Satellite constellation comprehensive application capability assessment method and device based on clustering analysis

Abstract

The invention discloses a clustering analysis-based satellite constellation comprehensive application capability evaluation method and equipment, and relates to the technical field of satellite constellation comprehensive application capability evaluation. The satellite constellation comprehensive application capability assessment method based on clustering analysis mainly comprises the following steps: constructing a constellation performance index system based on satellite constellation comprehensive capability characteristics, carrying out quantification and standardization processing on the constellation performance index system, carrying out aggregation by utilizing a Pearson correlation coefficient and a significance evaluation index, and carrying out clustering analysis according to a clustering result. And obtaining a clustering comprehensive index system by using a variable coefficient, screening out an effective clustering comprehensive index system based on an order degree judgment criterion, and obtaining system efficiency by using an analytic hierarchy process and an entropy weight method. By implementing the satellite constellation comprehensive application capability assessment method based on clustering analysis, the constellation comprehensive efficiency can be accurately assessed, and the capability of distinguishing alternative schemes is improved.

Description

Technical Field

[0001] This invention relates to the field of satellite constellation integrated application capability assessment technology, and more specifically, to a method and device for assessing satellite constellation integrated application capability based on cluster analysis. Background Technology

[0002] With the rapid increase in the number of satellites worldwide, satellite constellation systems are being used more and more widely in navigation, remote sensing, and communications. Satellite constellation systems typically consist of multiple satellites and possess characteristics such as wide coverage and continuous monitoring, thus playing an important role in various fields such as national defense, meteorology, and geographic information. However, how to scientifically and comprehensively evaluate the integrated application capabilities of satellite constellations remains a current technical challenge.

[0003] Traditional satellite constellation performance evaluation methods have certain limitations. Regarding the construction of indicator systems, some related studies have incomplete or redundant indicator systems. In terms of performance evaluation methods, classic methods such as the analytic hierarchy process (AHP) and fuzzy comprehensive method rely on too few factors to determine weights. While classic combined weighting evaluation methods comprehensively consider both subjective and objective factors, the weights assigned based on subjective experience suffer from excessive dependence on subjective factors. Therefore, a more effective method is needed to evaluate the performance of satellite constellations. Summary of the Invention

[0004] The purpose of this invention is to provide a method for evaluating the comprehensive application capabilities of satellite constellations based on cluster analysis, which can accurately assess the overall effectiveness of constellations and improve the ability to distinguish between alternative solutions.

[0005] This invention provides a method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis, comprising the following steps: S1: Construct a constellation performance index system based on the comprehensive capability characteristics of the satellite constellation; S2: Quantify and standardize the constellation performance index system to obtain the processed constellation performance index system; S3: Aggregate the processed constellation performance index system using Pearson correlation coefficient and significance evaluation index to obtain the aggregated constellation performance index system; S4: Perform clustering operations on the aggregated constellation performance index system to obtain clustering results; S5: Based on the clustering results, the comprehensive clustering index system is obtained using the coefficient of variation; S6: Based on the evaluation criterion of orderliness, determine the effectiveness and usability of the clustering comprehensive index system, and select effective clustering comprehensive index systems; S7: Based on the clustering comprehensive index system, the system efficiency is obtained using the analytic hierarchy process (AHP) and the entropy weight method.

[0006] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis.

[0007] The method and equipment for evaluating the integrated application capabilities of satellite constellations based on cluster analysis provided by this invention have the following beneficial effects: This invention addresses the challenges of satellite constellations as complex integrated systems, characterized by diverse mission types, powerful performance, and large-scale performance indicators generated during mission execution. Through research and analysis of constellation mission types and characteristics, it proposes a comprehensive performance evaluation index system based on missions, encompassing multiple constellation mission types. This system is suitable for evaluating the overall effectiveness of constellations. A clustering algorithm is used to cluster mission-oriented constellation indicators based on correlation coefficients, eliminating similar indicators and reducing their size. Pearson correlation coefficients are then used to cluster highly similar variables, extracting representative typical indicators. Finally, an effectiveness research method based on ordination is proposed to accurately determine... This paper improves upon the scientific validity and usability of the indicator system by combining the advantages of subjective and objective evaluation methods. Based on classical evaluation methods, it proposes a combined weighted constellation performance evaluation method. Objective evaluation is incorporated into the evaluation process, adjusting subjective evaluation results based on the contribution of indicator data to the information entropy of performance evaluation. An objective evaluation criterion based on orderliness and maximum variance is adopted, effectively reducing the reliance on subjective factors in determining method weights. This enhances the ability to differentiate between alternative schemes while ensuring accurate evaluation of the overall constellation performance. The method is used for comprehensive performance evaluation of multi-satellite constellation systems, covering dimensions such as timeliness, coverage, resource utilization, and reliability, reducing redundancy and improving evaluation efficiency. Attached Figure Description

[0008] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of the satellite constellation integrated application capability evaluation method based on cluster analysis provided by the present invention; Figure 2 This is a schematic diagram of the satellite constellation integrated application capability evaluation method provided by the present invention; Figure 3 This is a flowchart of the performance evaluation based on cluster analysis provided by the present invention; Figure 4 This is a flowchart of the performance evaluation based on combined weighting provided by the present invention; Figure 5 This is a schematic diagram comparing the relationship between evaluation quality and value changes provided by the present invention; Figure 6 This is a structural block diagram of the computer device provided by the present invention. Detailed Implementation

[0009] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0010] Figure 1 This diagram illustrates the satellite constellation integrated application capability assessment method based on cluster analysis according to this embodiment. In this embodiment, the satellite constellation integrated application capability assessment method based on cluster analysis includes the following steps: S1: Construct a constellation performance index system based on the comprehensive capability characteristics of the satellite constellation; In one exemplary embodiment, the constellation performance index system includes timeliness index, coverage index, resource utilization index, and reliability index; The timeliness indicators include coverage time percentage, maximum revisit period, average revisit period, average response time, single orbit working time, single operation time, and visible satellite duration; The coverage indicators include regional cumulative coverage rate, regional overlap rate, average coverage area percentage, regional coverage multiple, number of observation windows, and observation coverage elevation angle; The resource utilization rate indicators include resource utilization rates such as maximum single-satellite occupancy rate, minimum single-satellite occupancy rate, and average satellite system occupancy rate. The reliability indicators include equipment maintainability, equipment standardization, number of satellites in orbit in the constellation, number of spare satellites in the constellation, and DOP value.

[0011] S2: Quantify and standardize the constellation performance index system to obtain the processed constellation performance index system; In one exemplary embodiment, the normalization process is a standardization process.

[0012] In one exemplary embodiment, the normalization process is the z-score method; as shown in the formula:

[0013] in, Indicates the first Individual indicators The result of normalization, This represents the average value of the dataset. The standard deviation of the dataset, To determine the data scale.

[0014] S3: Aggregate the processed constellation performance index system using Pearson correlation coefficient and significance evaluation index to obtain the aggregated constellation performance index system; As an exemplary embodiment, in step S3, the similarity calculation method includes distance-based and similarity-based metrics to distinguish the differences and similarities between feature vectors of different individuals. Considering both the direction and magnitude of the feature vectors, this embodiment uses a distance-based metric to measure the spatial distance between different indicators. For indicators where the feature vector size is insensitive or where there are different ranges of variation within the feature vector, this embodiment uses the Pearson correlation coefficient to calculate indicator similarity, reflecting the degree of linear correlation between two indicators. The coefficient ranges from -1 to 1; a larger absolute value indicates a stronger correlation between the two indicators, and vice versa. The positive or negative sign of the coefficient represents a positive or negative correlation between the variables. This embodiment calculates indicator similarity to distinguish the differences and similarities between feature vectors of different individuals, and aggregates variables with high similarity based on the Pearson correlation coefficient.

[0015] In one exemplary embodiment, the formula for calculating the Pearson correlation coefficient is:

[0016] in, Represents a set of variable data and The Pearson correlation coefficient; This represents the expected value.

[0017] In one exemplary embodiment, the formula for calculating the Pearson correlation coefficient is as follows:

[0018] in, As a significance evaluation indicator; The correlation coefficient; This represents the dimension of the indicator's feature vector.

[0019] S4: Perform clustering operations on the aggregated constellation performance index system to obtain clustering results; As an exemplary embodiment, in step S4, clustering operations are performed on the indicator set according to the indicator system architecture. The indicator system is clustered based on the strength of the correlation between indicators, and indicators that provide similar information are aggregated into one class. Representative indicators are selected and weakly representative indicators are filtered out. During the iterative process of clustering, the distance between clusters is measured and calculated, and an inter-cluster distance matrix is ​​constructed. The clusters with the smallest distance are merged to form a new cluster. The distance between the newly generated cluster and all other clusters is calculated, and the inter-cluster distance matrix is ​​updated. This process is repeated until all individuals are aggregated into one cluster or the expected threshold is reached.

[0020] In one exemplary embodiment, step S4 specifically includes: S41: Obtain multiple sets of different experimental parameters, calculate them according to the aggregated constellation performance index system, and obtain an index data set; preprocess the index data set to eliminate differences in dimensions and differences between maximum and minimum values, calculate the Pearson correlation coefficient and significance index between the indicators, and judge the magnitude of the linear correlation and the significance of the linear correlation between the indicators. S42: Treat each object as a separate cluster, calculate the pairwise distances between all clusters to form an inter-class distance matrix, and set the final number of clusters according to requirements. m The specific calculation is as follows:

[0021]

[0022]

[0023]

[0024] S43: Based on the values ​​of the inter-cluster distance matrix, merge the clusters with the smallest distance to form a new cluster; S44: Calculate the distance between the newly generated cluster and all other clusters, and update the inter-cluster distance matrix with the values; S45: Return to step S43 until all individuals are aggregated into a cluster or the expected threshold is reached, then end the clustering process.

[0025] S5: Based on the clustering results, the comprehensive clustering index system is obtained using the coefficient of variation; As an exemplary embodiment, based on the clustering results, a coefficient of variation analysis is performed on the indicator set to calculate the ratio of the standard deviation of the original data to the mean of the original data, which measures the degree of dispersion of the dataset. By calculating the degree of information contribution of similar indicators within the group to the evaluation results, the indicator with the highest coefficient of variation or the indicator that meets the threshold is selected. That is, the most representative indicators in each factor layer are selected to form a comprehensive indicator system. Here, the coefficient of variation represents the ratio of the standard deviation of the original data to the mean of the original data, which measures the degree of dispersion of the indicator dataset.

[0026] In one exemplary embodiment, the formula for calculating the coefficient of variation is:

[0027] in, The first in the cluster The coefficient of variation of each indicator; The first in the cluster The standard deviation of the data for each indicator; The first in the cluster The average data of each indicator The number of indices in the cluster.

[0028] S6: Based on the evaluation criterion of orderliness, determine the effectiveness and usability of the clustering comprehensive index system; As an exemplary embodiment, in step S6, an evaluation criterion based on ordination is used to determine the effectiveness and usability of the clustering comprehensive index system. Specifically, this embodiment proposes a method for evaluating the effectiveness of the dimensionality reduction index system: first, multiple satellite constellation schemes are constructed, and performance evaluations are performed based on the original index system and the clustering index system, respectively. Let the experimental results of the original index set evaluation be ranked as follows: The results are ranked based on the dimensionality reduction index as follows: Let vector A be an ordered sequence, and vector B be an unordered sequence based on the criteria of vector A. For each element, if... , ,in Indicates the position of element i in the set, describing the element. The relationship is ordered. Based on the evaluation of the comprehensive orderliness of vector B, the effectiveness of the dimensionality reduction index system can be fully verified; Define To assess the effectiveness of the dimensionality reduction metric, the CHAOS function is used to evaluate the disorder of sequence B based on sequence A.

[0029] In one exemplary embodiment, the formula for calculating the degree of order is:

[0030] in, For degree of order; ={ 1, 2, … , The experimental results are ranked based on the original set of indicators. This indicates the number of indicators in sequence A. ; The results are ranked based on a clustering comprehensive index system; Based on sequence Based on A function to evaluate sequence disorder; and They are respectively The Middle and the Each element.

[0031] S7: Based on the clustering comprehensive index system, the system efficiency is obtained using the analytic hierarchy process (AHP) and the entropy weight method. In one exemplary embodiment, the system performance is calculated using the following formula:

[0032]

[0033]

[0034] in, Representation scheme System efficiency; plan The performance value, , ,..., Let n represent the values ​​of each performance indicator, and n represent the number of performance indicators in the plan. Weighting of subjective and objective factors; It refers to the proportion of subjective and objective weights in the analysis; The number of subjective empowerment methods; The number of objectively empowering methods; and They represent Subjective empowerment method and The weights assigned to each objective weighting method, and the following conditions must be met. ; Indicates the first The first subjective evaluation method calculated the Weight of each indicator; Indicates the first The first objective weight assignment method calculates the Each indicator has a weight.

[0035] As an exemplary embodiment, in step S7, a combined weighting evaluation method is proposed by combining the subjective judgment criteria of the analytic hierarchy process (AHP) and the objective data information of the entropy weight method, specifically including: The set of methods for weight calculation was selected. Subjective evaluation methods and An objective evaluation method, the evaluation problem system includes Alternative options Various evaluation criteria; The index weights calculated by the subjective evaluation method are: The weights meet the conditions. ;against The set of index weight vectors calculated by the objective weight assignment method is as follows: The weights meet the conditions. The overall weight is determined by the set of indicator weight vectors. and meet the conditions Let the first Group of alternative solutions The normalized values ​​of each indicator are , thus calculating The overall capability of the group of alternative solutions is shown in the formula:

[0036] In selecting the deviation metric, distance is used for calculation. Since it's a combined subjective and objective evaluation method, it's necessary to calculate the deviation between the combined weights and the subjective evaluation method, and the deviation from the objective evaluation method, respectively. The error between the combined weights and the subjective evaluation method in terms of Euclidean distance is given by the formula above. Similarly, the deviation from the objective evaluation method can be obtained as shown in the formula:

[0037]

[0038] To ensure more accurate calculation of the combined weights, specifically to minimize the sum of deviations between the combined weights and the subjective and objective weights, the planning function is constructed as follows:

[0039] In the above formula, the parameters The weighting of subjective and objective factors in the analysis indicates the importance of the subjective and objective analysis method; when This indicates that objective weighting plays a dominant role at this time, and is the main influencing factor on the comprehensive calculation result; when This indicates that subjective weighting plays a dominant role in the overall weighting calculation at this point; when This represents that subjective and objective factors account for an equal proportion of influence, parameters It reflects the decision-maker's preference for both subjective and objective factors.

[0040] conventional methods The selection of values ​​is based on experience; this embodiment is based on two criteria. The selection criteria include: the degree of orderliness of the ranking results, and the degree of separation of the overall evaluation scores of the schemes; the evaluation results based on subjective analysis methods. The larger the value, the greater the orderliness of the evaluation results and the smaller the separation of the scheme groups; conversely, the smaller the value, the smaller the orderliness of the evaluation results and the greater the separation. The separation degree between the value and the comprehensive evaluation result of system effectiveness shows a linear relationship, and as... As the value increases, the separation of evaluation results decreases, and the quality of performance evaluation results deteriorates; with As the value increases, the orderliness of the evaluation results increases, and the quality of the effectiveness assessment results is better; therefore, under the premise of ensuring the orderliness and quality of the evaluation, the separation of the evaluation results of each scheme group should be increased as much as possible.

[0041] and They represent Subjective empowerment method and The weights assigned to each objective weighting method, distinguishing the importance of different evaluation methods, and the weights satisfying the formulas and the final calculation expressions for the subjective-objective combined weights are as follows:

[0042]

[0043] plan The efficiency value is ,plan The system performance is calculated as follows: .

[0044] In some embodiments, the above-described method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis can also be implemented in the following ways.

[0045] like Figure 2 As shown, the clustering analysis-based satellite constellation integrated application capability evaluation method in this embodiment is mainly used to solve the problem of integrated capability evaluation of satellite constellation systems. This type of problem is very important in practical applications, especially in the fields of satellite observation, communication, and navigation. The purpose of this embodiment is to provide a comprehensive evaluation framework to scientifically analyze the overall effectiveness of the constellation. It includes the following steps: Step 1: Based on the comprehensive capability characteristics of the satellite constellation, an indicator system structure is proposed, and based on the computability of the indicator system, four types of indicators are defined and calculated, including timeliness indicators, coverage indicators, resource utilization rate, and reliability. Step 2: Quantify qualitative indicators and standardize quantitative indicators; Step 3: Calculate the similarity of indicators to distinguish the differences and similarities between feature vectors of different individuals, and aggregate variables with high similarity based on the Pearson correlation coefficient; Step 4: Perform clustering operations on the indicator set according to the system structure of the indicators. Based on the strength of the correlation between the indicators, perform cluster analysis on the indicator system, aggregate the indicators that provide similar information into one class, select the representative indicators, and filter out the indicators with weaker representativeness. Step 5: During the iterative process of clustering, the distance between clusters is measured and calculated, an inter-cluster distance matrix is ​​constructed, and the clusters with the smallest distance are merged to form a new cluster; Step 6: Calculate the distance between the newly generated cluster and all other clusters, update the inter-cluster distance matrix, and repeat Step 5 until all individuals are aggregated into one cluster or the expected threshold is reached; Step 7: Based on the clustering results, perform coefficient of variation analysis on the indicator set, calculate the ratio of the standard deviation of the original data to the mean of the original data to measure the degree of dispersion of the dataset, and select the most representative indicators in each factor layer to form a comprehensive indicator system by calculating the degree of information contribution of similar indicators within the group to the evaluation results. Step 8: Use the evaluation criteria based on orderliness to determine the effectiveness and usability of the clustering comprehensive index system; Step 9: Combining the subjective judgment criteria of the Analytic Hierarchy Process (AHP) and the objective data information of the entropy weight method, a combined weighting evaluation method is proposed.

[0046] Step 1 specifically includes: based on the characteristics of the satellite constellation's comprehensive capabilities, an in-depth analysis of the hierarchical structure of the main criteria affecting the constellation system's effectiveness is conducted. Combining relevant literature research and summarization, a hierarchical structure of four main effectiveness influencing factors is proposed, including timeliness, coverage, resource utilization, and reliability. This system defines and calculates timeliness indicators such as coverage time percentage, maximum revisit period, average revisit period, average response time, single orbit working time, single operation time, and visible satellite duration; coverage indicators such as regional cumulative coverage rate, regional overlap rate, average coverage area percentage, regional coverage overlap, number of observation windows, and observation coverage elevation angle; resource utilization indicators (maximum single-satellite occupancy rate, minimum single-satellite occupancy rate, and average satellite system occupancy rate); and reliability indicators (equipment maintainability, equipment standardization, number of satellites in orbit, number of spare satellites, and DOP value). This indicator system is more comprehensive and richer, enabling a more accurate multi-dimensional assessment of the constellation system's overall effectiveness.

[0047] Step 2 specifically includes: In the constellation performance index system, some important indicators cannot be directly quantitatively described, and qualitative descriptive language cannot be directly used in performance evaluation through mathematical modeling methods. Therefore, qualitative quantification is required. After qualitative quantification of the index system, several problems still need to be addressed: ① Inconsistent dimensions hinder comparisons between indicators, requiring solutions to the incommensurability problem; ② Inconsistent value ranges hinder comparison calculations; ③ Indicators include maximum and minimum values. Maximum values ​​represent higher performance, while minimum values ​​are the opposite. Therefore, data normalization before clustering is one of the most important tasks. It uses mathematical formulas to unify indicators in different ranges to the same range, avoiding inaccuracies in clustering results due to differences in data variation ranges. This embodiment uses the z-score method for normalization. Assume the data size is... The indicator dataset is , express The result of normalization, This represents the average value of the dataset. The z-score is calculated as shown in formula (1), where z represents the standard deviation of the dataset.

[0048] (1)

[0049] Step 3 specifically includes: Similarity calculation methods include distance-based and similarity-based methods, used to distinguish the differences and similarities between feature vectors of different individuals. Considering both the direction and magnitude of the feature vectors, this embodiment uses a distance-based method to measure the spatial distance between different indicators. For indicators that are insensitive to the magnitude of the feature vectors or have different ranges of variation within the feature vectors, this embodiment uses the Pearson correlation coefficient to calculate indicator similarity, reflecting the degree of linear correlation between two indicators. The coefficient ranges from -1 to 1; a larger absolute value indicates a stronger correlation between the two indicators, and vice versa. The positive or negative sign of the coefficient represents a positive or negative correlation between the variables.

[0050] Let the two variable data sets be... Pearson correlation coefficient The calculation method is shown in formula (2): (2) When using the Pearson correlation coefficient, significance assessment indicators are also required. Because there may be non-linear correlations between the data. The value reflects the degree of significance of the linear correlation between the two indicators. The value used The distribution and calculation method are shown in formula (3), where The correlation coefficient, This represents the dimension of the indicator's feature vector.

[0051] (3)

[0052] like Figure 3 The diagram shows the performance evaluation flowchart based on cluster analysis; steps 4, 5, and 6 specifically include: (1) Design multiple sets of different experimental parameters and calculate the index data set based on the indicators. Preprocess the data to eliminate differences in dimensions and differences between maximum and minimum values, and calculate the Pearson correlation coefficient between the indicators. r and significance index p This involves judging the magnitude of the linear correlation between indicators and assessing significant linear correlation. r and p The calculation is shown in formulas (4) and (5).

[0053] (4) (5) (2) Initialize clustering state: Treat each object as a separate cluster, calculate the distance between all pairs of clusters to form an inter-cluster distance matrix, and set the final number of clusters according to requirements. m The specific calculations are shown in formulas (6) to (9).

[0054] (6) (7) (8) (9) (3) Merging clusters: Based on the values ​​of the inter-cluster distance matrix, the clusters with the smallest distance are merged to form a new cluster; (4) Update the inter-cluster distance matrix: Calculate the distance between the newly generated cluster and all other clusters, and update the value in the inter-cluster distance matrix; (5) Repeat (3) and (4) until all individuals are aggregated into a cluster or the expected threshold is reached, and then end the clustering process.

[0055] like Figure 4 The diagram shows the performance evaluation flowchart based on combined weighting in the evaluation method for the integrated application capabilities of satellite constellations; step 7 specifically includes: The coefficient of variation (CV) represents the ratio of the standard deviation to the mean of the original data, measuring the degree of dispersion of the indicator dataset. Based on the clustering results, CV analysis is performed on the indicator set, selecting the indicator with the highest CV in each cluster or the indicator that meets the threshold. For each cluster... The first in The coefficients of variation for the indicators are shown in formula (10), where For clusters No. The standard deviation of the data for each indicator For the first The average data of each indicator n The number of indicators.

[0056] (10)

[0057] Step 8 specifically includes: This embodiment proposes a method for evaluating the effectiveness of a dimensionality reduction index system. First, multiple satellite constellation schemes are constructed, and their effectiveness is evaluated based on both the original index system and a clustering index system. Let the experimental results of the original index set be ranked as follows: The results are ranked based on the dimensionality reduction index as follows: Let vector A be an ordered sequence, and vector B be an unordered sequence based on the criteria of vector A. For each element, if... , ,in Indicates the position of element i in the set, describing the element. The relationships are ordered. Based on the evaluation of the comprehensive orderliness of vector B, the effectiveness of the dimensionality reduction index system can be fully verified. Definition To determine the effectiveness of the dimensionality reduction index, its calculation formula is defined as shown in formula (11), where the CHAOS function is a judgment of the disorder of sequence B based on sequence A.

[0058] (11)

[0059] Step 9 specifically includes: The set of methods for weight calculation was selected. Subjective evaluation methods and An objective evaluation method, the evaluation problem system includes Alternative options Various evaluation criteria. The index weights calculated by the subjective evaluation method are: The weights meet the conditions. .against The set of index weight vectors calculated by the objective weight assignment method is as follows: The weights meet the conditions. .

[0060] The overall weight is determined by the set of indicator weight vectors. and meet the conditions Let the first... Group of alternative solutions The normalized values ​​of each indicator are , thus calculating The overall capability of the group of alternative schemes is shown in formula (12).

[0061] (12) In selecting the deviation metric, distance is used for calculation. Since it is a comprehensive subjective and objective evaluation method, it is necessary to calculate the deviation between the combined weight and the subjective evaluation method and the objective evaluation method separately. The error between the combined weight and the subjective evaluation method in Euclidean distance is given by the above formula. Similarly, the deviation between the combined weight and the objective evaluation method can be obtained as shown in formulas (13) and (14).

[0062] (13) (14) To make the calculation results of the combined weights more accurate, that is, to minimize the sum of the deviations between the combined weights and the subjective and objective weights, the planning function is constructed as shown in formula (15).

[0063] (15) In the above formula, the parameters This represents the proportion of subjective and objective weights in the analysis, indicating the importance of the subjective-objective analysis method. When This indicates that objective weighting plays a dominant role at this time, and is the main influencing factor on the comprehensive calculation result; when This indicates that subjective weighting plays a dominant role in the overall weighting calculation at this point; when This represents that subjective and objective factors account for an equal proportion of influence, parameters It reflects the decision-maker's preference for both subjective and objective factors.

[0064] conventional methods The selection of values ​​is based on experience; this embodiment is based on two criteria. The selection criteria are based on: the degree of orderliness of the ranking results and the degree of separation of the overall evaluation scores of the schemes. The evaluation results are based on subjective analysis. A larger value indicates a greater degree of order in the evaluation results and a smaller degree of separation among the scheme groups. Conversely, a smaller value indicates a smaller degree of order in the evaluation results and a greater degree of separation. The separation degree between the value and the comprehensive evaluation result of system effectiveness shows a linear relationship, and as... As the value increases, the separation of evaluation results decreases, and the quality of performance evaluation results deteriorates. As the value increases, the orderliness of the evaluation results increases, and the quality of the performance evaluation results improves. Therefore, while ensuring the orderliness and quality of the evaluation, the separation of the evaluation results of each scheme group should be maximized.

[0065] and They represent Subjective empowerment method and The weights assigned to each objective weighting method are used to distinguish the importance of different evaluation methods. The weights satisfy the formula and the final calculation expression of the subjective and objective combined weights are shown in formula (16) and formula (17), respectively.

[0066] (16) (17) plan The efficiency value is ,plan The system performance is calculated as shown in formula (18).

[0067] (18) To verify the effectiveness of the indicator system, the experimental scheme group was evaluated based on the entropy weight method, using both the original indicator system and the cluster comprehensive efficiency indicator system. The results of the efficiency evaluations for the original indicators and the cluster comprehensive indicators are shown in Table 1. Table 1: Comparison of Evaluation Results of Original Indicators and Cluster Indicators

[0068] Table 1 yields the original index system ranking result vector. , From formula (18), the result of calculating the orderliness of the clustering comprehensive index is:

[0069] The standard deviation of the evaluation results using the original indicators was 0.116, while the standard deviation using the clustering indicators was 0.114, which is 98.1% of the original standard deviation. The experimental results show that the clustering comprehensive indicator system has higher accuracy in ranking the comprehensive capabilities of the candidate schemes compared to the original indicator system, and it also better preserves the ability to distinguish between different candidate schemes, demonstrating the practicality of the clustering comprehensive indicator system.

[0070] This embodiment provides case studies of constellation effectiveness using the Analytic Hierarchy Process (AHP), entropy method, and combinatorial analysis. The experimental comparison data for the three methods are shown in Table 2.

[0071] Table 2: Comparison of experimental results of AHP, entropy weight method, and combined weighting method

[0072] like Figure 5 The diagram shows a comparison of the relationship between evaluation quality and value changes. The Analytic Hierarchy Process (AHP) is an evaluation method that meets practical needs, and the experimental results are usable. However, due to the limitation of AHP's complete reliance on subjectivity, an objective method is used to reduce the dependence of the experimental results on subjective factors. The experimental results in the table show that all three evaluation schemes have the ability to completely distinguish the top-performing candidate schemes and can effectively screen out the high-performing experimental schemes. Compared to AHP, the entropy weight analysis method increases the distribution range of the scheme's comprehensive score by 36.84% and the standard deviation by 23.92%, demonstrating stronger scheme discrimination ability. This is consistent with the design philosophy of the entropy weight method, which assigns higher weights to indicators that have better identifiability of the schemes, making the results better distinguish the comprehensive ability of the schemes. The combined weighting method is a performance evaluation scheme that modifies the subjective evaluation method by providing an objective evaluation basis.

[0073] This embodiment provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the steps of the above-described method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0074] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis.

[0075] like Figure 6As shown, the computer device 120 may include: at least one processor 121, such as a central processing unit (CPU), at least one communication interface 123, memory 124, and at least one communication bus 122. The communication bus 122 is used to enable communication between these components. The communication interface 123 may include a display screen and a keyboard; optionally, the communication interface 123 may also include a standard wired interface or a wireless interface. The memory 124 may be high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Optionally, the memory 124 may also be at least one storage device located remotely from the aforementioned processor 121. The memory 124 stores application programs, and the processor 121 calls the program code stored in the memory 124 to execute any of the aforementioned method steps. The communication bus 122 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus 122 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6The term 124 is represented by a single line, but this does not imply a single bus or a single type of bus. The memory 124 may include volatile memory, such as random-access memory (RAM); it may also include non-volatile memory, such as flash memory, hard disk drive (HDD), or solid-state drive (SSD); or it may include combinations of the above types of memory. The processor 121 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP. The processor 121 may further include hardware chips. These hardware chips may be application-specific integrated circuits (ASICs), programmable logic devices (PLDs), or combinations thereof. The PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. Optionally, the memory 124 is also used to store program instructions. The processor 121 can call the program instructions to implement the satellite constellation integrated application capability evaluation method based on cluster analysis as described in this embodiment.

[0076] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for evaluating the integrated application capabilities of satellite constellations based on cluster analysis, characterized in that, Includes the following steps: S1: Construct a constellation performance index system based on the comprehensive capability characteristics of the satellite constellation; S2: Quantify and standardize the constellation performance index system to obtain the processed constellation performance index system; S3: Aggregate the processed constellation performance index system using Pearson correlation coefficient and significance evaluation index to obtain the aggregated constellation performance index system; S4: Perform clustering operations on the aggregated constellation performance index system to obtain clustering results; S5: Based on the clustering results, the comprehensive clustering index system is obtained using the coefficient of variation; S6: Based on the evaluation criterion of orderliness, determine the effectiveness and usability of the clustering comprehensive index system, and select effective clustering comprehensive index systems; S7: Based on the clustering comprehensive index system, the system efficiency is obtained using the analytic hierarchy process (AHP) and the entropy weight method.

2. The method for evaluating the comprehensive application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The constellation performance index system includes timeliness indicators, coverage indicators, resource utilization indicators, and reliability indicators. Timeliness indicators include coverage time percentage, maximum revisit period, average revisit period, average response time, single orbit working time, single operation time, and visible satellite duration. Coverage indicators include regional cumulative coverage rate, regional overlap rate, average coverage area percentage, regional coverage multiples, number of observation windows, and observation coverage elevation angle. Resource utilization indicators include maximum single-satellite occupancy rate, minimum single-satellite occupancy rate, and average satellite system occupancy rate. Reliability indicators include equipment maintainability, equipment standardization level, number of satellites in orbit, number of spare satellites, and DOP value.

3. The method for evaluating the comprehensive application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The normalization process is a standardization process.

4. The method for evaluating the comprehensive application capability of satellite constellations based on cluster analysis according to claim 3, characterized in that, The normalization process is the z-score method, as shown in the formula: ， in, Indicates the first Individual indicators The result of normalization, This represents the average value of the dataset. The standard deviation of the dataset, To determine the data scale.

5. The method for evaluating the integrated application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The formula for calculating the Pearson correlation coefficient is as follows: ， in, Represents a set of variable data and The Pearson correlation coefficient; This represents the expected value.

6. The method for evaluating the integrated application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The formula for calculating the Pearson correlation coefficient is as follows: ， in, As a significance evaluation indicator; The correlation coefficient; This represents the dimension of the indicator's feature vector.

7. The method for evaluating the integrated application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The formula for calculating the coefficient of variation is: ， in, The first in the cluster The coefficient of variation of each indicator; The first in the cluster The standard deviation of the data for each indicator; The first in the cluster The average data of each indicator The number of indices in the cluster.

8. The method for evaluating the integrated application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The formula for calculating the degree of order is: ， in, For degree of order; ={ 1, 2, … , The experimental results are ranked based on the original set of indicators. This indicates the number of indicators in sequence A. ; The results are ranked based on a clustering comprehensive index system; Based on sequence Based on A function to evaluate sequence disorder; and They are respectively The Middle and the Each element.

9. The method for evaluating the integrated application capability of satellite constellations based on cluster analysis according to claim 1, characterized in that, The formula for calculating the system performance is as follows: ， ， ， in, Representation scheme System efficiency; Representation scheme The performance value, , ,..., Let n represent the values ​​of each performance indicator, and n represent the number of performance indicators in the plan. Weighting of subjective and objective factors; It refers to the proportion of subjective and objective weights in the analysis; The number of subjective empowerment methods; The number of objectively empowering methods; and They represent Subjective empowerment method and The weights assigned to each objective weighting method, and the following conditions must be met. ; Indicates the first The first subjective evaluation method calculated the Weight of each indicator; Indicates the first The first objective weight assignment method calculates the Each indicator has a weight.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the satellite constellation integrated application capability evaluation method based on cluster analysis as described in any one of claims 1-9.

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