Equipment support efficiency evaluation method based on fuzzy mathematics

Abstract

The invention relates to an equipment support efficiency evaluation method based on fuzzy mathematics. The method comprises the steps of evaluation index system determination, weight distribution, normalization processing and fuzzy comprehensive evaluation. Firstly, an evaluation system comprising primary and secondary indexes is established according to guarantee requirements and evaluation targets of aerospace equipment, the primary indexes reflect main features, and the secondary indexes describe guarantee factors of different levels. Secondly, performing fuzzy weight distribution on the indexes by adopting an expert scoring method, and unifying the indexes through normalization processing; and then, based on a fuzzy comprehensive evaluation method, carrying out comprehensive calculation on the normalized index value and the corresponding weight value to obtain a guarantee efficiency evaluation result expressed in a fuzzy membership degree form, and using the guarantee efficiency evaluation result to reflect the comprehensive guarantee efficiency of the equipment under different use conditions. And finally, an evaluation result is analyzed, key factors influencing the equipment guarantee efficiency are identified, and targeted improvement measures are put forward to improve the comprehensive guarantee level of the equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of equipment support effectiveness evaluation, and in particular to an equipment support effectiveness evaluation method based on fuzzy mathematics. Background Art

[0002] In the existing technology, the evaluation of equipment support effectiveness usually relies on a fixed indicator system and static analysis methods. Traditional methods mostly use simple numerical analysis and weight distribution methods to evaluate the support performance of equipment, but fail to effectively consider the multi-factor influence and uncertainty in complex systems.

[0003] In recent years, fuzzy mathematics has been introduced into the field of equipment support to process multi-level and multi-dimensional fuzzy information, which has improved the accuracy and flexibility of evaluation to a certain extent. However, when applying fuzzy mathematics, most common evaluation methods in the prior art are limited to fuzzy comprehensive evaluation of a single dimension, lacking dynamic adjustment and comprehensive analysis of evaluation indicators. In addition, weight allocation usually relies on subjective experience, resulting in insufficient objectivity and adaptability of evaluation results. These shortcomings limit the application effect of existing methods in the evaluation of complex equipment support effectiveness, especially when dealing with changing conditions and environments, the evaluation results are difficult to accurately reflect the actual effectiveness.

[0004] Therefore, it is urgent to develop a new equipment support effectiveness evaluation method. Summary of the invention

[0005] The present application provides an equipment support effectiveness evaluation method based on fuzzy mathematics to improve the accuracy of the evaluation results.

[0006] The present application provides an equipment support effectiveness evaluation method based on fuzzy mathematics, including:

[0007] According to the support requirements and evaluation objectives of aerospace equipment, determine the index system for equipment support effectiveness evaluation; wherein the index system includes primary indicators and secondary indicators, the primary indicators are used to reflect the main characteristics of equipment support effectiveness, and the secondary indicators are used to specifically describe support factors at different levels;

[0008] Using the expert scoring method in fuzzy mathematics to assign weights to each indicator in the indicator system;

[0009] Normalizing each indicator in the indicator system;

[0010] Based on the fuzzy comprehensive evaluation method in fuzzy mathematics, the normalized index value and its corresponding weight value are comprehensively calculated to obtain the equipment support effectiveness evaluation result; wherein the equipment support effectiveness evaluation result is expressed in the form of fuzzy membership, which is used to reflect the comprehensive support effectiveness of aerospace equipment under different use conditions;

[0011] Analyze the support effectiveness evaluation results of the equipment and identify the main factors affecting the support effectiveness of the equipment; propose targeted improvement measures for the identified main factors affecting the support effectiveness of the equipment to improve the comprehensive support level of the equipment.

[0012] Furthermore, the indicator system for equipment support effectiveness evaluation is determined based on the support requirements and evaluation objectives of aerospace equipment, including:

[0013] Collect historical support data of aerospace equipment, including reliability, maintainability, availability and safety, and preliminarily build a set of primary and secondary indicators based on the collected historical support data;

[0014] The primary and secondary indicators were screened and prioritized by fuzzy analytic hierarchy process;

[0015] Combined with the suggestions of experts in the field, the initially constructed indicator system was revised and improved to form the final evaluation indicator system.

[0016] Furthermore, the normalization of each indicator in the indicator system includes:

[0017] According to the following formula 1, each indicator in the indicator system is normalized:

[0018]

[0019] Among them, x norm is the initial normalization result; x is the original index value; x min and x max are the minimum and maximum values ​​of the indicator respectively;

[0020] According to the following formula 2, the dynamic weighting factor D is calculated: i :

[0021]

[0022] Among them, β is the adjustment parameter; R i is the rate of change of the ith indicator; max(R i ) is the maximum change rate among all indicators; the change rate R i Use the following formula 3 to calculate:

[0023]

[0024] Among them, x ij is the value of the i-th indicator under the j-th evaluation condition; is the average value of the ith indicator under all evaluation conditions; M is the total number of evaluation conditions, where the evaluation conditions include environmental conditions, task conditions, usage conditions, external interference conditions, and resource conditions;

[0025] Use the following formula 4 to adjust the normalized result:

[0026] x dyn =x norm ·D i (4)

[0027] Among them, x dyn is the normalized value after dynamic adjustment; x norm is the preliminary normalization result; D i is the dynamic weighting factor.

[0028] Furthermore, the fuzzy comprehensive evaluation method based on fuzzy mathematics comprehensively calculates the normalized index value and its corresponding weight value to obtain the equipment support effectiveness evaluation result, including:

[0029] The index value x of the normalized i-th index norm,i , using multiple fuzzy membership functions for multi-layer mapping to form a membership vector U composed of different membership functions i = {u i1 ,u i2 ,…,u iL}, where u il represents the membership value of the i-th indicator under the l-th fuzzy membership function, L is the number of layers of the fuzzy membership function, wherein the multiple fuzzy membership functions include triangular, trapezoidal and Gaussian membership functions;

[0030] According to the following formula 5, the fuzzy comprehensive evaluation score of each indicator is calculated:

[0031]

[0032] Among them, S i is the fuzzy comprehensive evaluation score of the i-th index; u il is the membership value under the membership function of the lth layer; x norm,i is the normalized value of the ith indicator; w l is the fuzzy weight of the lth layer; α is the adjustment parameter; μ l is the center point of the l-th layer membership function;

[0033] According to the calculated fuzzy comprehensive evaluation score of each indicator, the equipment support effectiveness evaluation result is obtained according to the following formula 6:

[0034]

[0035] Among them, E total is the comprehensive support effectiveness evaluation result of the equipment; S i is the fuzzy comprehensive evaluation score of the i-th index; ω i is the global fuzzy weight of the i-th indicator.

[0036] Furthermore, the equipment support effectiveness evaluation results are analyzed to identify the main factors affecting the equipment support effectiveness, including:

[0037] A fuzzy decision tree is used to decompose the equipment support effectiveness evaluation result into different nodes, wherein each node represents a main factor affecting the equipment support effectiveness;

[0038] Through the path analysis of fuzzy decision tree, the primary and secondary indicators with the greatest impact on the evaluation results are identified, and their contribution to the equipment support effectiveness is quantified;

[0039] Through fuzzy logic reasoning, the primary and secondary indicators that have the greatest impact on the evaluation results are analyzed and ranked to determine the main factors affecting the equipment support effectiveness.

[0040] Furthermore, targeted improvement measures are proposed for the main factors that affect the equipment support effectiveness, including:

[0041] Constructing a fuzzy rule base, wherein the fuzzy rule base includes a plurality of improved rules for different evaluation results;

[0042] Based on the rules in the fuzzy rule base, the fuzzy reasoning mechanism is used to reason and evaluate different improvement plans and select the optimal improvement plan;

[0043] The optimal improvement plan is verified by fuzzy simulation, and the feasibility and effectiveness of the improvement measures are evaluated through simulation results to ensure that the proposed improvement measures can effectively improve the comprehensive support efficiency of the equipment after implementation.

[0044] Furthermore, the expert scoring method in fuzzy mathematics is used to assign weights to the various indicators in the indicator system, which is implemented using the following formula 7:

[0045]

[0046] Where n represents the total number of experts involved in the evaluation; W i represents the final weight of the i-th indicator; μ ij represents the membership of the jth expert to the i-th indicator; δ ij represents the dynamic credibility coefficient of the jth expert; ω ij is the original score of the jth expert on the i-th indicator; Ci is the relative importance coefficient of the ith indicator; C max is the maximum relative importance coefficient in the indicator system; R i represents the mean of the historical evaluation results of the ith indicator; R ij is the historical evaluation value of the j-th expert on the i-th indicator; α and β are adjustment parameters.

[0047] Furthermore, the membership degree μ ij This is achieved using the following formula 8:

[0048]

[0049] Among them, x ij is the original score of the jth expert on the i-th indicator; m ij is the most trusted score of the jth expert for the i-th indicator, determined according to the historical evaluation trend of the expert on the indicator; σ ij is the standard deviation, which is used to reflect the volatility or uncertainty of the j-th expert's evaluation of the i-th indicator.

[0050] Furthermore, the dynamic credibility coefficient δ ij This is achieved using the following formula 9:

[0051]

[0052] Among them, E ijt A is the predicted value of the i-th indicator by the j-th expert in the t-th evaluation; it is the actual performance result of the ith indicator in the tth evaluation; r jt is the historical evaluation accuracy of the jth expert in the tth evaluation; d t is the environmental factor of the tth evaluation, which is used to reflect the different external conditions of the evaluation; η is the adjustment parameter of the environmental factor, which is used to adjust the impact of different environmental factors on the credibility coefficient; M is the total number of historical evaluations.

[0053] Furthermore, the relative importance coefficient C i This is achieved by the following formula 10:

[0054]

[0055] Where K is the total number of clusters; u ik is the membership degree of the ith indicator in the kth cluster; d ik is the distance between the i-th index and the k-th cluster center; σ k is the density of the kth cluster, which is used to reflect the concentration of indicators in the cluster; β k is the weight coefficient of the kth cluster; L is the weight coefficient of the lth cluster βl The γ is a weight adjustment parameter.

[0056] The beneficial effects of the technical solution provided by this application include:

[0057] (1) By adopting a multi-level indicator system and fuzzy comprehensive evaluation method, the performance characteristics of equipment under different use conditions can be comprehensively considered, reducing the limitations of single-dimensional evaluation, thereby more accurately reflecting the actual support effectiveness of the equipment. (2) The introduction of expert scoring method and dynamic weight allocation mechanism in fuzzy mathematics enables the evaluation process to flexibly adapt to changes in various use environments and task conditions, thereby improving the applicability of the evaluation results. (3) Through in-depth analysis of the evaluation results, the main factors affecting the support effectiveness of equipment can be effectively identified, and targeted improvement suggestions can be provided for equipment design optimization, resource allocation and maintenance strategies, thereby improving the comprehensive support level of equipment. (4) Through normalization processing and fuzzy membership representation, the subjective factors in the evaluation are minimized, making the evaluation process more standardized and normalized, and improving the objectivity and credibility of the evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of an equipment support effectiveness evaluation method based on fuzzy mathematics provided in the first embodiment of the present application. DETAILED DESCRIPTION

[0059] Many specific details are described in the following description to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without violating the connotation of the present application, so the present application is not limited by the specific implementation disclosed below.

[0060] The first embodiment of the present application provides an equipment support effectiveness evaluation method based on fuzzy mathematics. Figure 1 , which is a schematic diagram of the first embodiment of the present application. Figure 1 A method for evaluating equipment support effectiveness based on fuzzy mathematics is described in detail in the first embodiment of the present application.

[0061] Step S101: Determine an index system for evaluating equipment support effectiveness based on the support requirements and evaluation objectives of aerospace equipment; wherein the index system includes primary indicators and secondary indicators, the primary indicators are used to reflect the main characteristics of equipment support effectiveness, and the secondary indicators are used to specifically describe support factors at different levels.

[0062] In step S101, the indicator system for equipment support effectiveness evaluation is determined according to the support requirements and evaluation objectives of aerospace equipment. The implementation of this step requires detailed operations and specific implementations from the following aspects.

[0063] First, the support requirements and evaluation objectives of aerospace equipment should be clarified. Support requirements refer to the performance requirements that need to be achieved during the daily maintenance and combat readiness of equipment, including but not limited to key performance indicators such as equipment reliability, maintainability, availability and safety. Evaluation objectives are specifically reflected in the results that are expected to be obtained through the evaluation, such as whether it is necessary to evaluate the adaptability of equipment in different mission environments, or whether it is necessary to analyze the resource allocation efficiency of equipment. In this step, it is necessary to clarify specific support requirements and evaluation objectives through analysis of historical data, consultation with field experts, and research on existing evaluation standards.

[0064] After the support needs and evaluation objectives are clear, preliminary indicator selection and classification are required. First, by analyzing the performance characteristics of aerospace equipment, a group of first-level indicators are preliminarily selected. These indicators are used to reflect the main characteristics of equipment support effectiveness. For example, first-level indicators may include reliability (reflecting the probability of equipment running without failure within a specific time period), maintainability (reflecting the ability of equipment to recover quickly after a failure), availability (reflecting the ability of equipment to be used normally within a specific mission time) and safety (reflecting the ability of equipment to be used without danger during use). After determining the first-level indicators, it is necessary to further subdivide these first-level indicators and select related second-level indicators. The second-level indicators are used to specifically describe the various dimensions and levels of the first-level indicators. For example, for reliability, the second-level indicators that can be selected include mean time between failures (MTBF), failure rate, and component durability.

[0065] Based on the preliminary selection of primary and secondary indicators, the fuzzy hierarchical analysis method is used to screen and optimize these indicators. Specifically, the fuzzy hierarchical analysis method needs to construct a pairwise comparison matrix to quantitatively compare the relative importance of different indicators. This comparison process can be achieved through the scoring of domain experts, and the scoring results are converted into fuzzy numbers through fuzzification processing to form a fuzzy pairwise comparison matrix. Based on this matrix, the fuzzy weights of each indicator can be further calculated, and the weights can be checked for consistency to ensure the rationality and consistency of the indicator system. If the consistency test fails, the pairwise comparison matrix needs to be adjusted according to the feedback from experts until the consistency test passes.

[0066] After completing the above steps, the index system that has been initially constructed needs to be further revised and improved. The main basis for the revision is the opinions of experts and the verification of historical data. The collection of expert opinions can be carried out through questionnaire surveys, expert group discussions, etc., to ensure that the selection of each first-level and second-level indicator is reasonable and can fully reflect the equipment support effectiveness. The verification of historical data verifies the applicability and accuracy of the index system by comparing and analyzing the actual support effectiveness of existing equipment.

[0067] Finally, when determining the final evaluation index system, it is necessary to clearly define the hierarchical relationship of the indicators, that is, the affiliation of each secondary indicator with its corresponding primary indicator, and the contribution of each primary indicator in the overall guarantee effectiveness evaluation. After the definition is completed, a complete and hierarchical evaluation index system can be formed, which provides a basis for the weight allocation, normalization processing and fuzzy comprehensive evaluation in the subsequent steps.

[0068] Furthermore, the indicator system for equipment support effectiveness evaluation is determined based on the support requirements and evaluation objectives of aerospace equipment, including:

[0069] Collect historical support data of aerospace equipment, including reliability, maintainability, availability and safety, and preliminarily build a set of primary and secondary indicators based on the collected historical support data;

[0070] The primary and secondary indicators were screened and prioritized by fuzzy analytic hierarchy process;

[0071] Combined with the suggestions of experts in the field, the initially constructed indicator system was revised and improved to form the final evaluation indicator system.

[0072] In this embodiment, the indicator system for evaluating equipment support effectiveness is determined according to the support needs and evaluation objectives of aerospace equipment, which is achieved through a series of specific steps. First, a large amount of historical support data of aerospace equipment needs to be collected. These data include but are not limited to key performance indicators such as equipment reliability, maintainability, availability and safety. The source of these data can be the operation and maintenance records of the equipment in actual use, the data output of the equipment monitoring system, the fault repair log, the daily inspection report and the related task execution feedback. Through the detailed analysis of these historical data, the actual performance and potential support effectiveness characteristics of the equipment under various conditions of use can be revealed.

[0073] After obtaining and summarizing historical support data, preliminary indicator construction is required. This process involves extracting a set of primary and secondary indicators from historical data. Primary indicators refer to the main characteristics that reflect the comprehensive support effectiveness of equipment, such as reliability, which indicates the ability of equipment to operate without failure within a specified time; maintainability, which indicates the ability to recover quickly after a failure; availability, which involves the ability of equipment to be used within a specific mission time, and safety, which involves the ability of equipment to not cause danger during use. Secondary indicators are the refinement and decomposition of primary indicators. For example, for reliability, secondary indicators may include mean time between failures, failure rate, durability of components, etc.; for maintainability, secondary indicators may include mean repair time, fault diagnosis accuracy, etc.

[0074] After constructing the primary and secondary indicator sets, these indicators need to be further screened and prioritized. At this time, the Fuzzy Analytic Hierarchy Process (FAHP) is introduced to ensure the scientific nature of the screening and sorting process. The Fuzzy Analytic Hierarchy Process is a multi-criteria decision-making method that simplifies the complex judgment process into pairwise comparisons through fuzzy mathematics. In specific operations, a pairwise comparison matrix needs to be constructed in which each indicator is compared with other indicators in terms of relative importance. This comparison process is based on the form of fuzzy numbers, which enables experts to make relative importance judgments under conditions of uncertainty and ambiguity. For example, experts can use triangular fuzzy numbers to represent the difference in importance between two indicators. This fuzzy processing can better reflect the decision-making process in complex situations. By calculating the fuzzy weights, the primary and secondary indicators can be prioritized to determine the relative importance of each indicator in the equipment support effectiveness evaluation.

[0075] After completing the screening and sorting of the fuzzy hierarchical analysis, the initially constructed indicator system needs to be further revised and improved in combination with the suggestions of domain experts. Domain experts usually have rich experience in aerospace equipment support, and they can evaluate and adjust the importance, operability and applicability of indicators based on actual conditions. Experts can make suggestions through group discussions, questionnaires or interviews. Experts' suggestions may involve adding or deleting certain indicators, or adjusting the weights of certain indicators. For example, experts may believe that some uncommon failure modes require the addition of corresponding indicators, or that some indicators are difficult to quantify in actual operations and need to be weighted.

[0076] After the experts' suggestions were adopted and applied, the final evaluation index system was formed. This system not only retains the objective reflection of historical support data, but also combines the scientific nature of the fuzzy hierarchical analysis method and the practical feasibility of expert experience. This evaluation index system, which has been verified and revised multiple times, can comprehensively and accurately reflect the comprehensive support effectiveness of equipment, laying a solid foundation for subsequent weight allocation, normalization processing and fuzzy comprehensive evaluation.

[0077] Step S102: using the expert scoring method in fuzzy mathematics to assign weights to the various indicators in the indicator system.

[0078] In step S102, the expert scoring method in fuzzy mathematics is used to assign weights to the various indicators in the indicator system. To achieve this step, it is first necessary to select experts to participate in the scoring. These experts should have rich experience in the field of aerospace equipment support and be able to provide scores based on their professional knowledge and practical experience. The number of experts should be representative to ensure the objectivity and comprehensiveness of the scoring. Usually, at least 5 to 10 experts should be invited to participate.

[0079] After the experts are determined, they will score each primary and secondary indicator according to the evaluation indicator system established in step S101. The score ranges from 0 to 10, where 0 represents the lowest importance of the indicator and 10 represents the highest. During the scoring process, each expert needs to independently score the relative importance of each indicator in the equipment support effectiveness evaluation based on his or her professional experience to ensure the independence and objectivity of each score. In order to make the experts' scoring standards consistent, a set of detailed scoring guidelines can be provided to help experts understand the scoring range and scoring standards.

[0080] After collecting all the experts' scores, the scores need to be standardized and fuzzified. The purpose of standardization is to adjust the scores of different experts to a unified scale and eliminate the impact of differences in scores between experts. The standardized score results are further fuzzified. The fuzzification process can be in the form of triangular fuzzy numbers or trapezoidal fuzzy numbers to convert the scores into fuzzy membership to reflect the uncertainty and ambiguity in the scores. For example, the score can be converted into a fuzzy number interval to represent the expert's fuzzy judgment on the importance of the indicator.

[0081] After the fuzzification is completed, the fuzzy scores of different experts need to be combined to calculate the fuzzy weight of each indicator. This step usually adopts the fuzzy weighted average method, combining the fuzzy scores of experts with their credibility for weighting. The credibility of experts can be determined based on the accuracy of their historical evaluations, professional background, and the depth of their understanding of specific indicators. Through weighted comprehensive calculation, the fuzzy weight of each indicator will reflect the comprehensive evaluation results of the experts, ensuring the rationality and scientificity of the weights.

[0082] After the fuzzy weights of all indicators are calculated, consistency checks are required to ensure the rationality and consistency of weight distribution. If inconsistencies are found, further discussion or re-scoring by experts is required to achieve a reasonable fuzzy weight distribution. This process ensures the accuracy of the scoring and the objectivity of the evaluation results, laying the foundation for the implementation of subsequent steps.

[0083] Furthermore, the expert scoring method in fuzzy mathematics is used to assign weights to the various indicators in the indicator system, which is implemented using the following formula 7:

[0084]

[0085] Where n represents the total number of experts involved in the evaluation; W i represents the final weight of the i-th indicator; μ ij represents the membership of the jth expert to the i-th indicator; δ ij represents the dynamic credibility coefficient of the jth expert; ω ijis the original score of the jth expert on the i-th indicator; C i is the relative importance coefficient of the ith indicator; C max is the maximum relative importance coefficient in the indicator system; R i represents the mean of the historical evaluation results of the ith indicator; R ij is the historical evaluation value of the j-th expert on the i-th indicator; α and β are adjustment parameters.

[0086] Furthermore, the membership degree μ ij This is achieved using the following formula 8:

[0087]

[0088] Among them, x ij is the original score of the jth expert on the i-th indicator; m ij is the most trusted score of the jth expert for the i-th indicator, determined according to the historical evaluation trend of the expert on the indicator; σ ij is the standard deviation, which is used to reflect the volatility or uncertainty of the j-th expert's evaluation of the i-th indicator.

[0089] Furthermore, the dynamic credibility coefficient δ ij This is achieved using the following formula 9:

[0090]

[0091] Among them, E ijt A is the predicted value of the i-th indicator by the j-th expert in the t-th evaluation; it is the actual performance result of the ith indicator in the tth evaluation; r jt is the historical evaluation accuracy of the jth expert in the tth evaluation; d t is the environmental factor of the tth evaluation, which is used to reflect the different external conditions of the evaluation; η is the adjustment parameter of the environmental factor, which is used to adjust the impact of different environmental factors on the credibility coefficient; M is the total number of historical evaluations.

[0092] Furthermore, the relative importance coefficient C i This is achieved by the following formula 10:

[0093]

[0094] Where K is the total number of clusters; u ik is the membership degree of the ith indicator in the kth cluster; d ik is the distance between the i-th index and the k-th cluster center; σ k is the density of the kth cluster, which is used to reflect the concentration of indicators in the cluster; β kis the weight coefficient of the kth cluster; L is the weight coefficient of the lth cluster β l The γ is a weight adjustment parameter.

[0095] In this embodiment, the expert scoring method in fuzzy mathematics is used to assign weights to each indicator in the indicator system. In order to ensure the rationality and scientificity of the weight of each indicator, a complex calculation formula is used to comprehensively consider the uncertainty in the expert scoring and the relative importance of the indicators.

[0096] First, the final weight W of each indicator is determined according to Formula 7 i :

[0097]

[0098] Where n is the total number of experts involved in the evaluation. By integrating multiple factors, such as expert scoring membership, dynamic credibility coefficient, original scoring value and relative importance coefficient, the formula can effectively integrate the evaluations of different experts and quantify the relative importance of each indicator.

[0099] μ in the formula ij It represents the membership of the jth expert to the ith indicator. The membership is used to reflect the degree of match between the expert's scoring result for a certain indicator and its expected value. The specific calculation method is shown in Formula 8:

[0100]

[0101] In this formula, x ij is the original score of the jth expert for the i-th indicator, indicating the expert's assessment of the importance of the indicator. For example, experts can score indicators based on factors such as equipment reliability or maintainability. ij is the most trusted score of the jth expert for the i-th indicator, that is, the score that the expert is most likely to choose based on his historical evaluation trend. ij is the standard deviation, which is used to quantify the volatility or uncertainty of experts in their historical evaluations. For example, if an expert's scores on the same indicator vary little over multiple evaluations, then σ ij A lower value indicates that the expert's score on this indicator is relatively stable.

[0102] The δ in the formula ij is the dynamic credibility coefficient of the jth expert, which is used to measure the credibility of the expert under different evaluation conditions. Its calculation method is shown in Formula 9:

[0103]

[0104] In this formula, E ijt is the predicted value of the i-th indicator by the j-th expert in the t-th evaluation, and Ait is the actual performance result of the ith indicator in the tth evaluation. jt It represents the historical evaluation accuracy of the jth expert in the tth evaluation, reflecting the quality of the expert's historical judgment. t It is a variable that describes different evaluation conditions, such as temperature, humidity, load and other external factors, indicating the degree of influence of these environmental conditions on the evaluation results. The adjustment parameter η is used to control the influence of different environmental factors on the credibility coefficient. Through this dynamic credibility calculation method, the reliability of experts under different evaluation conditions can be accurately reflected.

[0105] Relative importance coefficient C i Indicates the relative importance of the ith indicator in the entire indicator system. Formula 10 is used to calculate the relative importance coefficient:

[0106]

[0107] In this formula, u ik is the degree of membership of the ith indicator in the kth cluster, indicating the performance of the indicator in a specific cluster. Clustering is used to classify indicators into different categories, such as reliability, maintainability, availability, etc. ik is the distance between the ith index and the kth cluster center, reflecting the importance of the index in the cluster. The density of the cluster σ k It is used to describe the concentration of indicators in a cluster. If the indicators in a cluster are relatively concentrated, it means that the indicators in the cluster have high similarity and consistency. k is the weight coefficient of the kth cluster, which is used to measure the relative importance of different clusters in the entire evaluation. The adjustment parameter γ controls the nonlinear amplification effect of the relative importance coefficient. By calculating the logarithm of different clusters, the discrimination of the relative importance coefficient can be enhanced.

[0108] Membership degree u ik It is used to measure the degree of belonging of an indicator in a specific cluster. In order to determine the degree of membership, all indicators need to be clustered first, and the indicators are divided into multiple categories according to certain similarities. Each category represents a specific performance attribute, such as reliability, maintainability, or availability. For each indicator, the calculation of the degree of membership requires comparing the difference between the actual value of the indicator and the characteristic value of the category. If the value of an indicator is close to the characteristic value of a category, its degree of membership in the category is high; conversely, if the difference is large, the degree of membership is low. Specifically, the degree of membership reflects the degree of match between the indicator and the cluster center, and is expressed as a value between 0 and 1 through fuzzy logic, where 0 means that it does not belong to the cluster at all, and 1 means that it belongs to the cluster completely.

[0109] The distance d between cluster centersik Refers to the degree of difference between an indicator and a specific cluster center. When calculating, you need to first determine the center point of each cluster, which is the average or weighted average of all indicators belonging to the cluster. For example, if a cluster represents the "reliability" category, then its center point may be the average of all reliability-related indicators. Then, the degree of difference of an indicator is determined by calculating the distance between an indicator and the center point. The size of the distance directly reflects the similarity between the indicator and the cluster center. The smaller the distance, the smaller the difference between the indicator and the cluster center, that is, the indicator better reflects the characteristics of the category; conversely, the larger the distance, the greater the difference between the indicator and the characteristics of the category.

[0110] The density of the cluster is σ k Used to describe the distribution of all indicators in a cluster. The density reflects the concentration of indicators within the cluster. If most of the indicators in a cluster are close to the cluster center, it means that the indicators in the cluster are relatively consistent and its density is high. Specifically, the calculation of density is usually based on the average distance between the indicator and the cluster center. If the average value of these distances is small, it means that the indicators in the cluster are more concentrated and the density is higher; if the average value of these distances is large, it means that the indicators in the cluster are more dispersed and the density is lower. The density can also be used to measure the relative importance of the cluster, because a cluster with a higher density usually means that the indicators in the category are more consistent and representative.

[0111] Through the above formula and calculation method, the weight W of each indicator is finally obtained. i , these weights can accurately reflect the comprehensive evaluation results of experts and the relative importance of indicators. For example, in the evaluation of the support effectiveness of aerospace equipment, if a reliability indicator has been stable and highly important in the historical evaluation of experts, then its weight will be relatively high through the above formula, thus occupying a larger proportion in the comprehensive evaluation.

[0112] Step S103: normalizing each indicator in the indicator system.

[0113] In step S103, each indicator in the indicator system is normalized. The purpose of normalization is to convert the value range of different indicators to a unified scale so as to perform comprehensive calculations in subsequent evaluations. Since the dimensions of different indicators may be different, such as reliability indicators may be in the form of time or probability, and maintainability indicators may be in the form of time or cost, it is necessary to map all indicator values ​​to a standardized interval of 0 to 1 through normalization to ensure that each indicator is comparable in the evaluation.

[0114] First, it is necessary to obtain the minimum and maximum values ​​of each indicator in the historical data, or the minimum and maximum scores determined based on the expert scoring method. The minimum and maximum values ​​represent the possible upper and lower limits of the indicator in the specific evaluation process. This step needs to ensure that the selected minimum and maximum values ​​can cover all possible actual situations, thereby reflecting the extreme conditions of the indicator in the evaluation process. In order to avoid the influence of outliers on normalization, extreme data can be appropriately excluded when determining the minimum and maximum values, and the upper and lower limits of regular data can be used for normalization calculations.

[0115] After determining the minimum and maximum values, the original value of each indicator will be adjusted to the range of 0 to 1. Specifically, the value of each indicator will be linearly converted according to its relative distance from the minimum and maximum values, so that the minimum value corresponds to the normalized 0, the maximum value corresponds to the normalized 1, and the values ​​in between will be linearly converted to the corresponding normalized values ​​according to their relative positions. This linear normalization method can ensure the intuitiveness and operability of the normalization results and maintain the relative relationship between different indicators.

[0116] After the initial normalization is completed, dynamic adjustments need to be made based on the changes in each indicator under different evaluation conditions. This adjustment is to reflect the sensitivity and variability of the indicator under different environments. Specifically, the dynamic weighting factor of each indicator needs to be calculated based on its rate of change under different evaluation conditions. The rate of change reflects the fluctuation of the indicator under different scenarios and is a quantitative description of the stability of the indicator. The introduction of dynamic weighting factors will further correct the results of the initial normalization so that the final normalized indicator value can accurately reflect the performance of the equipment under different conditions.

[0117] After the dynamic adjustment is completed, the normalization results need to be checked and corrected to ensure that the normalized values ​​of all indicators are within the range of 0 to 1. If the normalized results of some indicators exceed this range, they need to be corrected to limit them to between 0 and 1. The correction method can be direct truncation, setting the excess part to 0 or 1, so as to keep the standardized results in line with the basic requirements of normalization. The entire normalization process ensures the comparability of different indicators under the standard scale, providing a basis for subsequent fuzzy comprehensive evaluation.

[0118] Furthermore, the normalization of each indicator in the indicator system includes:

[0119] According to the following formula 1, each indicator in the indicator system is normalized:

[0120]

[0121] Among them, x norm is the initial normalization result; x is the original index value; xmin and x max are the minimum and maximum values ​​of the indicator respectively;

[0122] According to the following formula 2, the dynamic weighting factor D is calculated: i :

[0123]

[0124] Among them, β is the adjustment parameter; R i is the rate of change of the ith indicator; max(R i ) is the maximum change rate among all indicators; the change rate R i Use the following formula 3 to calculate:

[0125]

[0126] Among them, x ij is the value of the i-th indicator under the j-th evaluation condition; is the average value of the ith indicator under all evaluation conditions; M is the total number of evaluation conditions, where the evaluation conditions include environmental conditions, task conditions, usage conditions, external interference conditions, and resource conditions;

[0127] Use the following formula 4 to adjust the normalized result:

[0128] x dyn =x norm ·D i (4)

[0129] Among them, x dyn is the normalized value after dynamic adjustment; x norm is the preliminary normalization result; D i is the dynamic weighting factor.

[0130] In this embodiment, the normalization process is used to convert the values ​​of various indicators in the equipment support effectiveness evaluation into a unified range, so that different indicators are comparable on the same scale. Specifically, the purpose of the normalization process is to eliminate the dimensional differences between different indicators, so that the subsequent fuzzy comprehensive evaluation is more accurate and effective.

[0131] First, a preliminary normalization process is required. To this end, the original value x of each indicator is converted into a normalized result using Formula 1:

[0132]

[0133] In this formula, x is the original indicator value, which represents the actual value of a specific indicator in the equipment support effectiveness evaluation. This value can come from historical data, real-time monitoring data, or expert evaluation data. For example, for reliability indicators, x can be the mean time between failures (MTBF) of the equipment under certain test conditions; for maintainability indicators, x can be the mean time to repair (MTTR). In order to ensure the accuracy and comprehensiveness of normalization, it is necessary to determine the minimum value x of each indicator. min and the maximum value x max .x min and x max Respectively represent the minimum and maximum values ​​that may appear in the historical data. For example, in task intensity evaluation, x min It can be the minimum failure interval of the equipment under low-intensity tasks, and x max It is the maximum failure interval time of the equipment under high-intensity tasks.

[0134] Through the calculation of formula 1, the initial normalized result x of each indicator norm It is limited to between 0 and 1, where 0 represents the worst performance of the indicator and 1 represents the best performance of the indicator. This normalization process can eliminate the dimensional differences of different indicators and provide a basis for subsequent weighted processing.

[0135] After the initial normalization, the dynamic weighting factor D needs to be calculated based on the change rate of each indicator under different evaluation conditions. i , in order to dynamically adjust the normalized results. The dynamic weighting factor reflects the volatility of the indicator under different conditions, thereby ensuring that the normalized results are more adaptable. Formula 2 is used to calculate the dynamic weighting factor D i :

[0136]

[0137] In this formula, β is an adjustment parameter used to control the influence of the dynamic weighting factor. Its value can be adjusted according to specific evaluation needs. For example, when it is necessary to strengthen the focus on indicators with greater volatility, the value of β can be appropriately increased. i It represents the rate of change of the ith indicator, reflecting the degree of fluctuation of the indicator under different evaluation conditions. i It is calculated by formula 3:

[0138]

[0139] In formula 3, x ij is the value of the ith indicator under the jth evaluation condition. For example, for environmental conditions, x ij It can be the performance of this indicator in a high temperature environment; for task conditions, xij is the performance of the indicator under high-load tasks. The evaluation condition M is the total number of different scenarios, including environmental conditions (such as temperature and humidity), task conditions (such as load intensity and operation frequency), usage conditions (such as maintenance frequency and operation complexity), external interference conditions (such as electromagnetic interference and vibration), and resource conditions (such as energy supply status and human input level). is the average value of the i-th indicator under all evaluation conditions, which is used to reflect the overall level of the indicator. In this way, the rate of change R i The volatility of this indicator under different conditions is quantified.

[0140] In obtaining the rate of change R i After that, by calculating the maximum rate of change max(R i ), the rate of change of each indicator is normalized to ensure that the calculation of the dynamic weighting factor has a unified standard. This normalization allows the volatility of different indicators to be compared on the same scale.

[0141] Finally, the preliminary normalization result is dynamically adjusted using Formula 4:

[0142] x dyn =x norm ·D i (4)

[0143] In this formula, x dyn Represents the dynamically adjusted normalized value, which is obtained by converting the initial normalized result x norm Multiply by the dynamic weighting factor D i This process ensures that the normalized results can reflect the actual performance under different evaluation conditions. For example, if a certain indicator fluctuates greatly under a high-load task, then through the adjustment of the dynamic weighting factor, the normalized result of the indicator will be appropriately enlarged or reduced, thereby more accurately reflecting its performance under the high-load task.

[0144] The entire normalization and dynamic adjustment process ensures that each indicator in the equipment support effectiveness evaluation has stronger adaptability and accuracy after standardization, providing more stable input data for subsequent fuzzy comprehensive evaluation.

[0145] After dynamic adjustment, all normalized results can be checked to ensure that all normalized indicator values ​​are still within the range of 0 to 1. If the adjusted value exceeds the range, the excess value is set to the adjacent boundary value (0 or 1) to ensure that the final normalized result meets the standardization requirements.

[0146] Step S104: Based on the fuzzy comprehensive evaluation method in fuzzy mathematics, the normalized index value and its corresponding weight value are comprehensively calculated to obtain the equipment support effectiveness evaluation result; wherein, the equipment support effectiveness evaluation result is expressed in the form of fuzzy membership, which is used to reflect the comprehensive support effectiveness of aerospace equipment under different use conditions.

[0147] In step S104, based on the fuzzy comprehensive evaluation method in fuzzy mathematics, the normalized index value and its corresponding weight value are comprehensively calculated to obtain the equipment support effectiveness evaluation result. The core of this step is to use the fuzzy comprehensive evaluation method to combine multiple normalized index values ​​and their weights to perform fuzzy multi-level comprehensive calculations, thereby achieving a comprehensive evaluation of the comprehensive support effectiveness of the equipment.

[0148] First, it is necessary to convert the fuzzy membership of each normalized indicator. Specifically, the normalized value of each indicator needs to be mapped through different fuzzy membership functions, which can be in the form of triangular membership functions, trapezoidal membership functions or Gaussian membership functions. Different fuzzy membership functions are selected and adjusted according to the characteristics of the indicators to ensure that the fuzzified membership can accurately reflect the different levels of equipment support effectiveness. For example, for linearly changing indicators, a triangular membership function can be selected, while for nonlinearly changing indicators, a Gaussian membership function can be used. The specific parameters of the membership function (such as center point, range, etc.) need to be set based on historical data or expert experience to ensure accurate calculation of the membership.

[0149] After completing the calculation of the membership, the fuzzy membership of each indicator and the corresponding fuzzy weight need to be weighted and integrated. The weight of each indicator is based on the fuzzy weight value obtained by the expert scoring method in step S102, and these weights reflect the relative importance of each indicator in the overall evaluation. In the process of comprehensive calculation, the weighted average method can be adopted, that is, the fuzzy membership of each indicator is weighted and accumulated according to the weight, so as to obtain the fuzzy comprehensive evaluation score of each indicator. It should be noted that, since different indicators may have different membership functions and fuzzy weights, the membership needs to be properly normalized in the weighting process to maintain the comparability between different memberships.

[0150] After obtaining the fuzzy comprehensive evaluation scores of each indicator, it is necessary to summarize the evaluation scores of all indicators to obtain the overall support effectiveness evaluation results of the equipment. At this time, the fuzzy comprehensive evaluation scores of all indicators can be further weighted and accumulated according to their global fuzzy weights to form a comprehensive fuzzy membership value, which represents the comprehensive support effectiveness of the equipment under different use conditions. The evaluation results are presented in the form of fuzzy membership, usually in the range of 0 to 1. The higher the value, the stronger the comprehensive support effectiveness of the equipment, and the lower the value, the relatively weaker the support effectiveness.

[0151] In order to ensure the accuracy and rationality of the final evaluation results, the comprehensive calculation results need to be fuzzy decoded. Fuzzy decoding refers to converting the fuzzy membership value into a specific effectiveness score, which can be used to intuitively express the support effectiveness of the equipment. This process can be converted through the corresponding relationship between the membership value and the actual score. For example, if the fuzzy membership is 0.8, it can correspond to a higher support effectiveness score, while if the membership is 0.3, it can correspond to a lower effectiveness score.

[0152] In summary, step S104 achieves a comprehensive evaluation of equipment support effectiveness through fuzzy mapping, weighted synthesis and fuzzy decomposition, and reflects the comprehensive support effectiveness of equipment under different use conditions in the form of fuzzy membership. This evaluation result provides an important basis for subsequent analysis and improvement.

[0153] Furthermore, the fuzzy comprehensive evaluation method based on fuzzy mathematics comprehensively calculates the normalized index value and its corresponding weight value to obtain the equipment support effectiveness evaluation result, including:

[0154] The index value x of the normalized i-th index norm,i , using multiple fuzzy membership functions for multi-layer mapping to form a membership vector U composed of different membership functions i = {u i1 ,u i2 ,…,u iL}, where u il represents the membership value of the i-th indicator under the l-th fuzzy membership function, L is the number of layers of the fuzzy membership function, wherein the multiple fuzzy membership functions include triangular, trapezoidal and Gaussian membership functions;

[0155] According to the following formula 5, the fuzzy comprehensive evaluation score of each indicator is calculated:

[0156]

[0157] Among them, S i is the fuzzy comprehensive evaluation score of the i-th index; u ilis the membership value under the membership function of the lth layer; x norm,i is the normalized value of the ith indicator; w l is the fuzzy weight of the lth layer; α is the adjustment parameter; μ l is the center point of the l-th layer membership function;

[0158] According to the calculated fuzzy comprehensive evaluation score of each indicator, the equipment support effectiveness evaluation result is obtained according to the following formula 6:

[0159]

[0160] Among them, E total is the comprehensive support effectiveness evaluation result of the equipment; S i is the fuzzy comprehensive evaluation score of the i-th index; ω i is the global fuzzy weight of the i-th indicator.

[0161] In this embodiment, a fuzzy comprehensive evaluation method based on fuzzy mathematics is used to comprehensively calculate the normalized index value and its corresponding weight, thereby obtaining the equipment support effectiveness evaluation result. This process uses multi-level and multi-dimensional fuzzy mapping and calculation to ensure that the evaluation result can accurately reflect the comprehensive support effectiveness of the equipment under different use conditions.

[0162] First, for each normalized index value x norm,i , multiple fuzzy membership functions need to be used for multi-layer mapping to form a membership vector U i = {u i1 ,u i2 ,…,u iL}, where u il represents the membership value of the i-th indicator under the l-th fuzzy membership function, and L is the number of layers of the fuzzy membership function. The purpose of multi-layer fuzzy membership mapping is to capture various characteristics of indicators through different types of membership functions. Triangular membership function, trapezoidal membership function and Gaussian membership function are commonly used types of fuzzy membership functions. In this embodiment, L can be 3, including triangular membership function, trapezoidal membership function and Gaussian membership function.

[0163] The triangular membership function is suitable for situations with linear changes, such as the linear changes of some reliability indicators under different task intensities; the trapezoidal membership function is suitable for situations where the indicators are stable in certain intervals but change dramatically in the boundary intervals, such as the durability of a certain component is basically stable within a certain period of use, but shows a significant decrease near the critical point of use; the Gaussian membership function is suitable for describing situations with nonlinear changes, such as safety assessment in complex environments, and the Gaussian function can better reflect this nonlinear feature. By selecting the appropriate membership function type, multi-level fuzzy mapping of different indicators can be achieved, thereby forming a comprehensive membership vector.

[0164] After completing the calculation of the membership vector, it is necessary to perform a weighted comprehensive calculation on the membership of each layer to obtain the fuzzy comprehensive evaluation score of each indicator. Specifically, the calculation is performed according to Formula 5:

[0165]

[0166] In this formula, S i is the fuzzy comprehensive evaluation score of the i-th indicator, which is obtained by weighted comprehensive calculation of the membership of each layer. il is the membership value under the membership function of the lth layer, indicating the fuzzy belonging of the i-th indicator under the membership function of this layer. l is the fuzzy weight of the lth layer, which is used to reflect the relative importance of different membership functions. l The determination can be based on expert scoring method, fuzzy hierarchical analysis method or statistical results of historical data to ensure that the contribution of membership functions at different levels can accurately reflect the importance of the indicator.

[0167] The formula also includes an exponential decay factor exp(-α·|x norm,i -μ l |), used to adjust the membership at different center points μ l The distribution of the near center point. Among them, α is an adjustment parameter used to control the decay speed. When α takes a larger value, the decay speed of the membership is faster, which can better highlight the membership characteristics near the specific center point; when α takes a smaller value, the distribution of the membership will be smoother, which is suitable for the fuzzy distribution of indicators in a larger range. The center point μ l It is the central value of the membership function of the first layer, which is usually determined by analyzing historical data or expert experience and reflects the main performance range of the indicator. For example, for a reliability indicator, its central point can be a specific mean time between failures.

[0168] After obtaining the fuzzy comprehensive evaluation score S of each indicator i Finally, the comprehensive support effectiveness evaluation result of the equipment needs to be calculated according to Formula 6:

[0169]

[0170] In this formula, E total It represents the comprehensive support effectiveness evaluation result of the equipment. It is calculated by combining the simulation and comprehensive evaluation score S of each indicator. i Its global fuzzy weight ω i The global fuzzy weight ω is obtained by weighted accumulation. i It reflects the relative importance of each indicator in the overall evaluation, which can be determined based on the comprehensive contribution of the indicator, historical performance or expert opinion. Global fuzzy weight ω i It can also be obtained by the above formula 7. Through this weighted accumulation method, the evaluation scores of all indicators can be combined into an overall evaluation result.

[0171] For example, if the comprehensive support effectiveness evaluation result of a space equipment is 0.85, it can be considered that the equipment performs well under the evaluated conditions and is close to the optimal state; if the evaluation result is 0.45, it means that there is a large room for improvement in the support effectiveness of the equipment. In this way, the comprehensive support effectiveness of the equipment can be clearly quantified, providing a reliable basis for subsequent analysis and decision-making.

[0172] This calculation process based on fuzzy comprehensive evaluation achieves a comprehensive evaluation of equipment support effectiveness through multi-layer membership mapping, weighted synthesis and global weighted accumulation, so that the evaluation results can accurately reflect the comprehensive performance of the equipment under different usage conditions.

[0173] Step S105: Analyze the equipment support effectiveness evaluation results to identify the main factors affecting the equipment support effectiveness; propose targeted improvement measures for the identified main factors affecting the equipment support effectiveness to improve the comprehensive support level of the equipment.

[0174] In step S105, the equipment support effectiveness evaluation results are analyzed to identify the main factors affecting the equipment support effectiveness. The key to this process is to find the indicators that play a major role in the evaluation results through in-depth analysis of the comprehensive evaluation results, thereby providing a clear direction for subsequent optimization and improvement.

[0175] First, the comprehensive evaluation results need to be interpreted. Since the evaluation results of step S104 are presented in the form of fuzzy membership, the analysis process should start with interpreting the fuzzy membership of each indicator, especially focusing on those indicators with low membership, because these indicators may perform relatively poorly in equipment support effectiveness. By comparing the membership of each indicator, it can be intuitively seen which indicators contribute more to the comprehensive effectiveness of the equipment and which indicators are insufficient under specific conditions of use.

[0176] Based on the interpretation of fuzzy membership, the fuzzy decision tree is used to conduct a structured analysis of the evaluation results. Fuzzy decision tree is an analysis tool based on fuzzy logic, which can decompose the evaluation results into different decision nodes, each of which represents a key factor affecting the effectiveness of equipment support. When constructing a fuzzy decision tree, each primary and secondary indicator needs to be used as a potential decision node, and sorted and branched according to its contribution to the overall effectiveness. The construction of the decision tree is based on information gain or fuzzy entropy calculation to ensure that the division of each node can maximize the reflection of the relationship and influence between indicators.

[0177] Through the path analysis of the fuzzy decision tree, the primary and secondary indicators that have the greatest impact on the evaluation results can be identified. These indicators are usually factors that contribute more to the equipment support effectiveness or change more significantly, and they may directly affect the reliability, maintainability, availability or safety of the equipment. For example, if an indicator appears as a decision node multiple times in the fuzzy decision tree, and its fuzzy membership has a high degree of distinction in different branches, then the indicator may be one of the main factors affecting the equipment support effectiveness. Further analysis of these key indicators can clarify their performance differences under different mission conditions, environmental factors and usage conditions.

[0178] After identifying the main influencing factors, targeted improvement measures need to be proposed. These measures should be based on the analysis results and combined with the opinions of experts in the field to ensure the feasibility and effectiveness of the improvement plan. For example, for the identified key indicators, specific optimization suggestions can be made from the aspects of equipment design improvement, maintenance cycle adjustment, and resource optimization allocation. If an indicator performs poorly in extreme environments, you can consider strengthening the durability design of related components or adjusting the operating strategy. If the fuzzy membership of an indicator is low in multiple evaluations, the measurement method or evaluation standard of the indicator needs to be adjusted to improve its accuracy and adaptability.

[0179] After proposing improvement measures, it is necessary to conduct preliminary feasibility verification of the improvement plan. This can be done through simulation or actual testing to ensure that the proposed improvement measures can effectively improve the comprehensive support effectiveness of the equipment in actual applications. At the same time, the effectiveness of the improved equipment needs to be re-evaluated to verify whether the effect of the improvement is significant. If the improvement measures show obvious performance improvement in the evaluation results, they can be implemented as a long-term optimization plan.

[0180] Furthermore, the equipment support effectiveness evaluation results are analyzed to identify the main factors affecting the equipment support effectiveness, including:

[0181] A fuzzy decision tree is used to decompose the equipment support effectiveness evaluation result into different nodes, wherein each node represents a main factor affecting the equipment support effectiveness;

[0182] Through the path analysis of fuzzy decision tree, the primary and secondary indicators with the greatest impact on the evaluation results are identified, and their contribution to the equipment support effectiveness is quantified;

[0183] Through fuzzy logic reasoning, the primary and secondary indicators that have the greatest impact on the evaluation results are analyzed and ranked to determine the main factors affecting the equipment support effectiveness.

[0184] In this embodiment, the analysis of the evaluation results aims to identify and quantify the main factors affecting the equipment support effectiveness. In order to achieve this goal, the fuzzy decision tree is used as an analysis tool. The fuzzy decision tree is an analysis method that combines the decision tree structure and fuzzy logic to deal with the uncertainty and ambiguity involved in the evaluation of equipment support effectiveness. Through this method, the evaluation results can be decomposed into multiple nodes, each node representing a main factor affecting the support effectiveness.

[0185] In the specific implementation, it is necessary to first establish the initial structure of the fuzzy decision tree. The equipment support effectiveness evaluation results are composed of the comprehensive evaluation scores of multiple primary and secondary indicators, which will be used as the input of the decision tree. When constructing a decision tree, each primary and secondary indicator needs to be regarded as a potential decision node. For example, if the primary indicators include reliability, maintainability, availability, and safety, then each indicator can become a main node of the decision tree. Secondary indicators are further branched under the corresponding primary indicators. For example, secondary indicators under reliability indicators may include mean time between failures, failure rate, etc.

[0186] Each node of the fuzzy decision tree is split and selected through fuzzy logic. When splitting a node, it is necessary to calculate the fuzzy contribution of different indicators to the evaluation results, which is quantified by information gain or fuzzy entropy. For example, if a secondary indicator appears repeatedly in multiple nodes and has a high information gain, then the indicator may be one of the key factors affecting the equipment support effectiveness. Through in-depth analysis of the decision tree path, the primary and secondary indicators that have the greatest impact on the evaluation results can be identified. For example, in the analysis results, a primary indicator (such as reliability) may contribute 40% to the overall support effectiveness, while a secondary indicator (such as average maintenance time) may contribute 30% to the maintainability indicator.

[0187] In order to further quantify the contribution of these key indicators, it is necessary to analyze the paths of each node in the fuzzy decision tree. Specifically, the most influential factors can be identified by calculating the changes in the fuzzy membership of each indicator on different paths and their contribution to the final evaluation results. Through this path analysis, it is not only possible to clarify which indicators have the greatest impact on the equipment support effectiveness under different mission conditions, but also to further refine their degree of influence. For example, in a high temperature environment, a safety indicator may show a large change in fuzzy membership, indicating that it has a significant impact on the evaluation results; while under normal temperature conditions, the contribution of this indicator may be reduced.

[0188] After identifying the primary and secondary indicators that have the greatest impact on the evaluation results, fuzzy logic reasoning is used to further analyze and sort these key factors. Fuzzy logic reasoning is a reasoning method based on a fuzzy rule base, which can reason and sort the impact of different factors according to the fuzzy characteristics of the evaluation results. For example, if a certain first-level indicator shows a high fuzzy membership in multiple evaluations and always contributes more to the evaluation results, then the indicator will occupy a higher position in the sorting. Similarly, if the fuzzy membership of a secondary indicator varies greatly under different conditions, the indicator may be ranked higher in the sorting. Through this reasoning and sorting, it is possible to ultimately determine which primary and secondary indicators are the main factors affecting the effectiveness of equipment support.

[0189] In summary, the entire analysis process achieves an in-depth understanding of the equipment support effectiveness evaluation results and accurate identification of key factors through the decomposition of the fuzzy decision tree, path analysis, and fuzzy logic reasoning. For example, if a certain equipment shows low reliability in multiple mission evaluations, through the fuzzy decision tree and fuzzy logic reasoning, it may be possible to identify the specific secondary indicators that lead to low reliability, such as high failure rate or long maintenance time. This identification result not only helps to understand the current support effectiveness of the equipment, but also provides a clear direction for subsequent optimization and improvement.

[0190] Furthermore, targeted improvement measures are proposed for the main factors that affect the equipment support effectiveness, including:

[0191] Constructing a fuzzy rule base, wherein the fuzzy rule base includes a plurality of improved rules for different evaluation results;

[0192] Based on the rules in the fuzzy rule base, the fuzzy reasoning mechanism is used to reason and evaluate different improvement plans and select the optimal improvement plan;

[0193] The optimal improvement plan is verified by fuzzy simulation, and the feasibility and effectiveness of the improvement measures are evaluated through simulation results to ensure that the proposed improvement measures can effectively improve the comprehensive support efficiency of the equipment after implementation.

[0194] In this embodiment, targeted improvement measures are proposed for the main factors affecting the equipment support efficiency. This process is achieved by building a fuzzy rule base, performing fuzzy reasoning evaluation, and verifying through fuzzy simulation. Through these steps, it can be ensured that the proposed improvement measures are scientific and operational, and can effectively improve the comprehensive support efficiency of equipment.

[0195] First, a fuzzy rule base needs to be built. The fuzzy rule base is a knowledge base based on fuzzy logic, which contains multiple improvement rules related to different evaluation results. These rules are formulated based on the key influencing factors identified in the early stage, and combine the knowledge of domain experts and the experience in actual equipment use. Each rule usually consists of an "if-then" statement, which describes the improvement measures to be taken under specific conditions. For example, for a key maintainability indicator, if its evaluation result is lower than a certain fuzzy threshold (such as the fuzzy membership is less than 0.4), the fuzzy rule may recommend increasing the number of spare parts or improving the response speed of maintenance personnel. Similarly, if a certain reliability indicator performs poorly in a high temperature environment, the fuzzy rule may recommend introducing materials with higher heat resistance or optimizing the heat dissipation system in the design of the equipment.

[0196] After the fuzzy rule base is built, fuzzy reasoning is required based on these rules. The fuzzy reasoning mechanism is a decision-making method based on fuzzy logic. It selects the best improvement plan by reasoning and evaluating different improvement plans. In specific implementation, the fuzzy reasoning mechanism will combine the actual evaluation results of the equipment and the rules in the fuzzy rule base to determine the pros and cons of various possible improvement plans. For example, if a rule recommends increasing the number of maintenance personnel and another rule recommends shortening the maintenance process, the fuzzy reasoning mechanism will compare the feasibility and effectiveness of the two plans. During the reasoning process, the effectiveness of each plan will be fuzzily represented, such as quantifying its contribution to improving the effectiveness of support through the form of membership. Finally, the reasoning mechanism will select the improvement plan with the greatest contribution as the optimal plan based on these membership values.

[0197] After selecting the optimal improvement plan, it is necessary to conduct fuzzy simulation verification on the plan. Fuzzy simulation verification is a method to verify the feasibility and effectiveness of improvement measures through computer simulation models. Specifically, it is necessary to build a simulation model that can simulate the actual use of equipment, which should take into account different task conditions, environmental factors and resource allocation. During the simulation process, the optimal improvement plan is applied to the simulation environment to observe its impact on the comprehensive support effectiveness of the equipment. For example, in the scenario of improved maintainability, the change in fault handling speed after adding maintenance personnel can be simulated; in the scenario of improved reliability, the durability performance of new materials in high temperature environments can be simulated. Through multiple simulation runs, the performance data of the improvement measures under different conditions can be collected, and these data can be analyzed in the form of fuzzy membership. If the simulation results show that the improvement measures have significant performance improvements in most cases, the improvement plan can be considered feasible and effective.

[0198] After the simulation verification is completed, further evaluation and adjustment are required to ensure that the improvement measures can be successfully implemented in actual applications. If the improvement effect under certain conditions in the simulation results is not obvious, it is necessary to adjust and optimize the improvement plan based on the actual situation. For example, if the effect of an improvement measure is not obvious under certain extreme conditions, you can consider adding new rules to the rule base to deal with these special situations. Through this iterative optimization method, the effectiveness and operability of the improvement measures in actual implementation are ultimately ensured, thereby significantly improving the comprehensive support effectiveness of the equipment.

[0199] For example, if the maintainability index of a certain equipment is found to be low during the evaluation, after fuzzy reasoning and simulation verification, the best improvement plan may be to increase the number of spare parts and adjust the shift system of maintenance personnel. This plan can be verified through simulation to verify its effect under different mission conditions, such as maintenance response time and equipment availability during high-intensity missions. Through this verification process, it can be ensured that the improvement plan can truly improve the comprehensive support effectiveness of the equipment after implementation.

[0200] A second embodiment of the present application provides an electronic device, the electronic device comprising:

[0201] processor;

[0202] The memory is used to store a program, and when the program is read and executed by the processor, the program executes the equipment support effectiveness evaluation method based on fuzzy mathematics provided in the first embodiment of the present application.

[0203] The third embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the equipment support effectiveness evaluation method based on fuzzy mathematics provided in the first embodiment of the present application is executed.

[0204] Although the present application is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present application. Any technical personnel in this field may make possible changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be based on the scope defined by the claims of the present application.

Claims

1. A method for evaluating equipment support effectiveness based on fuzzy mathematics, characterized in that: include: According to the support requirements and evaluation objectives of aerospace equipment, determine the index system for equipment support effectiveness evaluation; wherein the index system includes primary indicators and secondary indicators, the primary indicators are used to reflect the main characteristics of equipment support effectiveness, and the secondary indicators are used to specifically describe support factors at different levels; Using the expert scoring method in fuzzy mathematics to assign weights to each indicator in the indicator system; Normalizing each indicator in the indicator system; Based on the fuzzy comprehensive evaluation method in fuzzy mathematics, the normalized index value and its corresponding weight value are comprehensively calculated to obtain the equipment support effectiveness evaluation result; wherein the equipment support effectiveness evaluation result is expressed in the form of fuzzy membership, which is used to reflect the comprehensive support effectiveness of aerospace equipment under different use conditions; Analyze the support effectiveness evaluation results of the equipment and identify the main factors affecting the support effectiveness of the equipment; propose targeted improvement measures for the identified main factors affecting the support effectiveness of the equipment to improve the comprehensive support level of the equipment.

2. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: According to the support requirements and evaluation objectives of aerospace equipment, the indicator system for equipment support effectiveness evaluation is determined, including: Collect historical support data of aerospace equipment, including reliability, maintainability, availability and safety, and preliminarily build a set of primary and secondary indicators based on the collected historical support data; The primary and secondary indicators were screened and prioritized by fuzzy analytic hierarchy process; Combined with the suggestions of experts in the field, the initially constructed indicator system was revised and improved to form the final evaluation indicator system.

3. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: The normalization of each indicator in the indicator system includes: According to the following formula 1, each indicator in the indicator system is normalized: Among them, x norm is the initial normalization result; x is the original index value; x min and x max are the minimum and maximum values ​​of the indicator respectively; According to the following formula 2, the dynamic weighting factor D is calculated: i : Among them, β is the adjustment parameter; R i is the rate of change of the ith indicator; max(R i ) is the maximum change rate among all indicators; the change rate R i Use the following formula 3 to calculate: Among them, x ij is the value of the i-th indicator under the j-th evaluation condition; is the average value of the ith indicator under all evaluation conditions; M is the total number of evaluation conditions, where the evaluation conditions include environmental conditions, task conditions, usage conditions, external interference conditions, and resource conditions; Use the following formula 4 to adjust the normalized result: x dyn =x norm ·D i (4) Among them, x dyn is the normalized value after dynamic adjustment; x norm is the preliminary normalization result; D i is the dynamic weighting factor.

4. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: The fuzzy comprehensive evaluation method based on fuzzy mathematics comprehensively calculates the normalized index value and its corresponding weight value to obtain the equipment support effectiveness evaluation result, including: The normalized index value x of the i-th index norm,i , using multiple fuzzy membership functions for multi-layer mapping to form a membership vector U composed of different membership functions i = {u i1 ,u i2 ,…,u iL }, where u il represents the membership value of the i-th indicator under the l-th fuzzy membership function, L is the number of layers of the fuzzy membership function, wherein the multiple fuzzy membership functions include triangular, trapezoidal and Gaussian membership functions; According to the following formula 5, the fuzzy comprehensive evaluation score of each indicator is calculated: Among them, S i is the fuzzy comprehensive evaluation score of the i-th index; u il is the membership value under the membership function of the lth layer; x norm,i is the normalized value of the ith indicator; w l is the fuzzy weight of the lth layer; α is the adjustment parameter; μl is the center point of the membership function of the lth layer; According to the calculated fuzzy comprehensive evaluation score of each indicator, the equipment support effectiveness evaluation result is obtained according to the following formula 6: Among them, E total is the comprehensive support effectiveness evaluation result of the equipment; S i is the fuzzy comprehensive evaluation score of the i-th index; ω i is the global fuzzy weight of the i-th indicator.

5. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: Analyze the equipment support effectiveness evaluation results to identify the main factors affecting equipment support effectiveness, including: A fuzzy decision tree is used to decompose the equipment support effectiveness evaluation result into different nodes, wherein each node represents a main factor affecting the equipment support effectiveness; Through the path analysis of fuzzy decision tree, the primary and secondary indicators with the greatest impact on the evaluation results are identified, and their contribution to the equipment support effectiveness is quantified; Through fuzzy logic reasoning, the primary and secondary indicators that have the greatest impact on the evaluation results are analyzed and ranked to determine the main factors affecting the equipment support effectiveness.

6. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: The above-mentioned proposed targeted improvement measures for the main factors that affect the equipment support effectiveness, including: Constructing a fuzzy rule base, wherein the fuzzy rule base includes a plurality of improved rules for different evaluation results; Based on the rules in the fuzzy rule base, the fuzzy reasoning mechanism is used to reason and evaluate different improvement plans and select the optimal improvement plan; The optimal improvement plan is verified by fuzzy simulation, and the feasibility and effectiveness of the improvement measures are evaluated through simulation results to ensure that the proposed improvement measures can effectively improve the comprehensive support efficiency of the equipment after implementation.

7. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 1 is characterized in that: The expert scoring method in fuzzy mathematics is used to assign weights to each indicator in the indicator system, which is implemented by the following formula 7: Where n represents the total number of experts involved in the evaluation; W i represents the final weight of the i-th indicator; μ ij represents the membership of the jth expert to the i-th indicator; δ ij represents the dynamic credibility coefficient of the jth expert; ω ij is the original score of the jth expert on the i-th indicator; C i is the relative importance coefficient of the ith indicator; C max is the maximum relative importance coefficient in the indicator system; R i represents the mean of the historical evaluation results of the ith indicator; R ij is the historical evaluation value of the j-th expert on the i-th indicator; a and β are adjustment parameters.

8. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 7 is characterized in that: Membership degree μ ij This is achieved using the following formula 8: Among them, x ij is the original score of the jth expert on the i-th indicator; m ij is the most trusted score of the jth expert for the i-th indicator, determined according to the historical evaluation trend of the expert on the indicator; σ ij is the standard deviation, which is used to reflect the volatility or uncertainty of the j-th expert's evaluation of the i-th indicator.

9. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 7 is characterized in that: The dynamic credibility coefficient δ ij This is achieved using the following formula 9: Among them, E ijt A is the predicted value of the i-th indicator by the j-th expert in the t-th evaluation; it is the actual performance result of the ith indicator in the tth evaluation; r jt is the historical evaluation accuracy of the jth expert in the tth evaluation; d t is the environmental factor of the tth evaluation, which is used to reflect the different external conditions of the evaluation; η is the adjustment parameter of the environmental factor, which is used to adjust the impact of different environmental factors on the credibility coefficient; M is the total number of historical evaluations.

10. The equipment support effectiveness evaluation method based on fuzzy mathematics according to claim 7 is characterized in that: The relative importance coefficient C i This is achieved by the following formula 10: Where K is the total number of clusters; u ik is the membership degree of the ith indicator in the kth cluster; d ik is the distance between the i-th index and the k-th cluster center; σ k is the density of the kth cluster, which is used to reflect the concentration of indicators in the cluster; β k is the weight coefficient of the kth cluster; L is the weight coefficient of the lth cluster β l The γ is a weight adjustment parameter.

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