; The specific rules for the input nodes and their state values ​​are as follows: Taking the orbital threats faced by spacecraft as the research object, the threat distance, threat velocity, threat anomaly, threat payload behavior status, and threat level are selected as input nodes for the decision-making method; node C1 represents the threat distance, node C2 represents the threat velocity, node C3 represents the threat anomaly, node C4 represents the threat payload behavior status, and node C5 represents the threat level. The rules for selecting the value of node C1 are as follows: Where e=2.72, l represents the actual relative distance between the threat and the spacecraft, l1 represents the maximum observable distance of the threat from the spacecraft, and l2 represents the minimum safe distance for the spacecraft to avoid a collision. The rules for selecting the value of node C2 are as follows: where v0= (v max +v min ) / 2, σ = a(v max +v min ), v represents the actual relative speed of the threat approaching the spacecraft, v max and v min are the maximum and minimum speeds of the threat approaching the spacecraft, respectively, and a represents a fuzz factor and is a constant between 0 and 1; The value of node C3 is described by a switch. If a threat suddenly attacks or harasses the node, C3=1; otherwise, C3=0. The value of node C4 is between 0 and 1. The specific rules need to be represented by a set of fuzzy values ​​according to the type of load. If the load is a camera, the set of fuzzy values ​​is {silent: 0.1, aiming: 0.4, extending: 0.7}. The value of node C5 is between 0 and 1 and can be obtained directly. The larger the value, the higher the threat level. The specific rules for the output nodes and their status values ​​are as follows: The behavior strategy selected by the spacecraft is selected as the output node. Node C6 is defined to represent the behavior strategy selected by the spacecraft, including 5 behavior strategies: normal operation, attitude maneuver, orbital maneuver, emergency avoidance, and release of interference. The value of node C6 is between 0 and 1, and is represented by a fuzzy membership set: {normal operation: 0.1, attitude maneuver: 0.3, orbital maneuver: 0.5, emergency avoidance: 0.7, release interference: 0.9}; S2. Establish a decision-making model for spacecraft to avoid orbital threats based on FGCM; S3. Optimize the FGCM grey causal association weights of the avoidance decision model based on scene data and genetic algorithm; S4. Apply the optimized avoidance decision model to orbital threat avoidance decision-making.

2. The spacecraft orbital threat avoidance decision-making method based on FGCM according to claim 1, characterized in that, The method for establishing a spacecraft's decision-making model for mitigating orbital threats based on FGCM in step S2 is as follows: Using a fuzzy grayscale cognitive map as a medium, the mathematical expression for the grayscale state value of each node is as follows: in, This represents the gray state value of the j-th node at time t+1, where j represents the result node, and j=1,2,…,6. Let represent the gray state value of the i-th node at time t, where i represents the cause node, i=1,2,…,6, and S represents the set of all nodes in the FGCM. Let f represent the gray causal association weights from node i to node j, and let f represent the node update function. ∈[ , ]and ≤ , This represents the lower bound of the state value of the j-th node at time t+1. This represents the upper bound of the state value of the j-th node at time t+1. ∈[ , ]and ≤ , This represents the lower bound of the state value of the i-th node at time t. This represents the upper bound of the state value of the i-th node at time t. ∈[ , ]and ≤ , This represents the lower bound of the causal association weights from node i to node j. This represents the upper bound of the causal association weights from the i-th node to the j-th node; The mathematical form of the node update function is: Where λ is a constant greater than 0; The operation rules are as follows: Here, min() means taking the minimum value of the element within the parentheses, and max() means taking the maximum value of the element within the parentheses; The computational expression for transforming the j-th node of a fuzzy gray cognitive graph from a gray state value to a state value is: Here, η is the adjustment factor, and its value is between 0 and 1.

3. The spacecraft orbital threat avoidance decision-making method based on FGCM according to claim 2, characterized in that, The method for optimizing the gray causal association weights of FGCM based on scene data and genetic algorithm described in step S3 is as follows: S31. Update the causal weight matrix of the decision model. ; S32. Use a genetic algorithm to optimize the model parameters.

4. The spacecraft orbital threat avoidance decision-making method based on FGCM according to claim 3, characterized in that, The causal correlation weight matrix of the avoidance decision model described in step S31 The form is: In this matrix, the elements equal to 0 indicate that there is no causal relationship between the two nodes of FGCM, and the remaining elements need to be obtained through optimization using a genetic algorithm.

5. The spacecraft orbital threat avoidance decision-making method based on FGCM according to claim 4, characterized in that, The specific method for optimizing model parameters using a genetic algorithm as described in step S32 is as follows: ① Initialize the decision model Assume the population size H = 500, the maximum number of generations G = 200, and the crossover probability P. c =0.7, mutation probability P m =0.1, evolutionary algebra calculator g=1; Each chromosome is encoded using real numbers: Each element in L is randomly initialized, ensuring that each element is between -1 and 1. ② Calculate the fitness function Where ε represents the data training error, and the specific calculation formula is as follows: Where N represents the number of training samples, This represents the actual value of the j-th node of the n-th sample in the FGCM model. This represents the predicted value of the j-th node for the n-th sample in the FGCM model; ③ Select Operation Calculate the probability of each chromosome being selected: Among them, P h Let h represent the probability of the h-th chromosome being selected, where h = 1, 2, …, H, and fitness. h This represents the fitness of the h-th chromosome; According to the rules of roulette, a new population is formed based on the fitness of each chromosome, and the new population then proceeds to steps ④ and ⑤ in sequence. ④ Cross operations Randomly generate a constant p between 0 and 1 c If p c <P c Then, randomly select H / 4 pairs of chromosomes to swap the corresponding coding elements, ensuring that the crossover operation is performed on a per-weight basis corresponding to the FGCM node; if p c ≥P c If so, proceed directly to step ⑤; ⑤ Mutation operation Randomly generate a constant p between 0 and 1 m If p m <P m Then, a chromosome is randomly selected and mutated at a random position, ensuring that the mutation operation is performed on a unit of weight corresponding to the FGCM node; if p m ≥P m If so, proceed directly to step ⑥; ⑥ Termination condition judgment Update g = g + 1. If g ≤ G, then jump to step ②; if g > G, then terminate the loop and select the chromosome with the highest fitness as the optimal grey causal association weight for the FGCM model.

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