Assessment method of constellation system elasticity

Abstract

The invention provides a constellation system elasticity evaluation method comprising the following steps: S1, normalizing the coverage area of a constellation system in each working mode, and fitting to obtain a performance function; s2, determining the transfer type of the working mode, and determining the performance change condition of the constellation system before and after disturbance; s3, analyzing a minimum cut set Yk according to a preset fault tree; s4, calculating the elasticity of each minimum cut set Yk after an abnormal event occurs at the moment ti and a specific mode is implemented; s5, averagely taking m discrete time points from one work period of the constellation system, setting perturbation and the like to possibly occur at the m time points, and calculating the average projectile degree and the projectile degree satisfaction rate after a specific mode is implemented in the minimum cut set Yk; s6, calculating the average projectile degree and the projectile degree satisfaction rate of the minimum cut set Yk; s7, calculating the average elastic degree and the elastic degree satisfaction rate of the working mode transfer; and S8, calculating the average elastic degree and the elastic degree satisfaction rate of the constellation system.

Description

Technical Field

[0001] This invention belongs to the field of reliability assessment technology, and in particular relates to a method for assessing the resilience of a constellation system. Background Technology

[0002] Satellite constellations have emerged as a rapidly developing satellite mission mode in recent years. Their diverse composition, flexible operating modes, and high mission efficiency have garnered increasing favor among users. However, with the rapid and large-scale development of constellations, shortcomings in reliability prediction and assessment have become apparent. These shortcomings primarily include: 1. Traditional reliability prediction and assessment methods mainly focus on satellites capable of performing missions independently, lacking research on satellites forming constellations and collaborating to complete missions; 2. Traditional methods fail to consider the adaptability and recovery capabilities of constellation satellites in the face of external disturbances and internal failures during the assessment process.

[0003] The term "resilience" originates from the Latin word "resiliere," meaning "bounce back." It describes a system's ability to resist, adapt to, and recover from external disturbances and internal faults. It encompasses all possible states of continuous performance degradation and represents a new "process-oriented" reliability requirement. In recent years, resilience has gained widespread attention in the design of numerous complex systems, including power systems, water supply networks, communication networks, and transportation networks.

[0004] Failures are inevitable. When a system is disturbed and experiences failure or performance degradation, the system's ability to withstand disturbances and recover quickly is also very important. This ability is also part of the overall characteristics of the system, namely "resilience". Summary of the Invention

[0005] At least one objective of this application is to provide a method for evaluating the resilience of constellation systems, in order to address the problem of insufficient effectiveness in evaluating constellation resilience in the prior art.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for evaluating the resilience of a constellation system is provided. The method includes: S1: normalizing the coverage area of ​​the constellation system under each operating mode and fitting a performance function; S2: determining the type of operating mode transition and clarifying the performance changes of the constellation system before and after a disturbance; S3: conducting fault tree analysis with operating mode transition as the top event and abnormal events as the bottom events, and analyzing the minimum cut set Y of the fault tree. k S4: Collect minimum cut set information; S5: Calculate each minimum cut set Y k In t i Resilience in the event of an anomaly and the implementation of specific methods, including autonomous recovery of the constellation system, ground-based intervention, and failure to recover. i For minimal cut set Yk The occurrence time; S5: Take m discrete time points on average for one working cycle of the constellation system, assume that the disturbance can occur at m time points with equal probability, and calculate the minimum cut set Y. k Average elasticity and elasticity satisfaction rate after implementing a specific method; S6: Calculate the minimum cut set Y k The probability of being in different specific modes, and the minimum cut set Y is calculated using the law of total probability. k Average elasticity and elasticity satisfaction rate; S7: Minimum cut sets Y under a certain working mode transition k S8: Based on the average elasticity and elasticity satisfaction rate of all working mode transitions, and combined with the working mode probability and state transition probability of the constellation system before disturbance obtained through constellation assurance reliability analysis, calculate the average elasticity and elasticity satisfaction rate of the constellation system.

[0007] Furthermore, the performance function in S1 above is:

[0008]

[0009] In the formula, Q CA.i (ω) represents the normalized performance of the constellation system at latitude ω in the i-th operating mode, CA i (ω) represents the coverage area of ​​the constellation system at latitude ω when operating in the i-th mode; CA N,L CA is the critical value for the usable coverage area of ​​the constellation system. UA,U This is the critical value for coverage area failure of the constellation system.

[0010] Furthermore, in S2 above, the number of working modes ranges from 3 to 8, and the working mode transfer mode is: from a working mode with a larger coverage area to a working mode with a smaller coverage area.

[0011] Furthermore, in S3 above, the minimum cut set information includes the type of abnormal event, the probability of occurrence of the disturbance mode, the probability of occurrence of the failure mode, the success rate and recovery time of autonomous recovery of the constellation system, the success rate and recovery time of recovery by ground handling, and the probability of failure to recover.

[0012] Furthermore, in S4 above, the method for calculating the elasticity is as follows:

[0013]

[0014] In the formula, For t i Time-limited minimal cut set Y k The occurrence and recovery mechanisms are β and β, respectively. j Elasticity at time, X jFor abnormal events, β j For a specific method, For abnormal event X j Through all specific methods β respectively j Minimum recovery time under recovery conditions; T a The maximum recovery time allowed by the user; Q CA,0 (t) represents the normalized performance of the constellation system coverage area at time t under normal conditions; Q CA,y (t) represents the normalized performance of the coverage area of ​​a single constellation when the constellation system switches to working mode y at time t, where T is the normalized performance of the constellation coverage area. a This refers to the recovery time allowed by the constellation system.

[0015] Furthermore, in S5 above, the minimum cut set Y k The formula for calculating the average elasticity after implementing a specific method is as follows: ,in For minimal cut set Y k The average elasticity recovered through some means, the minimum cut set Y k The formula for calculating the elasticity satisfaction rate after implementing a specific method is as follows: ,in For minimal cut set Y k The elasticity satisfaction rate is restored through some means.

[0016] Furthermore, the aforementioned minimal cut set Y k The formula for calculating the average elasticity is: Minimal cut set Y k The formula for calculating the elasticity satisfaction rate is as follows: ,in, The average elasticity is the average elasticity of the system under multiple disturbances; p r For probability; The elasticity satisfaction rate is the probability that the system will elastically satisfy the requirements after receiving a disturbance.

[0017] Furthermore, the formula for calculating the average elasticity of the above-mentioned working mode transition is as follows: , among which Let p be the elasticity and p be the probability. The formula for calculating the elasticity satisfaction rate of working mode transition is: , among which Let p be the elasticity, and p be the probability.

[0018] Furthermore, the formula for calculating the average elasticity of the aforementioned constellation system is as follows: Elasticity satisfaction rate of constellation system , where p x This represents the probability that the constellation was in pattern x before the disturbance occurred. This represents the state transition probability.

[0019] According to one aspect of the present invention, a computer-readable storage medium having software instructions stored thereon is provided, which, when executed, implement any of the methods described above.

[0020] The advantages of this invention compared to existing technologies are:

[0021] 1) Based on the confidence reliability theory framework, this invention selects two key positioning performance parameters, coverage area and maximum revisit time, and judges faults by whether the above parameters reach the threshold requirements, which is more in line with the characteristics of constellation systems;

[0022] 2) This invention considers constellation operating mode degradation during the resilience measurement process. Even with a degraded constellation operating mode, the constellation positioning requirements can still be met within a relatively small range of activity. This ensures that the constellation system's resilience, adaptability, and recovery capabilities in the face of disturbances and faults can be objectively assessed. Attached Figure Description

[0023] The following description, in conjunction with the accompanying drawings, will further illustrate the above-mentioned features, technical characteristics, advantages, and implementation methods of this application in a clear and understandable manner. The accompanying drawings are for illustrative and explanatory purposes only and do not limit the scope of this application. Wherein:

[0024] Figure 1 This illustration shows a schematic diagram of the resilient behavior of the system after being disturbed in one embodiment of this application;

[0025] Figure 2 This paper illustrates a flowchart of a single constellation elastic modeling and simulation process in one embodiment of this application.

[0026] Figure 3 A flowchart of multiple constellation elastic modeling and simulation processes is shown in one embodiment of this application. Detailed Implementation

[0027] To provide a clearer understanding of the technical features, objectives, and effects of this application, specific embodiments of this application will now be described with reference to the accompanying drawings.

[0028] Currently, the resilience assessment of constellation systems is still in its developmental stage, and a targeted resilience assessment framework has not yet been established. To facilitate understanding of the technical solution, the resilience concepts and measurement methods involved in the constellation system resilience modeling and simulation assessment method provided in this application will be briefly explained first, with reference to the accompanying drawings.

[0029] The following are some concepts

[0030] (1) Elasticity: Elasticity refers to a system's ability to withstand disturbances and recover after the disturbance. For example, Figure 1As shown, the system's resilient behavior mainly includes: the system is subjected to a disturbance at time t0, resulting in performance degradation, and then, through recovery measures, its performance gradually returns to the original state or a new stable state. The system's ability to predict, resist, absorb, adapt to, and recover from disturbances determines the performance degradation and recovery process.

[0031] (2) Average elasticity: The average elasticity of the system under multiple disturbances, one of the parameters for measuring the elasticity of the system, and is calculated as follows:

[0032]

[0033] In the formula, Let E represent the average elasticity, and E() represent the expected value. Represents the elasticity under the i-th perturbation, which is the allowable recovery time T of the system after a single perturbation. a The performance integral within the time frame and T under normal conditions a The ratio of the performance integral within the timeframe is calculated as follows:

[0034]

[0035] In the formula, Q i Let Q(t) be the normalized performance of the system at time t after the i-th perturbation, and Q0(t) be the expected normalized performance curve of the system. T a t0 is the system's allowed recovery time, and t0 is the disturbance start time.

[0036] (3) Elasticity satisfaction rate: The probability that the system will meet the elasticity requirements after being disturbed. It is one of the parameters that measures the elasticity of the system. The calculation method is as follows:

[0037]

[0038] In the formula, p r ( ) represents probability. This is the elasticity requirement value.

[0039] (4) Working mode: The operating status or operation mode of a satellite or constellation when performing a mission, which is usually switched according to mission requirements, resource allocation or environmental conditions.

[0040] (5) Coverage area: The geographical area that a satellite or constellation can effectively observe or serve within its orbit or sensor field of view.

[0041] (6) Working cycle: The time required for a satellite or constellation to complete a full mission or operating cycle, which may involve orbital cycle, mission execution cycle or resource management cycle.

[0042] (7) Single constellation system: a formation unit consisting of multiple satellites that work together to build a satellite network with global coverage.

[0043] (8) Multiple constellation systems: formation units consisting of multiple satellites, with multiple such units operating in concert to build a global satellite network.

[0044] As described in the background section of this application, the existing technology for evaluating constellation resilience is insufficient. To address this issue, this application provides a method for evaluating the resilience of constellation systems.

[0045] In a typical embodiment of this application, a method for evaluating the resilience of a constellation system is provided. The method includes: S1: Normalizing the coverage area of ​​the constellation system under each operating mode and fitting a performance function; S2: Determining the type of operating mode transition and clarifying the performance changes of the constellation system before and after a disturbance; S3: Using the operating mode transition as the top event and the abnormal event as the bottom event, conducting fault tree analysis and analyzing the minimum cut set Y of the fault tree. k S4: Collect minimum cut set information; S5: Calculate each minimum cut set Y k In t i Resilience in the event of an anomaly and the implementation of specific methods, including autonomous recovery of the constellation system, ground-based intervention, and failure to recover. i For minimal cut set Y k The occurrence time; S5: Take m discrete time points on average for one working cycle of the constellation system, assume that the disturbance can occur at m time points with equal probability, and calculate the minimum cut set Y. k Average elasticity and elasticity satisfaction rate after implementing a specific method; S6: Calculate the minimum cut set Y k The probability of being in different specific modes, and the minimum cut set Y is calculated using the law of total probability. k Average elasticity and elasticity satisfaction rate; S7: Minimum cut sets Y under a certain working mode transition k S8: Based on the average elasticity and elasticity satisfaction rate of all working mode transitions, and combined with the working mode probability and state transition probability of the constellation system before disturbance obtained through constellation assurance reliability analysis, calculate the average elasticity and elasticity satisfaction rate of the constellation system.

[0046] The method of the present invention first normalizes the coverage area of ​​the constellation system in each working mode and fits it to obtain a performance function. Then, it determines the type of working mode transition and clarifies the performance changes of the constellation system before and after the disturbance. In one embodiment, the working mode transition can be recorded using the table below.

[0047] Table 1. Transfer between different operating modes (taking 5 operating modes after a failure as an example)

[0048]

[0049] Subsequently, using the working mode transition as the top event and the abnormal event as the bottom event, fault tree analysis was conducted to analyze the minimum cut set Y of the fault tree. k Next, we will calculate the minimum cut set Y and collect information on the minimum cut sets. k In t i The elasticity that occurs at any given moment and is recovered through specific methods, for a minimal cut set, can have 3 recovery scenarios. n (where n is the number of anomalous events in the cut set, and 3 represents the three specific modes of each type of failure (autonomous recovery of the constellation system, ground handling, and unrecoverable failure), calculate these 3...) n The probability of each scenario and its corresponding elasticity are calculated. Then, the minimum cut set Y is calculated using the total probability. k In t i The resilience is determined by the occurrence of an abnormal event and the implementation of a specific method. Then, to reflect the impact of the disturbance on the system's resilience at different times, m discrete time points are averaged over one working cycle, assuming the disturbance occurs at each of these m time points with equal probability, and the minimum cut set Y is calculated. k The average elasticity and elasticity satisfaction rate after implementing a specific method are calculated. Then, the minimum cut set Y is calculated sequentially. k The probability of being in different specific modes, and the minimum cut set Y is calculated using the law of total probability. k Average elasticity and elasticity satisfaction rate; based on the minimum cut sets Y under a certain working mode transition. k The average elasticity and elasticity satisfaction rate are calculated to determine the average elasticity and elasticity satisfaction rate of the working mode transition. Based on the average elasticity and elasticity satisfaction rate of all working mode transitions, and combined with the working mode probability and state transition probability of the constellation system before disturbance obtained through constellation assurance reliability analysis, the average elasticity and elasticity satisfaction rate of the constellation system are calculated.

[0050] In one embodiment, the performance function in S1 above is:

[0051]

[0052] In the formula, Q CA.i (ω) represents the normalized performance of the constellation system at latitude ω in the i-th operating mode, CA i (ω) represents the coverage area of ​​the constellation system at latitude ω when operating in the i-th mode; CA N,L CA is the critical value for the usable coverage area of ​​the constellation system. UA,UThis is the critical value for coverage area failure of the constellation system.

[0053] In one embodiment, in S2 above, the number of working modes ranges from 3 to 8, and the working mode transfer mode is: transferring from a working mode with a larger coverage area to a working mode with a smaller coverage area.

[0054] In one embodiment, the minimum cut set information in S3 above includes the abnormal event type, the probability of disturbance mode occurrence, the probability of failure mode occurrence, the autonomous recovery success rate and recovery time of the constellation system, the recovery success rate and recovery time of ground handling, and the probability of failure to recover.

[0055] Table 2. Minimum cut set information (operational performance) for transitioning from operating mode x to y.

[0056]

[0057] In one embodiment, the elasticity is calculated in S4 as follows:

[0058]

[0059] In the formula, For t i Time-limited minimal cut set Y k The occurrence and recovery mechanisms are β and β, respectively. j Elasticity at time, X j For abnormal events, β j For a specific method, For abnormal event X j Through all specific methods β respectively j Minimum recovery time under recovery conditions; T a The maximum recovery time allowed by the user; Q CA,0 (t) represents the normalized performance of the constellation system coverage area at time t under normal conditions; Q CA,y (t) represents the normalized performance of the coverage area of ​​a single constellation when the constellation system switches to working mode y at time t, where T is the normalized performance of the constellation coverage area. a This refers to the recovery time allowed by the constellation system.

[0060] In one embodiment, in S5 above, the minimum cut set Y k The formula for calculating the average elasticity after implementing a specific method is as follows: ,in For minimal cut set Y k The average elasticity recovered through some means, the minimum cut set Y k The formula for calculating the elasticity satisfaction rate after implementing a specific method is as follows: ,in For minimal cut set Y kThe elasticity satisfaction rate is restored through some means.

[0061] In one embodiment, the aforementioned minimal cut set Y k The formula for calculating the average elasticity is: Minimal cut set Y k The formula for calculating the elasticity satisfaction rate is as follows: ,in, The average elasticity is the average elasticity of the system under multiple disturbances; p r For probability; The elasticity satisfaction rate is the probability that the system will elastically satisfy the requirements after receiving a disturbance.

[0062] In one embodiment, the formula for calculating the average elasticity of the above-mentioned working mode transition is: , among which Let p be the elasticity and p be the probability. The formula for calculating the elasticity satisfaction rate of working mode transition is: , among which Let p be the elasticity, and p be the probability.

[0063] In one embodiment, the formula for calculating the average elasticity of the constellation system described above is: Elasticity satisfaction rate of constellation system , where p x This represents the probability that the constellation was in pattern x before the disturbance occurred. This represents the state transition probability.

[0064] According to another typical embodiment of this application, a computer-readable storage medium having software instructions stored thereon is provided, which, when executed, perform any of the methods described above.

[0065] The present invention will be further described below with reference to embodiments.

[0066] Example 1 - Single Constellation Elasticity Simulation

[0067] Using the Monte Carlo method, fault and recovery behaviors of a single constellation are sampled. Through simulation, the average elasticity and elasticity satisfaction rate of a single constellation system with coverage area as the performance parameter are calculated.

[0068] Before the simulation begins, it is first assumed that the constellation is in normal operating mode before the disturbance or fault. Relevant information about the operating mode is collected as shown in the table below. The modeling and simulation process is as follows: Figure 2 As shown.

[0069] Table 3 Elastic behavior of a single constellation after disturbance / fault

[0070]

[0071] Step 1: Based on the occurrence rate of anomalous events, use Monte Carlo sampling to obtain t. i The fault occurs at time t, and the fault time of each abnormal event within time Ta is sampled and recorded in [t]. i , t i +T a The fault that occurred within a certain time period.

[0072] Step 2: Based on the probabilities of various recovery methods for the fault, use Monte Carlo sampling to obtain the recovery method and recovery time of the fault in this simulation.

[0073] Step 3: Determine [t] based on the job transfer fault tree. i , t i + T a Determine the system performance at each time point within the time interval to establish the system performance curve in this simulation. Calculate the resilience of this fault.

[0074] Step 4: Calculate the elasticity when the fault occurs at different times in a working cycle, and calculate the average elasticity and elasticity satisfaction rate.

[0075] Step 5: Repeat steps one through four to obtain n sets of average elasticity and elasticity satisfaction rate samples, and calculate the system average elasticity and system elasticity satisfaction rate.

[0076] Example 2 - Simulation of Multiple Constellation Elasticity

[0077] Multiple constellations, using maximum revisit time as a performance parameter, are sampled for fault and recovery behaviors using the Monte Carlo method. Their average elasticity and elasticity satisfaction rate are calculated through simulation. The modeling and simulation process is detailed below. Figure 3 .

[0078] Step 1: Calculation and Normalization of Maximum Revisit Time. Different combinations of constellation operating modes correspond to different maximum revisit times. The maximum revisit time of a constellation system depends on the time interval between any two adjacent constellation groups reaching the required coverage area. Assume that the time when the Nth constellation group cannot meet the positioning coverage requirement is T. N,out The time when the N+1th constellation satisfies the positioning coverage area is T. N+1,in Therefore, the revisit time RT is:

[0079]

[0080] Then, following the normalization method for small parameters, the performance values ​​Q under multiple constellation working mode combinations i are obtained. MRT,i Since the maximum revisit time is a constant under the same combination of multiple constellation working modes, there is no need to perform function fitting.

[0081] Step 2: Assuming the constellation was in normal operating mode before the disturbance or fault, collect relevant information about the operating mode as shown in the table below:

[0082] Table 4 Elastic behavior of multiple constellations after disturbance / fault

[0083]

[0084] Step 3: According to Figure 3 The process involves conducting Monte Carlo simulations to determine information after multiple constellation disturbances / faults, with specific steps similar to those for single-constellation system simulations.

[0085] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0086] The above are merely illustrative embodiments of this application and are not intended to limit the scope of this application. Any equivalent changes, modifications, and combinations made by those skilled in the art without departing from the concept and principles of this application shall fall within the scope of protection of this application.

Claims

1. A method for evaluating the resilience of a constellation system, wherein, The methods for assessing the resilience of the constellation system include: S1: Normalize the coverage area of ​​the constellation system in each working mode and fit it to obtain the performance function; S2: Determine the transition type of the working mode and clarify the performance changes of the constellation system before and after the disturbance occurs; S3: Using the working mode transition as the top event and the abnormal event as the bottom event, conduct fault tree analysis and analyze the minimum cut set Y of the fault tree. k And collect minimum cut set information; S4: Calculate each of the minimum cut sets Y k In t i Resilience after the aforementioned abnormal event occurs and a specific method is implemented, wherein the specific method includes autonomous recovery of the constellation system, ground handling, and failure to recover. i For minimal cut set Y k The time of occurrence; S5: Take m discrete time points on average for one working cycle of the constellation system, and assume that the disturbance can occur at an equal probability at m time points, calculate the minimum cut set Y. k The average elasticity and elasticity satisfaction rate after implementing one of the specific methods described above; S6: Calculate the minimum cut set Y k The probability of being in different specific modes, and the minimum cut set Y is calculated using the law of total probability. k The average elasticity and elasticity satisfaction rate; S7: According to the minimum cut set Y under the working mode transition described in one class, k The average elasticity and elasticity satisfaction rate are calculated for the working mode transition. S8: Based on the average elasticity and elasticity satisfaction rate of all the aforementioned operating mode transitions, and combined with the operating mode probability and state transition probability of the constellation system before the disturbance obtained through constellation assurance reliability analysis, calculate the average elasticity and elasticity satisfaction rate of the constellation system.

2. The method for evaluating the resilience of a constellation system according to claim 1, characterized in that, The performance function in S1 is: In the formula, Q CA.i (ω) represents the normalized performance of the constellation system at latitude ω in the i-th operating mode, CA i (ω) represents the coverage area of ​​the constellation system at latitude ω in the i-th operating mode; CA N,L CA is the critical value for the usable coverage area of ​​the constellation system. UA,U This is the critical value for the coverage area failure of the constellation system.

3. The method for evaluating the resilience of a constellation system according to claim 1, characterized in that, In S2, the number of working modes ranges from 3 to 8, and the working mode transfer mode is: transferring from the working mode with a larger coverage area to the working mode with a smaller coverage area.

4. The method for evaluating the resilience of a constellation system according to claim 1, characterized in that, In S3, the minimum cut set information includes the abnormal event type, the probability of disturbance mode occurrence, the probability of failure mode occurrence, the autonomous recovery success rate and recovery time of the constellation system, the recovery success rate and recovery time of ground handling, and the probability of failure to recover.

5. The method for evaluating the resilience of a constellation system according to claim 1, characterized in that, In step S4, the elasticity is calculated as follows: In the formula, For t i Time-limited minimal cut set Y k The occurrence and recovery mechanisms are β and β, respectively. j Elasticity at time, X j For the aforementioned abnormal event, β j For the specific method, For the abnormal event X j Each through all the specific methods β j Minimum recovery time under recovery conditions; T a The maximum recovery time allowed by the user; Q CA,0 (t) represents the normalized performance of the constellation system's coverage area at time t under normal conditions; Q CA,y (t) represents the normalized performance of the coverage area of ​​a single constellation when the constellation system transitions to working mode y at time t, where T is the normalized performance of the constellation coverage area of ​​a single constellation. a This refers to the allowed recovery time for the constellation system.

6. The method for evaluating the resilience of a constellation system according to claim 5, characterized in that, In S5, the minimum cut set Y k The formula for calculating the average elasticity after implementing one of the specific methods is as follows: ,in For minimal cut set Y k The minimum cut set Y is the average elasticity recovered in some way. k The formula for calculating the elasticity satisfaction rate after implementing one of the specific methods is as follows: ,in For minimal cut set Y k The elasticity satisfaction rate is restored through some means.

7. The method for evaluating the resilience of a constellation system according to claim 6, characterized in that, The minimum cut set Y k The formula for calculating the average elasticity is: The minimum cut set Y k The formula for calculating the elasticity satisfaction rate is as follows: ,in, The average elasticity is the average elasticity of the system under multiple disturbances; p r For probability; The elasticity satisfaction rate is the probability that the system will elastically satisfy the requirements after receiving a disturbance.

8. The method for evaluating the resilience of a constellation system according to claim 7, characterized in that, The formula for calculating the average elasticity during the working mode transition is as follows: ,in Let p be the elasticity and p be the probability. The formula for calculating the elasticity satisfaction rate of the working mode transition is: ,in Let p be the elasticity, and p be the probability.

9. The method for evaluating the resilience of a constellation system according to claim 8, characterized in that, The formula for calculating the average elasticity of the constellation system is as follows: The elasticity satisfaction rate of the constellation system , where p x This represents the probability that the constellation was in pattern x before the disturbance occurred. This represents the state transition probability.

10. A computer-readable storage medium having software instructions stored thereon, which, when executed, perform the method according to any one of claims 1-9.

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