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摘要:
为了提高航空器、飞机等大型复杂装备的费用预测精度,根据相似信息优先原理和熵理论,将相似装备的选取看作是一个信息融合的过程,引入距离熵和灰关联熵,构建综合相似度指标来度量装备样本与待预测装备之间的相似程度,对不同样本进行赋权,建立加权最小二乘法对装备费用进行预测。针对装备样本数量小于参数数量的情形,通过构建装备参数对费用的驱动效应矩阵及计算相应熵权,选择熵权较大的参数作为测算模型的自变量。通过实例对比分析,表明基于熵理论的加权回归测算模型具有较高的预测精度和稳定性。
Abstract:In order to improve the cost prediction accuracy of large and complex equipment such as aircraft and airplanes, based on the principle of similar information priority and entropy theory, the selection of similar equipment is regarded as a process of information fusion, and distance entropy and grey relational entropy are introduced to construct a comprehensive similarity index in order to measure the similarity between the equipment sample and the equipment to be predicted, assign weights to different samples, and establish a weighted least squares method to predict equipment costs. In the situation where the number of equipment samples is less than the number of parameters, the cost driven effect matrix is established and the calculation of the corresponding entropy weight is performed by constructing equipment parameters. The parameter with larger entropy weight is selected as the independent variable of the prediction model.The comparative analysis of examples shows that the weighted regression calculation model based on entropy theory has high prediction accuracy and stability.
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Key words:
- complex equipment /
- distance entropy /
- grey relational entropy /
- driving effect /
- entropy weight
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表 1 机体研制费用数据
Table 1. Airframe development cost data
飞机型号 研制周期x1/a 机体空重x2/kg 最大平飞速度x3/(km·h-1) 作战半径x4/m 爬升率x5/(m·s-1) 外挂质量x6/kg 机体首翻期x7/h 研制费用c/万元 A 5 3 650 1 450 400 125 1 500 600 4 167 B 7 4 170 1 320 400 115 1 000 800 4 516 C 7 3 830 2 180 400 135 1 500 800 6 549 D 7 4 470 2 260 420 150 1 500 1 000 8 457 E 6 4 060 2 180 400 150 1 500 1 000 7 613 F 7 5 530 1 240 400 106 1 500 800 4 877 G 10 6 850 2 340 750 180 2 000 1 000 17 138 H 9 7 430 2 340 800 200 2 500 1 200 25 631 I 9 7 750 2 340 900 220 2 500 1 200 31 263 J 14 12 160 1 880 850 200 3 500 1 200 63 674 K 18 6 780 2 130 1 250 235 6 000 2 000 166 340 表 2 四种预测方法的结果比较
Table 2. Comparison of results of four prediction methods
表 3 机载电子设备费用样本
Table 3. Sample of airborne electronic equipment cost
飞机型号 首飞时间x1/a 质量x2/kg 体积x3/m3 功率x4/kW 实际平均费用c/(103美元) A-6E 70 624.25 0.569 1 6.4 1 069 A-7D 68 508.93 0.710 1 10.5 669 F-4D 65 790.41 0.843 8.2 582 A-10A 72 265.14 0.239 4 3.1 315 E-4E 67 566.14 0.677 3 5.3 662 F-4J 66 1 021.05 0.982 4 19.4 1 329 F-15A 72 717.32 0.833 1 22.5 2 488 F-111A 64 805.4 0.877 4 5.6 1 267 F-111D 68 1 068.72 0.910 2 12.5 2 392 F-111A 71 933.88 1.061 1 8.9 1 577 FB-111A 70 1 136.36 1.343 2 7.9 1 965 F-14A 70 998.35 1.062 8 29.4 2 383 A-7E 68 653.76 0.841 3 8.3 828 F-111E 69 987 1.105 4 8.9 1 564 表 4 三种预测方法的结果比较
Table 4. Comparison of results of three prediction methods
表 5 运输机性能数据与费用
Table 5. Performance data and price of transport aircraft
飞机型号 最大起飞重量x1/kg 机身长x2/m 机高x3/m 起飞距离x4/m 满油航程x5/km 最大平飞速度x6/(m·s-1) 空重x7/kg 载油量x8/kg 费用/ 万元 A 13 494 23.5 8.43 867 4 262 425 6 597 5 683 6 666.7 B 6 849 14.39 4.57 987 3 701 746 3 655 2 640 3 624.3 C 9 979 16.9 5.12 1 581 4 679 874 5 357 3 350 6 569.9 D 5 670 13.34 4.57 536 3 641 536 3 656 1 653 5 586.23 E 63 503 39.75 9.3 1 859 6 764 925 33 183 21 273 27 768.8 F 22 000 29.87 6.75 1 200 2 870 907 34 360 5 500 17 575.2 G 21 500 27.17 7.65 1 050 2 000 580 12 200 5 000 18 137.6 H 70 310 29.79 11.66 1 091 7 876 602 36 300 36 300 50 476 I 21 000 24.615 7.3 1 300 3 100 819.2 11 700 6 000 14 250 -
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