The Evaluation of Effectiveness for the Collaborative Combat of an Unmanned Aerial Vehicle Based on Grey Minimum Entropy
Journal of Aerospace Technology and Management
The main points to the evaluation of effectiveness for the collaborative combat of the unmanned aerial vehicle (UAV) lie within the construction of a reasonable indicator system and an accurate contribution model. As for point one, this article introduces a new method combining the Delphi consulting method and the principal component analysis method to avoid the underlying subjective and time-consuming defects of the existing methods. As for another point, a weighting method is adopted
... the subjective and objective parameters to minimize the errors caused by a single entity. Firstly, the modified grey relational degree analysis method is used to obtain the subjective weight, which can reduce the influence of the extreme values and outliers by enhancing the selection process of the reference sequence. Secondly, this paper adopts the weight of minimum entropy weight method to obtain the objective weight; it can avoid the information loss caused by the original method, which only determines the weight based on the frequency of each element present in the effective combination. At last, the principle of minimum relative entropy is adopted to obtain a more reasonable weight distribution coefficient. The simulation experiments established the rationality and effectiveness of the proposed method. At present, the UAV cluster collaborative combat system is still in the developmental stage, and there are only a few research achievements regarding its evaluation in combat effectiveness. Since the actual combat environment is complex and unstable, the effectiveness in combat is affected by a variety of uncertain factors. However, a financial loss is created if a large number of physical tests are used to evaluate the effectiveness (Fan et al. 2018) . Therefore, it is particularly important to evaluate the effectiveness of the multi-aircraft cooperative combat, whether from the perspective of promoting the integration of new combat forces with the joint combat system, improving the actual level of combat training of the troops, or improving the theoretical system of the weapon and the combat equipment (Jiang et al. 2020) . The effectiveness evaluation process of the UAV collaborative combat mainly consists of two parts, that is, the establishment of a reasonable indicator system and an accurate contribution model. While constructing the indicator system, the Delphi consulting method is commonly used from the existing literature to select the indicator. The Delphi consultation method was used to efficiently evaluate new models based on expert experience (Zhang and Xi 2021), which makes the entire evaluation process more authoritative and scientific. However, there are disadvantages regarding the factors of strong subjectivity and time consumption. To solve the subjective problem of the traditional Delphi consultation method, some studies suggested few solutions, which include improving the design content of the consultation form, statistical analysis methods, and the process of repeated consultation (Hanson et al. 2020; Wang et al. 2016) . However, because of the timeconsuming defect of the Delphi method, there is no efficient method that can be adopted to improve it. Currently, the principal component analysis (PCA) method is widely used in the construction of various evaluation indicator systems as a method for mathematical dimensionality reduction. An earlier study adopted the PCA method to establish a comprehensive decision-making model concerning the threat of the artillery target, which helps in quickly processing data and make effective decisions (Wang et al. 2017) . Accurate contribution modeling on the basis of the established indicator system is the key to solve the problem of the effectiveness evaluation in the UAV collaborative combat system. The contribution is a measure of how much an indicator contributes to the whole system, and it is commonly referred to as weight. The methods used to evaluate the contribution of the system include subjective weighting, objective weighting, and combination weighting. Subjective weighting methods include the analytic hierarchy process, fuzzy matter-element analysis, grey relational analysis, and so on. In an earlier study by Qin et al. (2020) , the analytic hierarchy process was used to determine the subjective weights in the effectiveness of evaluation in the anti-ship missile combat system, which effectively solves the problem of quantification of the qualitative indicators by constructing a relative importance matrix. However, the disadvantage of strong subjectivity still exists. In an earlier study by Li et al. (2020) , gray correlation was used to construct an evaluation model for the water conservancy project risk analysis, but there are outliers which affect greatly while selecting the optimal sequence. The objective weighting methods mainly include the method of the coefficient of variation, the maximum deviation method, and the entropy weighting method, respectively. The coefficient of variation method was adopted to determine the objective weight, which can eliminate the effect of different dimensions and does not need to consider the normalization of the indicator value (Li et al. 2020) . However, it often leads to uncertainty and incorrect weight estimation once the outliers appear in the data. In an earlier study (Tian et al. 2004) , the maximum deviation method was adopted, which is based on the difference in the indicator value. However, a greater difference between the values of an indicator does not mean that the indicator is more important, which results in a significant difference between the weighting results and the actual importance of the indicator. The entropy weight method was adopted, which can avoid the problem of bias caused by the subjective weighting method (Luo et al. 2019; Tong et al. 2011) . However, there is a defect that may ignore the importance of indicators themselves. The principle of minimum entropy analysis was applied to obtain the objective weight, and the mutual influence between the indicators is considered, which greatly improves the objectivity of the selection of an indicator (Shan et al. 2014) . The same study also applied the principle of minimum entropy analysis to obtain the objective weight, which takes into account the interaction between the indicators and greatly improves the objectivity of the indicator selection. However, it only determines the weights based on the frequency of each indicator in the effective combination, ignoring the difference in the relative entropy among different combinations.